H. Stüben

The nucleon mass in Nf=2 lattice QCD: Finite size effects from chiral perturbation theory

Abstract In the framework of relativistic SU(2) f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O ( p 4 ). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N f =2 simulations of the UKQCD and QCDSF Collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD Collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.

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.

A determination of the Lambda parameter from full lattice QCD

We present a determination of the QCD parameter Lambda in the quenched approximation (n_f=0) and for two flavours (n_f=2) of light dynamical quarks. The calculations are performed on the lattice using O(a) improved Wilson fermions and include taking the continuum limit. We find Lambda_{n_f=0} = 259(1)(20) MeV and Lambda_{n_f=2} = 261(17)(26) MeV}, using r_0 = 0.467 fm to set the scale. Extrapolating our results to five flavours, we obtain for the running coupling constant at the mass of the Z boson alpha_s(m_Z) = 0.112(1)(2). All numbers refer to the MSbar scheme.

The pion form factor from lattice QCD with two dynamical flavours

We compute the electromagnetic form factor of the pion, using non-perturbatively O(a) improved Wilson fermions. The calculations are done for a wide range of pion masses and lattice spacings. We check for finite size effects by repeating some of the measurements on smaller lattices. The large number of lattice parameters we use allows us to extrapolate to the physical point. For the square of the charge radius we find

Determination of light and strange quark masses from two-flavour dynamical lattice QCD

\langle{r^2}\rangle= 0.444(20)

Tuning the strange quark mass in lattice simulations

fm2, in good agreement with experiment.

BQCD - Berlin quantum chromodynamics program

We compute the light and strange quark masses m_l = (m_u+m_d)/2 and m_s, respectively, in full lattice QCD with N_f=2 flavors of light dynamical quarks. The renormalization constants, which convert bare quark masses into renormalized quark masses, are computed nonperturbatively, including the effect of quark-line disconnected diagrams. We obtain m_l=4.7(2)(3) MeV and m_s=119(5)(8) MeV in the MSbar scheme at the scale 2 GeV.

Spin structure of the pion.

Abstract QCD lattice simulations with 2 + 1 flavours typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass to its physical value and then the up-down quark mass. An alternative method of tuning the quark masses is discussed here in which the singlet quark mass is kept fixed, which ensures that the kaon always has mass less than the physical kaon mass. It can also take into account the different renormalisations (for singlet and non-singlet quark masses) occurring for non-chirally invariant lattice fermions and so allows a smooth extrapolation to the physical quark masses. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Results show the correct order for the baryon octet and decuplet spectrum and an extrapolation to the physical pion mass gives mass values to within a few percent of their experimental values.

IS THERE A LANDAU POLE PROBLEM IN QED

We publish BQCD as free software under the GNU General Public License. BQCD is a Hybrid Monte-Carlo program that simulates lattice QCD with dynamical Wilson fermions. It is one of the main production programs of the QCDSF collaboration. The program can simulate 2 and 2+ 1 fermion flavours with pure, clover improved, and stout smear ed fat link Wilson fermions as well as standard plaquette, and an improved (rectangle) gauge action. The single flavour is simulated with the Rational Hybrid Monte-Carlo algorithm.

Dirac and Pauli form factors from lattice QCD

We present the first calculation of the transverse spin structure of the pion in lattice QCD. Our simulations are based on two flavors of nonperturbatively improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to (2.1 fm)(3) and lattice spacings below 0.1 fm. We find a characteristic asymmetry in the spatial distribution of transversely polarized quarks. This asymmetry is very similar in magnitude to the analogous asymmetry we previously obtained for quarks in the nucleon. Our results support the hypothesis that all Boer-Mulders functions are alike.