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Register a new userNucleon form factors with 2+1 flavor dynamical domain-wall fermions
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Authors
Takeshi Yamazaki
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We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axialvector currents: the vector, induced tensor, axialvector, and induced pseudoscalar form factors. The calculation is carried out with the gauge configurations generated with N_f=2+1 dynamical domain wall fermions and Iwasaki gauge actions at beta = 2.13, corresponding to a cutoff 1/a = 1.73 GeV, and a spatial volume of (2.7 fm)^3. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, 0.2 < q^2 < 0.75 GeV^2. The vector and induced tensor form factors are well described by the conventional dipole forms and result in significant underestimation of the Dirac and Pauli mean-squared radii and the anomalous magnetic moment compared to the respective experimental values. We show that the axialvector form factor is significantly affected by the finite spatial volume of the lattice. In particular in the axial charge, g_A/g_V, the finite volume effect scales with a single dimensionless quantity, m_pi L, the product of the calculated pion mass and the spatial lattice extent. Our results indicate that for this quantity, m_pi L > 6 is required to ensure that finite volume effects are below 1%.
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We report lattice-volume independence of low moments of nucleon structure functions from the coarse RIKEN-BNL-Columbia (RBC) and UKQCD joint dynamical (2+1)-flavor domain-wall fermions (DWF) ensembles at the lattice cut off of (a^{-1}sim1.7) GeV. The isovector quark momentum fraction, (< x >_{u-d}), and helicity fraction, (< x >_{Delta u - Delta d}), both fully non-perturbatively renormalized are studied on two spatial volumes of ((sim {rm 2.7 fm})^3) and ((sim {rm 1.8 fm})^3). Their naturally renormalized ratio, (< x >_{u-d}/< x >_{Delta u - Delta d}), is not affected by any finite-size effect. It does not depend strongly on light quark mass and does agree well with the experiment. The respective absolute values, fully non-perturbatively renormalized, do not show any finite-size effect either. They show trending toward the respective experimental values at the lightest up- and down-quark mass. This trending down to the experimental values appears to be a real physical effect driven by lighter quarks. The observations are in contrast to the huge finite-size effect seen in the axial-current form factors.
We present results for the nucleon axial charge g_A at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16^3x32 and 24^3x64lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_pi is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m_pi= 330 MeV. We also find that g_A exhibits a scaling with the single variable m_pi L which can also be seen in previous two-flavor domain wall and Wilson fermion calculati ons. Using this scaling to eliminate the finite-volume effect, we obtain g_A = 1.20(6)(4) at the physical pion mass, m_pi = 135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when Vge (2.4 fm)^3. We argue this is a dynamical quark effect.
We present a quenched lattice calculation of the weak nucleon form factors: vector (F_V(q^2)), induced tensor (F_T(q^2)), axial-vector (F_A(q^2)) and induced pseudo-scalar (F_P(q^2)) form factors. Our simulations are performed on three different lattice sizes L^3 x T=24^3 x 32, 16^3 x 32 and 12^3 x 32 with a lattice cutoff of 1/a = 1.3 GeV and light quark masses down to about 1/4 the strange quark mass (m_{pi} = 390 MeV) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about (3.6 fm)^3, where the finite volume effects on form factors become negligible and the lower momentum transfers (q^2 = 0.1 GeV^2) are accessible. The q^2-dependences of form factors in the low q^2 region are examined. It is found that the vector, induced tensor, axial-vector form factors are well described by the dipole form, while the induced pseudo-scalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling g_A/g_V=F_A(0)/F_V(0)=1.219(38) and the pseudo-scalar coupling g_P=m_{mu}F_P(0.88m_{mu}^2)=8.15(54), where the errors are statistical erros only. These values agree with experimental values from neutron beta decay and muon capture on the proton. However, the root mean squared radii of the vector, induced tensor and axial-vector underestimate the known experimental values by about 20%. We also calculate the pseudo-scalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.
Nucleon-structure calculations of isovector vector- and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki $times$ dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.
We present updated results on the nucleon electromagnetic form factors and axial coupling calculated using CLS ensembles with $N_mathrm{f}=2+1$ dynamical flavours of Wilson fermions. The measurements are performed on large, fine lattices with a pseudoscalar mass reaching down to 200 MeV. The truncated-solver method is employed to reduce the variance of the measurements. Estimation of the matrix elements is challenging due to large contamination from excited states and further investigation is necessary to bring these effects under control.
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