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M. Göckeler

Publications and source records attributed to M. Göckeler.

At least 19 recordsLinked to original sources
arXiv2025

Updated determination of light-cone distribution amplitudes of octet baryons in lattice QCD

We present updated results on the wave function normalization constants and the first moments of the light cone distribution amplitudes for the lowest-lying baryon octet. The analysis is carried out on a large number of $n_f=2+1$ lattice gauge ensembles, including ensembles at physical pion (and kaon) masses. These are spread across five different lattice spacings, enabling a controlled continuum limit. The main differences with respect to our earlier work are the use of two-loop conversion factors to an $\overline{\mathrm{MS}}$-like scheme and of an updated set of low-energy constants in the parametrization of the quark mass dependence. As a byproduct, for the first time, the anomalous dimensions for local three-quark operators with one derivative are obtained.

hep-lat↗
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.

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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↗
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.

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arXiv2017

Non-perturbative renormalization of flavor singlet quark bilinear operators in lattice QCD

We report on our studies of the renormalization of flavor singlet quark bilinear operators in lattice QCD. The renormalization constants are determined non-perturbatively using gauge field ensembles with Nf=2 dynamical clover improved fermions. The renormalization is performed in the RI'-MOM scheme. The difference between flavor singlet and non-singlet quark bilinear operators is a disconnected contribution, which has to be evaluated by stochastic estimators. We compare our results for the running with perturbation theory.

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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.

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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.

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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.

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arXiv2013

Pion structure from lattice QCD

We report on the lowest moment of parton distribution functions and generalized form factors for the pion at several values of the momentum transfer. Calculations are performed for N_f=2 flavors of O(a) improved Wilson fermions with pion masses down to 150 MeV.

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arXiv2013

Moments of structure functions for $N_f=2$ near the physical point

We report on our on-going study of the lower moments of iso-vector polarised and unpolarised structure functions, $g_A$ and $\langle x\rangle_{u-d}$, respectively, and the iso-vector scalar and tensor charge, for $N_f=2$ non-perturbatively improved clover fermions. With pion masses which go down to about 150 MeV, we investigate finite volume effects and excited state contributions.

hep-lat↗
arXiv2012

Perturbative and Nonperturbative Renormalization in Lattice QCD

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.

hep-lat↗
arXiv2012

Scattering phases for meson and baryon resonances on general moving-frame lattices

A proposal by Lüscher enables one to compute the scattering phases of elastic two-body systems from the energy levels of the lattice Hamiltonian in a finite volume. In this work we generalize the formalism to S--, P-- and D--wave meson and baryon resonances, and general total momenta. Employing nonvanishing momenta has several advantages, among them making a wider range of energy levels accessible on a single lattice volume and shifting the level crossing to smaller values of $m_πL$.

hep-lat↗
arXiv2012

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

We analyze Nf=2 nucleon mass data with respect to their dependence on the pion mass down to mpi = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon sigma-term. Our lattice data below mpi = 435 MeV is well described by O(p^4) BChPT and we find sigma=37(8)(6) MeV for the sigma-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r_0=0.501(10)(11) fm.

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arXiv2012

First moments of the nucleon generalized parton distributions from lattice QCD

We report on our lattice calculations of the nucleon's generalized parton distributions (GPDs), concentrating on their first moments for the case of N_f=2. Due to recent progress on the numerical side we are able to present results for the generalized form factors at pion masses as low as 260 MeV. We perform a fit to one-loop covariant baryon chiral perturbation theory with encouraging results.

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arXiv2011

An Update on Distribution Amplitudes of the Nucleon and its Parity Partner

The calculation of baryon wave functions at small inter-quark separations is an ongoing effort within the QCDSF collaboration. In this update on normalization constants and distribution amplitudes of the nucleon and its negative parity partner, N* (1535), we present new lattice data which helps us controlling finite size effects. We use new chiral perturbation theory results to perform the extrapolation to the physical point.

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arXiv2011

Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks

QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1+1+1 flavour case and then for the 2+1 flavour case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the 2+1 flavour case confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this programme to include partially quenched results is given.

hep-lat↗
arXiv2011

Dirac and Pauli form factors from lattice QCD

We present a comprehensive analysis of the electromagnetic form factors of the nucleon from a lattice simulation with two flavors of dynamical O(a)-improved Wilson fermions. A key feature of our calculation is that we make use of an extensive ensemble of lattice gauge field configurations with four different lattice spacings, multiple volumes, and pion masses down to m_π~ 180 MeV. We find that by employing Kelly-inspired parametrizations for the Q^2-dependence of the form factors, we are able to obtain stable fits over our complete ensemble. Dirac and Pauli radii and the anomalous magnetic moments of the nucleon are extracted and results at light quark masses provide evidence for chiral non-analytic behavior in these fundamental observables.

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