Effect of heavy-quark energy loss on the muon differential production cross section in Pb-Pb collisions at \sqrtsNN=5.5 TeV

We study the nuclear modification factors RAA and RCP of the high transverse momentum 5<pt<60 GeV/c distribution of muons in Pb--Pb collisions at LHC energies. We consider two pseudo-rapidity ranges covered by the LHC experiments: $|\eta|<2.5$ and $2.5<\eta<4$. Muons from semi-leptonic decays of heavy quarks (c and b) and from leptonic decays of weak gauge bosons (W and Z) are the main contributions to the muon pt distribution above a few GeV/c. We compute the heavy quark contributions using available pQCD-based programs. We include the nuclear shadowing modification of the parton distribution functions and the in-medium radiative energy loss for heavy quarks, using the mass-dependent BDMPS quenching weights. Muons from W and Z leptonic decays, that dominate the yield at high pt, can be used as a medium-blind reference to observe the medium-induced suppression of beauty quarks.


Introduction
Heavy quarks are regarded as effective probes of the strongly-interacting medium produced in ultra-relativistic heavy-ion collisions, since they are produced in the initial hard-scattering processes and they may subsequently interact with the medium itself. At the Relativistic Heavy Ion Collider (RHIC), a significant suppression of the so called 'non-photonic electrons', expected to be produced in the semi-leptonic decay of charm and beauty hadrons, has been measured in central Au-Au collisions at centre-of-mass energy √ s NN = 200 GeV per nucleon-nucleon collision, indicating a substantial energy loss of heavy quarks in a strongly-interacting medium [1,2].
In Pb-Pb collisions at the Large Hadron Collider (LHC), the energy per nucleon-nucleon collision will be of 5.5 TeV, about 30 times larger than at RHIC, opening up a new era for the study of strongly-interacting matter at high energy density ('QCD medium'). Heavy-quark medium-induced energy loss will be one of the most captivating topics to be addressed in this novel energy domain [3]. In hadron-hadron collisions at LHC energies, muons are predominantly produced in semi-leptonic decays of heavy-flavoured hadrons -mostly beauty for muon p t > ∼ 4 GeV/c. Thus, in heavy-ion collisions, the muon p t distribution is sensitive to b-quark energy loss effects. In absence of nuclear effects, the initial heavy-quark production yields are expected to scale from proton-proton (pp) to nucleus-nucleus collisions in a given centrality class, according to the average number N coll of inelastic nucleon-nucleon collisions (binary scaling). Under this assumption, the in-medium energy loss of heavy quarks would induce a suppression of the high-p t muon yield with respect to the binary-scaled yield measured in pp collisions. The suppression can be quantified as a reduction with respect to unity of the nuclear modification factor: R AA (p t , η) = 1 N coll d 2 N AA /dp t dη d 2 N pp /dp t dη . (1) However, initial-state effects, like for example nuclear shadowing of the parton distribution functions, could significantly reduce the initial production yields in nucleus-nucleus collisions, thus making more difficult to relate a reduction of R AA to b-quark energy loss. At the LHC, muons from W and Z decays can provide an intrinsic calibration for the muon nuclear modification factor and a test of the binary scaling assumption. Due to the large amount of energy available at the LHC, W and Z bosons will be produced with significant cross sections in the hard parton-parton scatterings, and their initial yields are expected to scale with N coll . As we will show, the muons from the decays W → µν µ and Z → µµ are predicted to dominate the muon p t distribution for p t > ∼ 30 GeV/c.
Three experiments, ALICE [4,5], ATLAS [6], and CMS [7], will measure the production of muons in heavy-ion collisions, covering different acceptance regions. The ALICE Muon Spectrometer covers the pseudo-rapidity range 2.5 < η < 4 for p > 4 GeV/c (p t > ∼ 1 GeV/c) . ATLAS and CMS can measure muons at central pseudo-rapidity, |η| < ∼ 2.5, with a larger cutoff, p t > 3-4 GeV/c. As we will quantify in section 4, the high-p t reach for the measurement of the inclusive muon production spectrum is expected to extend well into the region where muons from W and Z decays become dominant over muons from beauty decays.
In this work, we study the effect of heavy-quark energy loss on the transverse momentum distribution of muons in Pb-Pb collisions at √ s NN = 5.5 TeV within the acceptance of the LHC experiments. The weak gauge bosons contributions (section 2.1) to the muon p t and rapidity distributions are obtained from the PYTHIA [8] event generator, taking into account the isospin content of the colliding nuclei and normalizing the cross section to the values predicted by the calculations in Refs. [9,10]. The heavy quark contributions (section 2.2) to the muon p t distribution are obtained from a NLO perturbative QCD(pQCD) calculation (MNR [11]) supplemented with the mass-dependent BDMPS quenching weights for radiative energy loss [12], quark fragmentatioǹ a la Peterson [13] and semi-muonic decay with the spectator model [14]. In the calculation of heavy-quark energy loss the decreased medium density at large rapidities is taken into account by assuming the BDMPS transport coefficientq to scale asq(η) ∝ dN ch /dη (section 3). In section 4 we present and discuss the resulting muon p t distribution in the 10% most central Pb-Pb collisions, the Pb-Pb-to-pp nuclear modification factor R AA (p t ) and the central-toperipheral nuclear modification factor R CP (p t ), without and with the inclusion of heavy-quark energy loss.

Muon p t distribution in hadron-hadron collisions
The muon p t distributions in pp and Pb-Pb collisions at LHC energies are calculated considering the semi-muonic decays of heavy-flavoured hadrons and the muonic decay of W and Z bosons. The procedure used to evaluate the production differential cross section per nucleon-nucleon collision is described in the following.

W and Z decay muons
At the LHC, the c.m.s. energy is large enough to allow the production of massive particles such as the W and Z bosons. The p t and rapidity distributions of W/Z and of their decay muons are obtained from the PYTHIA event generator [8], that reproduces the measured p t distributions in pp collisions at the Tevatron ( √ s = 1.8 TeV) [15,16]. Since in hadron-hadron collisions, at leading order, W and Z bosons are produced by quark-anti-quark annihilation, there could be a dependence of their production cross section on the isospin of the input channel. In nucleus-nucleus collisions this dependence can be mimicked by a weighted cocktail of proton-proton (pp), neutron-neutron (nn), proton-neutron (pn) and neutron-proton (np) collisions. The cross section per nucleon-nucleon binary collision can be expressed as where A and Z are the mass number and the atomic number of the colliding nuclei. CTEQ 4L [17] parton distributions functions (PDFs) are used, and nuclear shadowing is accounted for via the EKS98 parametrization [18]. The resulting p t distributions are normalized to the cross sections obtained from Refs. [9,10], that is a cross section per nucleon-nucleon collision of 6.56 (7.34) nb for the W and 0.63 (0.68) nb for the Z in Pb-Pb (pp) collisions at 5.5 TeV, including the muonic branching ratios (10.6% for W and 3.4% for Z [19]). Notice that the Z production cross section is about ten times smaller than that of the W [20,21]. The uncertainty due to neglecting higher order corrections (next-to-next-toleading order) was quantified as 1-2% in Ref. [9] by varying the values of the factorization and renormalization scales. The uncertainty due to the errors on the PDFs was quantified as about 10% in Ref. [22].

Heavy-quark decay muons
Within the pQCD collinear factorization framework, the expression for the production cross section of heavy-flavoured hadrons in the collision of two hadrons A and B can be schematically written as: where f i/A (x i/A ) and f j/B (x j/B ) are the parton distribution functions, the differential probabilities for the partons i and j to carry momentum fractions x i/A and x j/B of their respective nucleons.σ ij is the cross section of the partonic process ij → QQX. The fragmentation function D h/Q (z) is the probability for the heavy quark Q to fragment into a hadron h with transverse momentum p t = z p t,Q . To simplify the notation, we have dropped the √ s dependence of σ ij and the renormalization/factorization scale dependences of f i/A(j/B) ,σ ij and D h/Q (the squares of scales are normally of the order of the momentum transfer Q 2 ∼ p 2 t,Q of the hard scattering).
We use the NLO pQCD calculation implemented in the HVQMNR program [11] to obtain the heavy-quark p t -y double-differential cross sections, with the following parameters values: for charm, m c = 1.2 GeV/c 2 and factorization and renormalization scales µ F = µ R = 2µ 0 , where µ 0 ≡ m 2 Q + (p 2 t,Q + p 2 t,Q )/2; for beauty, m b = 4.75 GeV/c 2 and µ F = µ R = µ 0 . CTEQ 4M [17] parton distribution functions are used, and nuclear shadowing is taken into account with the EKS98 parametrization [18]. For the b quark, the perturbative uncertainty was quantified, by varying the scales, in about 30% for p t > 30 GeV/c [23]. Starting from the heavy-quark double-differential cross sections at NLO, we obtain the muon-level cross sections using the following Monte Carlo procedure. We sample p t and y of a c (or b) quark according to the shape of the NLO cross section and fragment it to a hadron using the Peterson [13] fragmentation function following the parameterization obtained in a recent analysis of e + e − data from LEP [23]. Finally, we decay the hadron into a muon according to the spectator model [24]. In the spectator model, the heavy quark in a meson is considered to be independent of the light quark and is decayed as a free particle according to the V − A weak interaction [14]. Thus, we assume the momentum of the hadron to be entirely carried by the constituent heavy quark and we perform the heavy-quark three-body decay, c → sµν µ or b → cµν µ , to obtain the muon transverse momentum and rapidity. The muon production cross sections per nucleon-nucleon collision from charm (beauty) at √ s NN = 5.5 TeV that we obtain are 0.415 mb (20 µb) in Pb-Pb collisions and 0.637 mb (23 µb) in pp collisions. A charm (beauty) semi-muonic branching ratio of 9.6% (11.0%) [19] has been considered. We do not include the muons from the cascade decay b → c → µ, because their yield is expected to become negligible with respect to that of the direct muons from b, for p t larger than a few GeV/c [25]. The uncertainty on the beauty component, which dominates the heavy-flavour muon yields in the p t range relevant to our study, can be quantified as about 30%, on the basis of a recent analysis [23] that considered the perturbative uncertainty (variation of the factorization and renormalization scales), the uncertainty on the PDFs and the uncertainty on the fragmentation.

Heavy-quark energy loss
Now we will compute the muon p t distribution taking into account the heavyquark energy loss in the strongly-interacting medium that is expected to be formed in central Pb-Pb collisions at LHC energies. For modelling the energy loss of heavy quarks by medium-induced gluon radiation, we used the quenching weights in the multiple soft scattering approximation, which were derived in Ref. [12] in the framework of the BDMPS formalism [26]. Schematically, energy loss is introduced by modifying Eq. (3) to: where E is the heavy-quark energy and ∆E is the radiated energy. The quenching weight, represented by P (∆E,q, L, m Q /E), is the probability for a heavy quark with mass m Q and energy E to lose an energy ∆E while propagating over a path length L inside a medium with transport coefficientq. The latter is defined as k 2 t /λ, the average transverse momentum, k t , squared transferred from the medium to the parton per unit mean free path λ. It is expected to be proportional to the volume density dN g /dV of gluons in the medium (thus, to its energy density) and to the typical momentum transfer per scattering.
We calculate the energy loss ∆E following the Monte Carlo approach introduced in Ref. [27] for light quarks and gluons, and adapted for heavy quarks in Refs. [12,28]. We start by sampling the heavy-quark kinematics, p t and y, according to the NLO double-differential cross section. Then, we sample the parton production point in the transverse plane (x, y) according to the Glauber-model [29] density ρ coll (x, y) of binary collisions, and we sample the azimuthal parton propagation direction. We calculate the path length L and the value ofq, which is a mean value of the local time-averaged ( ) transport coefficientq(x, y) along the path of the parton. We do not include the expansion of the medium in the longitudinal and transverse directions. However, it has been shown in Ref. [30] that, numerically, the effects of a time-dependent medium on parton energy loss can be accounted for by an equivalent static medium, specified in terms of the time-averaged transport coefficientq. This is confirmed by recent works (see e.g. Ref. [31]), showing that the inclusion of the medium evolution by a full hydrodynamical simulation does not significantly change or improve, with respect to the assumption of a static medium, the results for the suppression of the high-p t R AA in central Au-Au collisions at RHIC. We assume that our approach for the estimation of L is valid for rapidities belonging to the "central plateau" of the charged particle distribution [32], which is expected to be as large as |y| < 4.5 at LHC energies [3]. We now sample a ∆E value, according to the quenching weight P , and we modify the quark kinematics to (p ′ t = p t − ∆E, y ′ = y). As in Ref. [12], heavy quarks that lose all their energy (∆E > p t ) are redistributed according to the thermal distribution dN/dm t ∝ m t exp (−m t /T ) with T = 0.3 GeV. The muons from the decay of these thermalized quarks populate the region p t < ∼ 2 GeV/c, out-side the range of interest for the present study. We assume the heavy-quark rapidity to stay constant during the process of energy loss, since heavy quarks co-move with the longitudinally-expanding medium and any modification of the initial heavy-quark rapidity should remain small. Finally, we apply fragmentation and decay as described in section 2.2.
In Ref. [27] the localq transverse profile at central rapidity (y = 0) is assumed to be proportional to the density of binary collisions. Since we want to study muon production in a broad rapidity range (|y| < ∼ 4), we introduce a dependence of the localq on the pseudo-rapidity η in order to account for the reduced medium density in the forward direction. Namely, we assume the transport coefficientq to scale as a function of pseudo-rapidity according to the gluon pseudo-rapidity density of the medium dN g /dη, this choice being justified by the fact that dN g /dV scales in η according to dN g /dη. We assume the pseudo-rapidity density of charged particles and the pseudo-rapidity density of gluons to have the same dependence on η and we write [33]: where κ is a constant that sets the scale ofq. We use two values of κ that were estimated for central Pb-Pb collisions at √ s NN = 5.5 TeV by scaling the values extracted from an analysis of the light-flavour hadrons suppression at RHIC [27,34]. The corresponding values for the parton-averaged ( ) and time-averaged ( ) transport coefficient 1 are q = 25 and 100 GeV 2 /fm. For the pseudo-rapidity dependence we use the pseudo-rapidity distribution of charged particles predicted for Pb-Pb collisions at the LHC in Ref. [35]. The effect of this dependence on the suppression of muons from heavy-quark decays is expected to be small, because dN ch /dη is predicted to have only a modest variation in the range |η| < 4 (for illustration, for η = 3 it would be reduced by about 15% with respect to η = 0).
Before presenting our results, we point out that, in addition to radiative energy loss, there are other possible medium-induced effects (e.g.: collisional energy loss of heavy quarks [36], in-medium hadronization and dissociation of heavyflavour hadrons [37], formation of bound states and hadronization of heavy quarks via coalescence [38]) that could noticeably affect the muon spectrum for p t < ∼ 10 GeV/c. These effects have not been considered in the present study. And one has to keep in mind that all current jet quenching models do not describe the suppression of single non-photonic electron p t spectra at RHIC equally well as they do describe the suppression of pion spectra. It is with this caveat that one should view the predictions for LHC based on these models.

Results and discussion
We start by presenting, in the left-hand panel of Fig. 1, the muon production cross-section as a function of transverse momentum in the 10% most central Pb-Pb collisions at √ s NN = 5.5 TeV, when only nuclear shadowing is included.
The contributions from charm, beauty and weak gauge bosons are shown separately. Muons from charged pion and kaon decays and from Drell-Yan processes (qq → µ + µ − ) are ignored here, because both are expected to be negligible in the transverse momentum range 5 < ∼ p t < ∼ 60 GeV/c [4,7]. Due to their large masses, W and Z bosons are mainly produced with small transverse momentum, p t ≪ m W,Z . Therefore, the decay muons have typically p t ∼ m W,Z /2. The latest qualitatively explains the shape of the p t distribution of muons from the decay of the W and Z, which "peaks" at p t ≈ 40 GeV/c. Among the contributions that we compute, muons from charm decays are predominant in the low-p t range, 2-4 GeV/c. In the range 4-30 GeV/c beauty decays prevail, and at larger p t the W decays represent the largest contribution to the muon spectra. We may note that these values for the "crossing points" in p t are somewhat dependent on the perturbative uncertainties of NLO calculations (choice of the fragmentation and renormalization scales) and on other systematics in the fragmentation and decay kinematics. For example, a variation of ±30% of yield of the beauty component (see section 2.2) implies a shift of the crossing point by approximately ±2 GeV/c. As discussed in Refs. [20,21], the experimental measurement of the ratio of positive-to-negative muons could help to determine these crossing points. For illustration of the expected significance for high-p t muons, we quote the production yield of muons from W decay in minimum-bias Pb-Pb collisions at √ s NN = 5.5 TeV for an integrated luminosity of 5 × 10 32 cm −2 (the expected integrated luminosity to be collected by each of the three experiments within one month of data-taking).
In view of exploring the final-state effects (heavy-quark energy loss) on the muon spectrum, we first focus on the influence of the initial-state effects, i.e. nuclear shadowing, by analysing the nuclear modification factor R AA as a function of transverse momentum (right-hand panel of Fig. 1). The shortdashed and dotted lines represent the heavy-quark decays contributions; at low p t (2-4 GeV/c) they probe the small x range of the gluon PDF g(x), where, according to the EKS98 parametrization [18], we have shadowing: the PDF in the Pb nucleus is suppressed with respect to the PDF in the free proton (C shad (x, Q 2 ) = g Pb (x, Q 2 )/g p (x, Q 2 ) < 1). Thus, R AA < 1. For larger muon p t ( > ∼ 10 GeV/c) a higher x range is probed, and we begin to explore the anti-shadowing region (C shad > 1), so R AA > 1 as is observed in Fig. 1. For illustration, in table 1 we report a qualitative estimation of the probed (x 1 , x 2 ) values and of the corresponding EKS98 shadowing factors C shad = C shad (x 1 , Q 2 ) × C shad (x 2 , Q 2 ) for heavy quarks and W/Z bosons in Pb-Pb collisions at 5.5 TeV, as a function of the decay-muon rapidity and transverse momentum (C shad is the mean value of C shad ). The x values were obtained using the PYTHIA event generator for the leading order processes gg → QQ and qq → W/Z. For these two processes, we have, qualitatively, s NN x 1 x 2 = Q 2 ≈ 4 (p 2 t,µ + m 2 Q ) and s NN x 1 x 2 = Q 2 ≈ m 2 W (Z) ≈ 4 p 2 t,µ , respectively; and, for both, x 1 ≈ 2 p t,µ exp(+y µ )/ √ s NN , x 2 ≈ 2 p t,µ exp(−y µ )/ √ s NN . Weak gauge boson decays (long-dashed line in Fig. 1) probe the quarks nuclear shadowing, which fluctuates around its mean value of 0.9. The overall nuclear modification factor of muons (solid line in Fig. 1) increases rapidly with p t up to a value of about 1.1 and then decreases to about 0.9. In order to explore the uncertainties due to the limited knowledge of the nuclear PDFs in the kinematic region relevant to our study, we considered two other parametrizations of the nuclear parton distribution: nDS [39] and HKN07 [40]. The values of the corresponding shadowing factors are reported in table 1. We note that the shadowing factor uncertainty for heavy quarks at high p t is 7% and for weak gauge boson is less than 5%. For heavy quarks at low p t , it becomes as large as 20% for charm and 10% for beauty. Note that the study of proton-nucleus collisions at RHIC energies has been absolutely necessary to disentangle cold and hot nuclear matter effects. Cold nuclear matter effects at LHC energies remain relatively unknown. Therefore, p-Pb runs at the LHC will be needed in order to fully understand the nuclear modification factors measured in Pb-Pb.
We now include in the calculation the in-medium energy loss for heavy quarks. We start by considering the nuclear modification factor R AA (p t ) of muons Table 1 Qualitative estimation of Bjorken-x values and shadowing factors (according to EKS98 [18], nDS(NLO) [39] and HKN07(NLO) [40]) for heavy quarks and W/Z bosons produced in Pb-Pb collisions at √ s NN = 5.5 TeV as a function of the decaymuon y and p t (in GeV/c). Details in the text. from beauty decays in central (0-10%) Pb-Pb collisions, in order to study the effects of the b quark mass and of the dependence of the transport coefficientq on η according to dN ch /dη. The latter is relevant only in the large pseudo-rapidity range. The result is shown in Fig. 2. The shaded band represents our baseline result for theq range 25-100 GeV 2 /fm, with mass effect (m b = 4.75 GeV) and with pseudorapidity dependence ofq. The suppression obtained at high p t , where R AA becomes independent of p t , is about a factor 5 (10) forq = 25 (100) GeV 2 /fm. The suppression for electrons from beauty decays was calculated within the same framework (except for the treatment of hadronization and decay) in Ref. [12], for central rapidity and p t < ∼ 15 GeV/c. For the same p t range, we obtain similar values for R AA . With reference to Fig. 2, by comparing the thick solid line (m b = 4.75 GeV) and the long-dash line (m b = 0), we notice that the quark mass effect in parton energy loss increases R AA by up to a factor of three for p t ∼ 5 GeV/c, and that some effect persists even at 15 GeV/c. When going to p t > ∼ 20 GeV/c, the quark mass dependence becomes negligible since the quark mass becomes negligible with respect to the momentum. By comparing the thick and thin solid lines witĥ q = 100 GeV 2 /fm, which are with and without η dependence ofq respectively, we conclude that this dependence has basically no effect on the amount of suppression in the range 2.5 < η < 4. Figure 3 shows the muon p t -differential cross section and the nuclear modification factor for muons from W, Z, c and b decays in central (0-10%) Pb-Pb collisions at √ s NN = 5.5 TeV in the two pseudo-rapidity domains. The results with transport coefficient valuesq = 0, 25 and 100 GeV 2 /fm are reported, whereq = 0 corresponds to the case of no energy loss. With reference to the upper panels of Fig 3, note that, since muons from W and Z decays are unaffected by the energy loss, the crossing point in transverse momentum of the distributions of b-quark and W-boson decay muons shifts down by ≈ 5 GeV/c at large rapidities and by ≈ 7 GeV/c at mid-rapidity, when energy loss is included. Concerning the muon R AA (p t ) (lower panels of Fig. 3), at large pseudorapidities (on the left), with heavy-quark energy loss, the overall muon yield is suppressed by about a factor of 2-5 in the range 2 < p t < 20 GeV/c, where the beauty contribution dominates. For higher p t , R AA increases rapidly in the 20 < ∼ p t < ∼ 30 GeV/c range and flattens at around 0.8 above ≈ 30 GeV/c. Thê q-independence of the R AA of overall muons at large p t is due to the fact that the W/Z boson contribution to the yield becomes dominant (see upper panels of Fig. 3). At mid-rapidity the behaviour is similar (lower-right panel). The small difference of the R AA shape at different rapidities is due to the different proportion of heavy-quark and W/Z boson decays. For the same reason the  nuclear modification factor without energy loss (dot-dashed lines in the lower panels in Fig. 3) differs slightly from that obtained without acceptance cuts (solid line in Fig. 1).
Besides the Pb-Pb-to-pp nuclear modification factor R AA , also the central-to-peripheral nuclear modification factor R CP will provide information on the medium-induced suppression of b quarks. R CP is defined as: where the index C (P) stands for central (peripheral) collisions. From the experimental point of view, the R CP measurement will be more straight-forward than the R AA measurement, for the following two reasons. 1) The measurements in pp and in Pb-Pb will be affected by different systematic errors (especially for the cross section normalization), which will add up in the R AA uncertainty. 2) pp collisions at the LHC will have different c.m.s. energy (14 TeV) with respect to Pb-Pb (5.5 TeV), therefore the muon spectra measured in pp will have to be extrapolated from 14 TeV to 5.5 TeV with the guidance of perturbative QCD calculations, introducing an additional systematic error of the order of 10% on R AA [5].
In our calculation, the initial-state effects are assumed to be the same in central and peripheral collisions -namely, we do not include an impact parameter dependence for shadowing-thus, they cancel out in the central-to-peripheral ratio. As a consequence, the R CP of muons from weak gauge boson decays is equal to one. The central (0-10%) to peripheral (40-70%) ratios are shown in Fig. 4. In central (0-10%) collisions the yield might be reduced with respect to peripheral collisions (40-70%) by a factor 2-3 in the p t range from about 2 GeV/c to about 13 GeV/c, where the b-quark contribution dominates. When going to larger p t , the R CP of muons increases fast and then flattens at around 0.8 at mid-rapidity and 1.0 at forward rapidity. This difference at high p t between the two pseudo-rapidity regions is due to the different relative abundances of the heavy-quarks and weak bosons components. For the same reason, the curves forq = 25 GeV 2 /fm and 100 GeV 2 /fm cross each other at p t ≈ 20 GeV/c at large pseudo-rapidity and at p t ≈ 25 GeV/c at mid-rapidity. We have checked that the uncertainties on the cross sections of muons from W decays and of muons from beauty decays (approximately 10% and 30%, respectively, as discussed in section 2) translate into a variation smaller than 5% of the R AA and R CP values for p t > ∼ 35 GeV/c, while they have no effect at lower p t .

Conclusions
The effect of heavy-quark energy loss on the differential cross section of muons produced in Pb-Pb and pp collisions at LHC energies has been investigated. The most important contributions to the decay muon yield in the range 5 < p t < 60 GeV/c have been included: b (and c) quarks have been computed using a NLO pQCD calculation supplemented with the BDMPS mass-dependent quenching weights; weak gauge bosons muonic decays have been computed using the PYTHIA event generator. The heavy-quark mass-dependence of energy loss reduces the suppression of muon yields from beauty decays by about factor two for 5 < ∼ p t < ∼ 15 GeV/c. To account for the decrease of the medium density at large pseudo-rapidity, we assumed a decrease of the transport coefficient proportionally to dN ch /dη, and we found that the effect on the muon p t distribution is negligible, especially at large transverse momentum. We investigated the energy loss effect by means of the Pb-Pb-to-pp and of the Pb-Pb central-to-peripheral nuclear modification factors in the acceptance of the LHC experiments: ATLAS, ALICE, and CMS. In the p t interval below approximately 20 GeV/c, where the beauty component is dominant, R AA for 0-10% central Pb-Pb collisions relative to pp and R CP for 0-10% relative to 40-70% Pb-Pb collisions are found to be about 0.2-0.4 and 0.3-0.5, respectively. Then, we observe a steep rise in the beauty/W crossover interval 20-40 GeV/c, up to the values R AA ≈ 0.8 and R CP ≈ 1 in the interval above 40 GeV/c, dominated by W/Z decay muons. These muon nuclear modification factors could provide the first experimental observation of the b quark medium-induced suppression in Pb-Pb collisions at the LHC. The presence of a medium-blind component (muons from W and Z decays) that dominates the high-p t muon yield will allow an intrinsic calibration of the medium-sensitive probe (heavy quarks), because it will provide a handle on the strength of the initial-state effects that may alter the hard-scattering cross sections in nucleus-nucleus collisions at the unprecedented energies of the LHC.