arXiv subjects
Publications and source records attributed to Meinulf Göckeler.
In two recent papers Gonuguntla and Singleton claim that the Wu-Yang fiber bundle approach does not lead to to a consistent model for magnetic charge. We point out that this claim is false.
We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors. The calculation is carried out on 35 different CLS ensembles with $N_f=2+1$ flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to $a=0.039\,$fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane. The present arXiv version (v3) includes an Addendum where we update the results using the recently calculated three-loop matching factors for the conversion from the RI'/SMOM to the $\overline{\text{MS}}$ scheme. We find $a_2^π=0.116^{+19}_{-20}$ for the pion, $a_1^K=0.0525^{+31}_{-33}$ and $a_2^K=0.106^{+15}_{-16}$ for the kaon. We also include the previous values, which were obtained with two-loop matching.
We determine the generalized form factors, which correspond to the second Mellin moment (i.e., the first $x$-moment) of the generalized parton distributions of the nucleon at leading twist. The results are obtained using lattice QCD with $N_f=2$ nonperturbatively improved Wilson fermions, employing a range of quark masses down to an almost physical value with a pion mass of about 150 MeV. We also present results for the isovector quark angular momentum and for the first $x$-moment of the transverse quark spin density. We compare two different fit strategies and find that directly fitting the ground state matrix elements to the functional form expected from Lorentz invariance and parametrized in terms of form factors yields comparable, and usually more stable results than the traditional approach where the form factors are determined from an overdetermined linear system based on the fitted matrix elements.
We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039\,\mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit.
Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter $δ^π_2$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.
We present the current status of a non-perturbative lattice calculation of the moments of the pion and kaon distribution amplitudes by the RQCD collaboration. Our investigation is carried out using $N_f=2+1$ dynamical, non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5 different lattice spacings and pion masses down to the physical pion mass. A combined continuum and chiral extrapolation to the physical point is performed along two independent quark mass trajectories simultaneously. We employ momentum smearing in order to decrease the contamination by excited states and increase statistical precision.
Following the proposal in [1], we study the feasibility to calculate the pion distribution amplitude (DA) from suitably chosen Euclidean correlation functions at large momentum. In our lattice study we employ the novel momentum smearing technique [2,3]. This approach is complementary to the calculations of the lowest moments of the DA using the Wilson operator product expansion and avoids mixing with lower dimensional local operators on the lattice. The theoretical status of this method is similar to that of quasi-distributions [4], which has recently been applied to the same problem in [5]. The similarities and differences between these two techniques are highlighted.
We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized $ρ$ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between $0.060\,\text{fm}$ and $0.081\,\text{fm}$, different lattice volumes up to $m_πL = 6.7$ and pion masses down to $m_π=150\,\text{MeV}$. Bare lattice results are renormalized non-perturbatively using a variant of the RI'-MOM scheme and converted to the $\overline{\text{MS}}$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants $f_ρ^T/f_ρ^{\vphantom{T}} = 0.629(8)$ and the values of the second Gegenbauer moments $a_2^\parallel = 0.132(27)$ and $a_2^\perp = 0.101(22)$ at the scale $μ= 2\,\text{GeV}$ for the longitudinally and transversely polarized $ρ$ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of $ρ\toππ$ decay at the smaller pion masses is not taken into account.
We present selected results obtained by RQCD from simulations of $N_f=2+1$ flavours of non-perturbatively $\mathcal{O}(a)$ improved Wilson fermions, employing open boundary conditions in time. The ensembles were created within the CLS (Coordinated Lattice Simulations) effort at five different values of the lattice spacing, ranging from 0.085fm down to below 0.04fm. Many quark mass combinations were realized, in particular along lines where the sum of the bare quark masses was kept fixed as well as trajectories of an approximately physical renormalized strange quark mass. Several key observables, including meson and baryon masses and the axial charge of the nucleon have been computed, and preliminary results are presented here. In some cases an accurate and controlled extrapolation to the continuum limit has become possible.
Working with a pion mass $m_π\approx 150$ MeV, we study $ππ$ and $Kπ$ scattering using two flavours of non-perturbatively improved Wilson fermions at a lattice spacing $a\approx 0.071$ fm. Employing two lattice volumes with linear spatial extents of $N_s=48$ and $N_s=64$ points and moving frames, we extract the phase shifts for p-wave $ππ$ and $Kπ$ scattering near the $ρ$ and $K^*$ resonances.Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling $g_{ρππ}$ appears to be remarkably constant as a function of $m_π$.
We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using $N_f=2+1$ flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.
We determine generalized form factors of the nucleon from lattice simulations with $N_f = 2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions down to a pion mass of 150 MeV. We also present the resulting isovector quark angular momentum. Possible excited-state contaminations are investigated with correlated simultaneous fits.
We compute the axial, scalar, tensor and pseudoscalar isovector couplings of the nucleon as well as the induced tensor and pseudoscalar charges in lattice simulations with $N_f=2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions. The simulations are carried out down to a pion mass of 150 MeV and linear spatial lattice extents of up to 4.6 fm at three different lattice spacings ranging from approximately 0.08 fm to 0.06 fm. Possible excited state contamination is carefully investigated and finite volume effects are studied. The couplings, determined at these lattice spacings, are extrapolated to the physical pion mass. In this limit we find agreement with experimental results, where these exist, with the exception of the magnetic moment. A proper continuum limit could not be performed, due to our limited range of lattice constants, but no significant lattice spacing dependence is detected. Upper limits on discretization effects are estimated and these dominate the error budget.
We present an update of our analysis [1] which includes additional ensembles at different quark masses, lattice spacings and volumes, all with high statistics. We use $N_f=2$ mass-degenerate quark flavours, employing the non-perturbatively improved clover action. The lattice matrix elements are converted to the $\overline{\rm MS}$ scheme via renormalization factors determined non-perturbatively in the RI$^\prime$-MOM scheme. We have systematically investigated excited state contributions, in particular, at the smallest, near physical, pion mass. While our results~(with much increased precision) are consistent with Ref.~[1], comparing with previous determinations we find that excited state contributions can be significant if the quark smearing is not suitably optimized, in agreement with other recent studies. The difference with respect to the value for $\langle x\rangle_{u-d}$ extracted from experimental data is reduced but not resolved. Using lattice sizes in the range $L m_π\sim 3.4-6.7$, no significant finite volume effects were observed. Performing a controlled continuum limit that may remove the discrepancy will require simulations at lattice spacings $a< 0.06$ fm.
Using stochastic estimators for connected meson and baryon three-point functions has successfully been tried in the past years. Compared to the standard sequential source method we trade the freedom to compute the current-to-sink propagator independently of the hadron sink for additional stochastic noise in our observables. In the case of the nucleon we can use this freedom to compute many different sink-momentum/polarization combinations, which grants access to more virtualities. We will present preliminary results on the scalar, electro-magnetic and axial form factors of the nucleon in $N_f=2+1$ lattice QCD and contrast the performance of the stochastic method to the sequential source method. We find the stochastic method to be competitive in terms of errors at fixed cost.
We compare a recent lattice determination of the nucleon distribution amplitudes with other approaches and models. We study the nucleon distribution amplitudes up to twist 6 in next-to leading conformal spin and we also investigate conformal d-wave contributions to the leading twist distribution amplitude. With the help of light-cone sum rules one can relate the distribution amplitudes to the form factors of the nucleon or the $ N \to Δ$ transition at intermediate values of the momentum transfer. We compare our results with experimental data in the range 1 GeV$^2 \leq Q^2 \leq 10$ GeV$^2$. Keeping in mind that we are working only in LO QCD and NLO-QCD corrections might be sizeable we already obtain a surprisingly good agreement for the nucleon form factors $G_M^n$, $G_M^p$, $G_A^p$ and $G_T^p$ and for the $N \to Δ$ transition form factor ratios $R_{EM}$ and $R_{SM}$.
We compute moments of distribution amplitudes using gauge configurations with two flavors of clover fermions from QCDSF/DIK and operators which are optimized with respect to their behavior under the lattice symmetries. The knowledge of these quantities helps in understanding the internal structure of hadrons and in the analysis of (semi-)exclusive processes. We present results for the nucleon distribution amplitude which suggest that the asymmetries (the deviations from the asymptotic form) are smaller than indicated by sum rule calculations. Using the same approach we were also able to calculate the same quantities for the $N^\star(1535)$, the parity partner of the nucleon. These results show a stronger deviation from the asymptotic form.
We calculate low moments of the leading-twist and next-to-leading twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MSbar scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.