aa r X i v : . [ nu c l - t h ] J un Strange hadron ratios from quark coalescenceat RHIC and LHC energies
P. L´evai a a RMKI Research Institute for Particle and Nuclear Physics,P.O. Box 114, Budapest, 1525, Hungary
Abstract.
Quark coalescence models have been applied successfully to reproducemeasured hadron production data in relativistic heavy ion collisions at SPS and RHICenergies, which finding strongly supports the formation of deconfined quark matter inthese collisions. The investigation of meson and baryon production is an ideal toolto understand dynamical details of hadronization, especially strange hadron numbersand ratios. We display latest results on the production of strange particles in quarkcoalescence processes in heavy ion collisions at different collider energies.
After many years of investigating hadron-hadron and heavy ion collisions thestudy of hadron production remained an important research field. The lack of perfectknowledge of the microscopical mechanisms led to the application of many differentmodels, very often from completely opposite directions. Statistical models are basedon the introduced statistical weights for produced hadrons [1, 2, 3]. This idea hasbeen developed further and thermal models appeared with the introduction of thetemperature parameter and thermal weights for hadrons (see e.g. Ref. [3]). Thermalmodels became very successful reproducing soft particle production in different highenergy particle collisions [4], especially in heavy ion collisions (see e.g. Refs. [5, 6, 7, 8]).On the other hand, these models assume the formation of a sort of thermal and chemicalequilibrium in the hadronic phase and determine thermodynamical variables for theproduced hadron phase. The deconfined period of the time evolution dominated byquarks and gluons remains hidden: full equilibration generally washes out and destroyslarge amount of information about the early deconfined phase. The success of statisticalmodels implies the existence of such an information loss during hadronization, at least forcertain properties. It is a basic question which properties can survive the hadronizationand behave as messengers from the early (quark dominated) stages.Since our main goal is to create quark matter in heavy ion collisions and determineits properties, we can not be satisfied even with the most perfect hadronic statisticalmodel. We need to survey the messengers of the early phases and investigate hadronproduction by models based on quark degrees of freedom. Hadronization models withdirect quark degrees of freedom have been constructed from the beginning of the heavyion programme at CERN SPS. In this stream quark coalescence has been proposed manyyears ago to describe quark matter hadronization [9, 10, 11, 12]. Massive constituentquarks has been considered in the deconfined phase, which quarks and antiquarks are trange hadron ratios from quark coalescence at RHIC and LHC p T region and more widelyused because of their simplicity. At RHIC energy intense data collection has beenperformed in the intermediate- p T region (3 < p T < p T hadrons, heavyflavours) became the main focus of non-equilibrium models. The interest in coalescencehadronization mechanism has been increased and more applications appeared. Onesubfield is the strange hadron production: quark chemistry based on strange quarkcoalescence and annihilation became very successful to describe SPS and RHIC data.Furthermore, quark flow production also moved into the focus of interest. Therecognition of valence quark number scaling in asymmetric flow ( v ) strongly supportsquark matter formation and quark coalescence at RHIC and SPS energies [21].It is natural to ask, if quark coalescence is working properly for heavier flavourand at higher- p T , then what about the soft region, namely bulk hadron numbers,and ratios. During last decade we continously summarized the results of quarkcoalescence calculations and the successful reproduction of measured data, in parallelgiving predictions where it was possible. In this talk we gave a short summary again,analyzing latest SPS and RHIC data and predict the expected particle yields at LHCenergy. We would like to emphasize that quark coalescence models are capable todescribe large amount of experimental data, in the meantime supporting the formationof deconfined quark matter in heavy ion collisions at SPS and RHIC energies.Another question is connected to the validity of non-relativistic description in ahighly relativistic strongly interacting particle ensamble [22]. Although all particles,including quarks in the early stage, are moving with a velocity close to the speed oflight, but in a comoving system they can coalesce if only their relative velocity is small.This self-regularization gives the opportunity to describe the effective quark bindingsteps in a non-relativistic frame with coalescence. trange hadron ratios from quark coalescence at RHIC and LHC h consists of quark q and antiquark q , and production is proportional to densities of constituents, n and n : ∂ µ ( n h u µ ) = h σ h v i n n . (1)In an isotropic plasma state the rate, h σ h v i , is calculated as a momentum average: h σ h v i = R d ~p d ~p f q ( m , ~p ) f q ( m , ~p ) σv R d ~p d ~p f q ( m , ~p ) f q ( m , ~p ) (2)The quark coalescence cross section is determined from quantum mechanics, assuminga rearrangement (”pick-up”) reaction [25]. In the ALCOR model [10] quark plain wavescoalesce into a bound two-body system, described by a hydrogen-like wave function.Coalescence process is driven by a Coulomb-potential depending on relative distance, r : V ( r ) = α h λ i λ j i r (3)The colour factor h λ i λ j i is determined by the colour combination of the interactingparticles. This factor is − / − / N uu = N dd ).Strangeness production is controlled by the number of newly produced strange quark-antiquark pairs indicated by the ratio f s = N ss / ( N uu + N dd ). Baryon to meson ratio isfollowed by the α s effective coupling constant, because meson production is proportionalto α s , but two-steps baryon production depends on α s . Particle to antiparticle ratios arecontrolled by the stopping of incoming colliding nucleons into the mid-rapidity region. trange hadron ratios from quark coalescence at RHIC and LHC Table 1.
ALCOR results at SPS energies, E beam = 20, 30, 40, 80, 158 GeV/n.dN/dy at y=0 20 GeV/n 30 GeV/n 40 GeV/n 80 GeV/n 158 GeV/nInput data π − ± ± ± ± ± K − ± ± ± ± ± K + /K − ± ± ± ± ± + — 0.05 ± ± ± ± uu
45 50 62 88 123 f s strangeness 0.40 0.35 0.30 0.28 0.24Stopping 20 % 20 % 20 % 20 % 15 % α s coupling 0.80 0.80 0.80 0.80 0.72New QQ
252 270 322 450 610ALCOR results K + /π + /p − /K − − + Ω + ) /π − In Table 1 the latest results from quark coalescence calculations are summarized atdifferent CERN SPS energies in the mid-rapidity regions of
P b + P b collisions [26, 27].The four model parameters are determined from four experimental data, especiallyfrom π − and K − numbers indicating entropy and strangeness production, from K + /K − ratio indicating particle/antiparticle ratio, and from the absolute number of Ξ + particleconnected to the effective coupling constant. (At 20 GeV/n no data were available, inthis case Ξ − has been used.) Table 1 displays that entropy production is increasing, butrelative strangeness abundance ( f s ) is continously decreasing with increasing collisionenergy. One can see, the ratio K + /π + is decreasing, as well as the Λ /p − and Φ /K − ratios, as we expect from the decreasing of f s . The K − /π − ratio is slightly increasing,but this is an exception. The energy dependence of h Ω i /π − has a special structure,which should be investigated in details. The stopping is close to be constant, it startsto decrease at highest SPS energy, as well as the effective coupling constant.We repeat our analysis at RHIC energies. Table 2 displays recent ALCOR results at √ s = 200 AGeV in Au + Au collisions. We can see that entropy production is increasingfurther, but strangeness production is saturated at a certain value ( f s = 0 . √ s = 130 AGeV, also. The coupling constant is also saturatedaround α s = 0 .
55, founded at lower RHIC energy. The stopping is decreasing, as it isindicated by close to unity antibaryon to baryon ratios. The quark coalescence model canreproduce bulk particle ratios in most of the cases, except the Φ /K − . We investigaterecently if different wave-function setups could improve this agreement [22], keepingother ratios under good control. Another way to improve the quark coalescence resultsis to investigate the role of higher baryon and meson resonance production channels. trange hadron ratios from quark coalescence at RHIC and LHC Table 2.
ALCOR results at RHIC energy ( √ s = 200 AGeV) and predictions for LHCenergy ( √ s = 5500 AGeV).Particles Data ALCOR ALCOR ALCOR(dN/dy at y=0) RHIC RHIC LHC-I LHC-IINew uu
286 500 750 f s strangeness 0.22 0.22 0.22 α s coupling 0.55 0.55 0.55Stopping 3 % 1 % 1 %Total QQ h ± ±
40 780 1252 1830 π − ±
32 322 500 724 K + ± p +
19 37 62Ξ − ± K + /π + ± − /π − ± ρ /π ± /K − ± Combining quark coalescence results at SPS and RHIC energies, we can predictdifferent particle yields at LHC energies. We can expect from Table 1 and 2, thatstrangeness production and effective coupling constant will be very similar at RHICand LHC energies, on the other hand baryon number stopping into the mid-rapidityregion will drop to a minimal value (e.g. 1 %). The only question is connected to thevalue of entropy production, especially to the new light quark-antiquark pair production.Figure 1. displays the obtained values at SPS and RHIC energies and indicates a linearincrease in entropy production with increasing ln √ s . Applying a linear extrapolationwe obtain the estimated value N uu /dy = 500 for LHC energies in P b + P b collisions atmid-rapidity. Table 2 displays the ALCOR results for this light quark pair production,keeping the other parameter values, as we discussed above. In order to test the sensitivityof some ratios to the amount of produced entropy, we give, in the last column of Table2, results of our model assuming a 50 % higher entropy. Many strange particle ratios areinsensitive on the higher entropy production, thus other data are necessary to investigateentropy production at LHC energies, e.g. absolute particle numbers.This work has been supported in part by the Hungarian OTKA under grants No.NK062044 and IN71374. [1] E. Fermi, Prog. Theor. Phys. , 570 (1950).[2] I. Pomeranchuk, Proceedings of USSR Academy of Sciences , 889 (1951).[3] R. Hagedorn, Suppl. Nuovo Cim. , 147 (1965); Nuovo Cim. , 1336 (1967).[4] F. Becattini, Z. Phys. C69 , 485 (1996); F. Becattini, L. Ferroni, Eur. Phys. J.
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