D. Pleiter

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.

Generalized parton distributions from lattice QCD

We perform a quenched lattice calculation of the first moment of twist-two generalized parton distribution functions of the proton, and assess the total quark (spin and orbital angular momentum) contribution to the spin of the proton.

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.

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

Abstract We analyze N f = 2 nucleon mass data with respect to their dependence on the pion mass down to m π = 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 σ-term. Our lattice data below m π = 435 MeV is well described by O ( p 4 ) BChPT and we find σ = 37 ( 8 ) ( 6 ) MeV for the σ-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 .

Transverse spin structure of the nucleon from lattice QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.

Nucleon electromagnetic form factors on the lattice and in chiral effective field theory

We compute the electromagnetic form factors of the nucleon in quenched lattice QCD, using nonperturbatively improved Wilson fermions, and compare the results with phenomenology and chiral effective field theory.

Strangeness Contribution to the Proton Spin from Lattice QCD

We compute the strangeness and light-quark contributions Δs, Δu, and Δd to the proton spin in n(f)=2 lattice QCD at a pion mass of about 285 MeV and at a lattice spacing a≈0.073 fm, using the nonperturbatively improved Sheikholeslami-Wohlert Wilson action. We carry out the renormalization of these matrix elements, which involves mixing between contributions from different quark flavors. Our main result is the small negative value Δs(MS)(√(7.4) GeV)=-0.020(10)(4) of the strangeness contribution to the nucleon spin. The second error is an estimate of the uncertainty, due to the missing extrapolation to the physical point.

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

Axial coupling constant of the nucleon for two flavours of dynamical quarks in finite and infinite volume

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

Quark helicity flip generalized parton distributions from two-flavor lattice QCD

fm2, in good agreement with experiment.