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Register a new userNucleon form factors on the lattice with light dynamical fermions
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The electromagnetic form factors provide important insight into the internal structure of the nucleon and continue to be of major interest for experiment and phenomenology. For an intermediate range of momenta the form factors can be calculated on the lattice. However, the reliability of the results is limited by systematic errors mostly due to the required extrapolation to physical quark masses. Chiral effective field theories predict a rather strong quark mass dependence in a range which was yet inaccessible for lattice simulations. We give an update on recent results from the QCDSF collaboration using gauge configurations with dynamical Nf=2, non-perturbatively O(a)-improved Wilson fermions at pion masses as low as 350 MeV.
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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%.
The nucleon electromagnetic form factors continue to be of major interest for experimentalists and phenomenologists alike. They provide important insights into the structure of nuclear matter. For a range of interesting momenta they can be calculated on the lattice. The limiting factor continues to be the value of the pion mass. We present the latest results of the QCDSF collaboration using gauge configurations with two dynamical, non-perturbatively improved Wilson fermions at pion masses as low as 350 MeV.
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.
We present results on the nucleon form factors, momentum fraction and helicity moment for $N_f=2$ and $N_f=2+1+1$ twisted mass fermions for a number of lattice volumes and lattice spacings. First results for a new $N_f=2$ ensemble at the physical pion mass are also included. The implications of these results on the spin content of the nucleon are discussed taking into account the disconnected contributions at one pion mass.
We evaluate the isovector nucleon electromagnetic form factors in quenched and full QCD on the lattice using Wilson fermions. In the quenched theory we use a lattice of spatial size 3 fm at beta=6.0 enabling us to reach low momentum transfers and a lowest pion mass of about 400 MeV. In the full theory we use a lattice of spatial size 1.9 fm at beta=5.6 and lowest pion mass of about 380 MeV enabling comparison with the results obtained in the quenched theory. We compare our lattice results to the isovector part of the experimentally measured form factors.
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