New high statistics measurement of Ke4 decay form factors and ππ scattering phase shifts

Abstract

412The NA48/2 Collaboration: K e4 decay form factors and ππ scattering phase shifts Abstract. We report results from a new measurement of the K e4 decay K ± → π + π − e ± ν by the NA48/2 collaboration at the CERN SPS, based on a partial sample of more than 670 000 K e4 decays in both charged modes collected in 2003. The form factors of the hadronic current (F, G, H) and ππ phase difference (δ = δs − δp) have been measured in ten independent bins of the ππ mass spectrum to investigate their variation. A sizeable acceptance at large ππ mass, a low background and a very good resolution contribute to an improved experimental accuracy, a factor two better than in the previous measurement, when extracting the ππ scattering lengths a

Topological susceptibility on the lattice and the three-flavour quark condensate

“…As in our previous work, L 4 and L 6 do not show any sign of Zweig suppression and the competition between LO and NLO in three-flavour chiral expansions is clearly seen. We obtain values for the N f = 2 chiral order parameters in agreement with expectations from two-flavour chiral perturbation theory [13] as well as experimental information on ππ scattering, such as that from K l4 decays [1][2][3][4][5][6][7]. The values ofl 3 andl 4 given there can be compared to the one obtained from the RBC/UKQCD collaboration, ref.…”

“…(3.8) shows that in the physical case, the topological susceptibility has no sensitivity on the three-flavour condensate X(3). Indeed, up to 1/r-suppressed corrections (which are small since r ≥ 15 [3,7,46]), eq. (3.7) combines the (LO) three-flavour condensate and the (NLO) low-energy constant L 6 in the same way as F 2 π M 2 π , or equivalently the two-flavour condensate X(2):…”

“…which is determined from the study of ππ scattering through K ℓ4 decays [1][2][3][4][5][6][7]. As was discussed in ref.…”

“…This is sketched in a more quantitative way in figure 2 which compares the topological susceptibility at X(3) = 0 and X(3) = 1 in some illustrative cases. 3 The comparison between the two values indicates the sensitivity to the size of the three-flavour quark condensate, which tends to decrease the value of the topological susceptibility. We see that the contributions from X(3) are at least twice as small as the remaining contributions, and they in particular might be hidden in the uncertainties if q is small (e.g., of O(1/r) if the simulated quark masses are tuned to be close to the physical ones).…”

“…Over the recent years, a joint experimental and theoretical effort has provided new insight concerning low-energy dynamics of QCD, through the investigation of ππ (re)scattering in K ℓ4 [1][2][3][4][5][6][7] and K → 3π decays [8][9][10][11][12]. It turns out that, in the N f = 2 chiral limit (m u = m d = 0) [13], the breakdown of chiral symmetry (responsible for the presence of pseudoscalar Goldstone bosons corresponding to pions) is triggered by the quark condensate Σ(2) = − lim mu,m d →0 ūu .…”