Abstract
High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wave function and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS ¯ scheme at μ = 2 GeV .
Highlights
Distribution amplitudes play an essential role in the investigation of the internal nuclear structure
According to [2], for Q2 → ∞, the magnetic form factor of the nucleon can be written as a convolution of three amplitudes: first, the distribution amplitude Φ for finding the nucleon in the valence state with the three quarks having definite momentum fractions xi, second, the hard scattering kernel TH, which describes one of the three quarks absorbing the photon, and the complex conjugate of Φ
In this paper we have set up a lattice renormalization scheme for three-quark operators based on the RI-MOM approach
Summary
Distribution amplitudes play an essential role in the investigation of the internal nuclear structure. The soft subprocess, described by the nucleon distribution amplitude Φ(xi), contains the information about the distribution of the three valence quark momentum fractions xi inside the nucleon [1,2,3,4,5]. The great interest in this quantity stems from its importance for, e.g., the calculation of the electromagnetic form factors of the nucleon and their scaling behavior These form factors describe a nucleon absorbing a virtual photon of squared momentum −Q2 while remaining intact. According to [2], for Q2 → ∞, the magnetic form factor of the nucleon can be written as a convolution of three amplitudes: first, the distribution amplitude Φ for finding the nucleon in the valence state with the three quarks having definite momentum fractions xi, second, the hard scattering kernel TH , which describes one of the three quarks absorbing the photon, and the complex conjugate of Φ that gives the amplitude for the outgoing quarks to form a nucleon again: GM (Q2) =
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