The quantum mechanical formula for Mayer's second cluster integral for the gas of relativistic particles with hard-core interaction is derived. The proper pion volume calculated with quantum mechanical formula is found to be an order of magnitude larger than its classical evaluation. The second cluster integral for the pion gas is calculated in quantum mechanical approach with account for both ...

The study of ππ scattering is a classical subject in the field of strong interactions: it is a scattering process that may occur at very low energy, far away from the resonance region, and it only involves the quasi–Goldstone bosons of the chiral symmetry of strong interactions. If we stay at low energy, we could expect its dynamics to be strongly constrained by chiral symmetry: as Weinberg sho...

Two sources of strong phases in the decays B to ππ are identified: (1) “quasi-elastic scattering” corresponding to intermediate states like ππ and ρρ, (2) “cc̄” corresponding to intermediate states like DD̄ and D∗D̄∗. Possibilities of using data to identify these two sources are discussed and illustrated. Present data suggests both sources may be significant. The decay of B → ππ may be considered ...

We derive the generating functional of |∆S| = 1, 2 hadronic weak interactions at one loop for a generic number of flavours and its counterpart in the quenched approximation. A systematic analysis of the ultraviolet divergences in the full theory (with and without a singlet dynamical field) and in the quenched case is performed. We show that the quenched chiral logarithms in the presence of weak...

We propose a non relativistic effective Lagrangian approach to study hadronic atom observables in the framework of QCD (including photons). We apply our formalism to derive a general expression for the width of the ππ atom decaying into two neutral pions. It contains all terms at leading and next-to-leading order in isospin breaking. The result allows one to evaluate the combination a0 − a2 of ...

We re-investigate the impact of isospin violation for extracting the s-wave ππ scattering phase shift difference δ 0 (M K) − δ 2 (M K) from K → ππ decays. Compared to our previous analysis in 2003, more precise experimental data and improved knowledge of low-energy constants are used. In addition, we employ a more robust data-driven method to obtain the phase shift difference δ 0

We measure the CP -violating asymmetries in decays to the D → KK and D → ππ CP eigenstates using 540 fb of data collected with the Belle detector at or near the Υ(4S) resonance. Cabibbo-favored D → Kπ decays are used to correct for systematic detector effects. The results, A CP = (−0.43 ± 0.30 ± 0.11)% and A ππ CP = (+0.43± 0.52 ± 0.12)%, are consistent with no CP violation.

We have evaluated forward dispersion relations for scattering amplitudes that follow from direct fits to several sets of ππ scattering experiments, together with the precise K decay results, and high to energy data. We find that some of the most commonly used experimental sets, as well as some recent theoretical analyses based on Roy equations, do not satisfy these constraints by several standa...

We study a new K → ππ decay channel with gluons in intermediate state which is normally neglected within the factorization framework. Both short-distance and long-distance parts of the amplitude are calculated. The chiral Lagrangian approach is used for obtaining the long-distance contribution. The nonperturbative contribution gives an additional enhancement to K → ππ decay amplitude with ∆I = ...