The estimation of production rates of $\pi^+K^-, \pi^-K^+$ and $\pi^+\pi^-$ atoms in proton-Ni interactions at proton momentum of 450 GeV/c

In the DIRAC experiment at CERN the π+ K− , K+ π− and π+ π− atoms generated in proton-nucleus interaction at proton momentum Pp = 24 GeV/c were investigated. This work shows that the yields of π+ K− , K+ π− and π+ π− atoms in the p-nucleus interactions at Pp = 450 GeV/c and θ lab = 4◦ are 17, 38 and 16 times more than the one in the DIRAC experiment. The increased yields of the short-lived ππ ( πK ) atoms with minimum lifetime τ th = 2.9 . 10 − 15 s ( τ th = 3.5 . 10 − 15 s ) allows to improve the precisions of their lifetime measurement and ππ ( πK ) scattering length combinations | a 0 − a 2 | ( | a 1 / 2 − a 3/2 | ). In the DIRAC experiment the long-lived ππ atoms( τ th ≥ 1.2 . 10 − 11 s) were observed also. It was detected n A = 436 ± 61 π + π − pairs(atomic pairs) originating in the breakup of long-lived ππ atoms in the Pt foil with probability more than 90%. After the change of experiment scheme the number of produced long-lived π+ π− , π+ K− and K+ π− atoms per time unit at Pp = 450 GeV/c can be increased by 370, 1600 and 750 times accordingly. The background which gives the main contribution to the error in the n A will be reduced two orders of magnitude. It allows to use the resonance method to measure the Lamb shift in ππ atom and the new ππ scattering length combination 2a 0 + a2 . For the data analysis in the resonance method only Lorentz transformation and quantum mechanics will be used. The low energy QCD gives the precise predictions for values of ππ and πK scattering lengths and this precision will be improved in the future using Lattice calculations.