# Elliptic flow of muons from heavy-flavour hadron decays at forward rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV

The elliptic flow, $v_{2}$, of muons from heavy-flavour hadron decays at forward rapidity ($2.5 <~ y <~ 4$) is measured in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$~=~2.76 TeV with the ALICE detector at the LHC. The scalar product, two- and four-particle $Q$ cumulants and Lee-Yang zeros methods are used. The dependence of the $v_2$ of muons from heavy-flavour hadron decays on the collision centrality, in the range 0--40\%, and on transverse momentum, $p_{\rm T}$, is studied in the interval $3 <~ p_{\rm T} <~ 10$~GeV/$c$. A positive $v_2$ is observed with the scalar product and two-particle $Q$ cumulants in semi-central collisions (10--20\% and 20--40\% centrality classes) for the $p_{\rm T}$ interval from 3 to about 5 GeV/$c$. The $v_2$ magnitude tends to decrease towards more central collisions and with increasing $p_{\rm T}$. It becomes compatible with zero in the interval $6<~p_{\rm T}<~10~{\rm GeV/}c$. The results are compared to models describing the interaction of heavy quarks and open heavy-flavour hadrons with the high-density medium formed in high-energy heavy-ion collisions. The model calculations describe the measured $v_2$ within uncertainties.

Figures

## Figure 1

 $p_{\rm T}$-differential inclusive muon $v_2$ in $2.5 < y < 4$ and various centrality intervals, in Pb-Pb collisions at $\sqrt {s_{\rm NN}}$ = 2.76 TeV. The symbols are placed at the centre of the $p_{\rm T}$ interval and, for visibility, the points from two-particle $Q$ cumulants and Lee-Yang zeros with product generating function are shifted horizontally. The vertical error bars represent the statistical uncertainty, the horizontal error bars correspond to the width of the bin (not shown for the shifted data points) and the open boxes are the systematic uncertainties The $p_{\rm T}$ intervals used with the Lee-Yang zeros method are different with respect to the other methods Upper panels: results from two-particle correlation flow methods (scalar product and two-particle $Q$ cumulants)in the 0-10% (left) and 10-20% (right) centrality intervals Lower panels: results in the 20-40% centrality interval from two-particle correlation flow methods (scalar product and two-particle $Q$ cumulants) and from four-particle $Q$ cumulants (left), and from four-particle $Q$ cumulants and Lee-Yang zeros (right).

## Figure 2

 $p_{\rm T}$-differential elliptic flow of muons from heavy-flavour decays,$v_2^{\mu \leftarrow {\rm HF}}$, in $2.5 < y < 4$ and various centrality intervals, in Pb--Pb collisions at$\sqrt {s_{\rm NN}}$ = 2.76 TeV The symbols are placed at the centre of the $p_{\rm T}$ interval and, for visibility,the points from two-particle $Q$ cumulants and Lee-Yang zeros with product generating function are shifted horizontally The meaning of the symbols is the same as in Fig.[1] The horizontal error bars are not plotted for shifted data points The $p_{\rm T}$ intervals used with the Lee-Yang zeros method are different with respect to the other methods Upper panels: results from two-particle correlation flow methods (scalar product and two-particle $Q$ cumulants) in the 0-10% (left) and 10-20% (right) centrality intervals Lower panels: results in the 20-40% centrality interval from two-particle correlation flow methods (scalar product and two-particle $Q$ cumulants) and from four-particle $Q$ cumulants (left), and from four-particle $Q$ cumulants and Lee-Yang zeros (right) See the text for details.

## Figure 3

 Elliptic flow of muons from heavy-flavour hadron decays as a function of the collision centrality in $2.5 < y < 4$ and $3 < p_{\rm T} < 10$ GeV/$c$,in Pb-Pb collisions at $\sqrt {s_{\rm NN}}$ = 2.76 TeV. The results are obtained with scalar product and two-particle $Q$ cumulants Vertical bars (open boxes) represent the statistical(systematic) uncertainty, the horizontal error bars correspond to the width of the centrality bin. For visibility, the points from scalar product are shifted horizontally and the horizontal error bars are not plotted

## Figure 4

 Left: $p_{\rm T}$-differential elliptic flow of muons from heavy-flavour hadron decays in $2.5 < y < 4$, in Pb-Pb collisions at $\sqrt {s_{\rm NN}}$ = 2.76 TeV for the centrality class 20-40% compared to various transport model predictions:MC@sHQ + EPOS,TAMU and BAMPS. The TAMU model is shown with a theoretical uncertainty band Right: $p_{\rm T}$-differential $R_{\rm AA}$ of muons from heavy-flavour hadron decays for the centrality class 0-10% from [21] compared to the same models as for $v_2^{\mu \leftarrow {\rm HF}}$.