Production of muons from heavy-flavour hadron decays in pp collisions at $\sqrt{s}$ = 5.02 TeV

Production cross sections of muons from semi-leptonic decays of charm and beauty hadrons were measured at forward rapidity ($2.5<y<4$) in proton--proton (pp) collisions at a centre-of-mass energy $\sqrt{s}=5.02$ TeV with the ALICE detector at the CERN LHC. The results were obtained in an extended transverse momentum interval, $2<p_{\rm T}<20$ GeV/$c$, and with an improved precision compared to previous measurements performed in the same rapidity interval at centre-of-mass energies $\sqrt{s}= 2.76$ and 7 TeV. The $p_{\rm T}$- and $y$-differential production cross sections as well as the $p_{\rm T}$-differential production cross section ratios between different centre-of-mass energies and different rapidity intervals are described, within experimental and theoretical uncertainties, by predictions based on perturbative QCD.


Introduction
The measurement of heavy-flavour (charm and beauty) production cross sections in proton-proton (pp) collisions at the CERN LHC represents an important test of perturbative Quantum Chromodynamics (pQCD). Due to their large masses, heavy quarks are produced almost exclusively in initial hard partonic scatterings and consequently their production cross sections can be estimated in the framework of pQCD. The calculations are based on a factorisation approach and computed as a convolution of the hard parton scattering cross section, evaluated as a perturbative series of the coupling constant of the strong interaction, the parton distribution function (PDF) of the colliding protons and the fragmentation function of heavy quarks to heavy-flavour hadrons. Heavy-flavour production cross sections are predicted at nextto-leading order (NLO) using the fixed-order plus next-to-leading logarithms (FONLL) approach [1,2] or the general-mass variable-flavour-number scheme (GM-VFNS) [3,4]. Calculations at leading order based on k T factorisation [5] also exist. The forward rapidity range accessible by ALICE (2.5 < y < 4) allows us to test pQCD predictions in a region of small Bjorken x down to about 10 −5 (x being the longitudinal momentum fraction of initial-state partons, primarily gluons). In this region, the gluon distribution functions are affected by large uncertainties [6]. The systematic uncertainties on the theoretical production cross sections are larger than the experimental ones and are dominated by the uncertainties on renormalisation and factorisation scales. Recent theoretical developments have shown that the ratios of the open heavy-flavour production cross sections between different beam energies and different rapidity intervals are promising observables which are expected to be sensitive to the gluon PDFs [6], since the uncertainties on scales become negligible with respect to the PDF uncertainties when calculating such ratios. The production cross sections of charm, beauty and heavy-flavour hadron decay leptons measured over a wide energy domain at the Tevatron, RHIC and LHC (see e.g. [7] and references therein and, [8][9][10][11][12][13][14][15][16]) are described, within uncertainties, by these pQCD-based calculations at both forward and central rapidities in a large transverse momentum (p T ) range. Also the ratios of D-meson production cross sections between different rapidity intervals and centre-of mass energies recently measured by the ALICE and LHCb experiments [13,15,16] are described by pQCD-based predictions within uncertainties.
Furthermore, the measurement of heavy-flavour production cross sections in pp collisions provides the necessary baseline for the corresponding measurements in proton-nucleus and nucleus-nucleus collisions. These measurements allow us to study cold nuclear matter effects and effects related to the hot strongly-interacting medium, respectively. This letter describes the p T -and y-differential measurements of the production cross sections of muons from the decay of charm and beauty hadrons in pp collisions at √ s = 5.02 TeV, with the ALICE detector at the LHC. These measurements are performed at forward rapidity, in the interval 2.5 < y < 4. They are facilitated by an experimentally triggerable observable and relatively large decay branching ratios (about 10%), thus resulting in relatively large statistics allowing for differential measurements over a wide p T interval. The present measurements cover the interval 2 < p T < 20 GeV/c, where the beauty contribution is expected to dominate over the charm contribution in the high p T region i.e. for p T > 5 GeV/c [2]. They are complementary to those performed at the same centre-of-mass energy by the LHCb Collaboration for D-meson species in a kinematic region limited to hadron p T < 10 GeV/c [16]. Moreover, the present results are obtained in a significantly extended p T region and the total uncertainties are reduced by a factor larger than two, compared to previous published ALICE results for muons from heavy-flavour hadron decays [17,18].
The letter is structured as follows. Section 2 describes the apparatus with an emphasis on the detectors used in the analysis and the data taking conditions. Section 3 addresses the analysis details. Section 4 presents the results, namely the p T -and y-differential cross sections of muons from heavy-flavour hadron decays as well as the ratio of the p T -differential cross section between different centre-of-mass energies and rapidity intervals and their comparison with pQCD-based FONLL calculations. Finally, conclusions are drawn in Section 5.

Experimental apparatus and data taking conditions
The ALICE detector and its performance are described in detail in [19,20]. This analysis is based on muons reconstructed in the muon spectrometer which covers the pseudo-rapidity interval −4 < η lab < −2.5 1 in the laboratory frame. The muon spectrometer consists of i) a front absorber made of carbon, concrete and steel of 10 nuclear interaction lengths (λ I ), located between the interaction point (IP) and the tracking system, that reduces the hadron yield and decreases the yield of muons from light-particle decays by limiting the free path of primary pions and kaons, ii) a beam shield throughout its entire length, iii) a dipole magnet with a field integral of 3 T·m, iv) five tracking stations, each composed of two planes of cathode pad chambers, v) two trigger stations, each equipped with two planes of resistive plate chambers and vi) an iron wall of 7.2 λ I placed between the tracking and trigger systems, which absorbs secondary hadrons escaping from the front absorber as well as muons from light-hadron decays. In addition, the following detectors are also employed in the analysis. The Silicon Pixel Detector (SPD), which constitutes the two innermost layers of the Inner Tracking System, with pseudo-rapidity coverage |η lab | < 2 and |η lab | < 1.4 for the inner and outer layer, respectively, is used for reconstructing the position of the interaction vertex. Two scintillator arrays (V0) placed on each side of the IP, with pseudo-rapidity coverage 2.8 < η lab < 5.1 and −3.7 < η lab < −1.7, are used for triggering purposes and to reject offline beam-induced background events. Finally, the two T0 arrays, made of quartz Cerenkov counters and placed on both sides of the IP, covering the acceptance 4.6 < η lab < 4.9 and −3.3 < η lab < −3.0, are employed to determine the luminosity.
The results presented in this letter are based on the pp data sample at a centre-of-mass energy √ s = 5.02 TeV recorded by ALICE during a short data taking period of five days in November 2015. This data sample consists of muon-triggered events requiring the coincidence of the minimum-bias (MB) trigger condition and at least one track segment in the muon trigger system with a p T above the threshold of the online trigger algorithm. The MB trigger is formed by a coincidence between signals in the two V0 arrays. The samples of single muons were collected with the p T threshold of the online trigger algorithm set to provide a 50% efficiency for muon tracks with either p T ∼ 0.5 GeV/c or p T ∼ 4.2 GeV/c. In the following, the low-and high-p T trigger threshold samples are referred to as MSL and MSH, respectively. Beam-gas interactions are reduced at the offline level using the timing information of the V0 detector. The accepted events have at least one interaction vertex reconstructed from hits correlation in the two SPD layers. The pile-up rate, defined as the probability for multiple interactions in a bunch crossing, was smaller than 2.5% during the whole data taking period and taken into account in the luminosity determination. After the event selection described above, the integrated luminosities for the used data samples are L int = 53.7 ± 1.1 nb −1 and L int = 104.4 ± 2.2 nb −1 for MSL-and MSH-triggered events, respectively. The calculation of the integrated luminosities and associated uncertainties is discussed in Section 3.

Data analysis 3.1 Selection of muon candidates
Muon candidates are reconstructed using the algorithm described in [21]. They are further selected for the analysis applying same offline criteria as those described in [17,18]. The muon identification is performed by requiring that the reconstructed track in the tracking system matches a track segment in the trigger system satisfying the trigger condition. Muon candidates are required to be reconstructed in the pseudo-rapidity region −4 < η lab < −2.5 and to have a polar angle measured at the end of the absorber in the interval 170 • < θ abs < 178 • . The θ abs condition allows us to limit multiple scattering by rejecting HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration tracks passing through the high-density part of the front absorber. The contamination of fake tracks coming from the association of uncorrelated clusters in the tracking chambers and beam-induced background tracks is further reduced by applying a selection on the distance of the track to the primary vertex measured in the transverse plane (DCA, distance of closest approach) weighted with its momentum (p). The maximum value is set to 6σ p·DCA , where σ p·DCA is the resolution on this quantity. Finally, only muons with p T > 2 GeV/c are analysed since according to Monte Carlo simulations [18], the contribution of muons from the decay of secondary light hadrons produced inside the front absorber is expected to be small in this region. The statistics recorded by ALICE allows us to perform the measurement of the production of muons from heavy-flavour hadron decays up to p T = 20 GeV/c by combining MSL-and MSH-triggered events, which are used up to and above p T = 7 GeV/c, respectively. In the selected interval 2 < p T < 20 GeV/c, the main remaining background contributions consist of muons from the decay of light (charged) hadrons (mostly pions and kaons) produced at the IP and muons from W and Z/γ * decays, which dominate at low/intermediate p T (p T < 6 − 7 GeV/c) and high p T (p T > 16 − 17 GeV/c), respectively. Moreover, two additional background contributions, muons from secondary light (charged) hadron decays and muons from J/ψ decays, are also taken into account in the analysis, although they are small compared to the two other background sources.

Analysis procedure
The differential production cross section of muons from heavy-flavour hadron decays in a given p T and y interval is computed as: where d 2 σ µ ± /dp T dy is the p T -and y-differential production cross section of inclusive muons and, d 2 σ µ ± ←π /dp T dy, d 2 σ µ ± ←K /dp T dy, d 2 σ µ ± ←sec.π/K /dp T dy, d 2 σ µ ± ←W/Z/γ * /dp T dy and d 2 σ µ ± ←J/ψ /dp T dy are the estimated p T -and y-differential production cross sections of muons from primary charged-pion decays, primary charged-kaon decays, secondary (charged) pion and kaon decays, W and Z/γ * decays and J/ψ decays, respectively.
The inclusive muon production cross section is determined according to: where A × ε is the product of acceptance and efficiency and d 2 N µ ± /dp T dy is the measured p T -and ydifferential muon yield. The integrated luminosity L int is computed as N MSL ( The measured p T -and y-differential muon yields are corrected for the detector acceptance, tracking and trigger efficiencies (A × ε) using the same procedure as for previous analyses [  generated using the input p T and y distributions predicted by FONLL calculations [2]. These simulations are based on the GEANT3 transport code [24] for the detector description and response, and include the time evolution of the detector configuration as well as alignment effects. The resulting A × ε in MSLtriggered events is almost independent of p T and is about 90% for p T > 4 GeV/c, while in MSH-triggered events the A × ε plateau is reached at higher p T , about 15 GeV/c (Fig. 1).
The determination of the contribution of muons from charged pion and kaon decays, which dominates the background at low and intermediate p T , is based on a data-tuned Monte Carlo cocktail. The procedure uses as inputs the p T -differential mid-rapidity yields of charged pions and kaons per inelastic pp collision at √ s = 5.02 TeV, [d 2 N π ± (K ± ) /dp T dy] mid−y , resulting from an interpolation of data measured in pp collisions at √ s = 2.76 and 7 TeV, as described in [25][26][27]. These reference p T spectra, measured up to p T = 20 GeV/c, are extrapolated to higher p T using a power-law fit to extend the p T coverage to the p T interval relevant for the estimation of the contribution of decay muons up to p T = 20 GeV/c. Furthermore, the rapidity extrapolation of these distributions in a wider rapidity interval covering forward rapidities is performed according to: where F extrap (p T , y) is the p T -dependent rapidity extrapolation factor. The rapidity extrapolation is obtained from Monte Carlo simulations based on PYTHIA 6.4.25 [28] (Perugia-2011 [29]) and PHO-JET [30] event generators. Furthermore, PYTHIA 8 [31] simulations with various colour reconnection (CR) options ("default MPI (Multi-Parton Interactions)", "new QCD" and "no CR") are employed to account for the p T dependence of the rapidity extrapolation and to estimate the related systematic uncertainty. It was also checked that PYTHIA 8 [31] (Monash-2013 [32]) predictions give comparable results as PYTHIA 6 and PHOJET within uncertainties. Then, the p T and y distributions of muons from the decay of charged pions and kaons are generated with a fast detector simulation of the decay kinematics and absorber effect, using as inputs the extrapolated primary charged pion and kaon spectra. The decay vertex of muons from charged pion and kaon decays is parameterised using either a single exponential for decays occurring before the front absorber (z v ≥ −90 cm), or two exponentials for decays occurring HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration inside the front absorber (−503 cm < z v < −90 cm), in which case the first exponential represents the decay probability whereas the second corresponds to the hadron absorption probability. The fraction of reconstructed muons produced after the front absorber is negligible. Finally, the yields are converted into a cross section and subtracted from the inclusive muon distribution. The relative contributions of muons from primary charged pion decays and muons from primary charged kaon decays to inclusive muons are comparable. In the acceptance of the muon spectrometer, 2.5 < y < 4, the total contribution of muons from both charged pion and kaon decays decreases with increasing p T from about 39% at p T = 2 GeV/c down to 4% at p T = 20 GeV/c. This background contamination depends also on y, in particular at low p T where it amounts to 47% and 26% in the rapidity intervals 2.5 < y < 2.8 and 3.7 < y < 4, respectively.
The contribution of muons from secondary (charged) pion and kaon decays resulting from the interaction of light-charged hadrons with the material of the front absorber of the ALICE muon spectrometer is estimated by means of simulations using PYTHIA 6.425 [28] and the GEANT3 transport code [24]. This contribution affects the low p T region from p T = 2 GeV/c up to about p T = 5 GeV/c, only. The relative contribution with respect to inclusive muons decreases strongly with p T , from about 4% at p T = 2 GeV/c to become smaller than 1% at p T = 5 GeV/c. It also varies with rapidity, by decreasing down to about 3% at p T = 2 GeV/c in the interval 3.7 < y < 4.
At high p T , the W-boson decay muons and the dimuons from Z-boson decays and γ * decays (Drell-Yan process) are the main contributions to the background muon p T distribution. This background source is estimated with simulations using the POWHEG NLO event generator [33] paired with PYTHIA 6.425 [28] for parton shower simulation. These calculations use the CT10 PDFs [34]. The relative contribution of muons from W and Z/γ * decays to the inclusive muon yield in 2.5 < y < 4 is negligible for p T < 12 GeV/c and increases significantly with p T from about 1% at p T = 12 GeV/c up to 12% in 18 < p T < 20 GeV/c. It also depends on rapidity and varies as a function of rapidity in the range 3% − 6% in the interval 14 < p T < 20 GeV/c.
The background component of muons from J/ψ decays is estimated by means of a data-driven method similar to that implemented for the evaluation of muons from primary charged pion and kaon decays. The procedure uses the inclusive J/ψ p T -and y-differential cross sections measured by ALICE in the dimuon channel in the forward rapidity region (2.5 < y < 4) at √ s = 5.02 TeV [35]. The J/ψ p T distribution being limited to the interval p T < 8 GeV/c, it is fitted with the following function where C, p 0 and n are free parameters, and further extrapolated to higher p T values. The y distribution is also extended in a wider range by means of a second-order polynomial function in order to avoid edge effects. Finally, the contribution of muons from J/ψ decays is estimated with a simulation of the decay kinematics, using as inputs the extrapolated p T and y production cross sections. As expected, this contamination is small compared to the other sources. The relative contribution with respect to the inclusive muon yield in the full acceptance of the muon spectrometer is maximum at intermediate p T (p T ∼ 4 − 6 GeV/c) where it amounts to about 4% and decreases with increasing p T to become negligible for p T > 15 GeV/c (smaller than 1%). This background source exhibits a weak dependence on rapidity, with the maximum contribution at p T ∼ 4 − 6 GeV/c varying within 4% − 6%.

Systematic uncertainties
Several sources of systematic uncertainty affecting the measurement of the p T -and y-differential production cross section of muons from heavy-flavour hadron decays are evaluated. These are the systematic uncertainties on the inclusive muon yield, the estimated background sources and the determination of the integrated luminosity.
The systematic uncertainty on the inclusive muon yield contains the following contributions. The systematic uncertainty on the muon tracking efficiency amounts to 0.5% and is estimated by measuring the efficiency in data and Monte Carlo with a procedure that exploits the redundancy of the tracking chamber information [20,36]. The systematic uncertainty on the single muon trigger efficiency of 1.4% (3.2%) for MSL (MSH) trigger comes from the intrinsic efficiency of the trigger chambers and the response of the trigger algorithm. The first contribution is determined from the uncertainty on the trigger chamber efficiency measured in the data and applied to the simulations. The second one is estimated by comparing the p T dependence of the MSL and MSH trigger response function in data and Monte Carlo [36]. A 0.5% contribution related to the choice of the χ 2 cut implemented for the matching between tracker and trigger tracks is also taken into account. The magnitude of these systematic uncertainties is approximately independent of the kinematics, in the region of interest. Finally, an additional contribution related to the tracking chamber resolution and alignment needs to be taken into account. The procedure employed for the estimation of this uncertainty is based on the one described in [37]. It uses a Monte Carlo simulation modelling the tracker response of the muon spectrometer with a parameterisation of the tracking chamber resolution and systematic mis-alignment effects. The former is measured using the residual distance between the reconstructed tracks and their associated clusters. The latter is inferred by comparing the reconstructed p T distribution of positive and negative muons, which have opposite curvature in the dipole magnet field and thus opposite sensitivity to the mis-alignment. This parameterisation is tuned either on data or on the full Monte Carlo simulation. The comparison of the heavy-flavour decay muon p T -differential distributions obtained with the two parameterisations gives an estimation of the systematic uncertainty. It is negligible for p T < 7 GeV/c and then increases to about 15% in the interval 18 < p T < 20 GeV/c. HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration The systematic uncertainty on the estimated yield of muons from primary charged π (K) decays includes contributions from i) the measured mid-rapidity p T distributions of charged π (K) up to p T = 20 GeV/c and their extrapolation to higher p T , varying from about 7% (9%) to about 21% (22%) as a function of p T , ii) the rapidity extrapolation of about 8.5% (6%) for muons from charged π (K), estimated by comparing the results with PYTHIA 6 and PHOJET generators iii) the p T dependence of the rapidity extrapolation, negligible for p T < 4 GeV/c and increasing up to about 6% (3%) for charged π (K) decay muons, obtained by comparing the results with several colour reconnection options in PYTHIA 8 and iv) the simulation of hadronic interactions in the front absorber of about 4% for both charged π and K decay muons. The latter was estimated by comparing the p T distributions of muons from charged pion and kaon decays obtained in a fast detector simulation based on a parameterisation of the effects of the front absorber (Section 3.2) and a full simulation. Combining these sources, a total systematic uncertainty ranging from about 11% to 24% as a function of p T is obtained, with approximately no dependence on the decay particle type. On the other hand, in order to account for the systematics associated to the transport code [18], a conservative systematic uncertainty on the estimated yield of muons from secondary charged π (K) decays of 100% is considered and the obtained difference between the upper and lower limits is further divided by √ 12, corresponding to one RMS of a uniform distribution.
The systematic uncertainty of the estimated yield of muons from W and Z/γ * decays is determined by considering the CT10 PDF uncertainties. It amounts to about 8% (7%) for muons from W (Z/γ * ) decays 3 .
The systematic uncertainty on the extracted yield of muons from J/ψ originates from the measured J/ψ p T and y distributions and their extrapolation in a wider kinematic region, with a negligible effect on the extracted muon yield when using different functions for the rapidity extrapolation. This systematic uncertainty increases with increasing p T from about 10% to 34%.
The systematic uncertainty on the integrated luminosity reflects the 2.1% systematic uncertainty on the measurement of the T0 trigger cross section [22], the systematic uncertainty on the normalisation factor of muon-triggered events to the equivalent number of T0-triggered events based on the relative trigger rates being negligible. Indeed, compatible results are found when calculating the integrated luminosity for MSL (MSH) trigger by applying the corresponding trigger condition in the analysis of MB events, rather than using the relative trigger rates.

Source
Uncertainty vs p T Tracking efficiency 0.5% Trigger efficiency 1.4% (3.2%) for MSL (MSH) Matching efficiency 0.5% Resolution and alignment 0-15% (negligible for p T < 7 GeV/c) Background subtraction µ ← π 1 − 4.4% Background subtraction µ ← K 1 − 4.4% Background subtraction µ ← sec. π, K 0 − 4.3% Background subtraction µ ← W /Z/γ * 0 − 1.1% Background subtraction µ ← J/ψ 0 − 0.7% Integrated luminosity 2.1% Table 1: Summary of relative systematic uncertainties after propagation to the measurement of the p T -differential cross section of muons from heavy-flavour hadron decays at forward rapidity (2.5 < y < 4). See the text for details. For the p T -dependent uncertainties, the minimum and maximum values are given. They are shown for the lowest and highest p T interval with the exception of the light-hadron decay muon background, where this is the opposite trend, and of the background of muons from J/ψ decays with the maximum value being reached for 4 < p T < 6 GeV/c. The systematic uncertainty on the integrated luminosity is correlated as a function of p T .
HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration  Table 1 gives an overview of the systematic uncertainties assigned to the various contributions which enter in the measurement of the p T -differential cross section of muons from heavy-flavour hadron decays in 2.5 < y < 4. The total systematic uncertainty is the quadratic sum of the sources listed in Tab. 1, with the exception of the 2.1% contribution on the integrated luminosity which is fully correlated with p T . It varies from about 2% to 15%, the smaller (higher) value corresponding to p T = 6.5 GeV/c (18 < p T < 20 GeV/c). In the high-p T region (18 < p T < 20 GeV/c), the main contribution comes from the uncertainty on tracking chamber resolution and alignment.

Results and comparison with model predictions
The p T -differential cross section of muons from heavy-flavour hadron decays in 2.5 < y < 4 is presented in Fig. 3. The vertical bars represent the statistical uncertainties and are smaller than the symbols in most p T bins, while the empty boxes correspond to the systematic uncertainties. The symbols are positioned horizontally at the centre of each p T bin and the horizontal bars represent the width of the p T interval. These conventions are applied from here onwards to the figures discussed in the following. The measurement is carried out in a wider p T range with respect to previous measurements in pp collisions [17, 18], the p T reach being extended from p T = 10 GeV/c at √ s = 2.76 TeV (p T = 12 GeV/c at √ s = 7 TeV) to p T = 20 GeV/c by using MSL and MSH triggers. The total uncertainties (quadratic sum of statistical and systematic uncertainties) are reduced by a factor of about 2 − 4 with respect to previous measurements. These improvements have various sources: i) better understanding of the detector response, ii) new data-driven strategy for the estimation of the contribution of muons from light-hadron decays, iii) larger integrated luminosity and iv) use of a high-p T trigger. The measured production cross section HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration (Fig. 3, upper panel) is compared with FONLL predictions. The FONLL calculations [2,6] include the non-perturbative fragmentation into open heavy-flavour hadrons and their decay into final-state leptons. As described in [39], the production of leptons from charm-and beauty-hadron decays is controlled by measured decay spectra and branching ratios. These predictions which use the CTEQ6.6 PDFs [40] are represented with a black curve and a shaded band for the systematic uncertainty. The latter contains the uncertainties on the renormalization and factorization scales, on quark masses as well as on the PDFs. The FONLL predictions are also displayed for muons coming from charm and beauty decays, separately. The latter contribution includes direct decays and decays via D-hadron decays. The FONLL predictions are compatible with data within the experimental and theoretical uncertainties. However, one can notice that the central values of FONLL predictions systematically underestimate the measured production cross section at low and intermediate p T , i.e. up to p T 8 GeV/c. This is also illustrated in the bottom panel of Fig. 3, which shows the ratio between the measured production cross section and the FONLL calculations. This ratio is about 1.3 for 2 < p T < 8 GeV/c and then decreases with increasing p T to tend towards unity in the high p T region (p T > 11 − 12 GeV/c). Qualitatively, this behaviour was also reported at forward rapidity for muons from heavy-flavour hadron decays in previous analyses [ Fig. 4: Production cross section of muons from heavy-flavour hadron decays as a function of rapidity in pp collisions at √ s = 5.02 TeV for the p T intervals 2 < p T < 7 GeV/c (left) and 7 < p T < 20 GeV/c (right). Statistical uncertainties (bars, smaller than symbols) and systematic uncertainties (boxes) are drawn. The production cross sections are compared with FONLL predictions [2] (top). The ratios of the data to FONLL calculations are shown in the lower panels. See the text for details.
The p T -integrated production cross section of muons from heavy-flavour hadron decays is also studied as a function of rapidity for the p T intervals 2 < p T < 7 GeV/c and 7 < p T < 20 GeV/c, as shown in left and right panels of Fig. 4, respectively. The ratios between data and FONLL predictions are depicted in the bottom panels. The two measurements are consistent with FONLL predictions. As in the case of the p T -differential production cross section, the data lie in the upper part of the FONLL predictions. In √ s = 5.02 TeV ALICE Collaboration the interval 2 < p T < 7 GeV/c, muons from heavy-flavour hadron decays originate predominantly from charmed hadrons, while in the higher p T region, muons from beauty-hadron decays take over from charm HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration as the dominant source. One notices that in the higher p T interval, the agreement between data and the central values of FONLL calculations is better. The ratio of the measured production cross section to FONLL predictions is in the range ∼ 1 − 1.2, depending on the rapidity region.
The statistics collected with muon triggers allows us to perform measurements of the p T -differential cross section in five y intervals in the range 2.5 < y < 4. The results and comparisons with FONLL are presented in Fig. 5, upper panel. The corresponding ratios between data and FONLL calculations are also displayed in Fig. 5, lower panel. The data and FONLL exhibit a good agreement within experimental and theoretical uncertainties, the former being systematically higher than the model calculations with some fluctuations at high p T .  Fig. 6: Ratio of the p T -differential production cross section of muons from heavy-flavour hadron decays at forward rapidity in pp collisions at √ s = 7 TeV to that at √ s = 5.02 TeV. Statistical uncertainties (bars) and systematic uncertainties (boxes) are shown. The normalisation uncertainty contains the uncertainties on the luminosity at the two centre-of mass energies. The ratio is compared with FONLL predictions [2]. See the text for details.
The ratio of open heavy-flavour production cross sections between different centre-of-mass energies is considered as a powerful observable for sensitive tests of pQCD-based calculations and to constrain gluon PDF at forward rapidity [6]. While the absolute production cross sections as predicted by FONLL are associated with large systematic uncertainties, dominated by the scale uncertainties, the ratios of production cross sections at different centre-of-mass energies are predicted with a better accuracy [6]. The ratio of the measured p T -differential cross section of muons from heavy-flavour hadron decays in pp collisions at √ s = 7 TeV to that at √ s = 5.02 TeV in the rapidity interval 2.5 < y < 4 is reported in Fig. 6. The systematic uncertainties between the two measurements are considered as uncorrelated when forming the ratio and the main contribution comes from the measurement at √ s = 7 TeV. The ratio exhibits a smooth increase with increasing p T from about 1.5 (p T = 2 GeV/c) to 1.8 (p T = 12 GeV/c). The data are compared with FONLL predictions [2]. The measured ratio is well reproduced by FONLL calculations.
A reduction of the systematic uncertainty on the FONLL predictions is also expected from the ratio of open heavy-flavour cross sections between different rapidity intervals, which could provide constraints on the gluon PDF at small Bjorken-x values. This ratio, computed for heavy-flavour hadron decay muons between the two extreme rapidity intervals, i.e. 2.5 < y < 2.8 and 3.7 < y < 4, is presented in Fig. 7.
HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration When forming the ratio, the systematic uncertainty on integrated luminosity is correlated, while the systematic uncertainty on tracking chamber resolution and alignment is partially correlated. The other sources of systematic uncertainties are treated as uncorrelated. The ratio decreases significantly with increasing p T from about 0.5 down to 0.15. The measured ratio is compared with FONLL predictions, which describe the data within their uncertainties.  Fig. 7: Ratio of the p T -differential production cross section of muons from heavy-flavour hadron decays in 3.7 < y < 4 to that in 2.5 < y < 2.8 in pp collisions at √ s = 5.02 TeV. Statistical uncertainties (bars) and systematic uncertainties (boxes) are shown. The ratio is compared with FONLL predictions [2]. See the text for details.

Conclusions
In summary, the production of muons from heavy-flavour hadron decays has been measured in the forward rapidity region as a function of p T and y in pp collisions at √ s = 5.02 TeV with the ALICE detector at the CERN LHC. As compared to previously published measurements, the present results have an extended p T coverage, 2 < p T < 20 GeV/c, and a better precision with the total uncertainties reduced by a factor of about 2 − 4, depending on p T . The results provide the crucial reference for the study of the effects of the hot and dense matter on the production of muons from heavy-flavour hadron decays in Pb-Pb collisions at the same centre-of-mass energy. The measurements of the differential production cross sections are found to be in agreement with FONLL predictions over the full p T range, even though the central values of FONLL appear to underestimate the heavy-flavour hadron decay muon production. The p T -differential ratios of the production cross section between √ s = 7 TeV and √ s = 5.02 TeV and between two rapidity intervals within 2.5 < y < 4 are well described by FONLL calculations. √ s = 5.02 TeV ALICE Collaboration

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex.                 HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration

A The ALICE Collaboration
HF decay µ production in pp collisions at √ s = 5.02 TeV ALICE Collaboration