arXiv subjects
Publications and source records attributed to G. Schierholz.
We present calculations of matrix elements of 4-quark operators in the pion and in the nucleon extracted from quenched Monte Carlo simulations at beta = 6.0 using Wilson fermions. These operators are relevant for higher-twist effects. We are particularly careful to avoid mixing with lower-dimensional operators by choosing appropriate flavour structures.
We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg-Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.
In contrast to its counterpart in a vector theory, the effective action of a chiral gauge theory may have a non-vanishing imaginary part. It consists of the so-called Chern-Simons form, which encodes the anomaly and a gauge invariant piece related to the eta-invariant of some extended Dirac operator. We investigate the imaginary part of the effective action in the 4D chiral U(1) theory within the continuum fermion approach. Perturbative analysis indicates in general a non-vanishing imaginary part of the effective action. However, after anomaly cancellation we find only a small value of the imaginary part for the investigated configurations.
A numerical study of quenched QCD for light quarks is presented using O(a) improved fermions. Particular attention is paid to the possible existence and determination of quenched chiral logarithms. A `safe' region to use for chiral extrapolations appears to be at and above the strange quark mass.
We present quenched lattice QCD results for the contribution of higher-twist operators to the lowest non-trivial moment of the pion structure function. To be specific, we consider the combination $F_2^{π^+} + F_2^{π^-} - 2 F_2^{π^0}$ which has $I = 2$ and receives contributions from 4-Fermi operators only. We introduce the basis of lattice operators. The renormalization of the operators is done perturbatively in the $\bar{\rm{MS}}$ scheme using the 't Hooft-Veltman prescription for $γ_5$, taking particular care of mixing effects. The contribution is found to be of $O(f_π^2/Q^2)$, relative to the leading contribution to the moment of $F_2^{π^+}$.
The imaginary part of the effective action is investigated in the 4D chiral U(1) theory using the CFA.
We discuss the improvement of bilinear fermionic operators for Ginsparg-Wilson fermions. We present explicit formulae for improved Green's functions, which apply both on-shell and off-shell.
We present results for the mass spectrum and decay constants using non-perturbatively O(a) improved Wilson fermions. Three values of $β$ and 30 different quark masses are used to obtain the chiral and continuum limits. Special emphasis will be given to the question of taking the chiral limit and the existence of non-analytic behavior predicted by quenched chiral perturbation theory.
We address the problem of numerical simulations in the background non-trivial topology in the chiral Schwinger model. An effective fermionic action is derived which is in accord with established analytical results, and which satisfies the anomaly equation. We describe a numerical evaluation of baryon number violating amplitudes, specifically the 't Hooft vertex.
A recent lattice calculation of the spin-dependent structure function g_2 is revisited. It has been recognized that the twist-three operator, which gives rise to d_2, mixes non-perturbatively with operators of lower dimensions under renormalization. This changes the results substantially.
We evaluate the contribution of a class of higher-twist operators to the lowest moment of the Structure Functions, by computing appropriate matrix elements of six four-fermion operators in the quenched approximation. Their perturbative renormalization constants and mixing coefficients are calculated in the 't Hooft-Veltman scheme of dimensional regularization, using codes written in the algebraic manipulation computer language FORM.
The improvement of fermionic operators for Ginsparg-Wilson fermions is investigated. We present explicit formulae for improved Green's functions, which apply both on-shell and off-shell.
A completely non-perturbative estimate is given for the u/d and strange quark masses in quenched QCD using O(a) improved fermions and, for comparison, Wilson fermions. For improved fermions we find m_{u/d}^MSbar(μ=2 GeV) = 4.4(2) MeV, m_s^MSbar(μ=2 GeV) = 105(4) MeV when using r_0 to set the physical scale.
A fully non-perturbative lattice determination of the up/down and strange quark masses is given for quenched QCD using both, $O(a)$ improved Wilson fermions and ordinary Wilson fermions. For the strange quark mass with $O(a)$ improved fermions we obtain $m^{\msbar}_s(μ=2 {GeV}) = 105(4) {MeV}$, using the interquark force scale $r_0$. Due to quenching problems fits are only possible for quark masses larger than the strange quark mass. If we extrapolate our fits to the up/down quark mass we find for the average mass $m^{\msbar}_l(μ=2 {GeV}) = 4.4(2) {MeV}$.
A genuinely non-perturbative evaluation of higher-twist contributions to the structure functions of the nucleon, with all mixing effects and renormalon ambiguities taken care of, is presented. Higher-twist corrections turn out to be significant at moderate values of $q^2$.
Within the framework of lattice QCD a high statistics computation of the nucleon axial and tensor charges is given. Particular attention is paid to the chiral and continuum extrapolations.
We report new results on the lattice regularization of the chiral Schwinger model and the chiral U(1) model in four dimensions in the CFA.
We present first results for light hadron masses, quark masses and decay constants in the continuum limit using O(a) improved fermions at three different values of the gauge coupling β.