Abstract
We perform a first calculation for the unpolarized parton distribution function of the $\Delta^+$ baryon using lattice QCD simulations within the framework of Large Momentum Effective Theory. Two ensembles of $N_f=2+1+1$ twisted mass fermions are utilized with a pion mass of 270 MeV and 360 MeV, respectively. The baryon, which is treated as a stable single-particle state, is boosted with momentum $P_3$ with values $\{0.42,0.83,1.25\}$ GeV, and we utilize momentum smearing to improve the signal. The unpolarized parton distribution function of $\Delta^+$ is obtained using a non-perturbative renormalization and a one-loop formula for the matching, with encouraging precision. In particular, we compute the $\overline{d}(x)-\overline{u}(x)$ asymmetry and compare it with the same quantity in the nucleon, in a first attempt towards resolving the physical mechanism responsible for generating such asymmetry.
Highlights
Quantum chromodynamics (QCD) is established as the fundamental theory which describes the strong interaction among quarks and gluons, the basic constituents of all hadronic matter
We perform a first calculation for the unpolarized parton distribution function of the Δþ baryon using lattice QCD simulations within the framework of large momentum effective theory
The first ensemble is smaller in volume (243 × 48) and reproduces a mass for the Δ equal to mΔ 1⁄4 1.59ð4Þ GeV, i.e., around 30% heavier than its physical value
Summary
Quantum chromodynamics (QCD) is established as the fundamental theory which describes the strong interaction among quarks and gluons, the basic constituents of all hadronic matter. As such, it is valid in a wide range of energy scales, from the hadronic regime, where nonperturbative effects dominate, to high energy, where perturbation theory is applicable. An appropriate formulation is necessary to address the highly nonperturbative dynamics of QCD at low energies. Lattice QCD is an ideal nonperturbative tool, which relies on a space-time
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