arXiv subjects

A. Schäfer

Publications and source records attributed to A. Schäfer.

At least 19 recordsLinked to original sources

arXiv2023

Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions

We present the nonperturbative computation of renormalization factors in the RI'-(S)MOM schemes for the QCD gauge field ensembles generated by the CLS (coordinated lattice simulations) effort with three flavors of nonperturbatively improved Wilson (clover) quarks. We use ensembles with the standard (anti-)periodic boundary conditions in the time direction as well as gauge field configurations with open boundary conditions. Besides flavor-nonsinglet quark-antiquark operators with up to two derivatives we also consider three-quark operators with up to one derivative. For the RI'-SMOM scheme results we make use of the recently calculated three-loop conversion factors to the modified minimal subtraction scheme. The present version of the paper contains an Addendum with additional analytical expressions and updated results.

hep-lat↗

arXiv2022

Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon

Using lattice QCD, we calculate the twist-2 contribution $a_2$ to the third Mellin moment of the spin structure functions $g_1$ and $g_2$ in the nucleon. In addition we evaluate the twist-3 contribution $d_2$. Our computations make use of $N_f=2+1$ gauge field ensembles generated by the Coordinated Lattice Simulations (CLS) effort. Neglecting quark-line disconnected contributions we obtain as our best estimates $a_2^{(p)}= 0.069(17)$, $d_2^{(p)}= 0.0105(68)$ and $a_2^{(n)}= 0.0068(88)$, $d_2^{(n)}= -0.0009(70)$ for the proton and the neutron, respectively, where we use the normalizations given in Eqs. (58) and (59). While the $a_2$ results have been converted to the $\overline{\mathrm{MS}}$ scheme using three-loop perturbation theory, the numbers for $d_2$ are given in the regularization independent momentum subtraction (RI$^\prime$-MOM) scheme, i.e., the conversion has been performed only in tree-level perturbation theory. The $d_2$ results can be interpreted as corresponding to a transverse color Lorentz force on a quark in a transversely polarized proton of size $F^{(u)} = 116(61)$ MeV/fm and $F^{(d)} = -38(66)$ MeV/fm for $u$ and $d$ quarks, respectively. The error estimates quoted include statistical and systematic uncertainties added in quadrature.

hep-lat↗

arXiv2020

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining four single-spin and four double-spin asymmetries allowed in the one-photon-exchange approximation of the semi-inclusive deep-inelastic scattering process for target-polarization orientation perpendicular to the direction of the incoming lepton beam. Among those results, significant non-vanishing $\cos{ϕ-ϕ_S}$ modulations provide evidence for a sizable worm-gear (II) distribution, $g_{1T}$. Most of the other modulations are found to be consistent with zero with the notable exception of large $\sin{ϕ_S}$ modulations for charged pions and positive kaons.

hep-ex↗

arXiv2019

Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors

It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation functions, the corresponding relation for form factors (sometimes called the generalized Goldberger-Treiman relation in the literature) is broken rather badly. In this work we trace this difference back to excited state contributions and propose a new projection method that resolves this problem. We demonstrate the efficacy of this method by computing the axial and pseudoscalar form factors as well as related quantities on ensembles with two flavors of improved Wilson fermions using pion masses down to 150 MeV. To this end, we perform the $z$-expansion with analytically enforced asymptotic behaviour and extrapolate to the physical point.

hep-lat↗

arXiv2018

Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model

We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford (MSS) bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior - rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest time scale of all. We also find that while the bosonic matrix model becomes non-chaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and non-zero down to the lowest temperatures.

hep-th↗

arXiv2017

Shear viscosity of a hadron gas and influence of resonance lifetimes on relaxation time

We address a discrepancy between different computations of $η/s$ (shear viscosity over entropy density) of hadronic matter. Substantial deviations of this coefficient are found between transport approaches mainly based on resonance propagation with finite lifetime and other (semi-analytical) approaches with energy-dependent cross-sections, where interactions do not introduce a timescale. We provide an independent extraction of this coefficient by using the newly-developed SMASH (Simulating Many Accelerated Strongly interacting Hadrons) transport code, which is an example of a mainly resonance-based approach. We compare the results from SMASH with numerical solutions of the Boltzmann equation for simple systems using the Chapman-Enskog expansion, as well as previous results in the literature. Our conclusion is that the hadron interaction via resonance formation/decay strongly affects the transport properties of the system, resulting in significant differences in $η/s$ with respect to other approaches where binary collisions dominate. We argue that the relaxation time of the system ---which characterizes the shear viscosity--- is determined by the interplay between the mean-free time and the lifetime of resonances. We show how an artificial shortening of the resonance lifetimes, or the addition of a background elastic cross section nicely interpolate between the two discrepant results.

nucl-th↗

arXiv2017

Systematic errors in transport calculations of shear viscosity using the Green-Kubo formalism

The purpose of this study is to provide a reproducible framework in the use of the Green-Kubo formalism to extract transport coefficients. More specifically, in the case of shear viscosity, we investigate the limitations and technical details of fitting the auto-correlation function to a decaying exponential. This fitting procedure is found to be applicable for systems interacting both through constant and energy-dependent cross-sections, although this is only true for sufficiently dilute systems in the latter case. We find that the optimal fit technique consists in simultaneously fixing the intercept of the correlation function and use a fitting interval constrained by the relative error on the correlation function. The formalism is then applied to the full hadron gas, for which we obtain the shear viscosity to entropy ratio.

nucl-th↗

arXiv2017

Ratios of helicity amplitudes for exclusive $ρ^0$ electroproduction on transversely polarized protons

Exclusive $ρ^0$-meson electroproduction is studied by the HERMES experiment, using the 27.6 GeV longitudinally polarized electron/positron beam of HERA and a transversely polarized hydrogen target, in the kinematic region 1.0 GeV$^2$<Q$^2$<7.0 GeV$^2$, 3.0 GeV<W<6.3 GeV, and -t'<0.4 GeV$^2$. Using an unbinned maximum-likelihood method, 25 parameters are extracted. These determine the real and imaginary parts of the ratios of several helicity amplitudes describing $ρ^0$-meson production by a virtual photon. The denominator of those ratios is the dominant amplitude, the nucleon-helicity-non-flip amplitude $F_{0\frac{1}{2}0\frac{1}{2}}$, which describes the production of a longitudinal $ρ^{0}$-meson by a longitudinal virtual photon. The ratios of nucleon-helicity-non-flip amplitudes are found to be in good agreement with those from the previous HERMES analysis. The transverse target polarization allows for the first time the extraction of ratios of a number of nucleon-helicity-flip amplitudes to $F_{0\frac{1}{2}0\frac{1}{2}}$. Results obtained in a handbag approach based on generalized parton distributions taking into account the contribution from pion exchange are found to be in good agreement with these ratios. Within the model, the data favor a positive sign for the $π-ρ$ transition form factor. By also exploiting the longitudinal beam polarization, a total of 71 $ρ^0$ spin-density matrix elements is determined from the extracted 25 parameters, in contrast to only 53 elements as directly determined in earlier analyses.

hep-ex↗

arXiv2017

Second moment of the pion distribution amplitude with the momentum smearing technique

Using the second moment of the pion distribution amplitude as an example, we investigate whether lattice calculations of matrix elements of local operators involving covariant derivatives may benefit from the recently proposed momentum smearing technique for hadronic interpolators. Comparing the momentum smearing technique to the traditional Wuppertal smearing we find - at equal computational cost - a considerable reduction of the statistical errors. The present investigation was carried out using $N_f=2+1$ dynamical non-perturbatively order $a$ improved Wilson fermions on lattices of different volumes and pion masses down to 220 MeV.

hep-lat↗

arXiv2016

Spin density matrix elements in exclusive $ω$ electroproduction on $^1$H and $^2$H targets at 27.5 GeV beam energy

Exclusive electroproduction of $ω$ mesons on unpolarized hydrogen and deuterium targets is studied in the kinematic region of Q$^2$>1.0 GeV$^2$, 3.0 GeV < W < 6.3 GeV, and -t'< 0.2 GeV$^2$. Results on the angular distribution of the $ω$ meson, including its decay products, are presented. The data were accumulated with the HERMES forward spectrometer during the 1996-2007 running period using the 27.6 GeV longitudinally polarized electron or positron beam of HERA. The determination of the virtual-photon longitudinal-to-transverse cross-section ratio reveals that a considerable part of the cross section arises from transversely polarized photons. Spin density matrix elements are presented in projections of Q$^2$ or -t'. Violation of s-channel helicity conservation is observed for some of these elements. A sizable contribution from unnatural-parity-exchange amplitudes is found and the phase shift between those amplitudes that describe transverse $ω$ production by longitudinal and transverse virtual photons, $γ^{*}_{L} \to ω_{T}$ and $γ^{*}_{T} \to ω_{T}$, is determined for the first time. A hierarchy of helicity amplitudes is established, which mainly means that the unnatural-parity-exchange amplitude describing the $γ^*_T \to ω_T$ transition dominates over the two natural-parity-exchange amplitudes describing the $γ^*_L \to ω_L$ and $γ^*_T \to ω_T$ transitions, with the latter two being of similar magnitude. Good agreement is found between the HERMES proton data and results of a pQCD-inspired phenomenological model that includes pion-pole contributions, which are of unnatural parity.

hep-ex↗

arXiv2015

Pion Distribution Amplitude from Lattice QCD

We have calculated the second moment of the pion light-cone distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes, lattice spacings between $0.06 \, \mathrm {fm}$ and $0.08 \, \mathrm {fm}$ and pion masses down to $m_π\sim 150 \, \mathrm {MeV}$. Our result for the second Gegenbauer coefficient is $a_2 = 0.1364(154)(145)$ and for the width parameter $\langle ξ^2 \rangle = 0.2361(41)(39)$. Both numbers refer to the scale $μ=2 \, \mathrm {GeV}$in the $\overline{\text{MS}}$ scheme, the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.

hep-lat↗

arXiv2015

Bose-Einstein correlations in hadron-pairs from lepto-production on nuclei ranging from hydrogen to xenon

Bose-Einstein correlations of like-sign charged hadrons produced in deep-inelastic electron and positron scattering are studied in the HERMES experiment using nuclear targets of $^1$H, $^2$H, $^3$He, $^4$He, N, Ne, Kr, and Xe. A Gaussian approach is used to parametrize a two-particle correlation function determined from events with at least two charged hadrons of the same sign charge. This correlation function is compared to two different empirical distributions that do not include the Bose-Einstein correlations. One distribution is derived from unlike-sign hadron pairs, and the second is derived from mixing like-sign pairs from different events. The extraction procedure used simulations incorporating the experimental setup in order to correct the results for spectrometer acceptance effects, and was tested using the distribution of unlike-sign hadron pairs. Clear signals of Bose-Einstein correlations for all target nuclei without a significant variation with the nuclear target mass are found. Also, no evidence for a dependence on the invariant mass W of the photon-nucleon system is found when the results are compared to those of previous experiments.

hep-ex↗

arXiv2015

Lattice QCD study of the Boer-Mulders effect in a pion

The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentum-dependent parton distribution functions (TMDs). This work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. Particular emphasis is placed on the behavior as a function of a Collins-Soper evolution parameter quantifying the relative rapidity of the struck quark and the initial hadron, e.g., in a semi-inclusive deep inelastic scattering (SIDIS) process. The lattice calculation, performed at the pion mass m_pi = 518 MeV, utilizes a definition of TMDs via hadronic matrix elements of a quark bilocal operator with a staple-shaped gauge connection; in this context, the evolution parameter is related to the staple direction. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. In contrast to an earlier nucleon study, due to the lower mass of the pion, the calculated data enable quantitative statements about the physically interesting limit of large relative rapidity. In passing, the similarity between the Boer-Mulders effects extracted in the pion and the nucleon is noted.

hep-lat↗

arXiv2015

Second Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD

We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_π\sim 150 \, \mathrm {MeV}$. At lattice spacings between $0.06 \, \mathrm {fm}$ and $0.08 \, \mathrm {fm}$ we find for the second Gegenbauer moment the value $a_2 = 0.1364(154)(145)$ at the scale $μ=2 \, \mathrm {GeV}$ in the $\overline{\mathrm{MS}}$ scheme, where the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.

hep-lat↗

arXiv2014

Transition form factors $γ^γ\toη$ and $γ^γ\toη'$ in QCD

We update the theoretical framework for the QCD calculation of transition form factors $γ^*γ\toη$ and $γ^*γ\toη'$ at large photon virtualities including full next-to-leading order analysis of perturbative corrections, the charm quark contribution, and taking into account SU(3)-flavor breaking effects and the axial anomaly contributions to the power-suppressed twist-four distribution amplitudes. The numerical analysis of the existing experimental data is performed with these improvements.

hep-ph↗

arXiv2014

Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions in an external magnetic field

We study the influence of an external magnetic field on the deconfinement transition in two-flavour lattice QCD with physical quark charges. We use dynamical overlap fermions without any approximation such as fixed topology and perform simulations on a $16^3 \times 6$ lattice and at a pion mass around $500MeV$. The pion mass (as well as the lattice spacing) was determined in independent runs on $12^3 \times 24$ lattices. We consider two temperatures, one of which is close to the deconfinement transition and one which is above. Within our limited statistics the dependence of the Polyakov loop and chiral condensate on the magnetic field supports the "inverse magnetic catalysis" scenario in which the transition temperature decreases as the field strength grows for temperature not to far above the critical temperature.

hep-lat↗

arXiv2014

Reevaluation of the parton distribution of strange quarks in the nucleon

An earlier extraction from the HERMES experiment of the polarization-averaged parton distribution of strange quarks in the nucleon has been reevaluated using final data on the multiplicities of charged kaons in semi-inclusive deep-inelastic scattering obtained with a kinematically more comprehensive method of correcting for experimental effects. General features of the distribution are confirmed, but the rise at low x is less pronounced than previously reported.

hep-ex↗

arXiv2014

Light-cone Distribution Amplitudes of the Nucleon and Negative Parity Nucleon Resonances from Lattice QCD

We present the results of a lattice study of light-cone distribution amplitudes (DAs) of the nucleon and negative parity nucleon resonances using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to m_pi = 150 MeV. We find that the three valence quarks in the proton share their momentum in the proportion 37% : 31% : 31%, where the larger fraction corresponds to the u-quark that carries proton helicity, and determine the value of the wave function at the origin in position space, which turns out to be small compared to the existing estimates based on QCD sum rules. Higher-order moments are constrained by our data and are all compatible with zero within our uncertainties. We also calculate the normalization constants of the higher-twist DAs that are related to the distribution of quark angular momentum. Furthermore, we use the variational method and customized parity projection operators to study the states with negative parity. In this way we are able to separate the contributions of the two lowest states that, as we argue, possibly correspond to N*(1535) and a mixture of N*(1650) and the pion-nucleon continuum, respectively. It turns out that the state that we identify with N*(1535) has a very different DA as compared to both the second observed negative parity state and the nucleon, which may explain the difference in the decay patterns of N*(1535) and N*(1650) observed in experiment.

hep-lat↗