Two-point functions at two loops in three flavour chiral perturbation theory

Abstract

The vector and axial-vector two-point functions are calculated to nextto-next-to-leading order in Chiral Perturbation Theory for three light flavours. We also obtain expressions at the same order for the masses, m 2 π , m 2 K and m 2 η , and the decay constants, F π , F K and F η . We present some numerical results after a simple resonance estimate of some of the new O(p 6 ) constants.

From Hadronic τ Decays to the Chiral Couplings and

“…Our determinations of L r 10 (M ρ ) and C r 87 (M ρ ) agree within errors with the large-N C estimates based on lowest-meson dominance [24,29,37,42],…”

“…It is useful to classify the O(p 6 ) contributions through their ordering within the 1/N C expansion. The tree-level term G 6 0L (µ) contains the only O(p 6 ) correction in the large-N C limit, 4m 2 π (C r 61 −C r 12 −C r 80 ); this correction is numerically small because of the m 2 π suppression and can be estimated with a moderate accuracy [27,28,[37][38][39]. At NLO G 6 0L (µ) contributes with a term of the form m 2 K (C r 62 − C r 13 −C r 81 ).…”

New strategy for the lattice evaluation of the leading order hadronic contribution to(g−2)μ

“…It has been known for some time that the next-to-leading-order (NLO) representation [37][38][39][40] is not adequate for this purpose, its slope with respect to Q 2 being much less than what is seen in either lattice data [10] or the continuum version of the I = 1 subtracted polarization discussed above. The source of the problem is the absence, in the NLO representation, of NLO low-energy-constant (LEC) contributions encoding the large contributions associated with the prominent vector meson peaks in the relevant spectral functions.…”

The chiral logs of the K→ππ amplitude

“…For the former, the loop integrals are factorized, leading only to chiral logs of the form m 2 X L X , from which follows that m M = m K or t = 0 for this class of diagrams. For the sunrise topology, however, terms of the form m 4 [17,4], presumably shifting t to a nonzero value. I am not aware of a method how to accurately estimate the value of t. However, it was already noted by Bijnens et al in [6], discussing the double logs in the strong sector, that a large value of t leads to unrealistic large double log contributions ( They used t = 1/2 ).…”

“…In the case of three flavor CHPT , the double log contributions are however not as prominent. Table 1 shows the chiral corrections up to NNLO to the pion and Kaon decay constants and the vector form factor of K l3 [4,5,6]. The double logs amount to 20 − 35% of the NNLO order result, corresponding to around 10% of the total corrections at NNLO to the leading order result.…”