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Baryon Number Fluctuation and the Quark-Gluon Plasma

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Baryon Number Fluctuation and the Quark-Gluon Plasma Baryon Number Fluctuation and the Quark-Gluon Plasma Z. W. Lin and C. M. Ko Because of the fractional baryon number Using the generating function at of quarks, baryon and antibaryon number equilibrium, fluctuations in the quark-gluon plasma is less than those in the hadronic matter, making them plausible signatures for the quark-gluon plasma expected to be formed in relativistic heavy ion with g(l) = ∑ Pn = 1 due to normalization of collisions. To illustrate this possibility, we have the multiplicity probability distribution, it is introduced a kinetic model that takes into straightforward to obtain all moments of the account both production and annihilation of equilibrium multiplicity distribution. In terms of quark-antiquark or baryon-antibaryon pairs [1]. the fundamental unit of baryon number bo in the In the case of only baryon-antibaryon matter, the mean baryon number per event is production from and annihilation to two mesons, given by i.e., m1m2 ↔ BB , we have the following master equation for the multiplicity distribution of BB pairs: while the squared baryon number fluctuation per baryon at equilibrium is given by In obtaining the last expressions in Eqs. (5) and In the above, Pn(ϑ) denotes the probability of ϑ 〈σ 〉 (6), we have kept only the leading term in E finding n pairs of BB at time ; G ≡ G v 〈σ 〉 corresponding to the grand canonical limit, and L ≡ L v are the momentum-averaged cross sections for baryon production and E 1, as baryons and antibaryons are abundantly produced in heavy ion collisions at annihilation, respectively; Nk represents the total number of particle species k; and V is the proper RHIC. Since bo is 1/3 in quark-gluon plasma volume of the system. and 1 in hadronic matter, wB is smaller in the The equilibrium solution to Eq. (1) is quark-gluon plasma than in an equilibrated hadronic matter by a factor of 3. We note that the equilibrium multiplicity distribution in Eq. (2) is not Poisson. Furthermore, ΤB,eq has a value of bo/2 instead of the naive value of bo, that is expected from a Poisson multiplicity distribution. The non-Poisson distribution results from the and I0 being the modified Bessel function. quadratic dependence on the multiplicity n in the loss term of the master equation of Eq. (1) due to III-45 baryon number conservation. A Poisson pair production and annihilation tend to reduce distribution is obtained if the dependence on the their sensitivity to the quark-gluon plasma by multiplicity n is linear, which corresponds to driving their values towards those from an production of particles that do not carry equilibrated hadronic matter, the large baryon conserved charges. We also note that the master masses make it unlikely that baryon and equation of Eq. (1) gives a Poisson distribution antibaryon production is important in the final at early times (ϑ→0) when the loss term can be hadronic stage of ultra-relativistic heavy ion neglected. This corresponds to either production collisions. On the other hand, baryon- of particles with conserved U(I) charges during antibaryon production during the hadronization the early stage of heavy ion collisions or particle from the quark-gluon plasma to the hadronic production without chemical equilibration as in matter affects the baryon and antibaryon number e+e- collisions. fluctuations, in ways similar to that due to Because of experimental limitations, baryon and antibaryon inelastic scatterings. only protons and antiprotons in a certain rapidity To study this effect requires knowledge about and momentum range are usually measured. the hadronization process, which is at present Moreover, the net baryon number in heavy ion not well understood. collisions is in general non-zero even at mid- rapidity due to the presence of projectile and References target nucleons. Using a generalized master equation that includes these effects, we have [1] Z. W. Lin and C. M. Ko, Phys. Rev. Lett., shown that the above results remain essentially submitted; nucl-th/0103071. unchanged. [2] C. M. Ko, V. Koch, Z. W. Lin, K. Redlich, Unlike the net baryon number M. Stephanov and X.-N. Wang, Phys. Rev. Lett., fluctuation proposed in Ref. [3] and the net in press; nucl-th/0010004. charged particle fluctuation proposed in Ref. [4], [3] M. Asakawa, U. Heinz and B. Müller, baryon and antibaryou number fluctuations are Phys. Rev. Lett. 85, 2072 (2000). non-zero in the full phase space and are not [4] S. Jeon and V. Koch, Phys. Rev. Lett. 85, affected by elastic scatterings. Although 2076 (2000). inelastic reactions such as baryon-antibaryon III-46.
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