Suppression of Light Nuclei Production in Collisions of Small Systems at The

Suppression of light nuclei production in collisions of small systems at the Large Hadron Collider Kai-Jia Sun∗ and Che Ming Ko† Cyclotron Institute and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA Benjamin Dönigus‡ Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany (Dated: May 22, 2020) We show that the recently observed suppression of the yield ratio of deuteron to proton and of helium-3 to proton in p+p collisions compared to those in p+Pb or Pb+Pb collisions by the ALICE Collaboration at the Large Hadron Collider (LHC) can be explained if light nuclei are produced from the coalescence of nucleons at the kinetic freeze-out of these collisions. This suppression is attributed to the non-negligible sizes of deuteron and helium-3 compared to the size of the nucleon emission source in collisions of small systems, which reduces the overlap of their internal wave functions with those of nucleons. The same model is also used to study the production of triton and hypertriton in heavy-ion collisions at the LHC. Compared to helium-3 in events of low charged particle multiplicity, the triton is less suppressed due to its smaller size and the hypertriton is even more suppressed as a result of its much larger size. PACS numbers: 25.75.-q, 25.75.Dw I. INTRODUCTION TeV [38] compared to that in central Pb+Pb collisions at √sNN = 2.76 TeV [7]. Because of the high collision energies, the produced matter consists of nearly equal Besides the production of the quark-gluon plasma number of particles and antiparticles, and it reaches al- (QGP) [1–3], relativistic heavy-ion collisions have also led most the same temperature of Tc 154 MeV [40–43] to the production of anti-nuclei [4–7] and the discovery at which the initially produced QGP≈ is transformed to of anti-hypernuclei [8, 9]. More recently, light nuclei pro- the hadronic matter [44]. Therefore, almost the same duction in relativistic heavy-ion collisions have further chemical freeze-out temperature occurs in p+p, p+Pb been used to search for the possible critical point [10–13] and Pb+Pb collisions [45, 46], and the only difference in the phase diagram of strongly interacting quark mat- between these colliding systems is the size of produced ter [14–17]. However, how and when these light nuclei matter or the total number of produced particles. This are produced during relativistic heavy-ion collisions are is confirmed by the two-pion correlation measurements still under debate because of their small binding ener- through the Hanbury-Brown Twiss (HBT) interferome- gies and finite sizes [18–26]. On the one hand, they are try, which gives the Gaussian source radii in p+p and assumed to be produced at hadronization of the QGP Pb+Pb collisions that are about 2 fm and 10 fm, respec- created in these collisions as in the statistical model for tively [47, 48]. particle production [27, 28]. On the other hand, they are described by the coalescence of nucleons and lambda In the statistical hadronization approach based on the hyperons at the kinetic freeze-out of heavy-ion collisions grand canonical ensemble, all hadrons produced in heavy- arXiv:1812.05175v5 [nucl-th] 20 May 2020 when the temperature and density of the hadronic matter ion collisions at the LHC energies are in thermal and are low [29–36]. chemical equilibrium, and their yield ratios are deter- In recent measurements by the ALICE Collaboration mined only by the chemical freeze-out temperature, as at the LHC, the yield ratios d/p and 3He/p from p+p, the baryon chemical potential is nearly zero in collisions p+Pb and Pb+Pb collisions at center-of-mass energies at such high energies [45]. For instance, the measured proton to pion ratio is about 5 10−2 in p+p, p+Pb and ranging from 900 GeV to 7 TeV have been measured, and × they are found to decrease monotonically with decreas- Pb+Pb collisions, which is consistent with the statistical model prediction based on the grand canonical en- ing charged particle multiplicity in the collisions [7, 37– 3 39]. In particular, the ratio d/p is suppressed by more semble. For the yield ratios of d/p and He/p, the pre- dicted respective values of about 3.6 10−3 and 1.0 10−5 than a factor of 2 in p+p collisions at √sNN = 7 × × for central Pb+Pb collisions at √sNN = 2.76 TeV from the statistical model are also in nice agreement with the experimental data. These values are, however, much ∗email: [email protected] larger than those from p+p collisions at the LHC [38]. †[email protected] To explain the suppressed production of light nuclei in ‡[email protected] collisions of such a small system, the statistical model 2 has been modified to use the canonical ensemble to take For deuteron production in heavy-ion collisions, its num- into account the conservation of baryon number, electric ber from the coalescence model is given by charge and the strangeness [49]. The resulting ratios of 3 3 3 3 light nuclei to proton in these collisions are, however, too Nd = gd d x1 d k1 d x2 d k2fn(x1, k1) small compared with the experimental data unless the Z Z Z Z x k x x k k canonical correlation volume for exact charge conserva- fp( 2, 2)Wd( 1 2, ( 1 2)/2), (1) − − tions is taken to span three units of rapidity, instead of where g = 3/4 is the statistical factor for forming a the usual one unit of rapidity for collisions with large d spin one deuteron from spin half proton and neutron [35, particle multiplicity, or using a higher chemical freeze- 55], f (x, k) are the neutron and proton phase-space out temperature of 170 MeV than the usual value of 155 p,n distributions, and W (x, k) is the Wigner function of the MeV for collisions of large systems. d deuteron. In the coalescence model, the formation probability of Since the nucleon coalescence is a local process, one can a light nucleus in a heavy-ion collision depends not only neglect the effect of collective flow on nucleons and take on the thermal properties and volume of the nucleon and their phase-space distributions in a thermalized expand- hyperon emission source but also on the internal wave ing spherical fireball of kinetic freeze-out temperature T function of the light nucleus. The small size of the emis- K and radius R to be sion source in p+p collisions is expected to significantly 2 2 k x Np,n − − 2 reduce the phase-space volume in which a light nucleus x k 2mT 2R fp,n( , )= 3 e K , (2) 3 2 can be formed, leading to a suppression of its production. (2π) (mTK R ) 2 Using a schematic coalescence model based on nucleons from the UrQMD model by allowing a deuteron to be with m being the nucleon mass, and they are nor- formed from a pair of proton and neutron when their malized to their numbers Np,n according to Np,n = 3x 3k x k separation in phase-space is less than certain value, it is d d fp,n( , ). found in Ref. [50] that this model can give a good de- R UsingR the harmonic oscillator wave function for the in- scription of the experimental data on the d/p ratio in ternal wave function of the deuteron, which is usually as- p+p, p+A, and A+A collisions at the LHC. sumed in the coalescence model for deuteron production, In this Letter, we use a more realistic coalescence its Wigner function then has the Gaussian form [31–33], 2 model to study the system size or charged particle multi- x 2 2 x k − 2 −σ k plicity dependence of the d/p and 3He/p ratios by taking Wd( , )=8 e σ e , (3) 3 into account the finite size of deuteron and He through 3 3 3 with the normalization d x d k Wd(x, k) = (2π) . their internal wave functions. Our results on these yield x Transforming the protonR and neutronR coordinates 1 and ratios are found in good agreement with available exper- x k k 3 2 as well as their momenta 1 and 2 to their center- imental data. We also confirm that the He/p ratio has of-mass reference frame, a stronger system size dependence than the d/p ratio as x + x helium-3 has three nucleons and is thus more sensitive X = 1 2 , x = x x , to the spatial distribution of nucleons in the emission 2 1 − 2 source. For the triton 3H, we find that its production is k k K = k + k , k = 1 − 2 , (4) 10%-30% larger than that of helium-3 and thus less sup- 1 2 2 pressed in p+p collisions because of its smaller matter the integrals in Eq. (1) can then be straightforwardly radius. For the hypertriton 3 H, the 3 H/Λ ratio in colli- Λ Λ evaluated, leading to sions with small charged particle multiplicity is found, on 3 2 X 1 1 2 the other hand, much more suppressed than the He/p 8gdNpNn 3 − 2 3 −( 2 + 2 )x X R x σ 4R Nd = 6 2 3 d e d e ratio, and the suppression further depends on whether (2π) (mTK R ) Z Z 3 2 the ΛH is produced from the coalescence of n-p-Λ or d-Λ.

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