Multiperipheral Production of Large and Small Fireballs at Very High Energies

M. Hama, H. Suzuki
1979 Progress of theoretical physics  
In the multiparticle productions at cosmic ray energies the experimental data have been analysed by the small fireballs (Hquanta) and the large ones (SH-quanta) .u The masses 1'v1u=2~3 GeV and 1'.1sH=20 "-'30 Ge V; the average charged pion multiplicities (k"')H~4 and (k"')sH=20~30. On the other hand FNAL and ISR data on small Pr and large Pr have been analysed by the productions of H's and SH's respectively. 'l • 3 l "\Ve present here a simple one-dimensional multiperipheral model with Regge
more » ... exchange for SH production as well as for H production. 2 l The inclusive one pion cross section, momentum transfers between fireballs and the production cross section of SH are evaluated. Let us consider a one-dimensional (longitudial) multiperipheral production of n fireballs (Pi) and two leading nucleons (Po, Pn+1) in the proton-proton CPa, h) collision. In terms of rapidities the energy and momentum conservations are written where m and 1'.1 are masses of nucleon and fireball, respectively and 7Jh 7J2·"1Jn are rapidities of fireballs, 7Jo and 7Jn+ 1 (Ya and Yb) are those of leading (incident) protons; 7Jo <;;, 7J1 <;;, .. • S 7J n + b Yb-Ya :::= Y =In s, transverse momennta being ignored. For massive fireballs 1\ilym a simple relation holds at large Ins for the average multiplicity (n) =bIns+ canst, where /C is the average inelastisity, ~C~1/2, since in average events, equal spacing is expected, (7jj)= Ya+LI+JA, J..= (lns-2LI)/ ((n)+1), e-•=1-/C and then e-1 c-:'.m~C/ M(1-~C)~1/20~1 forM=MsH· The average four momentum transfer squared can also be evaluated using e-1.~1. (CPa -2.j~~oPi) 2 ) c-:' . -mMsH for sebsequent SH's and ((Po-Pa) 2 ) = ( (Pn+1-Po) 2 > c-:' . -m 2 /2 for a leading nucleon and next SH. The cross section for n fireball production may be given as 2 l g's are coupling constants at vertices. 'lJa and 7J 0 are the kinematical boundary of 'l) 1 "?:.7Ja and 7Jn<;;,·r;b. In c.m. system ·r;u= -rJa = Y/2 and Y :::= 7Jb-'f/a =2 cosh -1 [ {s+ (111 +m) 2 -m 2 }/2(M-i-m)vs], c-:'.ln{s/(M+m) 2 } for ln s/ lvf2y 1. This comes from the extreme case that a leading nucleon and a fireball are emitted with the same rapidity and another nucleon is emitted in the opposite direction, other fireballs being ignored. Taking K ( 7J) = 7JC 2 "" as discussed in Ref. 2) we have the fireball cross section, where 2a -1g-2 = 0 is used for the constant limit of up(=) =ga 2 gb 2 e-2 Y+ ( 2 a+olYj2g. The average multiplicity and inclusive one fireball cross section are given as (n)=~ gY(1+e-ol') (1-e-oF) -1/2, (4) drJp/d7J=r1p(=H g{1-e-o(2'i+Yl} Comparing each leading term m (1) and
doi:10.1143/ptp.62.1786 fatcat:abwkzqlp3zbxtlqzrawf5zpumy