Production of multistrange hadrons, light nuclei and hypertriton in central Au+Au collisions at $\sqrt{s_{NN}}=$ 11.5 and 200 GeV

The production of dibaryons, light nuclei and hypertriton in the most central Au+Au collisions at $\sqrt{s_{NN}}=$ 11.5 and 200 GeV are investigated by using a naive coalescence model. The production of light nuclei is studied and found that the production rate reduces by a factor of 330 (1200) for each extra nucleon added to nuclei at $\sqrt{s_{NN}}=$ 11.5 (200) GeV. The $p_{T}$ integrated yield of multistrange hadrons falls exponentially as strangeness quantum number increases. We further investigate strangeness population factor $S_{3}, S_{2}$ as a function of transverse momentum as well as $\sqrt{s_{NN}}$. The calculations for $\sqrt{s_{NN}}=$ 11.5 GeV presented here will stimulate interest to carry out these measurements during the phase-II of beam energy scan program at STAR experiment.


Introduction
The experiments at Relativistic Heavy Ion Collider (RHIC) have shown evidence for the hot and dense matter, also known as quark gluon plasma (QGP), created during the early stages of the collisions [1,2,3,4]. The high temperature and baryon density of the produced matter makes it most suitable environment for the production of light nuclei (p, d, 3 He, 4 He), hypertriton and dibaryons (ΛΛ, pΩ, ΞΞ, ΩΩ) as well as their antiparticles.
For long time the study of light (anti)nuclei and (anti)hypernuclei production has remained of interest for physicists [5,6]. These studies are important to understand the matter-antimatter symmetry, dark matter and structure of neutron star [7,8]. Antihypertriton ( 3 ΛH ) and antihelium-4 ( 4H e) have already been observed at RHIC [9,10] and Large Hadron Collider [11]. Very recently, interaction between antiproton pairs has been also measured by the STAR experiment [12].
The production of light (anti)nuclei and (anti)hypernuclei in heavy ion collisions is fairly described by the thermal model [13,14] and the coalescence model based on multiphase transport model as well as other transport models [15,16,17,18].

The production of light (anti)nuclei and (anti)hypernuclei in the most central
Au+Au collisions at √ s N N = 200 GeV has been studied using coalescence model and hydrodynamic blast-wave model in [19,20]. Using the same model of Ref. [19], the production of light (anti)nuclei and (anti)hypernuclei in the most central Au+Au collisions at √ s N N = 11.5 GeV are discussed in this article.
Different quantum chromodynamics (QCD) based models have proposed existence of dibaryons as exotic form of matter. The H dibaryon was first predicted by Jaffe [21] and then later many other dibaryon states were predicted, e.g. pΩ [22], ΞΞ [23] and ΩΩ [24].  [27,28,29,30,31]. However information about the invariant yield of dibaryons from heavy ion collisions remains scarce and more efforts are required in this direction. The invariant yield of dibaryons ΛΛ, pΩ, ΞΞ and ΩΩ are presented for central Au+Au collisions at √ s N N = 11.5 and 200 GeV.
The baryon-strangeness correlation coefficient C BS is proposed as a diagnostic tool to understand the nature of matter formed in heavy ion collisions [32,33].
For QGP state the C BS is expected to be unity, however a significant dependence of C BS on hadronic environment is observed by V. Koch, A. Majumder and J. Randrup [32]. Measurement of C BS in experiments is a technical challenge as one needs to measure baryon number and strangeness on event-byevent basis. Therefore the strangeness population factor S 3 was introduced by           [41,42,43,44] and different lines represent our calculations from the hydrodynamical blast-wave model plus a coalescence model. T. A. Armstrong et al. [34], which fairly depicts the local correlation between baryon number and strangeness [15]. Further we introduce S 2 , which represents the local strangeness-strangeness correlations. Keeping in mind the technical challenges to measure C BS , in this Letter, we concentrate on the strangeness population factor S 3 , S 2 for central Au+Au collisions at √ s N N = 11.5 and 200 GeV.

Coalescence Model
A naive coalescence model is used to study the production of multistrange hadrons, light nuclei and hypertriton in central Au+Au collisions at √ s N N = 11.5 and 200 GeV. It is assumed that the production of these particles occur at the kinetic freeze-out stage. In this case the particle production probability is proportional to the primordial hadron density and can be described by following equation [35]: In hydrodynamic blast-wave model [36], the system is characterized by these parameters: the kinetic freeze-out temperature T kin , the radial flow parameter ρ 0 and elliptic flow parameter ρ 2 , the spatial anisotropy a, the average transverse radius R, and the particle emission duration τ 0 . It is assumed that the fireball created in heavy ion collision is in local thermal equilibrium and moves outward with velocity u µ . The phase-space emission points for hadrons are defined as a Wigner function: where y is the rapidity, m t is transverse mass, p µ is four momentum, and (2s+1) is the degeneracy due to spin of hadrons.r is given bỹ where (x 1 , x 2 ) is the transverse position of the hadrons in coordinate space.
Then we can define the azimuthally integrated p T spectrum as  Results obtained for the invariant yields of multistrange hadrons, nuclei and hypertriton using equation 1 and 4 are discussed in next section.

Result and discussion
To study dibaryons, light nuclei and hypertriton production in the central   Table 1. We observe that expected yields of all the particles at √ s N N = 11.5 GeV are significantly higher than √ s N N = 200 except for ΩΩ, may be because of competition between strangeness production mechanism at this energy.  The filled symbols are data from the STAR experiment [42,43,44], the solid lines represent our calculations from the hydrodynamical blast-wave model plus a coalescence model and the dashed lines for the ΛΛ and ΩΩ dibaryons are from Ref [28].
dibaryon production yields at top RHIC energy were estimated by the ExHIC collaboration based on a realistic coalescence model and statistical model [27,28]. Those yields are compared with our calculations in the figure 3. We observe an exponential behavior of the invariant yield of multistrange hadrons similar to light nuclei [19]. The yield for baryon and dibaryon systems are fitted with where N i is number of initial strange hadrons, λ is penalty factor and S is the strangeness. The penalty factor quantitatively tells us how hard it is to produce a hadron with strangeness (|S|+1) compared to a hadron with strangeness (|S|). We obtain λ = 9.86 for baryons and λ  antimatter shows a significant energy (or temperature) dependence, which illustrate an increasing matter-antimatter asymmetry of the yields at lower energies (temperatures). If we make a rough extension to current Universe at room temperature, we can hardly observe the antimatter existence, which is consistent with the current observation of the cosmic rays from which neither antideutron nor antihelium are observed [45,46].
The strangeness population factor S 3 = 3 Λ H/( 3 He × Λ p ) contains the local baryon-strangeness correlation in the numerator and the baryon-baryon correlation in the denominator [15,35]. Therefore S 3 is quantitatively a good representation of χ BS 11 /χ B 2 , where χ is the second derivative of the free energy with respect to the chemical potential, from lattice QCD [47]. The ratio S 3 as a function transverse momentum is shown in figure 5 (left). Similarly we define

Conclusion
We presented an interesting calculation for the production of dibaryons, light Furthermore our study indicates that the suppression factor for nuclei produc- from STAR experiment [9]. tion at √ s N N = 11.5 GeV is roughly four times smaller than suppression factor at √ s N N = 200 GeV; leading to higher probability for observation of light nuclei candidates at lower energy. Our calculation will provide the motivation to carry out measurement of S 3 , light nuclei and dibaryons during the phase-II of beam energy scan program at STAR experiment at RHIC [48].

Acknowledgments
This work is supported in part by the