Accessing hadronic form factors at large momentum transfers has traditionally presented a challenge for lattice QCD simulations. Here, we demonstrate how a novel implementation of the ...Feynman-Hellmann method can be employed to calculate hadronic form factors in lattice QCD at momenta much higher than previously accessible. Our simulations are performed on a single set of gauge configurations with three flavors of degenerate mass quarks corresponding to mπ≈470 MeV. We are able to determine the electromagnetic form factors of the pion and nucleon up to approximately 6 GeV2, with results for the ratio of the electric and magnetic form factors of the proton at our simulated quark mass agreeing well with experimental results.
A
bstract
In this paper we present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED, concentrating particularly on violations of isospin symmetry. We calculate ...the
π
+
-
π
0
splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in 1. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the
u
and
d
quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashen’s theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as
M
S
¯
, in which Dashen’s theorem for neutral mesons is violated.
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.
By considering a flavor expansion about the SU(3) flavor symmetric point, we investigate how flavor blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference ...between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavor symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line-disconnected terms in the three-point correlation functions is also given. As we consider Wilson cloverlike fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavor-conserving matrix elements of the vector first-class form factors.
By introducing an additional operator into the action and using the Feynman–Hellmann theorem we describe a method to determine both the quark line connected and disconnected terms of matrix elements. ...As an illustration of the method we calculate the gluon contribution (chromo-electric and chromo-magnetic components) to the nucleon mass.
The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion ...decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann–Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.
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.
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.
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 \(\langle{r^2}\rangle= 0.444(20)\) fm2, in good agreement with experiment.
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