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First simultaneous global QCD analysis of kaon and pion parton distributions with lattice QCD constraints

P. C. Barry, Chueng-Ryong Ji, W. Melnitchouk, N. Sato, Fernanda Steffens

Abstract

We perform the first simultaneous global QCD analysis of pion and kaon parton distribution functions (PDFs), constrained by pion- and kaon-induced Drell-Yan (DY) and leading neutron electroproduction data, together with lattice QCD data on pion and kaon PDF moments. The analysis indicates a softer valence $\bar u$ distribution in the $K^-$ than in the $π^-$, and a significantly more peaked valence $s$-quark density in $K^-$ compared with the $\bar u$. The effective exponent governing the high-$x$ behavior of the PDF is found to be larger for $\bar u$ in the kaon, $β_{\bar u}^{K^-}\!= 1.6(2)$, than in the pion, $β_{\bar u}^{π^-}\!= 1.16(4)$, in the range $0.7 \leq x \leq 0.95$. From the gluon momentum fractions we find the pion's gluon content accounts for $\approx 1/3$ of the mass budget of the pion at $μ=2~{\rm GeV}$, but only $\approx 1/4$ for the kaon.

First simultaneous global QCD analysis of kaon and pion parton distributions with lattice QCD constraints

Abstract

We perform the first simultaneous global QCD analysis of pion and kaon parton distribution functions (PDFs), constrained by pion- and kaon-induced Drell-Yan (DY) and leading neutron electroproduction data, together with lattice QCD data on pion and kaon PDF moments. The analysis indicates a softer valence distribution in the than in the , and a significantly more peaked valence -quark density in compared with the . The effective exponent governing the high- behavior of the PDF is found to be larger for in the kaon, , than in the pion, , in the range . From the gluon momentum fractions we find the pion's gluon content accounts for of the mass budget of the pion at , but only for the kaon.

Paper Structure

This paper contains 3 equations, 4 figures, 1 table.

Figures (4)

  • Figure 1: Ratio of $K^-$ to $\pi^-$ DY cross sections from the NA3 experiment NA3:1980fhh (black circles) compared with the JAM analysis (blue bars). The inset compares kaon PDF moments from JAM (green bars) with lattice QCD (LQCD) results from the ETM Collaboration (open circles) ExtendedTwistedMass:2024kjf, shown for a 68% CI.
  • Figure 2: Valence quark PDFs $x q_v$ in the $K^-$ for the $s$ (red) and $\bar{u}$ (blue) quarks, and the $\bar{u}$ in the $\pi^-$ (yellow), at the input scale $\mu = m_c$ for the 95% CI. The inset shows the effective $\beta_q$ exponents at large $x$ as replicas.
  • Figure 3: Ratios of the $\bar{u}_v^{K^-}$ to $\bar{u}_v^{\pi^-}$ PDFs (upper panel) and $s_v^{K^-}$ to $\bar{u}_v^{K^-}$ PDFs (lower panel) for $1\sigma$ (darkest shading), $2\sigma$, and $3\sigma$ (lightest shading) CIs.
  • Figure 4: $Z$-score from the $t$-comparison statistic as a function of luminosity for the proposed kaon-induced AMBER experiment Denisov:2018unj. Luminosities above $2 \times 10^{-2}$ fb$^{-1}$ would be ideal for $3\sigma$ discrimination. The inset shows the distributions of the truncated $s_v^{K^-}$ and $\bar{u}_v^{K^-}$ moments.