# Precise tests of low energy QCD from decay properties

### Full-text

Italo Mannelli, Jul 06, 2015 Available from:- [Show abstract] [Hide abstract]

**ABSTRACT:**The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the pattern of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the eta propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three-flavour condensate in a particularly clean way in the case of three degenerate quarks.Journal of High Energy Physics 09/2012; 2012(12). DOI:10.1007/JHEP12(2012)080 · 6.22 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The DIRAC experiment at CERN has achieved a sizeable production of π+π− atoms and has significantly improved the precision on its lifetime determination. From a sample of 21 227 atomic pairs, a 4% measurement of the S-wave ππ scattering length difference |a0−a2|=(0.2533−0.0078+0.0080|stat|syst−0.0073+0.0078)Mπ+−1 has been attained, providing an important test of Chiral Perturbation Theory. -
##### Article: A new global fit of the $L^r_i$ at next-to-next-to-leading order in Chiral Perturbation Theory

[Show abstract] [Hide abstract]

**ABSTRACT:**A new fit is done to obtain numerical values for the order $p^4$ low-energy-constants $L_i^r$ in Chiral Perturbation Theory. This includes both new data and new calculated observables. We take into account masses, decay constants, $K_{\ell4}$, $\pi\pi$ and $\pi K$ scattering lengths and slopes and the slope of the pion scalar formfactor. We compare in detail where the changes w.r.t. to the 10 year old "fit 10" come from. We discuss several scenarios for estimating the order $p^6$ constants $C_i^r$ and search for possible values of them that provide a good convergence for the ChPT series. We present two such sets. One big change is that the fits do not have the expected behaviour in the limit of large $N_c$ as well as before.Nuclear Physics B 03/2011; 854(3). DOI:10.1016/j.nuclphysb.2011.09.013 · 3.95 Impact Factor