Through the Looking-Glass with ALICE into the Quark-Gluon Plasma: A New Test for Hadronic Interaction Models Used in Air Shower Simulations

Recently, the ALICE Collaboration reported an enhancement of the yield ratio of strange and multi-strange hadrons to charged pions as a function of multiplicity at mid-rapidity in proton-proton, proton-lead, lead-lead, and xenon-xenon scattering. ALICE observations provide a strong indication that a quark-gluon plasma is partly formed in high multiplicity events of both small and large colliding systems. Motivated by ALICE's results, we propose a new test for hadronic interaction models used for analyzing ultra-high-energy-cosmic-ray (UHECR) collisions with air nuclei. The test is grounded in the almost equal column-energy density in UHECR-air collisions and lead-lead collisions at the LHC. We applied the test to post-LHC event generators describing hadronic phenomena of UHECR scattering and show that these QCD Monte Carlo-based codes must be retuned to accommodate the strangeness enhancement relative to pions observed in LHC data.

Besides addressing key questions in astrophysics, ultra-high-energy cosmic ray (UHECR) experiments provide unique access to particle physics at energies an order-of-magnitude higher center-of-mass energy than pp collisions at the Large Hadron Collider (LHC) [1]. However, a precise characterization of the particle physics properties is usually hampered by the ambiguity of model predictions computed through extrapolation of hadronic interaction models tuned to accommodate collider data. These predictions have sizable differences [2][3][4], even among modern (post-LHC) models [5], and quite often overlap with the phase of particle physics observables. Disentangling one from the other is of utmost importance to study particle physics in unexplored regions of the phase-space. The development of new approaches to reduce the systematic uncertainties of hadronic interaction models represents one of the most compelling challenges in UHECR data analysis. In this letter we introduce a reliable model for extrapolation into the ultra-high-energy domain.
QCD calculations on the Lattice [6] predict that under certain critical conditions of baryon number density and temperature, normal nuclear matter undergoes a phase transition to a deconfined state of quarks and gluons where chiral symmetry is restored [7]. For many purposes, such a quark-gluon plasma (QGP) can be described as a near-perfect fluid with surprisingly large entropy-density-to-viscosity ratio. Therefore, once formed, like any other hot object, the QGP transfers heat internally by radiation. Several phases can be identified during the QGP evolution. The initial state contains only gluons as well as valence u and d quarks, but strangeness is produced in the very early stages via hard (perturbative) 2 → 2 partonic scattering processes (gg → ss and qq → ss). Strangeness is also predominantly produced during the subsequent partonic evolu-tion via gluon splittings (g → ss). This is because the very high baryochemical potential inhibits gluons from fragmenting into uū and dd, and therefore they fragment predominantly into ss pairs [8]. In the hadronization process that follows this leads to the strong suppression of pions (and hence photons), but allows the production of heavy hadrons with high transverse momentum (p T ) carrying away strangeness. At low p T non perturbative processes dominate the production of strange hadrons. Thus, the abundances of strange particles relative to pions provide a powerful discriminator to identify the QGP formation.
A QGP can be created by heating nuclear matter up to a temperature of 2 × 10 12 K, which amounts to 175 MeV per particle. Relativistic heavy-ion collisions are then the best tool one has to search for QGP production. Recently, the ALICE Collaboration reported enhancement of the yield ratio of multi-strange hadrons to charged pions as a function of multiplicity at mid-rapidity in LHC proton-proton (pp), proton-lead (pPb), lead-lead (PbPb), and xenon-xenon (XeXe) collisions [9][10][11]. More concretely: • the production rate of K 0 S , Λ, φ, Ξ, and Ω increases with multiplicity faster than that for charged particles; • the higher the strangeness content of the hadron, the more pronounced is the increase; • the ratios do not seem to depend on the system size or collision energies. Altogether, this provides unambiguous evidence for the formation of a QGP in high multiplicity small and large colliding systems [12]. Now, if the QGP is formed in relativistic heavy-ions collisions one would also expect to be formed in the scattering of UHECRs in the upper atmosphere [13,14]. Moreover, since the column-energy density in UHECR-air collisions is comparable to that in PbPb collisions at the LHC, the precise characterization of the QGP properties from ALICE data enables us to investigate QGP models describing the scattering of cosmic rays that impinge on the Earth's atmosphere with energy 10 9 E/GeV 10 11 . Indeed, as we show herein ALICE data straightforwardly constrain these models without the need to rely on energy extrapolation.
Before proceeding, we pause to note that the columnenergy density is the relevant parameter to compare QGP models with experimental data. This is because in the center-of-mass the particles are extremely Lorentz contracted so the time it takes to pass through each other is small compared to the time for signals to propagate transversely, and hence the pertinent parameter is the total surface energy density. The best way of getting this point across is to consider the collision of two nuclei of baryon number A 1 and A 2 in the center-of-mass frame. The energies per nucleon for each nucleus are written as , where s denotes the total center of mass energy squared. Approximating each nucleus in its rest-frame as a cube of side L = A 1/3 gives the surface energy density in GeV/nucleon-crosssection [15] For LHC PbPb scattering at a center-of-mass energy per nucleon pair √ s NN = 5.02 TeV, we can use (1) to obtain Σ PbPb LHC = 2.9 × 10 4 GeV , whereas for LHC XeXe scattering at √ s NN = 5.44 TeV, we have This must be compared to UHECR protons colliding with air nuclei at 10 10.5 s/GeV 2 10 12.5 , which leads to 9.8 × 10 4 < Σ pair UHECR /GeV < 9.8 × 10 5 , where we have taken A air = 14. For the same primary energy, if the UHECR is a nucleus instead of proton the column energy density is reduced. Now, using (1) it is straightforward to see that for helium and carbon nuclei with E 10 9 GeV, Σ A air UHECR > Σ PbPb LHC , but already for nitrogen (and of course nuclei with larger baryon number) there is a particular energy where Σ Aair UHECR Σ PbPb LHC . For example, when a nitrogen with E ∼ 10 9 GeV collides with an air nucleus has a column-energy density comparable to Σ PbPb LHC , and therefore the QGP model predictions of these two scattering processes must be roughly the same.
We now turn to compare the predictions of post-LHC hadronic interaction models (QGSJET II-04 [16] , EPOS-LHC [17], and SIBYLL 2.3c [18]) with the experimental data reported by the ALICE Collaboration [10]. We run Ω − +Ω + 10 6 collisions for each of the models, pair of primary particles, and center-of-mass energy. In analogy with the analyses presented by the ALICE Collaboration, we select those collisions containing at least one charged particle within the central (|η| < 1) pseudorapidity region. For those collisions, we first select the charged particles at midrapidity (|η| < 0.5). To estimate the observable dN ch /dη |η|<0.5 , we write it as the total number of charged particles at midrapidity which, for the i-th collision, is denoted by N c ch,i . For this collision, we measure the total number of particles N α,i of several groups of species α, as described in Table I. Armed with (5), we obtain the ratios to charged pions as In Fig. 1 we show the average ratios Γ α ≡ Γ α,i to all the collisions with the same N c ch for the six species (other than φ) listed in Table I. We conclude that none of the models correctly reproduce the main tendencies of ALICE data, especially for the description of multi-strange hadron production.
We end with two observations: • Over the last year there has been a tremendous amount of progress in modeling UHECR interactions with EPOS-LHC [19,20]. In particular, the new EPOS-QGP has been properly tuned to reproduce the particle to pion ratio for the Ω baryon versus multiplicity at mid-rapidity as reported by the ALICE Collaboration [20]. It will be interesting to see whether the EPOS-QGP predictions of NN collisions at √ s = 167 TeV also accurately match the experimental data.
• The formation of a QGP could play a significant role in the development of UHECR air-showers.
In particular, the enhanced production of multistrange hadrons in high-multiplicity small and large colliding systems would suppress the fraction of energy which is transferred to the electromagnetic shower-component. The formation of QGP blobs in air showers would then enhance the number of muons reaching ground level, and would also modify the shape of the muon density distribution ρ µ (r). The curvature of this distribution (d 2 ρ µ /dr 2 ) has been proposed as a possible discriminator between hadronic interaction models with sufficient statistics [21]. A thorough study of these phenomena is underway and will be pre-sented elsewhere [22].