Correlations between the strange quark condensate, strange quark mass, and kaon PCAC relation

Abstract

Correlations between the strange quark mass, strange quark condensate $⟨\bar{s}s⟩$, and the kaon partially conserved axial current (PCAC) relation are developed. The key dimensionless and renormalization-group invariant quantities in these correlations are the ratio of the strange to non-strange quark mass $r_m=m_s/m_q$, the condensate ratio $r_c=⟨\bar{s}s⟩/⟨\bar{q}q⟩$, and the kaon PCAC deviation parameter $r_p=-m_s⟨\bar{s}s+\bar{q}q⟩/2f_K^2{m}_K^2$. The correlations define a self-consistent trajectory in the $\{r_m,r_c,r_p\}$ parameter space constraining strange quark parameters that can be used to assess the compatibility of different predictions of these parameters. Combining the constraint with Particle Data Group (PDG) values of $r_m$ results in $\{r_c,r_p\}$ constraint trajectories that are used to asses the self-consistency of various theoretical determinations of $\{r_c,r_p\}$. The most precise determinations of $r_c$ and $r_p$ are shown to be mutually consistent with the constraint trajectories and provide improved bounds on $r_p$. In general, the constraint trajectories combined with $r_c$ determinations tend to provide more accurate bounds on $r_p$ than direct determinations. The $\{r_c,r_p\}$ correlations provide a natural identification of a self-consistent set of strange quark mass and strange quark condensate parameters.

arXiv comment9 pages, 6 figures, 1 table. Typo (factor of 1/2 in eq. (1)) corrected from PRD version

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