Intriguing similarities between high-$p_{\rm T}$ particle production in pp and A-A collisions

In this paper we study the particle production at high transverse momentum ($p_{\rm T}>8$ GeV/$c$) in both pp and Pb-Pb collisions at LHC energies. The characterization of the spectra is done using a power-law function and the resulting power-law exponent ($n$) is studied as a function of $x_{\rm T}$ for minimum-bias pp collisions at different $\sqrt{s}$. The functional form of $n$ as a function of $x_{\rm T}$ exhibits an approximate universal behavior. PYTHIA~8.212 reproduces the scaling properties and therefore, it is used to study the multiplicity-dependent particle production. Going from low to high multiplicities, the power-law exponent decreases. A similar behavior is also observed in heavy-ion collisions when one studies the centrality-dependent particle production. The interpretation of heavy-ion results requires the quantification of the impact of this correlation (multiplicity and high $p_{\rm T}$) on jet-quenching observables.

enhancement [7,8,9]) have been measured in the low-and intermediate-transverse momentum regimes (p T < 8 GeV/c). For higher transverse momenta, the traditional treatments intend to isolate the QGP effects using reference data where the formation of a medium is not expected. Minimum-bias proton-proton collisions have been used for this purpose. However, now this assumption is questionable [10,11].
The PHENIX collaboration has collected data of nucleus-nucleus collisions from √ s NN = 62.4 up to 200 GeV, and the results were compared with those from Pb-Pb collisions at √ s NN = 2.76 TeV. Using the so-called fractional momentum loss, particle production at high p T (p T > 8 GeV/c) in A-A collisions was compared with the one in minimum-bias pp collisions at the corresponding center-of-mass energy. Surprisingly, this quantity was found to scale better with dN ch /dη and with the Bjorken energy density times the equilibration time ( Bj τ 0 ) than with the number of participants obtained using the Glauber model [12]. These results motivated further studies which confirmed the scaling even at the top LHC energy of √ s NN = 5.02 TeV [13]. Similarly, recent results of the ALICE collaboration show that the nuclear modification factors (R AA ) in Pb-Pb collisions at √ s NN = 2.76 TeV and 5.02 TeV [14] and Xe-Xe collisions at √ s NN = 5.44 TeV [15] scale with dN ch /dη . This suggests that multiplicity (or energy density) may play an important role to describe the high-p T particle production in heavy-nuclei collisions.
The correlation between particle production at high transverse momentum and the large underlying event activity has been extensively documented for pp and p-Pb collisions [16,17,18,19,20]. Namely, for small systems the underlying event activity increases with increasing the leading particle transverse momentum. The production of high-momentum particles in Pb-Pb systems could also bias towards high-multiplicity nucleon-nucleon collisions. Therefore it is important to perform a systematic study of the system-size dependence of particle production at high p T . Moreover, the study of the transverse momentum spectra in a large momentum range is a very good laboratory to observe the successive dominance of the gluon and quark contributions [21].
In the present work we do a comprehensive study of the multiplicity dependence of particle production at high transverse momentum (p T > 8 GeV/c) in pp collisions at LHC energies. The results are then compared with LHC A-A data. Although this kind of studies is important to understand the propagation of a hard probe within the medium, they have not been reported so far. The message of the present paper is that the shape of R AA for high-p T particles is not fully attributed to the parton energy loss; since as we will demonstrate, a similar shape is observed for the analogous ratios in pp collisions, i.e., highmultiplicity p T spectra normalized to that for minimum-bias events.
The paper is organized as follows: Sec. 2 describes how the high-p T production is characterized in terms of a power-law function as well as the description of the data which were used in this analysis. The results and discussions are displayed in Sec. 3 and final remarks are presented in Sec. 4.

Particle production at large transverse momenta
In heavy-ion collisions particle production at high p T is commonly used to study the opacity of the medium to the jets. Experimentally, the medium effects are extracted by means of the nuclear modification factor, R AA , which is defined as: where d 2 N AA /dydp T and d 2 N pp /dydp T are the invariant yields measured in A-A and minimum-bias pp collisions, respectively. The ratio is scaled by the average number of binary nucleon-nucleon collisions (N coll ) occurring within the same A-A interaction, which is usually obtained using Glauber simulations [22,23]. The resulting ratio is supposed to account (at least from 8 GeV/c onward) for the so-called jet quenching whereby the high-momentum partons would be "quenched" in the hot system created in the nuclei collisions.
The definition of R AA involves two important aspects: 1. The absolute normalization of the p T spectra in minimum-bias pp collisions obtained from the Glauber model [22,23], means to represent the average number of minimum-bias pp collisions (binary collisions) that the colliding nucleons have suffered within the same heavy-ion collision.
2. The shape of R AA at high p T is determined by the different probability for the occurrence of a hard scattering which is larger in heavy-ion collisions than in pp collisions and is proportional to the path length in the medium and its characteristic transport coefficientq.
The rationale for the procedure is the following. The normalized ratio should give us the probability that partons normally produced in the multiple binary pp collision get degraded in the hot and dense system created in the heavy-ion collision, resulting in a suppression of the ratio (R AA < 1). For instance, in the 0-5% Pb-Pb collisions at the LHC energies the suppression is about 7-8 for p T of around 6-7 GeV/c [24,14]. For higher p T , R AA exhibits a continuous rise and approaches unity [24]. As suggested by the p T -differential baryon-to-meson ratio [25,26], for p T larger than 8 GeV/c radial flow effects are negligible and therefore, the shape of R AA is expected to be dominated by parton energy loss. The underlying assumption to that paradigm is that the pp spectrum does not have a marked dependence on event multiplicity. However, this is not true as indicated by the sphericity analysis as a function of charged-particle multi- The results indicate that even at high multiplicity the abundance of jetty-like events is not negligible, although its contribution is overestimated by the QCD-inspired Monte Carlo generators like PYTHIA 8.212 [28,29]. Based on models, in pp collisions the jet contribution increases with increasing multiplicity [30], this effect contributes to the increase of the particle production at high transverse momentum.
In the present paper we study the shape of the p T spectra of charged particles measured in heavy-ion and pp collisions separately. The aim is to discuss the origin of the rise of the R AA for p T > 6 GeV/c.    for minimum-bias pp collisions at different energies. The data have been taken from [34,35,24,36,37,38]. Results are compared with PYTHIA 8.212 predictions.  Figure 1 shows the multiplicity dependent p T spectra for pp collisions at √ s = 13 TeV. For p T > 8 GeV/c the spectra become harder with increasing multiplicity. This is a consequence of the multiplicity selection bias towards hard processes which is induced when one determines the event multiplicity and the p T spectrum within the same narrow pseudorapidity interval [29]. Figure 1 also shows the ratios of the p T spectra for the different multiplicity classes divided by that for minimum-bias pp collisions. They exhibit an important increase with p T , similar to the one observed in the R AA measured in Pb-Pb collisions [24]. To characterize the changes with multiplicity we fitted a powerlaw function (∝ p −n T ) to the p T spectrum of a specific colliding system and for a given multiplicity class [40]. The power-law exponents allow us to investigate in a bias-free manner various systems, multiplicities, and energies. Above, the spectra tend to have exponents that are smaller than observed for minimum bias. We observe that for all multiplicity classes there is a trend to have smaller exponents (softening of the spectra) at higher momenta; the tendency getting smaller for high multiplicities. Theoretically p T can range from 0 to half of the center-of-mass energy, √ s/2, of the collision. Therefore, the distribution can also be presented as a function of the dimensionless variable [41], which varies between 0 and 1.

Results and discussion
In Fig. 3 we show n as a function of p T for minimum-bias pp data at different √ s (0.2, 0.9, 2.76, 5.02, 7 and 13 TeV [34,35,24,36,37,38]). The results are compared with PYTHIA 8.212 [29] ( known that the mean p T continues rising with multiplicity both in pp and in heavy-ion collisions, implying that high multiplicity, which is proportional to the energy density, is correlated with the high momentum particle production.

Conclusion
We have studied the high-p T (p T > 8 GeV/c) charged-particle production in both pp and Pb-Pb collisions. Considering different p T subintervals, power-law functions were fitted to the transverse momentum distributions of minimum-bias pp collisions measured by experiments at the RHIC and LHC. The local exponents of the power-law fits were compared to those obtained from Pb-Pb data.
Using PYTHIA 8 simulations, we also studied the charged-particle multiplicity dependence of the exponent in pp collisions. With respect to minimum-bias pp collisions, we have determined the following: • The high-p T part of the p T spectra cannot be described by a single powerlaw function (same exponent value) within a wide p T interval (8-100 GeV/c).
• The minimum-bias p T spectra, when represented in terms of the local exponent as a function of the Bjorken variable x T , obey an approximate scaling behavior over a wide range of center-of-mass energy, √ s = 0.2 to 13 TeV.
• The p T spectral shape (characterized by local exponents) as a function of multiplicity exhibits a specific behavior. For 8 < p T < 30 GeV/c the local exponents are smaller than those for minimum-bias events, i.e. the p T spectra are harder for high-multiplicity events than that for minimumbias pp collisions. At higher p T (30-100 GeV/c) the exponents gradually increase to reach the values which describe the minimum-bias p T spectra.
• For heavy-ion collisions the evolution of the local exponent as a function of x T and collision centrality is qualitatively similar to that for pp collisions.
The only specific difference is that the heavy-ion data show a particular shape of the exponent evolution with a downward trend for lower values of x T (p T ) . This is not observed in pp collision, but one has to consider that PYTHIA 8 does not necessarily describe the multiplicity-dependent pp data. Unfortunately at the present, pp data for different multiplicity classes and wide p T intervals are not available.
It would be very important to produce experimental results on high-multiplicity pp collisions over a wide p T interval in order to be able to assess in details the source of the apparent similarity between pp and A-A data.