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Can Gluons Trace Baryon Number ?

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Can Gluons Trace Baryon Number ? CERN-TH/95-343 BI-TP 95/42 CAN GLUONS TRACE BARYON NUMBER ? D. KHARZEEV Theory Division, CERN, CH-1211 Geneva, Switzerland and Fakultat fur Physik, Universitat Bielefeld, D-33501 Bielefeld, Germany Abstract QCD as a gauge non-Ab elian theory imp oses severe constraints on the structure of the baryon wave function. We p oint out that, contrary to a widely accepted b elief, the traces of baryon numb er in a high-energy pro cess can reside in a non-p erturbative con guration of gluon elds, rather than in the valence quarks. We argue that this conjecture can b e tested exp erimentally, since it can lead to substantial baryon asymmetry in the central rapidity region of ultra-relativistic nucleus-nucleus collisions. CERN-TH/95-343 BI-TP 95/42 In QCD, quarks carry colour, avour, electric charge and isospin. It seems only natural to assume that they also trace baryon numb er. However, this latter assumption is not dictated by the structure of QCD, and therefore do es not need to b e true. Indeed, the assignment of the baryon number B =1=3 to quarks is based merely on the naive quark mo del classi cation. But anyphysical hadron state in QCD should b e represented by a state vector which is gauge-invariant{ the constraint which is ignored in most of the naive quark mo del formulations. This constraint turns out to b e very severe; in fact, there is only one wayto construct a gauge-invariant state vector of a baryon from quarks and gluons [1] (note however that there is a large amount of freedom in cho osing the paths connecting x to x ): i Z Z x x ij k B = P exp ig A dx q (x ) P exp ig A dx q (x ) 1 2 x x 1 2 i j Z x P exp ig q (x ) A dx : (1) 3 x 3 k The \string op erators" in (1) acting on the quark eld q (x ) make it transform n as a quark eld at p oint x instead of at x . The tensor then constructs a lo cal n colour singlet and gauge invariant state out of three quark elds (see Fig.1a). The B in eq. (1) is a set of gauge invariant op erators representing a baryon in QCD. With prop erly optimised parameters it is used extensively in the rst principle computations with lattice Monte Carlo attempting to determine the nucleon mass. The purp ose of this work is to study its phenomenological impact on baryon numb er pro duction in the central region of nucleus-nucleus collisions . It is evident from the structure of (1) that the trace of baryon numb er should b e asso ciated not with the valence quarks, but with a non-p erturbative con g- uration of gluon elds lo cated at the p oint x - the \string junction" [1]. This can b e nicely illustrated in the string picture: let us pull all of the quarks away from the string junction, whichwekeep xed at p oint x. This will lead toqq pair pro duction and string break-up, but the baryon will always restore itself around the string junction. The quark comp osition of this resulting baryon will in general di er from the comp osition of the initial baryon. It is imp ortantto note that the assignment of the trace of baryon numb er to gluons is not only a feature of a particular kind of the string mo del, but is a consequence of the lo cal gauge invariance principle applied to baryons. Surprisingly, at rst glance this non-trivial structure of baryons in QCD do es not seem to reveal itself in hadronic interactions in any appreciable way. This is b ecause to prob e the internal structure of baryons, we need hard interactions, which usually act on single quarks. The baryon numb er therefore can always b e asso ciated with the remaining diquark, without sp ecifying its internal structure. To really understand what traces the baryon numb er, one needs therefore to 2 study pro cesses in which the ow of baryon numb er can b e separated from the owofvalence quarks. In this Letter we suggest that studies of baryon pro duction in the central ra- pidity region of ultra-relativistic pp and esp ecially AA collisions provide a crucial p ossibili ty to test the baryon structure. Our ndings may prove imp ortant for understanding the prop erties of dense QCD matter pro duced in AA collisions at high energies. In what follows, we shall rst formulate our ideas qualitatively, and then give some quantitative estimates based on the top ological expansion of QCD [1, 2 ] and Regge phenomenology. Let us consider rst an ultra-relativisti c pp collision in its centre-of-mass frame, which coincides with the lab frame in collider exp eriments. At suciently high energies, the valence quark distributions will b e Lorentz-contracted to thin pancakes with the thickness of 1 z ' ; (2) V x P V where P is the c.m. momentum in the collision, and x 1=3isatypical V fraction of the proton's momentum carried bya valence quark. The typical time needed for the interaction of valence quarks from di erent protons with each other during the collision is given by the characteristic interquark distance in the impact parameter plane, t = const O (1 fm). However, the time available int 1 for this interaction in the collision is only t z (x P ) . It is therefore coll V V clear that at suciently high energies, when t << t , the valence quarks of coll int the colliding protons do not have time to interact during the collision and go through each other, p opulating the fragmentation regions. In the conventional picture, the baryon numb er follows the valence quarks. At rst glance, the argument lo oks correct, and is well supp orted exp erimen- tally - the leading e ect for baryons in high energy pp collisions is well established. However, the structure of the gauge-invariant baryon wave function (1) suggests that this scenario may not b e entirely consistent. As wehave stressed ab ove, in QCD the trace of the baryon numb er has to b e asso ciated with the non- p erturbative con guration of the gauge eld. This \string junction" contains an in nite numb er of gluons which, therefore, by virtue of momentum conservation, should carry on the average an in nitely small fraction x << x of the proton's S V momentum. We therefore exp ect that the \string junction" con guration may not b e Lorentz-contracted to a thin pancakeeven at asymptotically high energies (see Fig.2), since 1 z ' >> z : (3) S V x P S In this case the string junction will always have enough time to interact, and we may exp ect to nd stopp ed baryons in the central rapidity region even in a high- 3 energy collision (of course there will also b e baryon-antibaryon pair pro duction in addition). This argument leads to a p eculiar picture of a high-energy pp collision: in some events, one or b oth of the string junctions are stopp ed in the central rapidity region, whereas the valence quarks are stripp ed-o and pro duce three-jet events in the fragmentation regions. Immediately after collision, the central region is then lled by a gluon sea containing one or twotwists, which will later on b e dressed up by sea quarks and will form baryon(s). Note that the quark comp osition of the pro duced baryons will in general di er from the comp osition of colliding protons. Why then is the leading baryon e ect a gross feature of high-energy pp col- lisions? The reason may b e the following. The string junction, connected to all three of the valence quarks, is con ned inside the baryon, whereas pp collisions b ecome on the average more and more p eripheral at high energies. Therefore, in a typical high-energy collision, the string junctions of the colliding baryons pass far away from each other in the impact parameter plane and do not inter- act. One can however select only central events, triggering on high multiplicity of the pro duced hadrons. In this case, we exp ect that the string junctions will interact and may b e stopp ed in the central rapidity region. This should lead to the baryon asymmetry in the central rapidity region: even at very high energies, there should b e more baryons than antibaryons there. Fortunately, the data needed to test this conjecture already exist: the exp er- imental study of baryon and antibaryon pro duction with trigger on asso ciated hadron multiplicity has b een already p erformed at ISR, at the highest energy ever available in pp collisions [3]. This study has revealed that in the central ra- pidity region, the multiplicities asso ciated with a proton are higher than with an antiproton by ' 10%. It was also found that the numb er of baryons in the central rapidity region substantially exceeds the numberofantibaryons [4]. These two observations combined indicate the existence of an appreciable baryon stopping in central pp collisions even at very high energies [3]. Where else do we encounter central baryon-baryon collisions? In a high energy nucleus-nucleus collision, the baryons in each of the colliding nuclei are densely packed in the impact parameter plane, with an average inter-baryon distance 1=2 1=6 r ' A ; (4) where is the nuclear density, and A is the atomic numb er.
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