Partition temperature and fireballs of hadron-proton collisions

A geometric property is considered to relate the impact parameter b of hh collision at a given √s to the partition temperature Tp of produced nch pions. It is based on the overlapping of two Lorentz contracted fireballs (FB) associated to the primary hadrons, as is described in the partition temperature model (PTM), assuming for the FB radius R=r(3nch/2)1/3. For anti pp collisions at √s=540 GeV analyzed by the authors of the PTM, r=0.70±0.03 fm consistent with the pion radius, the computed Tp agree with their results for various nch. The energy dependence of Tp for anti pp from √s=13.8 to 900 GeV is accounted for by assuming the FB velocity with respect to the c.m.s., to behave like pp, i.e., βF=1-λ with λ=2/π and anti b=0.98 fm. Remarks are made on the relationship between Tp and the conventional temperature determined by in terms of the Lorentz factor of the FB. (orig.)