Model for Pion Produc t ion in Proton-Nucleus Interact ions

I N T R O D U C T I O N Reliable prediction of pion yield in hadron-nucleus (hA) collisions is vital in numerous applications, particularly in the planning of future experiments and accelerators. The newest examples include a #+#-coll ider project [1] and neutrino experiments at Fermilab Main Injector [2] and Booster [3]. There are a few models capable of generating pions in pA --, 7r• reactions, e. g., [4 9]. Theoretical calculations based on the intranuclear cascade model are reliable at proton momenta P0 <5 GeV/c, but drastically overestimate hadron yield at higher energies. Microscopic models, such as D P M J E T [5] (based on the dual topological unitarization approach) and FRITIOF [6] (based on the LUND model) were developed mainly for high energies >50 GeV/c. As it is shown in [1], there is an uncertainty up to a factor of 5 in the pion yield at p <1 GeV/c on heavy nuclei for proton momenta 5< P0 <30 GeV/c the region that is especially interesting for the #+#-coll ider project. On the other hand, there are many data on inclusive charged pion production in hA collisions obtained over the last three decades. Based on those data and our original model [4.9]. we develop a phenomenological model for a reliable description of inclusive pion production in the entire kinematic range for pA collisions at 5 GeV/c< P0 <10 TeV/(. 1) Work supported by" tile Universities Research Association, Inc., under contract DE-AC0276CH00300 with the U. S. Department of Energy. 2) Supported by Russian Foundation for Basic Research, under contract RFBR-96-07-89230. CP435. Workshop on the Front End of a Muon Collider edited by S. Geer and R. Raja 9 1998 The American Institute of Physics 1-56396-793-6/98/$15.00 453 Downloaded 04 Mar 2010 to 128.112.85.160. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp PHENOMENOLOGICAL MODEL Many reliable data and parameterizations exist on pion yield in pp-collisions. We can compensate for the lack of data for pA reactions by using the following form (see, e. g., [4,9]) for the double differential cross section of the pA ~ 7r• reaction: d2 crpA~Tr • X d2 ~pp~rr• x dpdf~ RPA~n• p,p.L) ~ , (1) where p and pz are the total and transverse momenta of 7r ~, and A is an atomic mass of the target nucleus. The function R pn-~• measured with much higher precision than the absolute yields, is almost independent of p• and its dependence on Po and p is much weaker than for the differential cross-section itself. Because of rather different properties of pion production on nuclei in the forward (xr >0) and backward (xF <0) hemispheres, where xF is the Feynman's longitudinal variable~ we treat these two regions differently. R a t xF >0 .05 . In this region we assume R pA~'• ~ A ~. The power c~ is almost independent of the pion sign. The following parameterization was proposed in [10] for P0 >70 GeV/c: ag = 0.8 0 .75 x r + 0 . 4 5 . x~/l=rl + 0 . 1 . p~. (_'2) Fig. l(a) shows our compilation of data [11-15] on c~ for 7r--production. It turns out tha t (2) describes data very well at P0 >24 GeV/c and can be successfully used at lower momenta (5_< Po _<24 GeV/c) if it is replaced with (see Fig. l(a)): = ~g 0.0087-(24 Po). (3) The R pA-*cr• ~ A ~ form doesn't extrapolate well to A = I because of the difference in the 7r-yield in proton-proton and proton-neutron collisions. This difference can be taken into account if one uses the following form for R pA~n• [10]: RPA~,• = ( A ) ~ . f(Po, Y) , (4) where f(Po, Y) = do, d • e, ~ ( p --~ 7r ) / ~ ( p p --, 7r• It turns out that. pion yields in pd and pp collisions are not very different, i. e. f(Po, Y) ~1. Using FRITIOF results, we found that f (Po ,Y)n= 1 + 0.225/Nnan9 Y~s , where N~is mean 7rmultiplicity in pp collisions and Y~s is pion rapidity in the center-ofmass system (CMS). Data [16] show linear dependence of N~on free energy W = (VT-2.rnF)~ T5 ,/~o2s , where ~ is the CMS collision energy. Our fit to the data gives N~= 0.81 (W 0.6). The other parameter an= 0.16 for p0 < 20 GeV/c, and depends on energy for higher momenta as a~= -0.055 + 0.747~log(s). f(Po, Y)~ is forced to be 1 if it becomes less than 1. For rc + production the approximation is