Scattering amplitudes at multi TeV energies
Abstract
Description
We show that a generalized Regge behaviour, $$Im F(s,t)\simeq Φ(t)(\log s/\hat{s})^{ν(t)}(s/\hat{s})^{α_P(t)},\quad{\rm for} |t|<|t_0|, s\to\infty$$ where $Φ(t)\simeq e^{bt}$, $α_P(t)\simeq α_P(0)+α'_P(0)t$, and $t_0$ is the first zero of $α_P(t)$, $α_P(t_0)=0$, implies that the corresponding cross section is bounded by $$σ_{\rm tot}(s)<({\rm Const.})\times\log s/\hat{s}.$$ This growth, however, is not sufficient to fit the experimental cross sections. If, instead of this, we assume saturation of the improved Froissart bound, i.e., a behaviour $$Im F(s,0)\simeq A(s/\hat{s})\log^2{{s}\over{s_1\log^{7/2} s/s_2}}, $$ a good fit is obtained to $ππ$, $πN$, $KN$ and $NN$ cross sections from c.m. kinetic energy $E_{\rm kin}\simeq1 $ GeV to 30 TeV (producing a cross section of $108\pm6$ mb at LHC energy). This suggests that the Regge-type behaviour only holds for values of the momentum transfer very near zero.
Plain TeX. Dedicated to Prof. Yuri Simonov in his 70th birthday
Plain TeX. Dedicated to Prof. Yuri Simonov in his 70th birthday