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B Meson Semileptonic Form Factors from Unquenched Lattice QCD: The semileptonic process, B --> \pi l \nu, is studied via full QCD Lattice
simulations. We use unquenched gauge configurations generated by the MILC
collaboration. These include the effect of vacuum polarization from three quark
flavors: the $s$ quark and two very light flavors ($u/d$) of variable mass
allowing extrapolations to the physical chiral limit. We employ Nonrelativistic
QCD to simulate the $b$ quark and a highly improved staggered quark action for
the light sea and valence quarks. We calculate the form factors $f_+(q^2)$ and
$f_0(q^2)$ in the chiral limit for the range 16 GeV$^2 \leq q^2 < q^2_{max}$
and obtain $\int^{q^2_{max}}_{16 GeV^2} [d\Gamma/dq^2] dq^2 / |v_{ub}|^2 =
1.46(35) ps^{-1}$. Combining this with a preliminary average by the Heavy
Flavor Averaging Group (HFAG'05) of recent branching fraction data for
exclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations,
leads to $|V_{ub}| = 4.22(30)(51) \times 10^{-3}$. PLEASE NOTE APPENDIX B with
an ERRATUM, to appear in Physical Review D, to the published version of this
e-print (Phys.Rev.D 73, 074502 (2006)). Results for the form factor $f_+(q^2)$
in the chiral limit have changed significantly. The last two sentences in this
abstract should now read; "We calculate the form factor $f_+(q^2)$ and
$f_0(q^2)$ in the chiral limit for the range 16 Gev$^2 \leq q^2 < q^2_{max}$
and obtain $\int^{q^2_{max}}_{16 GeV^2} [d\Gamma/dq^2] dq^2 / |V_{ub}|^2 =
2.07(57)ps^{-1}$. Combining this with a preliminary average by the Heavy Flavor
Averagibg Group (HFAG'05) of recent branching fraction data for exclusive B
semileptonic decays from the BaBar, Belle and CLEO collaborations, leads to
$|V_{ub}| = 3.55(25)(50) \times 10^{-3}$." | hep-lat |
Compact Gauge Fields on Causal Dynamical Triangulations: a 2D case study: We discuss the discretization of Yang-Mills theories on Dynamical
Triangulations in the compact formulation, with gauge fields living on the
links of the dual graph associated with the triangulation, and the numerical
investigation of the minimally coupled system by Monte Carlo simulations. We
provide, in particular, an explicit construction and implementation of the
Markov chain moves for 2D Causal Dynamical Triangulations coupled to either
$U(1)$ or $SU(2)$ gauge fields; the results of exploratory numerical
simulations on a toroidal geometry are also presented for both cases. We study
the critical behavior of gravity related observables, determining the
associated critical indices, which turn out to be independent of the bare gauge
coupling: we obtain in particular $\nu = 0.496(7)$ for the critical index
regulating the divergence of the correlation length of the volume profiles.
Gauge observables are also investigated, including holonomies (torelons) and,
for the $U(1)$ gauge theory, the winding number and the topological
susceptibility. An interesting result is that the critical slowing down of the
topological charge, which affects various lattice field theories in the
continuum limit, seems to be strongly suppressed (i.e., by orders of magnitude)
by the presence of a locally variable geometry: that may suggest possible ways
for improvement also in other contexts. | hep-lat |
Approximate forms of the density of states: We compare MC calculations of the density of states in SU(2) pure gauge
theory with the weak and strong coupling expansions. Surprisingly, the range of
validity of the two approximations overlap significantly, however the large
order behavior of both expansions appear to be similar to the corresponding
expansions of the plaquette. We discuss the implications for the calculation of
the Fisher's zeros of the partition function. | hep-lat |
$χ_{\textrm{top}}(T \gg T_{\textrm{c}})$ in pure-glue QCD through
reweighting: We calculate the topological susceptibility at 2.5 Tc and 4.1 Tc in SU(3)
pure Yang-Mills theory. We define topology with the help of gradient flow and
we largely overcome the problem of poor statistics at high temperatures by
applying a reweighting technique in terms of the topological charge, measured
after a specific small amount of gradient flow. This allows us to obtain a
sample of configurations which compares topological sectors with good
statistics, with enhanced tunneling between topologies. We quote continuum
extrapolated results at these two temperatures and conclude that our method is
viable and can be extended without new conceptual problems to the case of full
QCD with fermions. | hep-lat |
Deconfinement transition and dimensional cross-over in the 3D gauge
Ising model: We present a high precision Monte Carlo study of the finite temperature $Z_2$
gauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows
us to use powerful cluster algorithms for the simulations. For temporal
extensions up to $N_t=16$ we obtain the inverse critical temperature with a
statistical accuracy comparable with the most accurate results for the bulk
phase transition of the 3D Ising model. We discuss the predictions of T. W.
Capehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions.
Our precise data for the critical exponents and critical amplitudes confirm the
Svetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the
critical temperature of about 20%. | hep-lat |
Dirac-mode analysis for quark number density and its application for
deconfinement transition: The quark number density at finite imaginary chemical potential is
investigated in the lattice QCD using the Dirac-mode expansion. We find the
analytical formula of the quark number density in terms of the Polyakov loop in
the large quark mass regime. On the other hand, in the small quark mass region,
the quark number density is investigated by using the quenched lattice QCD
simulation. The quark number density is found to strongly depend on the
low-lying Dirac modes while its sign does not change. This result leads to that
the quark number holonomy is not sensitive to the low-lying Dirac modes. We
discuss the confinement-deconfinement transition from the property of the quark
number density and the quark number holonomy. | hep-lat |
Recent Developments of Muon g-2 from Lattice QCD: One of the most promising quantities for the search of signatures of physics
beyond the Standard Model is the anomalous magnetic moment $g-2$ of the muon,
where a comparison of the experimental result with the Standard Model estimate
yields a deviation of about $3.5~\sigma$. On the theory side, the largest
uncertainty arises from the hadronic sector, namely the hadronic vacuum
polarisation and the hadronic light-by-light scattering. I review recent
progress in calculating the hadronic contributions to the muon $g-2$ from the
lattice and discuss the prospects and challenges to match the precision of the
upcoming experiments. | hep-lat |
Towards corrections to the strong coupling limit of staggered lattice
QCD: We report on the first steps of an ongoing project to add gauge observables
and gauge corrections to the well-studied strong coupling limit of staggered
lattice QCD, which has been shown earlier to be amenable to numerical
simulations by the worm algorithm in the chiral limit and at finite density.
Here we show how to evaluate the expectation value of the Polyakov loop in the
framework of the strong coupling limit at finite temperature, allowing to study
confinement properties along with those of chiral symmetry breaking. We find
the Polyakov loop to rise smoothly, thus signalling deconfinement. The
non-analytic nature of the chiral phase transition is reflected in the
derivative of the Polyakov loop. We also discuss how to construct an effective
theory for non-zero lattice coupling, which is valid to $O(\beta)$. | hep-lat |
Impact of Dynamical Fermions on the Centre Vortex Gluon Propagator: The impact of $SU(3)$ centre vortices on the Landau-gauge gluon propagator is
calculated in the presence of dynamical fermions and compared to the pure
Yang-Mills case. The presence of dynamical fermions is found to alter the
behaviour of the centre vortex propagator when compared to the established
pure-gauge result. The gluon spectral representation is also explored from the
centre vortex perspective, where centre vortices are shown to exhibit clear
signs of positivity violation, which is an indicator of confinement. Vortex
removal subsequently restores positivity, demonstrating the crucial role centre
vortices play in the confinement of gluons. | hep-lat |
Enumerating Copies in the First Gribov Region on the Lattice in up to
four Dimensions: The covariant gauges are known to suffer from the Gribov problem: even after
fixing a gauge non-perturbatively, there may still exist residual copies which
are physically equivalent to each other, called Gribov copies. While the
influence of Gribov copies in the relevant quantities such as gluon propagators
has been heavily debated in recent studies, the significance of the role they
play in the Faddeev--Popov procedure is hardly doubted. We concentrate on
Gribov copies in the first Gribov region, i.e., the space of Gribov copies at
which the Faddeev--Popov operator is strictly positive (semi)definite. We
investigate compact U($1$) as the prototypical model of the more complicated
standard model group SU($N_{c}$). With our Graphical Processing Unit (GPU)
implementation of the relaxation method we collect up to a few million Gribov
copies per orbit. We show that the numbers of Gribov copies even in the first
Gribov region increase exponentially in two, three and four dimensions.
Furthermore, we provide strong indication that the number of Gribov copies is
gauge orbit dependent. | hep-lat |
Finite-volume effects in long-distance processes with massless leptonic
propagators: In Ref. [1], a method was proposed to calculate QED corrections to hadronic
self energies from lattice QCD without power-law finite-volume errors. In this
paper, we extend the method to processes which occur at second-order in the
weak interaction and in which there is a massless (or almost massless) leptonic
propagator. We demonstrate that, in spite of the presence of the propagator of
an almost massless electron, such an infinite-volume reconstruction procedure
can be used to obtain the amplitude for the rare kaon decay
$K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with
only exponentially small finite-volume corrections. | hep-lat |
Phase diagram of two-dimensional SU($N$) super-Yang--Mills theory with
four supercharges: We non-perturbatively study two-dimensional SU($N$) supersymmetric
Yang--Mills theory with four supercharges and large $12 \leq N \leq 20$.
Although this theory has no known holographic dual, we conduct numerical
investigations to check for features similar to the sixteen-supercharge theory,
which has a well-defined gravity dual. We carry out lattice field theory
calculations to determine the phase diagram, observing a spatial deconfinement
transition, similar to the maximally supersymmetric case. However, the
transition does not continue to strong couplings, implying the absence of a
holographic interpretation for this four-supercharge theory. | hep-lat |
Lattice QCD Study of the Pentaquark Baryons: We study the spin $\frac12$ hadronic state in quenched lattice QCD to search
for a possible $S=+1$ pentaquark resonance. Simulations are carried out on
$8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices
at $\beta$=5.7 at the quenched level with the standard plaquette gauge action
and Wilson quark action. We adopt two independent operators with I=0 and
$J^P=\frac12$ to construct a $2\times 2$ correlation matrix. After the
diagonalization of the correlation matrix, we successfully obtain the energies
of the ground-state and the 1st excited-state in this channel. The volume
dependence of the energies suggests the existence of a possible resonance state
slightly above the NK threshold in I=0 and $J^P=\frac12^-$ channel. | hep-lat |
Charmonium spectral functions from 2+1 flavour lattice QCD: Finite temperature charmonium spectral functions in the pseudoscalar and
vector channels are studied in lattice QCD with 2+1 flavours of dynamical
Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057 fm),
with a non-physical pion mass of $m_{\pi} \approx$ 545 MeV. The highest
temperature studied is approximately $1.4 T_c$. Up to this temperature no
significant variation of the spectral function is seen in the pseudoscalar
channel. The vector channel shows some temperature dependence, which seems to
be consistent with a temperature dependent low frequency peak related to heavy
quark transport, plus a temperature independent term at \omega>0. These results
are in accord with previous calculations using the quenched approximation. | hep-lat |
Lattice QCD results at finite T and μ: We propose a method to study lattice QCD at finite temperature (T) and
chemical potential (\mu). We test the method and compare it with the Glasgow
method using n_f=4 staggered QCD with imaginary \mu. The critical endpoint (E)
of QCD on the Re(\mu)-T plane is located. We use n_f=2+1 dynamical staggered
quarks with semi-realistic masses on L_t=4 lattices. Our results are based on
{\cal{O}}(10^3-10^4) configurations. | hep-lat |
Complex spacing ratios of the non-Hermitian Dirac operator in
universality classes AI$^\dagger$ and AII$^\dagger$: We consider non-Hermitian Dirac operators in QCD-like theories coupled to a
chiral U(1) potential or an imaginary chiral chemical potential. We show that
in the continuum they fall into the recently discovered universality classes
AI$^\dagger$ or AII$^\dagger$ of random matrix theory if the fermions transform
in pseudoreal or real representations of the gauge group, respectively. For
staggered fermions on the lattice this correspondence is reversed. We verify
our predictions by computing spacing ratios of complex eigenvalues, whose
distribution is universal without the need for unfolding. | hep-lat |
Light Hadron Masses from Lattice QCD: This article reviews lattice QCD results for the light hadron spectrum. We
give an overview of different formulations of lattice QCD, with discussions on
the fermion doubling problem and improvement programs. We summarize recent
developments in algorithms and analysis techniques, that render calculations
with light, dynamical quarks feasible on present day computer resources.
Finally, we summarize spectrum results for ground state hadrons and resonances
using various actions. | hep-lat |
Hopping Parameter Analysis of Leptonic and Semi-Leptonic Heavy-Light
Decays: We study leptonic and semi-leptonic decays of D and B mesons. Use of the
Hopping Parameter Expansion (HPE) for two-point functions allows us
continuously to vary the pseudoscalar mass from below m_D up towards m_B. We
compute the pseudoscalar decay constants f_D and f_B, and observe consistency
with the value calculated in the static limit. {}From the measurement of
three-point functions we compute the matrix element relevant to the decay \bar
B -> D l \bar nu_l and extract the Isgur-Wise function xi(v.v'). The HPE
enables us freely to vary the initial state pseudoscalar mass at constant v.v',
and we investigate the 1/m_Q corrections to the heavy-quark limit. | hep-lat |
Hadron correlators with improved fermions: We investigate point-to-point correlation functions for various mesonic and
baryonic channels using the ${\cal O}(a)$-improved Wilson action due to
Sheikholeslami and Wohlert. We consider propagators to both time slices 0 and
1. We find that discretisation effects are more pronounced than those reported
with unimproved Wilson fermions, but that the same procedure for removing
finite size effects is successful. Extrapolating to the chiral limit, we see
the notable features predicted phenomenologically: the ratio of interacting to
free correlators in the vector channel is roughly constant to about 1 fm, while
in the pseudoscalar channel the ratio increases markedly due to the strong
binding. | hep-lat |
Practical methods for a direct calculation of $ΔI=1/2$ $K$ to
$ππ$ Decay: A direct calculation of the complex $\Delta I=1/2$ kaon decay amplitude is
notoriously difficult because of the presence of disconnected graphs. Here we
describe and demonstrate two practical methods to defeat this problem: the
EigCG algorithm and the use of time-separated $\pi-\pi$ sources. With a fine
tuned EigCG implementation for domain wall fermions, the calculation of light
quark propagators is accelerated by a factor of 5-10 on a variety of lattices
from small ($16^3\times32\times16$) to large ($32^3\times64\times32$). In
addition, a substantial reduction in noise is achieved by separating each of
the sources for the two pions in the time direction by 2-5 lattice spacings.
These methods are combined in a calculation of $K$ to $\pi\pi$ threshold decay
using a $24^3\times64\times16$ volume and 329 MeV pions. These methods result
in non-zero signals for both Re($A_0$) and Im($A_0$) from 138 gauge
configurations. | hep-lat |
The Mellin moments $\langle x \rangle$ and $\langle x^2 \rangle$ for the
pion and kaon from lattice QCD: We present a calculation of the pion quark momentum fraction, $\langle x
\rangle$, and its third Mellin moment $\langle x^2 \rangle$. We also obtain
directly, for the first time, $\langle x \rangle$ and $\langle x^2 \rangle$ for
the kaon using local operators. We use an ensemble of two degenerate light, a
strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with
clover improvement. The quark masses are chosen so that they reproduce a pion
mass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the
ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze
several values of the source-sink time separation within the range of
$1.12-2.23$ fm to study and eliminate excited-states contributions. The
necessary renormalization functions are calculated non-perturbatively in the
RI$'$ scheme, and are converted to the $\overline{\rm MS}$ scheme at a scale of
2 GeV. The final values for the momentum fraction are $\langle x
\rangle^\pi_{u^+}=0.261(3)_{\rm stat}(6)_{\rm syst}$, $\langle x
\rangle^K_{u^+}=0.246(2)_{\rm stat}(2)_{\rm syst}$, and $\langle x
\rangle^K_{s^+}=0.317(2)_{\rm stat}(1)_{\rm syst}$. For the third Mellin
moments we find $\langle x^2 \rangle^\pi_{u^+}=0.082(21)_{\rm stat}(17)_{\rm
syst}$, $\langle x^2 \rangle^K_{u^+}=0.093(5)_{\rm stat}(3)_{\rm syst}$, and
$\langle x^2 \rangle^K_{s^+}=0.134(5)_{\rm stat}(2)_{\rm syst}$. The reported
systematic uncertainties are due to excited-state contamination. We also give
the ratio $\langle x^2 \rangle/\langle x \rangle$ which is an indication of how
quickly the PDFs lose support at large $x$. | hep-lat |
Chiral Limit of Staggered Fermions at Strong Couplings: A Loop
Representation: The partition function of two dimensional massless staggered fermions
interacting with U(N) gauge fields is rewritten in terms of loop variables in
the strong coupling limit. We use this representation of the theory to devise a
non-local Metropolis algorithm to calculate the chiral susceptibility. For
small lattices our algorithm reproduces exact results quite accurately.
Applying this algorithm to large volumes yields rather surprising results. In
particular we find $m_\pi \neq 0$ for all $N$ and it increases with $N$. Since
the talk was presented we have found reasons to believe that our algorithm
breaks down for large volumes questioning the validity of our results. | hep-lat |
Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems
with multiple right-hand sides: The technique that was used to build the EigCG algorithm for sparse symmetric
linear systems is extended to the nonsymmetric case using the BiCG algorithm.
We show that, similarly to the symmetric case, we can build an algorithm that
is capable of computing a few smallest magnitude eigenvalues and their
corresponding left and right eigenvectors of a nonsymmetric matrix using only a
small window of the BiCG residuals while simultaneously solving a linear system
with that matrix. For a system with multiple right-hand sides, we give an
algorithm that computes incrementally more eigenvalues while solving the first
few systems and then uses the computed eigenvectors to deflate BiCGStab for the
remaining systems. Our experiments on various test problems, including Lattice
QCD, show the remarkable ability of EigBiCG to compute spectral approximations
with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos.
Furthermore, our incremental EigBiCG followed by appropriately restarted and
deflated BiCGStab provides a competitive method for systems with multiple
right-hand sides. | hep-lat |
Status of Lattice QCD Determination of Nucleon Form Factors and their
Relevance for the Few-GeV Neutrino Program: Calculations of neutrino-nucleus cross sections begin with the
neutrino-nucleon interaction, making the latter critically important to
flagship neutrino oscillation experiments, despite limited measurements with
poor statistics. Alternatively, lattice QCD (LQCD) can be used to determine
these interactions from the Standard Model with quantifiable theoretical
uncertainties. Recent LQCD results of $g_{\mathrm{A}}$ are in excellent
agreement with data, and results for the (quasi-)elastic nucleon form factors
with full uncertainty budgets are expected within a few years. We review the
status of the field and LQCD results for the nucleon axial form factor,
$F_{\mathrm{A}}(Q^2)$, a major source of uncertainty in modeling sub-GeV
neutrino-nucleon interactions. Results from different LQCD calculations are
consistent, but collectively disagree with existing models, with potential
implications for current and future neutrino oscillation experiments. We
describe a road map to solidify confidence in the LQCD results and discuss
future calculations of more complicated processes, important to few-GeV
neutrino oscillation experiments. | hep-lat |
String breaking mechanisms induced by magnetic and electric condensates: The normal confining phase of gauge theories is characterised by the
condensation of magnetic monopoles and center vortices. Sometimes in coupled
gauge system one finds another phase with simultaneous condensation of electric
and magnetic charges. In both phases the confining string breaks down at a
given scale because of pair creation, however the mechanism is different. In
the former case the string breaking is a mixing phenomenon which is invisible
in the Wilson loop. On the contrary, in presence of both electric and magnetic
condensates the string breaking can be observed even in the Wilson loops.
Numerical experiments on a 3D $Z_2$ gauge-Higgs system neatly show this new
phenomenon. | hep-lat |
Finite-size scaling for the left-current correlator with non-degenerate
quark masses: We study the volume dependence of the left-current correlator with
non-degenerate quark masses to next-to-leading order in the chiral expansion.
We consider three possible regimes: all quark masses are in the
$\epsilon$-regime, all are in the $p$-regime and a mixed-regime where the
lighest quark masses satisfy $m_v \Sigma V \leq 1$ while the heavier $m_s
\Sigma V \gg 1$. These results can be used to match lattice QCD and the Chiral
Effective Theory in a large but finite box in which the Compton wavelength of
the lightest pions is of the order of the box size. We consider both the full
and partially-quenched results. | hep-lat |
Four-loop logarithms in 3d gauge + Higgs theory: We discuss the logarithmic contributions to the vacuum energy density of the
three-dimensional SU(3) + adjoint Higgs theory in its symmetric phase, and
relate them to numerical Monte Carlo simulations. We also comment on the
implications of these results for perturbative and non-perturbative
determinations of the pressure of finite-temperature QCD. | hep-lat |
Monopoles and hadron spectrum in quenched QCD: We report the preliminary results of the studies of hadron spectrum under the
background of abelian and monopole gauge fields in quenched Wilson SU(3) QCD.
Abelian gauge fields alone reproduce the same chiral limit as in the full case.
Critical hopping parameter $\kappa_c$ and $m_{\rho}$ are the same in both
cases. We need more time to get a definite result in the case of monopole
background. The photon contribution do not produce any mass gap in the chiral
limit ($\kappa=\kappa_c\sim 0.17$). The behavior is similar to those in the
free photon case for $\kappa_c= 0.125$. | hep-lat |
Nucleon to $Δ$ and $Δ$ form factors in Lattice QCD: We present recent lattice QCD results on the electroweak nucleon to $\Delta$
transition and $\Delta$ form factors using dynamical fermion gauge
configurations with a lowest pion mass of about 300 MeV, with special emphasis
in the determination of the sub-dominant quadrupole $N\gamma^*\rightarrow
\Delta$ and $\Delta$ electromagnetic form factors. | hep-lat |
Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave
Function on the Lattice: Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to
extend our previous approach for hadron-hadron interactions on the lattice.
Scattering states of hadrons with different energies encoded in the NBS
wave-function are utilized to extract non-local hadron-hadron potential. "The
ground state saturation", which is commonly used in lattice QCD but is hard to
be achieved for multi-baryons, is not required. We demonstrate that the present
method works efficiently for the nucleon-nucleon interaction (the potential and
the phase shift) in the 1S_0 channel. | hep-lat |
Higgs and W boson spectrum from lattice simulations: The spectrum of energy levels is computed for all available angular momentum
and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to
match experimental data from the Higgs-W boson sector of the standard model.
Several multi-boson states are observed, with and without linear momentum, and
all are consistent with weakly-interacting Higgs and W bosons. The creation
operators used in this study are gauge-invariant so, for example, the Higgs
operator is quadratic rather than linear in the Lagrangian's scalar field. | hep-lat |
Systematics of the HAL QCD Potential at Low Energies in Lattice QCD: The $\Xi\Xi$ interaction in the $^1$S$_0$ channel is studied to examine the
convergence of the derivative expansion of the non-local HAL QCD potential at
the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order
potential from the N$^2$LO analysis gives the scattering phase shifts
accurately at low energies, (ii) the full N$^2$LO potential gives only small
correction to the phase shifts even at higher energies below the inelastic
threshold, and (iii) the potential determined from the wall quark source at the
leading order analysis agrees with the one at the N$^2$LO analysis except at
short distances, and thus, it gives correct phase shifts at low energies. We
also study the possible systematic uncertainties in the HAL QCD potential such
as the inelastic state contaminations and the finite volume artifact for the
potential and find that they are well under control for this particular system. | hep-lat |
Distributing the chiral and flavour components of Dirac-Kahler fermions
across multiple lattices: We use a specific implementation of discrete differential geometry to
describe Dirac-Kahler fermions in such a way that we can separate their chiral
and flavour components. The formulation introduces additional lattices so that
on each lattice there is a single field of definate chirality. Within this
framework, we define an non-compact Abelian gauge theory. | hep-lat |
Correlation functions in lattice formulations of quantum gravity: We compare different models of a quantum theory of four-dimensional lattice
gravity based on Regge's original proposal. From Monte Carlo simulations we
calculate two-point functions between geometrical quantities and estimate the
masses of the corresponding interaction particles. | hep-lat |
Lattice QCD study of baryon-baryon interactions in the (S,I)=(-2,0)
system using the coupled-channel formalism: We investigate baryon-baryon interactions with strangeness $S=-2$ and isospin
I=0 system from Lattice QCD. In order to solve this system, we prepare three
types of baryon-baryon operators ($\Lambda-\Lambda$, $N-\Xi$ and
$\Sigma-\Sigma$) for the sink and construct three source operators
diagonalizing the $3\times3$ correlation matrix. Combining of the prepared sink
operators with the diagonalized source operators, we obtain nine effective
Nambu-Bethe-Salpeter (NBS) wave functions. The $3\times3$ potential matrix is
calculated by solving the coupled-channel Schr\"odinger equation. The flavor
SU(3) breaking effects of the potential matrix are also discussed by comparing
with the results of the SU(3) limit calculation. Our numerical results are
obtained from three sets of 2+1 flavor QCD gauge configurations provided by the
CP-PACS/JLQCD Collaborations. | hep-lat |
Chiral Phase Transition in Lattice QCD with Wilson Quarks: The nature of the chiral phase transition in lattice QCD is studied for the
cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice
with the temporal direction extension $N_t=4$. We find that the chiral phase
transition is continuous for the case of 2 flavors, while it is of first order
for 3 and 6 flavors. | hep-lat |
New Algorithm of the Finite Lattice Method for the High-temperature
Expansion of the Ising Model in Three Dimensions: We propose a new algorithm of the finite lattice method to generate the
high-temperature series for the Ising model in three dimensions. It enables us
to extend the series for the free energy of the simple cubic lattice from the
previous series of 26th order to 46th order in the inverse temperature. The
obtained series give the estimate of the critical exponent for the specific
heat in high precision. | hep-lat |
Chebyshev and Backus-Gilbert reconstruction for inclusive semileptonic
$B_{(s)}$-meson decays from Lattice QCD: We present a study on the nonperturbative calculation of observables for
inclusive semileptonic decays of $B_{(s)}$ mesons using lattice QCD. We focus
on the comparison of two different methods to analyse the lattice data of
Euclidean correlation functions, specifically Chebyshev and Backus-Gilbert
approaches. This type of computation may eventually provide new insight into
the long-standing tension between the inclusive and exclusive determinations of
the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$.
We report the results from a pilot lattice computation for the decay $B_s
\rightarrow X_c \, l\nu_l$, where the valence quark masses are approximately
tuned to their physical values using the relativistic-heavy quark action for
the $b$ quark and the domain-wall formalism for the other valence quarks. We
address the computation of the total decay rate as well as leptonic and
hadronic moments, discussing similarities and differences between the two
analysis techniques. | hep-lat |
Numerical tests of the electroweak phase transition and thermodynamics
of the electroweak plasma: The finite temperature phase transition in the SU(2) Higgs model at a Higgs
boson mass $M_H \simeq 34$ GeV is studied in numerical simulations on
four-dimensional lattices with time-like extensions up to $L_t=5$. The effects
of the finite volume and finite lattice spacing on masses and couplings are
studied in detail. The errors due to uncertainties in the critical hopping
parameter are estimated. The thermodynamics of the electroweak plasma near the
phase transition is investigated by determining the relation between energy
density and pressure. | hep-lat |
Systematics of the HAL QCD Potential at Low Energies in Lattice QCD: The $\Xi\Xi$ interaction in the $^1$S$_0$ channel is studied to examine the
convergence of the derivative expansion of the non-local HAL QCD potential at
the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order
potential from the N$^2$LO analysis gives the scattering phase shifts
accurately at low energies, (ii) the full N$^2$LO potential gives only small
correction to the phase shifts even at higher energies below the inelastic
threshold, and (iii) the potential determined from the wall quark source at the
leading order analysis agrees with the one at the N$^2$LO analysis except at
short distances, and thus, it gives correct phase shifts at low energies. We
also study the possible systematic uncertainties in the HAL QCD potential such
as the inelastic state contaminations and the finite volume artifact for the
potential and find that they are well under control for this particular system. | hep-lat |
Absolute X-distribution and self-duality: Various models of QCD vacuum predict that it is dominated by excitations that
are predominantly self-dual or anti-self-dual. In this work we look at the
tendency for self-duality in the case of pure-glue SU(3) gauge theory using the
overlap-based definition of the field-strength tensor. To gauge this property,
we use the absolute X-distribution method which is designed to quantify the
dynamical tendency for polarization for arbitrary random variables that can be
decomposed in a pair of orthogonal subspaces. | hep-lat |
Center Projection With and Without Gauge Fixing: We consider projections of SU(2) lattice link variables onto Z(2) center and
U(1) subgroups, with and without gauge-fixing. It is shown that in the absence
of gauge-fixing, and up to an additive constant, the static quark potential
extracted from projected variables agrees exactly with the static quark
potential taken from the full link variables; this is an extension of recent
arguments by Ambjorn and Greensite, and by Ogilvie. Abelian and center
dominance is essentially trivial in this case, and seems of no physical
relevance. The situation changes drastically upon gauge fixing. In the case of
center projection, there are a series of tests one can carry out, to check if
vortices identified in the projected configurations are physical objects. All
these criteria are satisfied in maximal center gauge, and we show here that
they all fail in the absence of gauge fixing. The non-triviality of center
projection is due entirely to the maximal center gauge-fixing, which pumps
information about the location of extended physical objects into local Z(2)
observables. | hep-lat |
Lattice gauge-fixing for generic covariant gauges: We propose a method which allows the generalization of the Landau lattice
gauge-fixing procedure to generic covariant gauges. We report preliminary
numerical results showing how the procedure works for $SU(2)$ and $SU(3)$. We
also report numerical results showing that the contribution of finite
lattice-spacing effects and/or spurious copies are relevant in the lattice
gauge-fixing procedure. | hep-lat |
Twisted mass ensemble generation on GPU machines: We present how we ported the Hybrid Monte Carlo implementation in the tmLQCD
software suite to GPUs through offloading its most expensive parts to the QUDA
library. We discuss our motivations and some of the technical challenges that
we encountered as we added the required functionality to both tmLQCD and QUDA.
We further present some performance details, focussing in particular on the
usage of QUDA's multigrid solver for poorly conditioned light quark monomials
as well as the multi-shift solver for the non-degenerate strange and charm
sector in $N_f=2+1+1$ simulations using twisted mass clover fermions, comparing
the efficiency of state-of-the-art simulations on CPU and GPU machines. We also
take a look at the performance-portability question through preliminary tests
of our HMC on a machine based on AMD's MI250 GPU, finding good performance
after a very minor additional porting effort. Finally, we conclude that we
should be able to achieve GPU utilisation factors acceptable for the current
generation of (pre-)exascale supercomputers with subtantial efficiency
improvements and real time speedups compared to just running on CPUs. At the
same time, we find that future challenges will require different approaches
and, most importantly, a very significant investment of personnel for software
development. | hep-lat |
Evidence for fine tuning of fermionic modes in lattice gluodynamics: We consider properties of zero and near-zero fermionic modes in lattice
gluodynamics. The modes are known to be sensitive to the topology of the
underlying gluonic fields in the quantum vacuum state of the gluodynamics. We
find evidence that these modes are fine tuned, that is exhibit sensitivity to
both physical (one can say, hadronic) scale and to the ultraviolet cutoff.
Namely, the density of the states is in physical units while the localization
volume of the modes tends to zero in physical units with the lattice spacing
tending to zero. We discuss briefly possible theoretical implications and also
include some general, review-type remarks. | hep-lat |
Towards the continuum limit of nucleon form factors at the physical
point using lattice QCD: We present results for the axial charge and root-mean-square (RMS) radii of
the nucleon obtained from 2+1 flavor lattice QCD at the physical point with a
large spatial extent of about 10 fm. Our calculations are performed with the
PACS10 gauge configurations generated by the PACS Collaboration with the six
stout-smeared $O(a)$ improved Wilson-clover quark action and Iwasaki gauge
action at $\beta$ = 1.82 and 2.00 corresponding to lattice spacings of 0.085 fm
and 0.063 fm respectively. We first evaluate the value of $g_A/g_V$ , which is
not renormalized in the continuum limit and thus ends up with the renormalized
axial charge. Moreover, we also calculate the nucleon elastic form factors and
determine three kinds of isovector RMS radii such as electric, magnetic and
axial ones at the two lattice spacings. We finally discuss the discretization
uncertainties on renormalized axial charge and isovector RMS radii towards the
continuum limit. | hep-lat |
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the
Schroedinger functional scheme: We present an evaluation of the quark mass renormalization factor for Nf=2+1
QCD. The Schroedinger functional scheme is employed as the intermediate scheme
to carry out non-perturbative running from the low energy to deep in the high
energy perturbative region. The regularization independent step scaling
function of the quark mass is obtained in the continuum limit. Renormalization
factors for the pseudo scalar density and the axial vector current are also
evaluated for the same action and the bare couplings as two recent large scale
Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which
covered the up-down quark mass range heavier than m_pi=500 MeV and that of
PACS-CS collaboration on the physical point using the reweighting technique. | hep-lat |
The Status of D-Theory: Field theories are usually quantized by performing a path integral over
configurations of classical fields. This is the case both in perturbation
theory and in Wilson's nonperturbative lattice field theory. D-theory is an
alternative nonperturbative formulation of field theory in which classical
fields emerge from the low-energy collective dynamics of discrete quantum
variables (quantum spins and their gauge analogs -- quantum links) which
undergo dimensional reduction. D-theory was developed some time ago as a
discrete approach to U(1) and SU(2) pure gauge theories, extended to SU(N)
gauge theories and full QCD, and also applied to a variety of other models. On
the practical side, D-theory provides a framework for the development of
efficient numerical methods, such as cluster algorithms. For example, in the
D-theory formulation of CP(N-1) models one can simulate efficiently at non-zero
chemical potential or at non-zero vacuum angle theta. On the conceptual side,
D-theory offers a natural solution for the nonperturbative hierarchy problem of
chiral symmetry in QCD. We also take a broader nonperturbative view on
fundamental physics and speculate that D-theory variables -- i.e. quantum spins
and quantum links -- may be promising candidates for the physical degrees of
freedom that Nature has chosen to regularize the standard model physics at
ultra-short distances. | hep-lat |
On-shell representations of two-body transition amplitudes: single
external current: This work explores scattering amplitudes that couple two-particle systems via
a single external current insertion, $2+\mathcal{J}\to 2$. Such amplitudes can
provide structural information about the excited QCD spectrum. We derive an
exact analytic representation for these reactions. From these amplitudes, we
show how to rigorously define resonance and bound-state form-factors.
Furthermore, we explore the consequences of the narrow-width limit of the
amplitudes as well as the role of the Ward-Takahashi identity for conserved
vector currents. These results hold for any number of two-body channels with no
intrinsic spin, and a current with arbitrary Lorentz structure and quantum
numbers. This work and the existing finite-volume formalism provide a complete
framework for determining this class of amplitudes from lattice QCD. | hep-lat |
Quenched charmonium near the continuum limit: We study relativistic charmonium on very fine quenched lattices (beta=6.4 and
6.6). We concentrate on the calculation of the hyperfine splitting between
eta_c and J/psi, aiming for a controlled continuum extrapolation of this
quantity. Results for the eta_c and J/psi wave functions are also presented. | hep-lat |
Lattice QCD Study for Confinement and Hadrons: Using SU(3) lattice QCD, we perform the detailed studies of the three-quark
and the multi-quark potentials. From the accurate calculation for more than 300
different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm
3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear
potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for
Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in
maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we
perform the accurate calculation for the 1st excited-state 3Q potential $V_{\rm
3Q}^{\rm e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three
quarks, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv
V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a
physical reason of the success of the quark model. $\Delta E_{\rm 3Q}$ is found
to be reproduced by the ``inverse Mercedes Ansatz'', which indicates a
complicated bulk excitation for the gluonic-excitation mode. We study also the
tetra-quark and the penta-quark potentials in lattice QCD, and find that they
are well described by the OGE Coulomb plus multi-Y type linear potential, which
supports the flux-tube picture even for the multi-quarks. | hep-lat |
Lattice QCD study of a five-quark hadronic molecule: We compute the ground-state energies of a heavy-light K-Lambda like system as
a function of the relative distance r of the hadrons. The heavy quarks, one in
each hadron, are treated as static. Then, the energies give rise to an
adiabatic potential Va(r) which we use to study the structure of the five-quark
system. The simulation is based on an anisotropic and asymmetric lattice with
Wilson fermions. Energies are extracted from spectral density functions
obtained with the maximum entropy method. Our results are meant to give
qualitative insight: Using the resulting adiabatic potential in a Schroedinger
equation produces bound state wave functions which indicate that the ground
state of the five-quark system resembles a hadronic molecule, whereas the first
excited state, having a very small rms radius, is probably better described as
a five-quark cluster, or a pentaquark. We hypothesize that an all light-quark
pentaquark may not exist, but in the heavy-quark sector it might, albeit only
as an excited state. | hep-lat |
Weak universality induced by $Q=\pm 2e$ charges at the deconfinement
transition of a (2+1)-d $U(1)$ lattice gauge theory: Matter-free lattice gauge theories (LGTs) provide an ideal setting to
understand confinement to deconfinement transitions at finite temperatures,
which is typically due to the spontaneous breakdown (at large temperatures) of
the centre symmetry associated with the gauge group. Close to the transition,
the relevant degrees of freedom (Polyakov loop) transform under these centre
symmetries, and the effective theory only depends on the Polyakov loop and its
fluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified
numerically, for the $U(1)$ LGT in $(2+1)$-d the transition is in the 2-d XY
universality class, while for the $Z_2$ LGT, it is in the 2-d Ising
universality class. We extend this classic scenario by adding higher charged
matter fields, and show that the notion of universality is generalized such
that the critical exponents $\gamma, \nu$ can change continuously as a coupling
is varied, while their ratio is fixed to the 2-d Ising value. While such weak
universality is well-known for spin models, we demonstrate this for LGTs for
the first time. Using an efficient cluster algorithm, we show that the finite
temperature phase transition of the $U(1)$ quantum link LGT in the spin
$S=\frac{1}{2}$ representation is in the 2-d XY universality class, as
expected. On the addition of $Q = \pm 2e$ charges distributed thermally, we
demonstrate the occurrence of weak universality. | hep-lat |
A quark action for very coarse lattices: We investigate a tree-level O(a^3)-accurate action, D234c, on coarse
lattices. For the improvement terms we use tadpole-improved coefficients, with
the tadpole contribution measured by the mean link in Landau gauge.
We measure the hadron spectrum for quark masses near that of the strange
quark. We find that D234c shows much better rotational invariance than the
Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to
smaller finite-lattice-spacing errors than plaquette tadpole improvement. We
obtain accurate ratios of lattice spacings using a convenient ``Galilean
quarkonium'' method.
We explore the effects of possible O(alpha_s) changes to the improvement
coefficients, and find that the two leading coefficients can be independently
tuned: hadron masses are most sensitive to the clover coefficient, while hadron
dispersion relations are most sensitive to the third derivative coefficient
C_3. Preliminary non-perturbative tuning of these coefficients yields values
that are consistent with the expected size of perturbative corrections. | hep-lat |
Controlling sign problems in spin models using tensor renormalization: We consider the sign problem for classical spin models at complex $\beta
=1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization
group method allows reliable calculations for larger Im$\beta$ than the
reweighting Monte Carlo method. For the Ising model with complex $\beta$ we
compare our results with the exact Onsager-Kaufman solution at finite volume.
The Fisher zeros can be determined precisely with the TRG method. We check the
convergence of the TRG method for the O(2) model on $L\times L$ lattices when
the number of states $D_s$ increases. We show that the finite size scaling of
the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless
transition assumption and predict the locations for larger volume. The location
of these zeros agree with Monte Carlo reweighting calculation for small volume.
The application of the method for the O(2) model with a chemical potential is
briefly discussed. | hep-lat |
Lee-Yang zeroes in the one flavour massive lattice Schwinger model: We study the partition function of the model formulated with Wilson fermions
with only one species, both analytically and numerically. At strong coupling we
construct the solution for lattice size up to $8\times 8$, a polynomial in the
hopping parameter up to $O(\ka^{128})$. At $\be>0$ we evaluate the expectation
value of the fermion determinant for complex values of $\ka$. From the Lee-Yang
zeroes we find support for the existence of a line of phase transitions from
$(\be=0, \ka\simeq 0.38)$ up to $(\be=\infty, \ka=1/4)$. | hep-lat |
Order a improved renormalization constants: We present non-perturbative results for the constants needed for on-shell
$O(a)$ improvement of bilinear operators composed of Wilson fermions. We work
at $\beta=6.0$ and 6.2 in the quenched approximation. The calculation is done
by imposing axial and vector Ward identities on correlators similar to those
used in standard hadron mass calculations. A crucial feature of the calculation
is the use of non-degenerate quarks. We also obtain results for the constants
needed for off-shell $O(a)$ improvement of bilinears, and for the scale and
scheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P).
Several of the constants are determined using a variety of different Ward
identities, and we compare their relative efficacies. In this way, we find a
method for calculating $c_V$ that gives smaller errors than that used
previously. Wherever possible, we compare our results with those of the ALPHA
collaboration (who use the Schr\"odinger functional) and with 1-loop
tadpole-improved perturbation theory. | hep-lat |
B, Bs, K and pi weak matrix elements with physical light quarks: Calculations of pseudoscalar decay constants of B, Bs, K and pi mesons with
physical light quarks are presented. We use HISQ ensembles that include u,d,s
and c sea quarks at three lattice spacings. HISQ is used for the valence light
quarks and a radiatively improved NRQCD action for the heavy quarks. The key
results are f_{B^+}=0.184(4)$ GeV, f_{B_s}=0.224(4) GeV,
f_{B_s}/f_{B^+}=1.217(8), f_{K^+}/f_{pi^+}=1.1916(21), f_{K^+}=155.37(34) MeV,
giving a significant improvement over previous results that required chiral
extrapolation. We also calculate the Wilson flow scale w_0, finding
w_0=0.1715(9) fm. | hep-lat |
Phase structure of two-color QCD at real and imaginary chemical
potentials; lattice simulations and model analyses: We investigate the phase structure of two-color QCD at both real and
imaginary chemical potentials mu, performing lattice simulations and analyzing
the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model.
Lattice QCD simulations are done on an 8^3 times 4 lattice with the
clover-improved two-flavor Wilson fermion action and the renormalization-group
improved Iwasaki gauge action. We test the analytic continuation of physical
quantities from imaginary mu to real mu by comparing lattice QCD results
calculated at real mu with the result of analytic function the coefficients of
which are determined from lattice QCD results at imaginary mu. We also test the
validity of the PNJL model by comparing model results with lattice QCD ones.
The PNJL model is good in the deconfinement region, but less accurate in the
transition and confinement regions. This problem is improved by introducing the
baryon degree of freedom to the model. It is also found that the vector-type
four-quark interaction is necessary to explain lattice data on the quark number
density. | hep-lat |
Monopoles and Spatial String Tension in the High Temperature Phase of
SU(2) QCD: We studied a behavior of monopole currents in the high temperature
(deconfinement) phase of abelian projected finite temperature SU(2) QCD in
maximally abelian gauge. Wrapped monopole currents closed by periodic boundary
play an important role for the spatial string tension which is a
non-perturbative quantity in the deconfinement phase. The wrapped monopole
current density seems to be non-vanishing in the continuum limit. These results
may be related to Polyakov's analysis of the confinement mechanism using
monopole gas in 3-dimensional SU(2) gauge theory with Higgs fields. | hep-lat |
The QCD equation of state in background magnetic fields: We determine the equation of state of 2+1-flavor QCD with physical quark
masses, in the presence of a constant (electro)magnetic background field on the
lattice. To determine the free energy at nonzero magnetic fields we develop a
new method, which is based on an integral over the quark masses up to
asymptotically large values where the effect of the magnetic field can be
neglected. The method is compared to other approaches in the literature and
found to be advantageous for the determination of the equation of state up to
large magnetic fields. Thermodynamic observables including the longitudinal and
transverse pressure, magnetization, energy density, entropy density and
interaction measure are presented for a wide range of temperatures and magnetic
fields, and provided in ancillary files. The behavior of these observables
confirms our previous result that the transition temperature is reduced by the
magnetic field. We calculate the magnetic susceptibility and permeability,
verifying that the thermal QCD medium is paramagnetic around and above the
transition temperature, while we also find evidence for weak diamagnetism at
low temperatures. | hep-lat |
Landau gauge gluon and ghost propagators from two-flavor lattice QCD at
T > 0: In this contribution we extend our unquenched computation of the Landau gauge
gluon and ghost propagators in lattice QCD at non-zero temperature. The study
was aimed at providing input for investigations employing continuum functional
methods. We show data which correspond to pion mass values between 300 and 500
MeV and are obtained for a lattice size 32**3 x 12. The longitudinal and
transversal components of the gluon propagator turn out to change smoothly
through the crossover region, while the ghost propagator exhibits only a very
weak temperature dependence. For a pion mass of around 400 MeV and the
intermediate temperature value of approx. 240 MeV we compare our results with
additional data obtained on a lattice with smaller Euclidean time extent N_t =
8, 10 and find a reasonable scaling behavior. | hep-lat |
Fermionic observables in Numerical Stochastic Perturbation Theory: We present technical details of fermionic observables computations in NSPT.
In particular we discuss the construction of composite operators starting from
the inverse Dirac operator building block, the subtraction of UV divergences
and the treatment of irrelevant contributions in extracting the continuum
limit. | hep-lat |
Lattice calculation of SU(3) flavor breaking ratios in B - anti-B mixing: We present an unquenched lattice calculation for the SU(3) flavor breaking
ratios of the heavy-light decay constants and the $\Delta B = 2$ matrix
elements. The calculation was performed on $16^3 \times 32$ lattices with two
dynamical flavors of domain-wall quarks and inverse lattice spacing $1/a =
1.69(5)$ GeV. Heavy quarks were implemented using an improved lattice
formulation of the static approximation. In the infinite heavy-quark mass limit
we obtain $f_{B_s}/f_{B_d} = 1.29(4)(6)$, $B_{B_s}/B_{B_d} = 1.06(6)(4)$, $\xi
= 1.33(8)(8)$ where the first error is statistical and the second systematic. | hep-lat |
Duality and scaling in 3-dimensional scalar electrodynamics: Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry,
is believed to be dual to a scalar theory with a global U(1) symmetry, near the
phase transition point. The conjectured duality leads to definite predictions
for the scaling exponents of the gauge theory transition in the type II region,
and allows thus to be scrutinized empirically. We review these predictions, and
carry out numerical lattice Monte Carlo measurements to test them: a number of
exponents, characterising the two phases as well as the transition point, are
found to agree with expectations, supporting the conjecture. We explain why
some others, like the exponent characterising the photon correlation length,
appear to disagree with expectations, unless very large system sizes and the
extreme vicinity of the transition point are considered. Finally, we remark
that in the type I region the duality implies an interesting quantitative
relationship between a magnetic flux tube and a 2-dimensional non-topological
soliton. | hep-lat |
Correlation Functions of Hadron Currents in the QCD Vacuum Calculated in
Lattice QCD: Point-to-point vacuum correlation functions for spatially separated hadron
currents are calculated in quenched lattice QCD on a $16^3\times 24$ lattice
with $6/g^2=5.7$. The lattice data are analyzed in terms of dispersion
relations, which enable us to extract physical information from small distances
where asymptotic freedom is apparent to large distances where the hadronic
resonances dominate. In the pseudoscalar, vector, and axial vector channels
where experimental data or phenomenological information are available,
semi-quantitative agreement is obtained. In the nucleon and delta channels,
where no experimental data exist, our lattice data complement experiments.
Comparison with approximations based on sum rules and interacting instantons
are made, and technical details of the lattice calculation are described. | hep-lat |
Delta I = 3/2, K to Pi Pi Decays with a Nearly Physical Pion Mass: The Delta I = 3/2 K to Pi Pi decay amplitude is calculated on RBC/UKQCD 32^3
x 64, L_s=32 dynamical lattices with 2+1 flavors of domain wall fermions using
the DSDR and Iwasaki gauge action. The calculation is performed with a single
pion mass (m_pi=141.9(2.3) MeV, partially quenched) and kaon mass
(m_K=507.4(8.5) MeV) which are nearly physical, and with nearly energy
conserving kinematics. Antiperiodic boundary conditions in two spatial
directions are used to give the two pions non-zero ground state momentum.
Results for time separations of 20, 24, 28 and 32 between the kaon and two-pion
sources are computed and an error weighted average is performed to reduce the
error. We find prelimenary results for Re(A_2)=1.396(081)_stat(160)_sys x
10^(-8) GeV and Im(A_2) = -8.46(45)_stat(1.95)_sys x 10^(-13) GeV. | hep-lat |
Simulating lattice QCD at finite temperature and zero quark mass: We simulate lattice QCD with an irrelevant chiral 4-fermion interaction which
allows us to simulate at zero quark mass. This enables us to study the
finite-temperature chiral-symmetry-restoring phase transition for 2 massless
quark flavours, which is believed to be second order. In particular, it enables
us to estimate the critical exponents which characterize the universality class
of this transition. Our earlier simulations on $N_t=4$ and $N_t=6$ lattices
revealed that finite lattice-spacing artifacts on such coarse lattices affect
the nature of the transition. We are now simulating on $N_t=8$ lattices ($12^3
\times 8$, $16^3 \times 8$ and $24^3 \times 8$ lattices) where we expect to
expose the continuum behaviour of this transition. | hep-lat |
Spectroscopy in finite density lattice field theory: An exploratory
study in the relativistic Bose gas: We analyze 2-point functions in the relativistic Bose gas on the lattice,
i.e., a charged scalar phi-4 field with chemical potential mu. Using a
generalized worm algorithm we perform a Monte Carlo simulation in a dual
representation in terms of fluxes where the complex action problem is overcome.
We explore various aspects of lattice spectroscopy at finite density and zero
temperature, such as the asymmetry of forward and backward propagation in time
and the transition into the condensed phase. It is shown that after a suitable
subtraction the exponents for forward and backward propagation are independent
of mu and agree with the mass obtained from the propagator at mu = 0. This
holds for mu < mu_c and shows that below the condensation transition the mass
is independent of mu as expected from the Silver Blaze scenario. | hep-lat |
A computational system for lattice QCD with overlap Dirac quarks: We outline the essential features of a Linux PC cluster which is now being
developed at National Taiwan University, and discuss how to optimize its
hardware and software for lattice QCD with overlap Dirac quarks. At present,
the cluster constitutes of 30 nodes, with each node consisting of one Pentium 4
processor (1.6/2.0 GHz), one Gbyte of PC800 RDRAM, one 40/80 Gbyte hard disk,
and a network card. The speed of this system is estimated to be 30 Gflops, and
its price/performance ratio is better than $1.0/Mflops for 64-bit (double
precision) computations in quenched lattice QCD with overlap Dirac quarks. | hep-lat |
Infrared fixed point in SU(2) gauge theory with adjoint fermions: We apply Schrodinger-functional techniques to the SU(2) lattice gauge theory
with N_f=2 flavors of fermions in the adjoint representation. Our use of
hypercubic smearing enables us to work at stronger couplings than did previous
studies, before encountering a critical point and a bulk phase boundary.
Measurement of the running coupling constant gives evidence of an infrared
fixed point g* where 1/g*^2 = 0.20(4)(3). At the fixed point, we find a mass
anomalous dimension gamma_m(g*) = 0.31(6). | hep-lat |
A new strategy for evaluating the LO HVP contribution to $(g-2)_μ$ on
the lattice: A highly physical model of the subtracted $I=1$ vector polarization, obtained
using a dispersive representation with precise hadronic $\tau$ decay data as
input, is used to investigate systematic issues in the lattice evaluation of
the leading order hadronic vacuum polarization contribution to the anomalous
magnetic moment of the muon. The model is also employed to study possible
resolutions of these problems. A hybrid approach to analyzing lattice data,
involving low-order Pad\'e, low-degree conformal-variable polynomial, or
supplemented NNLO ChPT fits for $Q^2$ below $\sim 0.1-0.2$ GeV$^2$ and direct
numerical integration of lattice data above this point, is shown to bring the
systematic issues identified under control at the sub-$1\%$ level. | hep-lat |
Atomic Bose Condensation and the Lattice: I show how interaction corrections to the Bose condensation temperature of an
atomic gas can be computed using a combination of perturbative effective field
theory and lattice techniques. | hep-lat |
The Landshoff-Nachtmann Pomeron on the Lattice: We investigate the Landshoff-Nachtmann two-gluon-exchange model of the
Pomeron using gluon propagators computed in the Landau gauge within quenched
lattice QCD calculations. We first determine an effective gluon-quark coupling
by constraining the Pomeron-quark coupling to its phenomenological value
$\beta_0 = 2\, \gev^{-1}$. We then provide predictions for a variety of
diffractive processes. As the propagators have been evaluated entirely from QCD
first principles (although in the quenched approximation), our results provide
a consistency check of the Landshoff-Nachtmann model. We address the issue of
the possible gauge-dependence of our results, which will be the object of a
future study. | hep-lat |
Display of probability densities for data from a continuous distribution: Based on cumulative distribution functions, Fourier series expansion and
Kolmogorov tests, we present a simple method to display probability densities
for data drawn from a continuous distribution. It is often more efficient than
using histograms. | hep-lat |
The vector and axial vector current in Wilson ChPT: We construct the vector and axial vector currents in Wilson Chiral
Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD
with Wilson fermions.
Our construction is slightly different compared to ChPT in continuum QCD,
where the currents are essentially the (partially) conserved currents
associated with the chiral symmetries. In WChPT, due to explicit chiral
symmetry breaking at non-zero lattice spacing, there appear O(a) terms in the
expressions for the currents which do not stem from the effective action. In
addition, the finite renormalization of the currents needs to be taken into
account in order to properly match the currents of the effective theory.
As an illustration we compute f_pi to one loop with the renormalized axial
vector current for a particular renormalization condition. It turns out that
for this particular condition some of the O(a) corrections are taken care of by
the renormalization. | hep-lat |
Glueball matrix elements: a lattice calculation and applications: We compute the matrix elements of the energy-momentum tensor between glueball
states and the vacuum in SU(3) lattice gauge theory and extrapolate them to the
continuum. These matrix elements may play an important phenomenological role in
identifying glue-rich mesons. Based on a relation derived long ago by the ITEP
group for J/psi radiative decays, the scalar matrix element leads to a
branching ratio for the glueball that is at least three times larger than the
experimentally observed branching ratio for the f_0 mesons above 1GeV. This
suggests that the glueball component must be diluted quite strongly among the
known scalar mesons. Finally we review the current best continuum determination
of the scalar and tensor glueball masses, the deconfining temperature, the
string tension and the Lambda parameter, all in units of the Sommer reference
scale, using calculations based on the Wilson action. | hep-lat |
Lattice Simulations using OpenACC compilers: OpenACC compilers allow one to use Graphics Processing Units without having
to write explicit CUDA codes. Programs can be modified incrementally using
OpenMP like directives which causes the compiler to generate CUDA kernels to be
run on the GPUs. In this article we look at the performance gain in lattice
simulations with dynamical fermions using OpenACC compilers. | hep-lat |
Approaching the chiral point in two-flavour lattice simulations: We investigate the behaviour of the pion decay constant and the pion mass in
two-flavour lattice QCD, with the physical and chiral points as ultimate goal.
Measurements come from the ensembles generated by the CLS initiative using the
O(a)-improved Wilson formulation, with lattice spacing down to about 0.05 fermi
and pion masses as low as 190 MeV. The applicability of SU(2) chiral
perturbation theory is investigated, and various functional forms, and their
range of validity, are compared. The physical scale is set through the kaon
decay constant, whose measurement is enabled by inserting a third, heavier
valence strange quark. | hep-lat |
Critical exponents of a three dimensional O(4) spin model: By Monte Carlo simulation we study the critical exponents governing the
transition of the three-dimensional classical O(4) Heisenberg model, which is
considered to be in the same universality class as the finite-temperature QCD
with massless two flavors. We use the single cluster algorithm and the
histogram reweighting technique to obtain observables at the critical
temperature. After estimating an accurate value of the inverse critical
temperature $\Kc=0.9360(1)$, we make non-perturbative estimates for various
critical exponents by finite-size scaling analysis. They are in excellent
agreement with those obtained with the $4-\epsilon$ expansion method with
errors reduced to about halves of them. | hep-lat |
(1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation: The color-flavor transformation, an identity that connects two integrals,
each of which is over one of a dual pair of Lie groups acting in the fermionic
Fock space, is extended to the case of the special unitary group. Using this
extension, a toy model of lattice QCD is studied: N_f species of spinless
fermions interacting with strongly coupled SU(N_c) lattice gauge fields in 1+1
dimensions. The color-flavor transformed theory is expressed in terms of gauge
singlets, the meson fields, organized into sectors distinguished by the
distribution of baryonic flux. A comprehensive analytical and numerical search
is made for saddle-point configurations of the meson fields, with various
topological charges, in the vacuum and single-baryon sectors. Two definitions
of the static baryon on the square lattice, straight and zigzag, are
investigated. The masses of the baryonic states are estimated using the
saddle-point approximation for large N_c. | hep-lat |
JLQCD IroIro++ lattice code on BG/Q: We describe our experience on the multipurpose C++ code IroIro++ designed for
JLQCD to run on the BG/Q installation at KEK. We discuss some details on the
performance improvements specific for the IBM Blue Gene Q. | hep-lat |
The spin content of the proton in quenched QCD: We present preliminary results on the proton spin structure function at zero
momentum, in the quenched approximation. Our calculation makes use of a
nonperturbative means of determining the multiplicative renormalization of the
topological charge density. | hep-lat |
Degeneracy of vector-channel spatial correlators in high temperature QCD: We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical
domain-wall fermions on $32^3\times 8$ lattices at temperatures up to 380 MeV
with various quark masses. We measure the correlators of spin-one isovector
operators including vector, axial-vector, tensor and axial-tensor. At
temperatures above $T_c$ we observe an approximate degeneracy of the
correlators in these channels, which is unexpected because some of them are not
related under $SU(2)_L \times SU(2)_R$ nor $U(1)_A$ symmetries. The observed
approximate degeneracy suggests emergent $SU(2)_{CS}$ (chiral-spin) and $SU(4)$
symmetries at high $T$. | hep-lat |
Testing universality and the fractional power prescription for the
staggered fermion determinant: In [Phys.Rev.Lett.92:162002 (2004), hep-lat/0312025] expressions for the
continuous Euclidean time limits of various lattice fermion determinants were
derived and compared in order to test universality expectations in Lattice QCD.
Here we review that work with emphasis on its relevance for assessing the
fractional power prescription for the determinant in dynamical staggered
fermion simulations. Some new supplementary material is presented; in
particular the status of the "universality anomaly" is clarified: it is shown
to be gauge field-independent and therefore physically inconsequential. | hep-lat |
A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac
operator in lattice QCD: Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in
several lattice QCD simulations, e.g., for noise reduction when evaluating
all-to-all propagators. In this paper we present a Davidson-type eigensolver
that utilizes the structural properties of the Hermitian Wilson-Dirac operator
$Q$ to compute eigenpairs of this operator corresponding to small eigenvalues.
The main idea is to exploit a synergy between the (outer) eigensolver and its
(inner) iterative scheme which solves shifted linear systems. This is achieved
by adapting the multigrid DD-$\alpha$AMG algorithm to a solver for shifted
systems involving the Hermitian Wilson-Dirac operator. We demonstrate that
updating the coarse grid operator using eigenvector information obtained in the
course of the generalized Davidson method is crucial to achieve good
performance when calculating many eigenpairs, as our study of the local
coherence shows. We compare our method with the commonly used software-packages
PARPACK and PRIMME in numerical tests, where we are able to achieve significant
improvements, with speed-ups of up to one order of magnitude and a near-linear
scaling with respect to the number of eigenvalues. For illustration we compare
the distribution of the small eigenvalues of $Q$ on a $64\times 32^3$ lattice
with what is predicted by the Banks-Casher relation in the infinite volume
limit. | hep-lat |
Investigating the critical properties of beyond-QCD theories using Monte
Carlo Renormalization Group matching: Monte Carlo Renormalization Group (MCRG) methods were designed to study the
non-perturbative phase structure and critical behavior of statistical systems
and quantum field theories. I adopt the 2-lattice matching method used
extensively in the 1980's and show how it can be used to predict the existence
of non-perturbative fixed points and their related critical exponents in many
flavor SU(3) gauge theories. This work serves to test the method and I study
relatively well understood systems: the $N_f=0$, 4 and 16 flavor models. The
pure gauge and $N_f=4$ systems are confining and chirally broken and the MCRG
method can predict their bare step scaling functions. Results for the $N_f=16$
model indicate the existence of an infrared fixed point with nearly marginal
gauge coupling. I present preliminary results for the scaling dimension of the
mass at this new fixed point. | hep-lat |
Progress on the QCD deconfinement critical point for $N_\text{f}=2$
staggered fermions: The global center symmetry of quenched QCD at zero baryonic chemical
potential is broken spontaneously at a critical temperature $T_c$ leading to a
first-order phase transition. Including heavy dynamical quarks breaks the
center symmetry explicitly and weakens the first-order phase transition for
decreasing quark masses until it turns into a smooth crossover at a
$Z(2)$-critical point. We investigate the $Z(2)$-critical quark mass value
towards the continuum limit for $N_\text{f}=2$ flavors using lattice QCD in the
staggered formulation. As part of a continued study, we present results from
Monte-Carlo simulations on $N_\tau=8,10$ lattices. Several aspect ratios and
quark mass values were simulated in order to obtain the critical mass from a
fit of the Polyakov loop to a kurtosis finite size scaling formula. Moreover,
the possibility to develop a Ginzburg-Landau effective theory around the
$Z(2)$-critical point is explored. | hep-lat |
QCD Thermodynamics: Recent results on QCD thermodynamics are presented. The nature of the T>0
transition is determined, which turns out to be an analytic cross-over. The
absolute scale for this transition is calculated. The temperature dependent
static potential is given. The results were obtained by using a Symanzik
improved gauge and stout-link improved fermionic action. In order to approach
the continuum limit four different sets of lattice spacings were used with
temporal extensions N_t=4, 6, 8 and 10 (they correspond to lattice spacings a
\sim 0.3, 0.2, 0.15 and 0.12 fm). A new technique is presented, which --in
contrast to earlier methods-- enables one to determine the equation of state at
very large temperatures. | hep-lat |
A Wilson-Majorana Regularization for Lattice Chiral Gauge Theories: We discuss the regularization of chiral gauge theories on the lattice
introducing only physical degrees of freedom. This is obtained by writing the
Wilson term in a Majorana form, at the expense of the U(1) symmetry related to
fermion number conservation. The idea of restoring chiral invariance in the
continuum by introducing a properly chosen set of counterterms to be added to
the tree level action is checked against one-loop perturbative calculations. | hep-lat |
Fighting topological freezing in the two-dimensional CP$^{N-1}$ model: We perform Monte Carlo simulations of the CP$^{N-1}$ model on the square
lattice for $N=10$, $21$, and $41$. Our focus is on the severe slowing down
related to instantons. To fight this problem we employ open boundary conditions
as proposed by L\"uscher and Schaefer for lattice QCD. Furthermore we test the
efficiency of parallel tempering in a line defect. Our results for open
boundary conditions are consistent with the expectation that topological
freezing is avoided, while autocorrelation times are still large. The results
obtained with parallel tempering are encouraging. | hep-lat |
Numerical study of lattice index theorem usingimproved cooling and
overlap fermions: We investigate topological charge and the index theorem on finite lattices
numerically. Using mean field improved gauge field configurations we calculate
the topological charge Q using the gluon field definition with ${\cal
O}(a^4)$-improved cooling and an ${\cal O}(a^4)$-improved field strength tensor
$F_{\mu\nu}$. We also calculate the index of the massless overlap fermion
operator by directly measuring the differences of the numbers of zero modes
with left- and right--handed chiralities. For sufficiently smooth field
configurations we find that the gluon field definition of the topological
charge is integer to better than 1% and furthermore that this agrees with the
index of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is
satisfied. This establishes a benchmark for reliability when calculating
lattice quantities which are very sensitive to topology. | hep-lat |
The pi-N Sigma term - an evaluation using staggered fermions: A lattice calculation of the pi-N sigma term is described using dynamical
staggered fermions. Preliminary results give a sea term comparable in magnitude
to the valence term. | hep-lat |
CP violation and Kaon weak matrix elements from Lattice QCD: In this short review, I present the recent lattice computations of kaon weak
matrix elements relevant to $K \to \pi\pi$ decays and neutral kaon mixing.
These matrix elements are key to the theoretical determination of the CP
violation parameters $\epsilon$ and $\epsilon'$ . Impressive progress have been
achieved recently, in particular the first realistic computation of
$\epsilon'/\epsilon$ with physical kinematics has been reported in [1]. The
novelty is the $\Delta I = 1/2$ channel, whereas the $\Delta I = 3/2$
contribution is now computed at several values of the lattice spacing and
extrapolated to the continuum limit. I will also present the status of $B_K$
and discuss its error budget, with a particular emphasis on the perturbative
error. Finally I will review the matrix elements of neutral kaon mixing beyond
the standard model and will argue that the discrepancy observed by different
collaborations could be explained by the renormalisation procedure of the
relevant four-quark operators. | hep-lat |
Anatomy of the sign-problem in heavy-dense QCD: QCD at finite densities of heavy quarks is investigated using the
density-of-states method. The phase factor expectation value of the quark
determinant is calculated to unprecedented precision as a function of the
chemical potential. Results are validated using those from a reweighting
approach where the latter can produce a significant signal-to-noise ratio. We
confirm the particle-hole symmetry at low temperatures, find a strong sign
problem at intermediate values of the chemical potential, and an inverse Silver
Blaze feature for chemical potentials close to the onset value: here, the phase
quenched theory underestimates the density of the full theory. | hep-lat |
Finite-Size Scaling at Phase Coexistence: {}From a finite-size scaling (FSS) theory of cumulants of the order parameter
at phase coexistence points, we reconstruct the scaling of the moments.
Assuming that the cumulants allow a reconstruction of the free energy density
no better than as an asymptotic expansion, we find that FSS for moments of low
order is still complete. We suggest ways of using this theory for the analysis
of numerical simulations. We test these methods numerically through the scaling
of cumulants and moments of the magnetization in the low-temperature phase of
the two-dimensional Ising model. (LaTeX file; ps figures included as shar file) | hep-lat |
Correlation Function in Ising Models: We simulated the fourier transform of the correlation function of the Ising
model in two and three dimensions using a single cluster algorithm with
improved estimators. The simulations are in agreement with series expansion and
the available exact results in $d=2$, which shows, that the cluster algorithm
can succesfully be applied for correlations. We show as a further result that
our data do not support a hypothesis of Fisher that in any $d=2$ lattice the
fourier transform of the correlation function depends on the lattice generating
function only. In $d=3$ our simulation are again in agreement with the results
from the series expansion, except for the amplitudes $f_{\pm}$, where we find
$f_+/f_-=2.06(1)$. | hep-lat |
Quark orbital dynamics in the proton from Lattice QCD -- from Ji to
Jaffe-Manohar orbital angular momentum: Given a Wigner distribution simultaneously characterizing quark transverse
positions and momenta in a proton, one can directly evaluate their
cross-product, i.e., quark orbital angular momentum. The aforementioned
distribution can be obtained by generalizing the proton matrix elements of
quark bilocal operators which define transverse momentum-dependent parton
distributions (TMDs); the transverse momentum information is supplemented with
transverse position information by introducing an additional nonzero momentum
transfer. A gauge connection between the quarks must be specified in the quark
bilocal operators; the staple-shaped gauge link path used in TMD calculations
yields the Jaffe-Manohar definition of orbital angular momentum, whereas a
straight path yields the Ji definition. An exploratory lattice calculation,
performed at the pion mass m_pi = 518 MeV, is presented which
quasi-continuously interpolates between the two definitions and demonstrates
that their difference can be clearly resolved. The resulting Ji orbital angular
momentum is confronted with traditional evaluations based on Ji's sum rule.
Jaffe-Manohar orbital angular momentum is enhanced in magnitude compared to its
Ji counterpart. | hep-lat |
The topological structures in strongly coupled QGP with chiral fermions
on the lattice: The nature of chiral phase transition for two flavor QCD is an interesting
but unresolved problem. One of the most intriguing issues is whether or not the
anomalous U(1) symmetry in the flavor sector is effectively restored along with
the chiral symmetry. This may determine the universality class of the chiral
phase transition. Since the physics near the chiral phase transition is
essentially non-perturbative, we employ first principles lattice techniques to
address this issue. We use overlap fermions, which have exact chiral symmetry
on the lattice, to probe the anomalous U(1) symmetry violation of 2+1 flavor
dynamical QCD configurations with domain wall fermions. The latter also
optimally preserves chiral and flavor symmetries on the lattice, since it is
known that the remnant chiral symmetry of the light quarks influences the
scaling of the chiral condensate in the crossover transition region. We observe
that the anomalous U(1) is not effectively restored in the chiral crossover
region. We perform a systematic study of the finite size and cut-off effects
since the signals of U(1) violation are sensitive to it. We also provide a
glimpse of the microscopic topological structures of the QCD medium that are
responsible for the strongly interacting nature of the quark gluon plasma
phase. We study the effect of these microscopic constituents through our first
calculations for the topological susceptibility of QCD at finite temperature,
which could be a crucial input for the equation of state for anomalous
hydrodynamics. | hep-lat |
High performance Beowulf computer for lattice QCD: We describe the construction of a high performance parallel computer composed
of PC components, as well as the performance test in lattice QCD. | hep-lat |
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