Isospin symmetry breaking

Abstract

We discuss the separation of isospin-symmetric and isospin-breaking contributions in the hadronic observables within the framework of QCD plus QED. Further, we briefly review some recent work on the low-energy hadron phenomenology, in which the isospin-breaking effect plays a prominent role.

Review of lattice results concerning low energy particle physics

“…There is an indirect phenomenological determination of ǫ, which is based on the decay η → 3π and does not rely on models. The result for the quark mass ratio Q, defined in (24) and obtained from a dispersive analysis of this decay, implies ǫ = 0.70 (28) (see Section 3.4). While the values found in older lattice calculations [32][33][34] are a little less than one standard deviation lower, the most recent determinations [40][41][42][43][44][45]50], though still preliminary, are in excellent agreement with this result and have significantly smaller error bars.…”

“…We divide them by the results for R and Q in (27), omitting the uncertainties due to e.m. We obtain R M /R ≃ 0.88 (8) and Q M /Q ≃ 0.91(5). We proceed analogously for N f = 2 + 1, using ǫ = 0.70(3) from ( 9) and R and Q from (28), and find R M /R ≃ 1.02(5) and Q M /Q ≃ 0.99 (3). The chiral corrections appear to be small for N f = 2 + 1, especially those in the relation of Q to Q M .…”

“…The input used in MILC 09A is ǫ = 1.2(5) [37], while the N f = 2 computation of RM123 13 finds ǫ = 0.79 (18) (18) [45]. As discussed in Section 3.5, the value of Q used by BMW 10A, 10B [22,23] gives ǫ = 0.70 (28) at NLO (see (31)). On the other hand, RBC 07 [34] and Blum 10 [32] obtain the results ǫ = 0.13(4) and ǫ = 0.5 (1).…”

Cusps in K --> 3pi decays: a theoretical framework

“…(1.2) could only be obtained through a combined effort of experiment and theory. Indeed, relating experimental data to the scattering lengths is a nontrivial affair [18,19,20], and a precise theoretical description of the cusp behavior in the amplitude for K ± → π 0 π 0 π ± turns out to be quite difficult.…”

QCD isospin breakingχPT low-energy constants from the instanton vacuum

“…where B and F are the leading order parameters in the chiral lagrangian, and m u , m d are the current quark masses. While experimentally the isospin breaking effects are known to a very high precision, separation of these effects on the "pure QCD" and electromagnetic parts has ambiguities and has been a subject of intensive debates [1,[6][7][8][9]. From phenomenology the constant l 7 is known only with an "order of magnitude" estimate [1],…”