Eur. Phys. J. C (18) 78:395 htts://doi.org/1.114/ejc/s15-18-5843-8 Regular Article - Exerimental Physics Ellitic flow of electrons from beauty-hadron decays extracted from Pb Pb collision data at s NN =.76 ev D. Moreira de Godoy 1,a, F. Herrmann 1,M.Klasen 1, C. Klein-Bösing 1,, A. A. P. Suaide 3 1 Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, Münster, Germany ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 6491 Darmstadt, Germany 3 Universidade de São Paulo, R. do Matão 1371, São Paulo, Brazil Received: 4 Setember 17 / Acceted: 6 Aril 18 / Published online: 1 May 18 he Author(s) 18 Abstract We resent a calculation of the ellitic flow of electrons from beauty-hadron decays in semi-central Pb Pb collisions at centre-of-mass energy er colliding nucleon air, reresented as s NN, of.76 ev. he result is obtained by the subtraction of the charm-quark contribution in the ellitic flow of electrons from heavy-flavour hadron decays in semi-central Pb Pb collisions at s NN =.76 ev recently made ublicly available by the ALICE collaboration. 1 Introduction he nuclear matter exosed to conditions of high temerature and energy density is exected to undergo a hase transition to a colour deconfined state of matter [1,], the Quark-Gluon Plasma (QGP). he conditions for the hase transition can be achieved in the laboratory with collisions of heavy ions at high energies [1]. he roerties of the medium formed in the laboratory can be robed with a unique degree of control by articles from decays of heavy flavours (charm and beauty), since heavy quarks are mainly roduced in hard arton scattering rocesses [3 5] at the initial stage of heavyion collisions [6,7] and articiate in the entire evolution of the created system. he artons traversing the medium lose energy via collisional and radiative rocesses [8 1] in the interaction with the medium constituents. he energy loss of artons is redicted to be deendent on their colour charge and mass, resulting in a hierarchy where beauty quarks lose less energy than charm quarks, charm quarks lose less energy than light quarks, and quarks lose less energy than gluons [1,13,14]. he heavy-flavour energy loss can be investigated exerimentally with the nuclear modification factor (R AA ) of heavy-flavour articles, defined as a e-mail: moreirad@uni-muenster.de R AA = 1 dn AA /d, (1) AA dσ /d where dn AA /d is the transverse momentum ( )differential yield in nucleus-nucleus (AA) collisions; AA is the average nuclear overla function in nucleus-nucleus collisions, given by the ratio of the average number of binary collisions and the inelastic cross section; and dσ /d is the -differential cross section in roton-roton () collisions. A suression of the yield of D mesons and letons from heavy-flavour hadron decays (R AA < 1) for > 3GeV/c was observed in gold gold (Au Au) collisions at s NN = GeV at the Relativistic Heavy Ion Collider (RHIC) [15 18] and in lead-lead (Pb Pb) collisions at s NN =.76 and 5. ev at the Large Hadron Collider (LHC) [19 5], indicating energy loss of heavy flavours in the medium. An exerimental hint to the quark mass deendence of the heavy-flavour energy loss has been found in the comarison of the R AA of D mesons and non-romt J/ψ from B-hadron decays in central Pb Pb collisions at snn =.76 ev at the LHC [,6,7]. he observed difference of these measurements is described by model calculations [8,9] as redominantly due to the quark mass deendence of the arton energy loss. he interaction of heavy quarks with the medium can be further investigated with the azimuthal anisotroy of heavyflavour articles, extracted from the coefficients v n of the Fourier decomosition of the article azimuthal distribution in the transverse lane [3] dn d (ϕ Ψ n ) 1 + v n cos [n (ϕ Ψ n )], () n=1 where ϕ is the azimuthal angle of the heavy-flavour articles and Ψ n is the symmetry-lane angle of the nth-order harmonic. he second Fourier coefficient v, called ellitic 13
395 Page of 1 Eur. Phys. J. C (18) 78 :395 flow, quantifies the ellitic azimuthal anisotroy of the emitted articles. he origin of the ellitic azimuthal anisotroy of heavy-flavour articles in non-central heavy-ion collisions deends on the transverse-momentum interval. While the v at low is sensitive to the collective motion of the medium constituents caused by ressure gradients, the v at high can constrain the ath-length deendence of the in-medium energy loss of heavy quarks, resulting from the direction of the articles that traverse the ellisoidal nuclear overla region. he ellitic flow of romt D mesons at midraidity is observed to be ositive in 3 5% Pb Pb collisions at s NN =.76 ev at the LHC [31,3] with 5.7σ significance in the interval < < 6GeV/c, indicating that charm quarks articiate in the collective motion of the system. Measurements of the romt D-meson v in Pb Pb collisions at s NN = 5. ev [33,34] have smaller uncertainties comared to the ones in Pb Pb collisions at snn =.76 ev. he results at the two collision energies are comatible within uncertainties. he romt D + s v in semi-central Pb Pb collisions at s NN = 5. ev is comatible within uncertainties with the average of romt D,D +, and D + v in the same collision system [34]. A ositive v is also observed for letons from heavy-flavour hadron decays at low and intermediate in semi-central Au Au collisions at s NN = GeV at RHIC [17,35] and in semi-central Pb Pb collisions at s NN =.76 ev at the LHC [5,36,37]. In articular, the v of electrons from heavy-flavour hadron decays is observed to be ositive with 5.9σ significance in the range < <.5 GeV/c in 4% Pb Pb collisions at s NN =.76 ev. In view of the exerimental results on the ellitic flow of heavy-flavour articles, an imortant question that remains oen is whether beauty quarks take art in the collective motion in the medium. he first measurement of the v of non-romt J/ψ mesons from B-hadron decays is comatible with zero within uncertainties in two kinematic regions, 6.5 < < 3 GeV/c and y <.4, and 3 < < 6.5 GeV/c and 1.6 < y <.4, in 1 6% Pb Pb collisions at s NN =.76 ev at the LHC [7]. In this aer, we resent a method to subtract the contribution of charm quarks in the ublished measurement of the ellitic flow of electrons from heavy-flavour hadron decays in semi-central Pb Pb collisions at s NN =.76 ev erformed by the ALICE collaboration. he calculation uses as inut the v coefficients of romt D mesons and electrons from heavyflavour hadron decays measured by the ALICE collaboration [3,36] and three different results for the relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays [38 41]. Methodology he article azimuthal distribution of electrons from heavyflavour hadron decays (e c + b) can be searated into the contributions of electrons from charm-hadron decays (e c) and from beauty-hadron decays (e b). Consequently, the ellitic flow of electrons from beauty-hadron decays can be exressed as v e b = ve c+b (1 R)v e c, (3) R where R reresents the relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavyflavour hadron decays. In the following, we resent the currently ublished measurements and, in case there is no available measurement, our calculations of the three observables required to obtain the ellitic flow of electrons from beauty-hadron decays. Based on available results on oen heavy flavours at RHIC and LHC, the most suitable system for this analysis is the Pb Pb collision system at s NN =.76 ev in the 4% centrality class, which corresonds to the centrality range where the measured v of electrons from heavy-flavour hadron decays is observed to be ositive with a maximum significance [36] and thus a ossible ellitic flow of electrons from beauty-hadron decays is exected to be more significant. In this analysis, the v and R AA of heavyflavour articles are assumed to be the same at slightly different mid-raidity ranges ( y <.5,.7 and.8) in which the measurements needed in the calculation are available. Indeed, no deendence on raidity was observed in recent ALICE results on those observables for electrons from heavy-flavour hadron decays at mid-raidity ( y <.7 for v and y <.6 forr AA measurements) and muons from heavy-flavour hadron decays at forward raidity (.5 < y < 4) [4,36]..1 Ellitic flow of electrons from heavy-flavour hadron decays he result on the ellitic flow of electrons from heavy-flavour hadron decays (v e c+b ) at mid-raidity ( y <.7) in 4% Pb Pb collisions at s NN =.76 ev ublished by the ALICE collaboration [36] is used in this analysis. he v e c+b is measured in the interval.5 < < 13 GeV/c with the event lane method [3]. A ositive value is observed in the interval < <.5 GeV/c with significance of 5.9σ [36]. 13
Eur. Phys. J. C (18) 78 :395 Page 3 of 1 395. Relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays he measurement of the relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays (R) has been ublished by the ALICE collaboration only in collisions at s =.76 ev [38,39]. he factor R is measured using the track imact arameter and electron-hadron azimuthal correlation methods. Results obtained with both techniques are comatible within uncertainties. he coefficient R measured in collisions with the electron-hadron azimuthal correlation method is used in the analysis with the caveat that initial- and final-state effects modify the yield of electrons from heavyflavour hadron decays in heavy-ion collisions. In articular, the coefficient R at high is exected to be higher in Pb Pb collisions comared to collisions, since the in-medium energy loss of charm quarks is redicted to be larger than the one of beauty quarks [3]. herefore, the factor R at high in Pb Pb collisions at s NN =.76 ev is exected to have an exclusive value between the measured factor R in collisions at s =.76 ev and unity. Consequently, according to Eq. 3, the minimum value of the v of electrons from beauty-hadron decays can be comuted with the R measured in collisions. In addition to the available measurement, the coefficient R is obtained with a Monte Carlo (MC) simulation based on POWHEG [4], which rovides the calculation of the heavyflavour roduction in hadronic collisions at Next-to-Leading Order (NLO) accuracy. he POWHEG results are interfaced to PYHIA [43,44] in order to generate the shower, hadronisation and decay. In agreement with other heavy-flavour roduction tools, e.g. QCD calculation at Fixed Order lus Next-to-Leading Logarithms (FONLL) [4,45] and earlier calculations [5], the square root of the quadratic sum of the quark mass (m Q ) and are used as renormalization and factorization scales, i.e. μ = μ f = μ r = m Q +.he charm- and beauty-quark masses are set as 1.5 and 4.75 GeV, resectively. Even though the calculated coefficient R is sensitive to the choice of heavy-quark masses and scales [5], only the central value is shown in this analysis. Admittedly, the described framework is designed for collisions, but by making use of the EPS9 [46] NLO nuclear Parton Distribution Functions (npdfs) the framework is able to account for initial-state cold nuclear effects. he npdf gluon shadowing results in reduced -differential cross sections for electrons from heavy-flavour hadron decays for < 6GeV/c and affects contributions from charm quarks stronger than those from beauty quarks. hus, it rovides a lower baseline for the factor R, which is suggested to be further enhanced by medium interactions as it will be discussed in this aer. In R = b( c) e / c+b e 1.9.8.7.6.5.4.3..1 s =.76 ev PYHIA(EPS9LO) POWHEG+PYHIA(EPS9NLO) FONLL 3 4 5 6 7 8 y <.8 Fig. 1 Comarison of the relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavyflavour hadron decays (R) at s =.76 ev obtained with POWHEG+PYHIA [4 44] at NLO accuracy using EPS9 NLO npdfs, with PYHIA at LO accuracy using EPS9 LO npdfs, and withfonll calculation [4,45] using CEQ6.6 PDFs. Only the central values are shown addition, the R coefficient is also obtained with a leading order (LO) calculation based on PYHIA using EPS9 LO npdfs to study the imact of NLO corrections [5]. he comarison of the calculations with LO and NLO aroaches, shown in Fig. 1, reveals that the factor R is reduced with the NLO corrections, stressing the imortance of NLO calculations. In fact, the additional rocesses of heavy-flavour roduction at NLO give rise to large logarithmic corrections to the charm- and beauty-quark cross sections deending on the heavy-flavour mass. he corresonding FONLL calculation of the factor R using CEQ6.6 PDFs, which is also shown in Fig. 1, is similar to the POWHEG+PYHIA(EPS9NLO) result at high. he result on the factor R from the BAMPS heavyflavour transort model [4,41], which includes collisional and radiative in-medium energy loss of heavy quarks, is also emloyed in the analysis to obtain the v of electrons from beauty-hadron decays. he choice of the BAMPS model is justified by the good agreement of the redictions for the R AA of electrons from beauty- and heavy-flavour hadron decays for > 3GeV/c in central Pb Pb collisions at snn =.76 ev with what measured by the ALICE collaboration [3,4]. In this analysis, the R coefficient measured in collisions using the electron-hadron azimuthal correlation technique and the ones obtained with POWHEG + PYHIA (EPS9NLO) and with the BAMPS model are used to estimate the ellitic flow of electrons from beauty-hadron decays..3 Ellitic flow of electrons from charm-hadron decays he ellitic flow of electrons from charm-hadron decays (v e c ) is estimated using a MC simulation of decays of D 13
395 Page 4 of 1 Eur. Phys. J. C (18) 78 :395 mesons into electrons with PYHIA. he MC simulation is based on two observables measured for D mesons in Pb Pb collisions at s NN =.76 ev: the -differential yield, which is used as a robability distribution for finding a D meson with a certain ; the -differential v, which is used to obtain the ϕ D Ψ robability distribution with Eq.. In fact, the -differential yield of D mesons at midraidity ( y <.8) in 4% Pb Pb collisions at s NN =.76 ev is estimated from the ALICE results on the - differential yield and R AA of romt D mesons at midraidity ( y <.5) in % Pb Pb collisions at the same collision energy [19]as (c/gev) dn/d romt D v 1 1 1 1 1 3 1 4 1 5 1.4.3-4% Pb-Pb, y <.8 s NN =.76 ev 4 6 8 1 1 14 16 y <.8 ( dnaa ) 4% = C Δy C AA C RAA ( dnaa ) %,. d d (4).1 where the coefficient C Δy = 1.6 corresonds to the scaling factor of the yield from y <.5 to y <.8 in collisions, assuming a uniform distribution of the D -meson yield within the raidity range. he terms C AA =.36 ±. [19] and C RAA are the ratios of the average nuclear overla function and the D -meson R AA, resectively, in Pb Pb collisions at s NN =.76 ev in the 4% centrality class to the ones in the % centrality class. Note that the terms C Δy and C AA are constant, so they do not lay a role in the determination of the D -meson robability distribution. he non-measured R AA of D mesons in 4% Pb Pb collisions at s NN =.76 ev is estimated by the average of the ALICE results on the D -meson R AA in Pb Pb collisions at the same collision energy in the and 4 8% centrality classes [19] weighted by the corresonding yield of D mesons in each centrality class. he resulting distribution of D mesons in 4% Pb Pb collisions obtained from Eq. 4 is then fitted by a ower-law function (to anel of Fig. ), considering the statistical uncertainty of the exerimental results. he fit function is used as the D -meson robability distribution. he v of romt D mesons in 4% Pb Pb collisions at s NN =.76 ev (bottom anel of Fig. ) is obtained by the arithmetic average of the measured romt D -meson v in Pb Pb collisions at the same collision energy in the 1 3 and 3 5% centrality classes [3]. Indeed, exerimental results show that the v of heavy-flavour articles increases with the centrality class [17,3,36,37], which is consistent with the qualitative exectation of increasing of the ellitic anisotroy from central to eriheral nucleus-nucleus collisions. he statistical and systematic uncertainties are roagated considering the romt D -meson v in the 1 3 and.1-4% Pb-Pb, s NN =.76 ev. 4 6 8 1 1 14 16 Fig. o: estimated -differential yield of D mesons in 4% Pb Pb collisions at s NN =.76 ev from ALICE results [19]. he dashed line corresonds to the ower-law fitted function. Bottom: estimated v of romt D mesons in 4% Pb Pb collisions at s NN =.76 ev from ALICE results [3]. he vertical error bars reresent the statistical uncertainties and the horizontal error bars indicate the bin widths. he emty and filled boxes reresent the systematic uncertainties from data and from the B feed-down subtraction, resectively, in the D -meson v measurement [3] 3 5% centrality classes as uncorrelated as a conservative estimation. In the D -meson v measurement by the ALICE collaboration, the central value was obtained by assuming that the v coefficients of romt D mesons and D mesons from B-meson decays are the same [3]. However, the systematic uncertainty related to this assumtion, referred to as systematic uncertainty from the B feed-down subtraction, was evaluated by the ALICE collaboration. It was assumed that the v of romt D mesons from B-meson decays should be between zero and v of romt D mesons, resulting in the uer and lower limits of the systematic uncertainty, resectively. herefore, the B feed-down contribution decreases the absolute value of the D -meson v and thus the systematic uncertainty is restricted to the uer (lower) limit when the v is ositive (negative). Since the measured D -meson v coefficients are negative in the 8 < < 1 and 1 < < 16 GeV/c intervals in the 1 3 and 3 5% centrality classes, resectively, the resulting roagated systematic uncertainty 13
Eur. Phys. J. C (18) 78 :395 Page 5 of 1 395 from the B feed-down subtraction contains lower and uer limits. Finally, the estimated and v distributions of D mesons in 4% Pb Pb collisions at s NN =.76 ev are used to obtain the v e c = cos [ (ϕ e Ψ )] in the same collision system using the PYHIA event generator. he azimuthal angle of electrons (ϕ e ) takes into account the angular searation between electrons and their arent D mesons..3.1 Statistical uncertainty he statistical uncertainty of the D -meson v is used as inut for the MC simulation to obtain the statistical uncertainty of the v e c. he statistical uncertainties of the measurements used to obtain the -differential yield of D mesons are considered in the fit of the D -meson robability distribution. Further variations are considered as systematic uncertainties..3. Systematic uncertainty he systematic uncertainties from data and from the B feeddown subtraction of the D -meson v (bottom anel of Fig. ) are used as inut for the MC simulation to obtain the systematic uncertainty of the v e c. he following is a discussion on other sources of systematic uncertainty that can influence the v e c estimation. In order to validate the Eq. 4,the -differential yield and R AA of romt D mesons in 4 8% Pb Pb collisions at snn =.76 ev [19] are also used as reference to obtain the -differential yield of D mesons in the 4% centrality class. he result is the same as the one obtained with the % centrality class (to anel of Fig. ). he ALICE result on the D -meson R AA in the 3 5% centrality class [3]isusedasanalternativefortheD -meson R AA estimation in the 4% centrality class. No significant difference is observed in the resulting v e c with resect to the one obtained with the R AA estimated by the average of the D -meson R AA measurements in the and 4 8% centrality classes weighted by the corresonding yield of D mesons in each centrality class. he systematic uncertainties of the measurements of the -differential yield and R AA of romt D mesons are considered in the fit of the D -meson distribution in 4% Pb Pb collisions. No significant difference is observed in the resulting v e c with resect to the one considering only the statistical uncertainty in the fit. For further investigation, he BAMPS result on the distribution of D mesons at y <.8 in 4% Pb Pb collisions at s NN =.76 ev [4,41] is also used to comute the v e c. he relative difference of the obtained v e c using the estimated distribution of D mesons and the BAMPS result, which increases from 1 to % in the interval < < 8GeV/c, is included in the systematic uncertainty. he effect of the D -meson v estimation in 4% Pb Pb collisions using the arithmetic average of the D - meson v measurements in the 1 3 and 3 5% centrality classes is investigated in this analysis. For this urose, the trend of the unidentified charged article v as a function of the average number of binary collisions ( N coll )[47] is assumed to be the same as the one for D mesons. he v as a function of N coll is obtained from a arametrisation of the centrality-deendent v measurement of unidentified charged articles integrated over the interval. < < 5GeV/c[48]. he corresonding result exhibits a linear deendence between v and N coll with a negative sloe for N coll >. For comarison, the arametrisation is also obtained from the centrality-deendent v measurement of unidentified charged articles integrated over the interval 1 < < GeV/c[49]. he linear deendence between v and N coll is the same as the one obtained for articles in a lower interval. he D -meson v is then obtained by the average of the D -meson v in the 1 3 and 3 5% centrality classes weighted by the v coefficients of the corresonding N coll values [47]. he relative difference of the obtained D -meson v with resect to the one obtained with the arithmetic average is negligible for < 8GeV/c and its average is 19% for > 8GeV/c, which is still comatible within uncertainties. he v e c coefficients obtained with the two aroaches show a relative difference of % in the range < < 8GeV/c. his deviation is considered as a consequence of statistical fluctuations in the D -meson v measurement for > 8GeV/c and thus no systematic uncertainty is assigned for this effect. In order to investigate the imact of the assumtion of the article mass ordering of the ellitic flow [5] used to determine the systematic uncertainty from the B feed-down subtraction in the D -meson v measurement, one can assume that the v of romt D mesons from B-meson decays should be between zero and the unidentified charged article v.he unidentified charged article v in 4% Pb Pb collisions is obtained by the average of the v measurements in the 3 and 3 4% centrality classes [49] weighted by the corresonding N coll values. he v coefficients of romt D mesons and unidentified charged articles are comatible within uncertainties as well as the v e c obtained with these two results. herefore, the lower limit of the systematic uncertainty from the B feed-down subtraction can be ositioned at the central values of the romt D-meson v and v e c without strictly considering that the B-meson v is exected to be lower than the D-meson v. As a consequence of the interval ( < < 16 GeV/c) of the D -meson v and -differential yield measurements, the v e c is obtained in the range < < 8GeV/c. he fraction of electrons with > GeV/c 13
395 Page 6 of 1 Eur. Phys. J. C (18) 78 :395 that come from D mesons with < GeV/c is negligible according to PYHIA simulations. he effect of the uer limit of the D -meson measurements is studied by evaluating the v e c with extraolation of the and v distributions of D mesons u to 6 GeV/c. he transverse momentum extraolation is obtained from the ower-law fit function shown in the to anel of Fig., while the imact of the v of D mesons is estimated by exlicitly setting its value, in the interval 16 < < 6 GeV/c, to either zero, or constant at high, or maximum value of the romt D - meson v (shown in Fig. ). he highest relative difference in these three scenarios, which increases from.3 to 4% in the interval < < 8GeV/c, is assigned as a conservative systematic uncertainty. he effect of the mid-raidity range of D mesons is investigated by obtaining the v e c using the D -meson distribution in the raidity range y < 1.6 as inut for the simulation. he D -meson v is considered to be the same in this raidity range, because no deendence on raidity was observed in ALICE results on letons from heavy-flavour hadron decays [4,36] as discussed reviously. he relative difference of the obtained v e c with resect to the one using the D -meson distribution in the raidity range y <.8 is negligible and thus no additional systematic uncertainty is considered due to the raidity effect. In this analysis, the v and shae of the -differential yields of charm hadrons are assumed to be the same as the ones measured for D mesons. his is justified by the fact that the v coefficients of D,D + and D + mesons are comatible within uncertainties in 3 5% Pb Pb collisions at snn =.76 ev [31], also the romt D + s v is comatible within uncertainties with the romt non-strange D meson v in 3 5% Pb Pb collisions at s NN = 5. ev [34]. In addition, the ratios of the yields of D + /D and D + /D were observed to be constant within uncertainties in collisions at s = 7 ev and no modification of the ratios was observed within uncertainties in central and semi-central Pb Pb collisions at s NN =.76 ev [51]. A ossible hint for an enhancement of the D + s /D ratio is observed in 1% Pb Pb collisions at s NN =.76 ev [5], but the current uncertainties do not allow for a conclusion. he effect of different decay kinematics of charm articles is estimated by simulating the v of electrons from combined D, D,D s, and Λ c article decays taking into account the fraction of charm quarks that hadronise into these articles [53] and using the same simulation inut as used in the analysis ( - differential yield and v of D mesons). he obtained v e c is comatible with the one using D -meson decay and thus no systematic uncertainty is considered due to this effect. In order to exemlify the imact of a ossible roduction enhancement of D + s and Λ c articles in Pb Pb collisions with resect to collisions, their fragmentation fractions are increased by a factor and 5, resectively, in the simulation of the combined charm meson v. he relative difference of the obtained v e c and the one using D -meson decay is negligible for < 3GeV/c and its average is 5% for > 3GeV/c. Finally, the D -meson v systematic uncertainty from data is summed in quadrature with other sources of systematic uncertainty that affect significantly the v e c estimation, which are the distribution of D mesons and the limited interval of the D -meson measurements. hey are considered as uncorrelated since the effect from the distribution of D mesons is obtained with the BAMPS result and the effect from the limited interval of the D -meson measurements is obtained by extraolations. he term from data is maintained later in this aer to distinguish all sources of systematic uncertainty from the systematic uncertainty related to the B feed-down subtraction of the D -meson v measurement, which is shown searately..4 Ellitic flow of electrons from beauty-hadron decays he v of electrons from beauty-hadron decays (v e b )is obtained from Eq. 3 using the R, v e c+b and v e c results resented in their resective sections. he three results are considered as statistically indeendent. First, the factor R was measured in a different collision system ( collisions) or obtained with calculations. Second, the v e c is obtained with a simulation using measurements of D mesons reconstructed via the hadronic decay channel D K π + in a different centrality class than in the v e c+b measurement. Even though the systematic uncertainties of the R, v e c+b results might be artially correlated, esecially and v e c concerning the article identification selection criteria, the limited ublic information revents a more accurate treatment of these uncertainties. herefore, they are assumed to be uncorrelated as a conservative estimation. As an examle of the effect of a ossible overestimation, if the systematic uncertainties of the v e c and v e c+b results decrease by 3% in the interval < < 8GeV/c, the systematic uncertainty from data of the v e b result is exected to decrease by aroximately 4%. herefore, the statistical and systematic uncertainties of the R, v e c+b and v e c results are roagated as indeendent variables. he v e b systematic uncertainties from data and from the B feed-down subtraction are asymmetric as a consequence of the systematic uncertainty asymmetry of the measurements used in this analysis. he systematic uncertainty from data is evaluated according to the method described in [54], where the ositive and negative deviations are obtained searately and their average is added in quadrature. For verification, the alternative aroach resented in [55] is also alied in this analysis. No signifi- 13
Eur. Phys. J. C (18) 78 :395 Page 7 of 1 395 cant difference between these methods is observed. Since the asymmetry of the systematic uncertainty from the B feeddown subtraction only comes from the v e c result, the limits of the v e b systematic uncertainty are the deviations resulting from the uer and lower limits of the v e c systematic uncertainty. 3 Results he relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays at s =.76 ev obtained with POWHEG + PYHIA at NLO accuracy using EPS9 NLO npdfs is shown in the to anel of Fig. 3. he result is comared with the R in collisions at s =.76 ev measured by the ALICE collaboration using the electron-hadron azimuthal correlation technique [38,39] and with the BAMPS result in 4% Pb Pb collisions at s NN =.76 ev [4]. he comarison shows that R is higher when in-medium effects are resent, which is consistent with the exectation of the mass hierarchy of the energy loss of charm and beauty quarks in the medium. he bottom anel of Fig. 3 shows the v of electrons from charm-hadron decays at mid-raidity in 4% Pb Pb collisions at s NN =.76 ev obtained with a MC simulation with PYHIA using as inut the - differential yield and v distributions of D mesons in the same collision system. A ositive v of electrons from charmhadron decays is found in all intervals, with a maximum significance of 3.σ, where σ is the combined statistical and systematic uncertainties of the lower limit, in the interval < < 3GeV/c. he v coefficients of electrons from beauty-hadron decays in 4% Pb Pb collisions at s NN =.76 ev obtained with different aroaches of the factor R (to anel of Fig. 3) areshowninfig.4. he result comuted with the coefficient R in collisions is an estimation of the minimum value, as discussed reviously. he v of electrons from beauty-hadron decays in 4% Pb Pb collisions at snn =.76 ev is comatible with zero within aroximately 1σ of the total uncertainty, obtained by summing in quadrature the different uncertainty contributions, in all intervals and different R coefficients. However, the large statistical and systematic uncertainties revent a definite conclusion. he result is consistent with the measured v of nonromt J/ψ mesons from B-hadron decays in 1 6% Pb Pb collisions at s NN =.76 ev [7], which is also comatible with zero within uncertainties. Figure 5 shows the v of electrons from charm- and beauty-hadron decays, inclusive [36] and searated, in 4% Pb Pb collisions at s NN =.76 ev. he v of electrons from beauty-hadron decays is lower than the v of electrons from charm-hadron decays, although they are R = b( c) e / c+b e c v e 1.9.8.7.6.5.4.3..1.3.5..15.1.5 s =.76 ev BAMPS, y <.8, -4% Pb-Pb, JPG 4 (15) 11516 ALICE, y <.7,, PLB 738 (14) 97 POWHEG+PYHIA(EPS9NLO) 3 4 5 6 7 8-4% Pb-Pb, y <.7 s NN =.76 ev 3 4 5 6 7 8 Fig. 3 o: relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays at s =.76 ev obtained with POWHEG+PYHIA at NLO accuracy using EPS9 NLO npdfs. he result is comared with the R in collisions at s =.76 ev measured by the ALICE collaboration using the electron-hadron azimuthal correlation technique [38,39] and with the BAMPS result in 4% Pb Pb collisions at s NN =.76 ev [4]. hestatisticalandsystematicuncertaintiesofthe R coefficient obtained with POWHEG + PYHIA and from the BAMPS model are zero. Bottom: ellitic flow of electrons from charm-hadron decays at mid-raidity in 4% Pb Pb collisions at s NN =.76 ev estimated using a MC simulation with PYHIA based on ALICE results [19,3]. he vertical error bars reresent the statistical uncertainties and the horizontal error bars indicate the bin widths. he emty and filled boxes reresent the systematic uncertainties from data and from the B feed-down subtraction, resectively, in the D -meson v measurement [3] comatible within uncertainties. he average of the v coefficients of electrons from charm- and beauty-hadron decays obtained in the interval < < 8GeV/c are listed in able 1. Because of the asymmetric uncertainties, the average is obtained numerically with an iterative sum of the likelihood functions arametrised by variable-width Gaussians [55,56]. he standard deviation, which is the combination of statistical and systematic uncertainties, is assumed to vary linearly. he maximum value of the summed likelihood function corresonds to the average v, while the oints at which the function is.5 corresond to the lower and uer limits of the total uncertainty. 13
395 Page 8 of 1 Eur. Phys. J. C (18) 78 :395 b e v.5. R from ALICE R from POWHEG+PYHIA(EPS9NLO) -4% Pb-Pb, =.76 ev s NN.15 R from BAMPS y <.7.1.5.5.1.15 3 4 5 6 7 8 3 4 5 6 7 8 3 4 5 6 7 8 Fig. 4 Ellitic flow of electrons from beauty-hadron decays at midraidity in 4% Pb Pb collisions at s NN =.76 ev using the aroaches of the factor R [38 4] shown in the to anel of Fig. 3. he vertical error bars reresent the statistical uncertainties and the horizontal error bars indicate the bin widths. he emty and filled boxes reresent the systematic uncertainties from data and from the B feeddown subtraction, resectively, in the D -meson v measurement [3] v.3..1.1-4% Pb-Pb, s NN =.76 ev y <.7 e c e c+b, ALICE, JHEP 9 (16) 8 e b, R from ALICE e b, R from POWHEG+PYHIA(EPS9NLO) e b, R from BAMPS. 3 4 5 6 7 8 Fig. 5 Ellitic flow of electrons from charm- and beauty-hadron decays, inclusive [36] and searated, in 4% Pb Pb collisions at snn =.76 ev. he vertical error bars reresent the statistical uncertainties and the horizontal error bars indicate the bin widths. he emty and filled boxes reresent the systematic uncertainties from data and from the B feed-down subtraction, resectively, in the D -meson v measurement [3] 4 Conclusions We resented a method to subtract the contribution of charm quarks in the ellitic flow of electrons from heavy-flavour hadron decays. he v of electrons from charm-hadron decays was estimated using a MC simulation of D -meson decays into electrons with PYHIA, based on measurements of the -differential yield and v of D mesons in Pb Pb collisions at s NN =.76 ev by ALICE. A ositive v of electrons from charm-hadron decays is found with a maximum significance of 3.σ in the interval < < 3GeV/c. he comuted v of electrons from charm-hadron decays was then subtracted from the v of electrons from able 1 Average of the v coefficients of electrons from charm- and beauty-hadron decays obtained in the transverse momentum interval < < 8GeV/cin 4% Pb Pb collisions at s NN =.76 ev. he reorted errors are the combined statistical and systematic uncertainties. See text for more details Result R aroach Average v e c.15.8 +.34 e b ALICE.14.4 +.39 e b POWHEG+PYHIA(EPS9NLO).1 +.47.5 e b BAMPS.3.3 +.8 heavy-flavour hadron decays in 4% Pb Pb collisions at snn =.76 ev measured by the ALICE collaboration. he subtraction was weighted by the relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays. Since this observable is not measured in Pb Pb collisions, three different aroaches were used as estimations in the analysis. he resulting v of electrons from beauty-hadron decays in 4% Pb Pb collisions at s NN =.76 ev from the subtraction is comatible with zero within aroximately 1σ of the total uncertainty in all intervals and different aroaches of the relative contribution of electrons from beauty-hadron decays to the yield of electrons from heavy-flavour hadron decays. However, the large statistical and systematic uncertainties revent a definite conclusion. he v of electrons from beauty-hadron decays is found to be lower than the v of electrons from charm-hadron decays. 5 Outlook In the resented method, the ellitic flow of electrons from beauty-hadron decays can be determined by using three 13
Eur. Phys. J. C (18) 78 :395 Page 9 of 1 395 observables that have largely been measured at the LHC and RHIC. Based on available results of these observables, the rocedure was alied using measurements erformed by the ALICE collaboration. he method demonstrated to be effective; however, the current statistical and systematic uncertainties of the ALICE results revent a definite conclusion whether the collective motion of the medium constituents influences beauty quarks. A better accuracy of the results on heavy-flavour articles has been achieved in measurements in Pb Pb collisions at s NN = 5. ev [34] and it is exected to be further imroved with the ALICE ugrade, which is foreseen to start in 19. In articular, the ugrade of the Inner racking System (IS) detector will imrove the determination of the distance of closest aroach to the rimary vertex, momentum resolution and readout rate caabilities [57]. hese imrovements will allow for more recise measurements of D mesons down to low transverse momenta and for reducing the systematic uncertainties from data and from the B feed-down subtraction. he latter will be ossible with the direct measurement of the fraction of romt D mesons and D mesons from B- meson decays, which is exected to be accessible with relative statistical and systematic uncertainties smaller than 1 and 5% [57], resectively, for romt D mesons. In addition, the IS ugrade will enable the tracking of electrons down to aroximately.5 GeV/c and enhance the caability to searate romt from dislaced electrons [57], imroving the reconstruction of electrons that do not originate from heavy-flavour hadron decays needed for the background subtraction. Moreover, the systematic uncertainty of the ellitic flow of electrons from beauty-hadron decays can be further imroved by taking into account correlations among different contributions. he caability of the heavy-flavour measurements will also enhance with the increase of luminosity. For instance, the current relative statistical uncertainty of the D-meson v measurement in Pb Pb collisions is 1% for an integrated luminosity of.1 nb 1, while it is exected to be.% for a scenario with an integrated luminosity of 1 nb 1 [57]. Also the ellitic flow coefficients of D s and Λ c articles are exected to be achievable with a relative statistical uncertainty of 8 and % [57], resectively. herefore, the resented method can be used to extract the ellitic flow of electrons from beauty-hadron decays with better recision with future measurements of the three needed observables. Acknowledgements We would like to thank Carsten Greiner and Florian Senzel for roviding the BAMPS results, as well as Francesco Prino for fruitful discussions. We are grateful for the suort of the Deutsche Forschungsgemeinschaft (DFG) through the Research raining Grou GRK 149: Strong and Weak Interactions from Hadrons to Dark Matter ; Bundesministerium für Bildung und Forschung (BMBF) under the roject number 5P15PMCA1; Conselho Nacional de Desenvolvimento Científico e ecnológico (CNPq); and Fundação de Amaro à Pesquisa do Estado de São Paulo (FAPESP). Oen Access his article is distributed under the terms of the Creative Commons Attribution 4. International License (htt://creativecomm ons.org/licenses/by/4./), which ermits unrestricted use, distribution, and reroduction in any medium, rovided you give aroriate credit to the original author(s) and the source, rovide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP 3. References 1. K. 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