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Register a new userTowards the nucleon hadronic tensor from lattice QCD
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We present the first calculation of the hadronic tensor on the lattice for the nucleon. The hadronic tensor can be used to extract the structure functions in deep inelastic scatterings and also provide information for the neutrino-nucleon scattering which is crucial to the neutrino-nucleus scattering experiments at low energies. The most challenging part in the calculation is to solve an inverse problem. We have implemented and tested three algorithms using mock data, showing that the Bayesian Reconstruction method has the best resolution in extracting peak structures while the Backus-Gilbert and Maximum Entropy methods are somewhat more stable for the flat spectral function. Numerical results are presented for both the elastic case (clover fermions on domain wall configuration with $m_pisim$ 370 MeV and $asim$ 0.06 fm) and a case (anisotropic clover lattice with $m_pisim$ 380 MeV and $a_tsim$ 0.035 fm) with large momentum transfer. For the former case, the reconstructed Minkowski hadronic tensor gives precisely the vector charge which proves the feasibility of the approach. While for the latter case, the nucleon resonances and possibly shallow inelastic scattering contributions around $ u=1$ GeV are clearly observed but no information is obtained for higher excited states with $ u>2$ GeV. A check of the effective masses of $rho$ meson with different lattice setups indicates that, in order to reach higher energy transfers, using lattices with smaller lattice spacings is essential.
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The path-integral formulation of the hadronic tensor W_{mu u} of deep inelastic scattering is reviewed. It is shown that there are 3 gauge invariant and topologically distinct contributions. The separation of the connected sea partons from those of the disconnected sea can be achieved with a combination of the global fit of the parton distribution function (PDF), the semi-inclusive DIS data on the strange PDF and the lattice calculation of the ratio of the strange to $u/d$ momentum fraction in the disconnected insertion. We shall discuss numerical issues associated with lattice calculation of the hadronic tensor involving a four-point function, such as large hadron momenta and improved maximum entropy method to obtain the spectral density from the hadronic tensor in Euclidean time. We also draw a comparison between the large momentum approach to the parton distribution function (PDF) and the hadronic tensor approach.
We present the first direct lattice calculation of the isovector sea-quark parton distributions using the formalism developed recently by one of the authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC Collaboration) and clover valence fermions with pion mass 310 MeV. We are able to obtain the qualitative features of the nucleon sea flavor structure even at this large pion mass: We observe violation of the Gottfried sum rule, indicating $overline{d}(x) > overline{u}(x)$; the helicity distribution obeys $Delta overline{u}(x) > Delta overline{d}(x)$, which is consistent with the STAR data at large and small leptonic pseudorapidity.
Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the computation of the nucleon form factors and moments of parton distribution functions, before proceeding to describe lattice studies of the Generalized Parton Distributions (GPDs). In particular, I show how lattice studies of GPDs contribute to building a three-dimensional picture of the proton. I conclude by describing the prospects for studying the structure of resonances from lattice QCD.
We calculate potentials between a proton and a $Xi^0$ (hyperon with strangeness -2) through the equal-time Bethe-Salpeter wave function, employing quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on (4.5 fm)^4 lattice at the lattice spacing $a simeq 0.14$ fm. The ud quark mass in our study corresponds to $m_{pi}simeq 0.37$ and 0.51 GeV, while the s quark mass corresponds to the physical value of $m_K$. The central $p Xi^0$ potential has a strong (weak) repulsive core in the $^1S_0$ ($^3S_1$) channel for $r lsim 0.6$ fm, while the potential has attractive well at the medium and long distances (0.6 fm $lsim r lsim 1.2$ fm) in both channels. The sign of the $p Xi^0$ scattering length and its quark mass dependence indicate a net attraction in both channels at low energies.
We present the N_f=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.
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