Universal rise of hadronic total cross sections based on forward πp and p¯p(pp) scatterings

Recently there are several evidences of the increase of the total cross section σtotσtot to be log2slog2s consistent with the Froissart unitarity bound, and the COMPETE collaborations in the PDG have further assumed σtot≃Blog2(s/s0)σtot≃Blog2(s/s0) to extend its universal rise with a common value of B   for all the hadronic scatterings. However, there is no rigorous proof yet based only on QCD. Therefore, it is worthwhile to prove this universal rise of σtotσtot even empirically. In this Letter we attempt to obtain the value of B for πp   scattering, BπpBπp, with reasonable accuracy by taking into account the rich πp data in all the energy regions. We use the finite-energy sum rule (FESR) expressed in terms of the πp   scattering data in the low and intermediate energies as a constraint between high-energy parameters. We then have searched for the simultaneous best fit to the σtotσtot and ρ   ratios, the ratios of the real to imaginary parts of the forward scattering amplitudes. The lower energy data are included in the integral of FESR, the more precisely determined is the non-leading term such as logslogs, and then helps to determine the leading terms like log2slog2s. We have derived the value of BπpBπp as Bπp=0.311±0.044 mbBπp=0.311±0.044 mb. This value is to be compared with the value of B   for p¯p,pp scattering, BppBpp, in our previous analysis [M. Ishida, K. Igi, Eur. Phys. J. C 52 (2007) 357], Bpp=0.289±0.023 mbBpp=0.289±0.023 mb. Thus, our result appears to support the universality hypothesis.