Baryon masses and σ terms in SU(3) BChPT × 1/Nc

Abstract

ChPT and the 1/N c expansion provide systematic frameworks for the strong interactions at low energy. A combined framework of both expansions has been developed and applied for baryons with three light-quark-flavors. The small scale expansion of the combined approach is identified as the ξ-expansion, in which the power counting of the expansions is linked accordingThe physical baryon masses as well as lattice QCD baryon masses for different quark mass masses are analyzed to O(ξ 3 ) in that framework. σ terms are addressed using the Feynman Hellmann theorem. For the nucleon, a useful connection between the deviation of the Gell-Mann-Okubo relation and the σ term σ 8N associated with the scalar densityūu +dd − 2ss is identified. In particular, the deviation from the tree level relation σ 8N = 1 3 (2m N − m Σ − m Ξ ), which gives rise to the so called σ-term puzzle, is studied in the ξ-expansion. A large correction non-analytic in ξ results for that relation, making plausible the resolution of the puzzle. Issues with the determination of the strangeness σ terms are discussed, emphasizing the need for lattice calculations at smaller m s for better understanding the range of validity of the effective theory.The analysis presented here leads to σ πN = 69(10) MeV and σ π∆ = 60(10) MeV.

CP violation in η muonic decays

“…[41], and those appearing in Ref. [43] 31 ; for the strange one, σ s 3 = N p | m ss s |N p , we restrict to the lattice results due to the large theoretical uncertainties. This results in σ p,n ud = 53(16), σ p 3 = 2.9(1.0), σ n 3 = −2.9(0.6), σ p,n s = 54(5),…”

“…[40]. 31 In doing so, we use the value arising from a χPT-based analysis m d /mu = 0.553 (43) [5] rather than lattice. Figure 5: Comparison of the half-width estimate for the-normalized-isovector form factor (orange band) to that in Ref.…”

Baryon $\sigma$ terms in SU(3) BChPT x 1/Nc

“…In the analysis of Ref. [10], both physical and LQCD baryon masses are considered. The LQCD baryon masses have been obtained for approximately fixed M K , varying m u = m d in a range from the physical limit up to M π ∼ 300 MeV [11].…”

“…In this note, the focus is on the determination of σ πN using the Feynman-Hellmann theorem and results for baryon masses in SU (3), as presented in Ref. [10], with additional brief discussions of σ terms of ∆ and hyperons, and the issue of the quark mass dependence of σ terms, namely the range in m q where the effective theory may be trusted in their description.…”

“…In this framework, the effective Lagrangians to O(ξ 3 ) can be found in Ref. [5,10]. The chiral Lagrangian relevant to the discussion of masses up to O(ξ 3 ) and including electromagnetic contributions is given by [5,10]:…”