PDF《Hidden-charm Pentaquark States in》

arXiv:1601.

02835v1 [hep-ph]

12 Jan

2016 Hidden-charm Pentaquark States in Heavy Ion Collisions at the Large Hadron Collider Rui-Qin Wang,1,2 Jun Song,3 Kai-Jia Sun,2 Lie-Wen Chen,2 Gang Li,1 and Feng-Lan Shao1, ?

1 College of Physics and Engineering, Qufu Normal University, Shandong 273165, China

2 Department of Physics and Astronomy and Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai 200240, China

3 Department of Physics, Jining University, Shandong 273155, China In the framework of the quark combination, we derive the yield formulas and study the yield ratios of the hidden-charm pentaquark states in ultra-relativistic heavy ion collisions. We propose some interesting yield ratios which clearly exhibit the production relationships between di?erent hidden-charm pentaquark states. We show how to employ a speci?c quark combination model to evaluate the yields of exotic P+ c (4380), P+ c (4450) and their partners on the basis of reproducing the yields of normal identi?ed hadrons, and execute the calculations in central Pb+Pb collisions at √ sNN = 2.76 TeV as an example. PACS numbers: 25.75.Dw, 25.75.Nq, 25.75.-q I. INTRODUCTION The LHCb Collaboration at the Large Hadron Collider (LHC) has recently announced two exotic resonances P+ c (4380) and P+ c (4450), consistent with pentaquark states, via the J/ψp invariant mass spectrum in Λ0 b decays in p+p reactions [1]. Thereupon, the study for the internal con?gurations of such resonances becomes a subject of an intensive discussion in literatures. The so-far suggested interpretations for P+ c (4380) and P+ c (4450) include molecular states bound of a charmed baryon and an anticharmed meson [2, 3], molecular states with J/ψ and an excited nucleon [4], composites containing colored baryonlike and mesonlike constituents [5], pentaquark states with one heavy-light diquark, one light-light diquark and a charm antiquark [6C8], pentaquark states with color-antitriplet diquark cu and color-triplet ? cud [9, 10], and so on. There are also some works about needing further con?rmation of whether such resonance is just a kinematical e?ect or a real exotic resonance by analyzing other processes, such as Λ0 b → K? χc1 p [11C14]. Further exploring for the intrinsic dynamical nature of such exotic resonances and searching for their partners are necessary for understanding some longstanding questions in hadronic physics, which requires more theoretical and experimental e?orts. Heavy ion collisions with ultra-relativistic collision energies, especially those at the LHC, provide preferable conditions for the creation of particles in heavy ?avor sectors. The studies of heavy ?avor exotic resonances in heavy ion collisions not only are complementary to those in the LHCb experiments, but also o?er unique insights into some of the fundamental questions in hadronic physics [15, 16]. As is well known, the Quark Combination Mechanism (QCM) is an e?ective phenomenological method to deal with the hadronization of the partonic system produced early in high energy heavy ion collisions. It has shown successes in reproducing multiplicities, yield ratios, momentum distributions, elliptic ?ows, etc., of normal identi?ed light, strange and heavy ?avor hadrons [17C23], and has also many applications in describing the production properties of exotic resonances [15, 16, 24C27]. Due to the produced bulk decon?ned ?reball and the hadronization through the quark combination in high energy heavy ion collisions, various kinds of exotic hadrons can be formed. The purpose of this paper is to investigate the yield ratios and estimate the yields of various hidden-charm pentaquark states with di?erent valence quark ingredients and di?erent intrinsic quantum numbers in the framework of the QCM in ultra-relativistic heavy ion collisions at the LHC. This can provide useful references for the exotic hadron search in future experiments and is helpful for understanding the production mechanism of the exotic resonances in heavy ion collisions. The rest of the paper is organized as follows. In Sec. II, we derive the yield formulas and study the yield ratios of hidden- charm pentaquark states from the basic ideas of the QCM. During the derivation, a few assumptions, approximations and/or simpli?cations are used and they are all clearly presented. In Sec. III, we show how to employ a speci?c quark combination model to estimate the yields of di?erent hidden-charm pentaquark states, and give the estimated results in central Pb+Pb collisions at √ sNN = 2.76 TeV as an example. Sec. IV summaries our work. ?Electronic address: [email protected]

2 II. YIELD RATIOS OF DIFFERENT HIDDEN-CHARM PENTAQUARK STATES In this section, we derive the yield formalism of the hidden-charm pentaquark states in the quark combination models based on the basic ideas. We ?rst begin with a quark-antiquark system as general as possible. Then we simplify the results by adopting a few explicit assumptions and/or approximations. Finally we present some interesting results for the yield ratios of di?erent hidden-charm pentaquark states. A. The yield formalism of the hidden-charm pentaquark states We start from a color-neutral quark-antiquark system with Nqi quarks of ?avor qi (qi = u, d, s, c) and N? qi antiquarks of ?avor ? qi (? qi = ? u, ? d, ? s, ? c). All these quarks and antiquarks can hadronize via the quark combination into not only normal mesons, baryons and antibaryons, but also exotic hadrons such as tetraquark states, pentaquark states and so on. The momentum distribution fPj (p;

Nqi , N? qi ) for the directly produced pentaquark state Pj with the known quark contents (q01q02q03q04 ? q05) after quark combination hadronization is given by fPj (p;

Nqi , N? qi ) = q1q2q3q4 ? q5 dp1dp2dp3dp4dp5 fq1q2q3q4 ? q5 (p1, p2, p3, p4, p5;

Nqi , N? qi )RPj,q1q2q3q4 ? q5 (p, p1, p2, p3, p4, p5;

Nqi , N? qi ), (1) where fq1q2q3q4 ? q5 is the ?ve-particle joint momentum distribution for (q1q2q3q4 ? q5). The kernel function RPj,q1q2q3q4 ? q5 stands for the probability density for q1, q2, q3, q4, and ? q5 with momenta p1, p2, p3, p4, and p5 to combine into a pentaquark state Pj of momentum p. Integrating over p from Eq. (1), we can obtain the average number of the directly produced Pj as NPj (Nqi , N? qi ) = q1q2q3q4 ? q5 dpdp1dp2dp3dp4dp5 fq1q2q3q4 ? q5 (p1, p2, p3, p4, p5;

Nqi , N? qi )RPj,q1q2q3q4 ? q5 (p, p1, p2, p3, p4, p5;

Nqi , N? qi ). (2) Eqs. (1) and (2) are the most general starting point of describing the production of pentaquark states with any ?avors of quark ingredients in high energy reactions based on the basic ideas of the QCM. Di?erent models are some special examples of the general case we consider in these equations. In speci?c models, di?erent methods and/or assumptions are introduced to construct the precise form of the kernel function. For example, the kernel function evolves into the Wigner function in the coalescence model [20] and the recombination function in the quark recombination model [28], respectively. For a special kind of hidden-charm pentaquark states Pc? c j with the known quark contents (l01l02l03c? c) distinguished by the superscript c? c, we from Eq. (2) easily have NPc? c j (Nqi , N? qi ) = l1l2l3 dpdp1dp2dp3dp4dp5 fl1l2l3c? c(p1, p2, p3, p4, p5;

Nqi , N? qi )RPc? c j ,l1l2l3c? c(p, p1, p2, p3, p4, p5;

Nqi , N? qi ), (3) where li = u, d, s. The joint momentum distribution fl1l2l3c? c is the number density that satis?es dp1dp2dp3dp4dp5 fl1l2l3c? c(p1, p2, p3, p4, p5;

Nqi , N? qi ) = Nl1l2l3c? c = Nl1l2l3 NcN? c, (4) where Nl1l2l3c? c and Nl1l2l3 = ? ? ? ? ? ? ? ? ? Nl1 Nl2 Nl3 for l1 l2 l3 Nl1 (Nl1 ? 1)Nl3 for l1 = l2 l3, Nl1 (Nl1 ? 1)(Nl1 ? 2) for l1 = l2 = l3 (5) are the numbers of all the possible (l1l2l3c? c)'

s and (l1l2l3)'

s, respectively, in the considered bulk quark-antiquark system. We rewrite fl1l2l3c? c(p1, p2, p3, p4, p5;

Nqi , N? qi ) = Nl1l2l3c? c f(n) l1l2l3c? c(p1, p2, p3, p4, p5;

Nqi , N? qi ), (6) so that the joint momentum distribution is normalized to one where is denoted by the superscript (n), i.e., dp1dp2dp3dp4dp5 f(n) l1l2l3c? c(p1, p2, p3, p4, p5;

Nqi , N? qi ) = 1. (7)

3 We adopt an assumption of u, d, s-?avor independence of the normalized joint momentum distribution of quarks and/or anti- quarks, i.e., f(n) l1l2l3c? c(p1, p2, p3, p4, p5;

Nqi , N? qi ) = f(n) lllc? c(p1, p2, p3, p4, p5;

Nl, N? l, Nq, N? q), (8) to simplify the formalism. Here, l stands for u, d or s;

Nl and N? l stand for the total number of u, d and s quarks and that of ? u, ? d and ? s antiquarks, respectively;

Nq and N? q stand for the total number of u, d, s, c quarks and that of ? u, ? d, ? s, ? c antiquarks in the considered quark-antiquark system. With the normalized u, d, s-?avor independent joint momentum distribution, we have NPc? c j (Nqi , N? qi ) = l1l2l3 Nl1l2l3c? c d........