Parton quasidistribution functions provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is ...the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the modified minimal subtraction (MSover ¯) scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters, we show the effect of renormalization on nucleon matrix elements with a pion mass of approximately 370 MeV and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI′ scheme. The proposed prescription addresses ...simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator.
We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS‾-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing.
We apply the methodology for the renormalization to an ensemble of twisted mass fermions with Nf=2+1+1 dynamical quarks, and a pion mass of around 375 MeV.
We present the first direct calculation of the renormalized transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the ...light quark mass fixed to its physical value and at one value of the lattice spacing. Apart from physically light quarks, novel elements of the calculations are nonperturbative renormalization and extraction of a formula for the matching to light-cone parton distribution functions. Final results are presented in the MS¯ scheme at a scale of 2 GeV.
Efficient discretisations of gauge groups are crucial with the long term perspective of using tensor networks or quantum computers for lattice gauge theory simulations. For any Lie group other than ...U(1), however, there is no class of asymptotically dense discrete subgroups. Therefore, discretisations limited to subgroups are bound to lead to a
freezing
of Monte Carlo simulations at weak couplings, necessitating alternative partitionings without a group structure. In this work we provide a comprehensive analysis of this freezing for all discrete subgroups of SU(2) and different classes of asymptotically dense subsets. We find that an appropriate choice of the subset allows unfrozen simulations for arbitrary couplings, though one has to be careful with varying weights of unevenly distributed points. A generalised version of the Fibonacci spiral appears to be particularly efficient and close to optimal.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
We present the QCD simulation of the first gauge ensemble of two degenerate light quarks, a strange and a charm quark with all quark masses tuned to their physical values within the twisted mass ...fermion formulation. Results for the pseudoscalar masses and decay constants confirm that the produced ensemble is indeed at the physical parameters of the theory. This conclusion is corroborated by a complementary analysis in the baryon sector. We examine cutoff and isospin breaking effects and demonstrate that they are suppressed through the presence of a clover term in the action.
We present a reliable nonperturbative calculation of the QCD correction, at leading order in the electromagnetic coupling, to the anomalous magnetic moment of the electron, muon, and tau leptons ...using two-flavor lattice QCD. We use multiple lattice spacings, multiple volumes, and a broad range of quark masses to control the continuum, infinite-volume, and chiral limits. We examine the impact of the commonly ignored disconnected diagrams and introduce a modification to the previously used method that results in a well-controlled lattice calculation. We obtain 1.513(43)×10(-12), 5.72(16)×10(-8), and 2.650(54)×10(-6) for the leading-order two-flavor QCD correction to the anomalous magnetic moment of the electron, muon, and tau, respectively, each accurate to better than 3%.
Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding ...of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use
2
+
1
dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.
We propose an explicit formulation of the physical subspace for a (1+1 )-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely ...general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.
Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space
H
. Here we give a prescription for gauge links and canonical ...momenta of an SU(2) gauge theory, such that the matrix representation of the former is diagonal in
H
. This is achieved by discretising the sphere
S
3
isomorphic to SU(2) and the corresponding directional derivatives. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts. Moreover, we directly construct the Casimir operator corresponding to the Laplace–Beltrami operator on
S
3
and show that the spectrum of the free theory is reproduced again up to discretisation effects. Qualitatively, these results do not depend on the specific discretisation of SU(2), but the actual convergence rates do.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral-projector method. We use ensembles ...with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cutoff effects. This finally yields a much smaller total error in the spectral-projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility.
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