Factorization and scaling in hadronic diffraction

Abstract

A bstractIn standard R egge theory,the contri buti on ofthe tri pe-pom eron am pl i tude to the t= 0 di erenti alcross secti on for si ngl e di racti on di ssoci ati on has the form d 2 =dM 2 dtj t= 0 (s=s 0 ) 2[ I P (0) 1] =(M 2 ) I P (0) ,w here I P (t) i s the pom eron trajectory. For I P (0)> 1,thi sform ,w hi ch i sbased on factori zati on,doesnotscal e w i th energy. From an anal ysi s ofpp and pp data from xed target to col l i der energi es, we nd that such scal i ng actual l y hol ds,si gnal i ng a breakdow n of factori zati on. Phenom enol ogi cal l y,thi s resul t can be obtai ned from a scal i ng l aw i n di racti on, w hi ch i s em bedded i n the hypothesi s ofpom eron ux renorm al i zati on i ntroduced to uni tari ze the tri pl e pom eron am pl i tude.y Fel l ow ofC N Pq,Brazi l . IntroductionIn R egge theory,the hi gh energy behavi or ofhadroni c cross secti ons i s dom i nated by pom eron exchange [ 1,2] . For a si m pl e pom eron pol e,the pp el asti c,total ,and si ngl e di racti ve (SD ) cross secti ons can be w ri tten as(1)w here I P (t)= I P (0)+ 0 t= (1+ )+ 0 ti sthepom eron R eggetrajectory, I P pp (t)i sthe coupl i ng ofthe pom eron to the proton,g(t) i s the tri pl e-pom eron coupl i ng,s 0 = M 2 i s the I P p centerofm assenergy squared, = 1 x F = s 0 =s = M 2 =s i sthe fracti on ofthe m om entum ofthe proton carri ed by the pom eron,and s 0 i s an energy scal e param eter, w hi ch i s assum ed throughout thi s paper to be 1 G eV 2 unl ess appeari ng expl i ci tel y. In anal ogy w i th Eq.2,the term i n brackets i n (3) i s i denti ed as the I P p total cross secti on,w here we have used g(t)= g(0),si nce i t was found experi m ental l y thatg(t) i s i ndependent oft [ 1] . T he rem ai ni ng factor i n (3),nam el y f I P =p ( ;t) 2 I P pp (t) 16w here K 2 I P pp (0)=16 , i s i nterpreted as the \pom eron ux". T hus, pp di racti on di ssoci ati on can bevi ewed asa processi n w hi ch pom eronsem i tted by one ofthe protons i nteract w i th the other proton [ 3] .T he functi on F (t) represents the proton form factor,w hi ch i s obtai ned from el asti c scatteri ng. A t sm al lt,F 2 (t) e 4:6t [ 4] . H owever, thi s si m pl e exponenti alexpressi on underesti m ates the cross secti on at l arge t. D onnachi e and Landsho proposed [ 5]that the appropri ate form factorforpp el asti c and di racti ve scatteri ng i s the i soscal ar form factor m easured i n el ectron-nucl eon scatteri ng,nam el yw here m i s the m ass ofthe proton. W hen usi ng thi s form factor,the pom eron ux i s referred to asthe D onnachi e-Landsho (D L) ux 1 .N ote thatatsm al l -tF 2 1 (t)can be approxi m ated w i th an exponenti alexpressi on w hose sl ope param eter,b(t)= d dt l n F 2 1 (t),i s 1 T he factor K i n the D L ux i s K D L = (3 I P qq ) 2 =4 2 ,w here I P qq i s the pom eron-quark coupl i ng.

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