Compilation of coupling constants and low-energy parameters

Energy-level displacement of excitednpstates of kaonic hydrogen

“…The phenomenological low-energy interaction of the resonance Σ 0 3 with octets lowlying baryons B(8) and pseudoscalar mesons P (8) is defined by [18,19,37] (see also [20]):…”

“…The real parts of the amplitudes f ℓ ′ + ( √ kq) and f ℓ ′ − ( √ kq) are defined by the ℓ ′ -wave scattering lengths of K − p scattering [18,14] Re…”

Finite-size effect on two-particle production in continuous and discrete spectrum

“…The two-channel effects in the production cross section, being quadratic in the amplitude f βα 0 , usually represent less than several percent of the strong FSI contribution (a fraction of percent in the cross section). Thus, for a near-threshold two-pion system produced according to a Gaussian r * -distribution (159) with the characteristic radius r G = 3 fm and, taking the two-pion s-wave amplitudes from [8] G , at r G = 3 fm it is still comparable to the contribution of the inelastic two-pion transition, composing 0.25% and 0.20% for the amplitudes from [8] and [5], respectively.…”

“…As this lifetime of order 10 −15 s is determined by the probability of the annihilation π + π − → π 0 π 0 : 1/τ 10 ∼ |a 0 0 − a 2 0 | 2 , the DIRAC measurement enables to determine the absolute value of the difference a 0 0 −a 2 0 of the s-wave isoscalar and isotensor ππ scattering lengths to 5%. This represents a factor of 4 improvement of the accuracy achieved in previous studies [5], and is comparable with the precision of the most recent experiments E865 at BNL [6] and NA48/2 at CERN [7]. The former is based on a study of K e4 decays and yields the statistical error of 6% in a 0 0 ; this measurement essentially exploits other experimental data together with dispersion relations (Roy equations), the systematic and theoretical errors being estimated on the level of several percent.…”

“…The possibility of the correlation measurement of the scattering amplitudes has been demonstrated [20] in a preliminary analysis of the NA49 π + π − correlation data within the RQMD transport model. For this, besides the r * -scale s r , the strong interaction scale s f has been introduced in the RQMD correlation function R(Q; s r , s f ), rescaling the original s-wave π + π − scattering amplitude taken from [5]:…”