Abstract
This work continues our program of lattice-QCD baryon physics using staggered fermions for both the sea and the valence quarks. We present a proof-of-concept study that demonstrates, for the first time, how to calculate baryon matrix elements using staggered quarks for the valence sector. We show how to relate the representations of the continuum staggered flavor-taste group $\mathrm{SU}(8{)}_{\mathrm{FT}}$ to those of the discrete lattice symmetry group. The resulting calculations yield the normalization factors relating staggered baryon matrix elements to their physical counterparts. We verify this methodology by calculating the isovector vector and axial-vector charges ${g}_{V}$ and ${g}_{A}$. We use a single ensemble from the MILC Collaboration with $2+1+1$ flavors of sea quark, lattice spacing $a\ensuremath{\approx}0.12\text{ }\text{ }\mathrm{fm}$, and a pion mass ${M}_{\ensuremath{\pi}}\ensuremath{\approx}305\text{ }\text{ }\mathrm{MeV}$. On this ensemble, we find results consistent with expectations from current conservation and neutron beta decay. Thus, this work demonstrates how highly improved staggered quarks can be used for precision calculations of baryon properties and, in particular, the isovector nucleon charges.
Highlights
Accurate first-principles calculations of nuclear cross sections are an important objective in the particle physics community
We have presented two key results in this work
We have shown how to analytically relate the staggered nucleonlike matrix elements with nontrivial tastes to the physical nucleon matrix elements. This step is crucial for our ongoing program of extracting high-precision nucleon results from staggered fermions
Summary
Accurate first-principles calculations of nuclear cross sections are an important objective in the particle physics community. [20], it can be advantageous to use unphysical nucleonlike states to carry out the calculation These states obtain the same properties as the physical nucleon in the continuum limit, where the full SUð8ÞFT flavor(isospin)taste symmetry emerges. For matrix elements such as charges and form factors, one must find the correct group-theoretic normalization factors relating nucleonlike matrix elements to their physical counterparts. This exercise is a straightforward if complicated application of the generalization of the Wigner-Eckart theorem to SU(8) To demonstrate this approach, we compute the nucleon vector and axial-vector charges on a single MILC HISQ ensemble with lattice spacing a ≈ 0.12 fm and pion mass Mπ ≈ 305 MeV. Appendixes A and B present the group theory relating the nucleonlike matrix elements to their physical counterparts, including a numerical demonstration that these derivations are correct
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