# Direct photon production in Pb-Pb collisions at $\sqrt{s_\rm{NN}}$ = 2.76 TeV

Direct photon production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}} = 2.76$ TeV was studied in the transverse momentum range $0.9 <~ p_\mathrm{T} <~ 14$ GeV$/c$. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the ALICE detector material with the $e^+e^-$ pair reconstructed in the central tracking system. The results of the two methods were combined and direct photon spectra were measured for the 0-20%, 20-40%, and 40-80% centrality classes. For all three classes, agreement was found with perturbative QCD calculations for $p_\mathrm{T} \gtrsim 5$ GeV$/c$. Direct photon spectra down to $p_\mathrm{T} \approx 1$ GeV$/c$ could be extracted for the 20-40% and 0-20% centrality classes. The significance of the direct photon signal for $0.9 <~ p_\mathrm{T} <~ 2.1$ GeV$/c$ is $2.6\sigma$ for the 0-20% class. The spectrum in this $p_\mathrm{T}$ range and centrality class can be described by an exponential with an inverse slope parameter of $(297 \pm 12^\mathrm{stat}\pm 41^\mathrm{syst})$ MeV. State-of-the-art models for photon production in heavy-ion collisions agree with the data within uncertainties.

Figures

## Figure 1

 Relative contributions of different hadrons to the total decay photon spectrum as a function of the decay photon transverse momentum (PCM case)

## Figure 2

 Comparison of inclusive photon spectra measured with PCM and PHOS in the 0-20%, 20-40%, and 40-80% centrality classes. The individual spectra were divided by the corresponding combined PCM and PHOS spectrum. The shown errors only reflect the uncertainties of the individual measurements. The boxes around unity indicate normalization uncertainties (type C)

## Figure 3

 Comparison of double ratios $R_\gamma$ measured with PCM and PHOS for the 0-20%, 20-40%, and 40-80% centrality classes. Error bars reflect the statistical and type A systematic uncertainty, the boxes represent the type B and C systematic uncertainties. The cancellation of uncertainties (energy scale, material budget) in the double ratio $R_\gamma$ is taken into account in the shown systematic uncertainties.

## Figure 4

 Combined PCM and PHOS double ratio $R_\gamma$ in the 0-20%, 20-40%, and 40-80% centrality classes compared with pQCD calculations for nucleon-nucleon collisions scaled by the number of binary collisions for the corresponding Pb-Pb centrality class. The dark blue curve is a calculation from Refs [51,52]. which uses the GRV photon fragmentation function [53]. The JETPHOX calculations were performed with two different parton distribution functions, CT10 [55] and EPS09 [56], and the BFG II fragmentation function [57].

## Figure 5

 Direct photon spectra in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20% (scaled by a factor 100), the 20-40% (scaled by a factor 10) and 40-80% centrality classes compared to NLO pQCD predictions for the direct photon yield in pp collisions at the same energy, scaled by the number of binary nucleon collisions for each centrality class.

## Figure 6

 Comparison of model calculations from Refs.[59-62] with the direct photon spectra in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20% (scaled by a factor 100), the 20-40% (scaled by a factor 10) and 40-80% centrality classes. All models include a contribution from pQCD photons. For the 0-20% and 20-40% classes the fit with an exponential function is shown in addition.

## Figure 1

 Inclusive photon ($\gamma_{\mathrm{incl}}$) spectra in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20% (scaled by a factor 100), the 20-40% (scaled by a factor 10) and 40-80% centrality classes

## Figure 2

 Combined PCM and PHOS double ratio $R_\gamma$ in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20%, 20-40%, and 40-80% centrality classes.

## Figure 3

 Combined PCM and PHOS double ratio $R_\gamma$ in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20%, 20-40%, and 40-80% centrality classes. The errors in this plot are split into fully uncorrelated errors (stat. $\oplus$ syst. A), displayed as error bars, systematic uncertainties correlated in $\pT$ (syst. B), shown as empty boxes around the points, and a normalization uncertainty (syst. C), shown as filled boxes around 1.

## Figure 4

 Direct photon spectra in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20% (scaled by a factor 100), the 20-40% (scaled by a factor 10) and 40-80% centrality classes compared to NLO pQCD predictions for the direct photon yield in pp collisions at the same energy, scaled by the number of binary nucleon collisions for each centrality class.

## Figure 5

 Comparison of model calculations from Refs.~ with the direct photon spectra in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20% (scaled by a factor 100), the 20-40% (scaled by a factor 10) and 40-80% centrality classes. All models include a contribution from pQCD photons.

## Figure 6

 Direct photon spectra in Pb-Pb collisions at $\snn$=2.76 TeV and $\snn$=0.2 TeV, in both cases for the 0-20% centrality class. The spectra in both cases are the measured direct photon spectra, i.e., the contribution of pQCD photons was not subtracted. In case of the ALICE data, the slope of the exponential shown in the figure was determined without the subtraction of a pQCD contribution, while in the PHENIX case, the slope was determined after subtracting a pQCD contribution. In PHENIX, the pQCD contribution was determined by parameterizing a direct photon measurement in pp collisions

## Figure 7

 Direct photon spectra in Pb-Pb collisions at $\snn$=2.76 TeV and $\snn$=0.2 TeV , in both cases for the 20-40% centrality class. Both spectra reflect the data without the subtraction of a contribution from pQCD photons. In case of the ALICE data, the slope of the exponential shown in the figure was determined without the subtraction of a pQCD contribution, while in the PHENIX case, the slope was determined after subtracting a pQCD contribution. In PHENIX, the pQCD contribution was determined by parameterizing a direct photon measurement in pp collisions

## Figure 8

 Direct photon nuclear modification factor $R_\mathrm{AA}$ in Pb-Pb collisions at $\snn$=2.76 TeV for the 0-20% centrality class. As a measured direct photon spectrum is not available at $\snn$=2.76 TeV, the pQCD calculation by the McGill group was taken as pp reference. The gray band indicates the error of the $\textit{JETPHOX}$ calculation with similar PDF and FF

## Figure 9

 Direct photon nuclear modification factor $R_\mathrm{AA}$ in Pb-Pb collisions at $\snn$=2.76 TeV for the 20-40% centrality class. As a measured direct photon spectrum is not available at $\snn$=2.76 TeV, the pQCD calculation by the McGill group was taken as pp reference. The gray band indicated the error of the $\textit{JETPHOX}$ calculation with similar PDF and FF

## Figure 10

 Direct photon nuclear modification factor $R_\mathrm{AA}$ in Pb-Pb collisions at $\snn$=2.76 TeV for the 40-80% centrality class. As a measured direct photon spectrum is not available at $\snn$=2.76 TeV, the pQCD calculation by the McGill group was taken as pp reference. The gray band indicated the error of the $\textit{JETPHOX}$ calculation with similar PDF and FF

## Figure 11

 Distribution of the test statistic $t$ for the direct-photon excess $R_\gamma$ in 0.9 $< p_T <$ 2.1 GeV/$c$ in the 0-20%, 20-40% $\&$ 40-80% classes for pseudo-experiments performed under the null hypothesis that there is no direct photon excess The model of the measurement of the direct-photon excess $R_\gamma$ is based on the type A, B, C systematic uncertainties. It is assumed that the actual measurement can be described by certain values of nuisance parameters $\varepsilon_B$ and $\varepsilon_C$. Our limited knowledge of the actual values of these parameters is parameterized by Gaussian distributions with mean $\mu=0$ and standard deviations $\sigma = 1$ ($N_{0,1}$), i.e., $\varepsilon_B$ and $\varepsilon_C$ are deviations from a central value in units of the standard deviation. We now perform pseudo-experiments by randomly drawing $\varepsilon_B$ and $\varepsilon_C$ from $N_{0,1}$. Suppose that $R_0$ is the true value of the photon excess. The actual measurement in the $p_T$ interval $i$ will now fluctuate around$R_{\mathrm{mod},i} = R_0 (1 + \varepsilon_B \sigma_{B,i,rel}) (1 + \varepsilon_C \sigma_{C,rel})$as given by the statistical and type A systematic uncertainties added in quadrature. The uncertainties $\sigma_{B,i,rel}$ are the relative systematic type B uncertainties and $\sigma_{C,rel}$ is the relative normalization uncertainty. A given pseudo data point in the $p_T$ interval $i$ is denoted by $R_{pd,i}$. The test statistic is defined by the following sum over pseudo-measurements in the different $p_T$ intervals $i$:$t = \sum_{i=1}^{n_\mathrm{data\;points}} \left( \frac{R_{pd,i}-R_0}{\sigma_{0,i}}\right)^2\quad \mathrm{where} \quad R_{0} = 1,\;\sigma_{0,i} = R_{\mathrm{mod},i} \sigma_{i,stat+A,rel}$. The line indicates the value $t_\mathrm{data}$ of the test statistic for the real data (Photon Conversion Method and PHOS combined). The $p\mbox{-values}$ (number of pseudo-experiments with $t>t_\mathrm{data}$ divided by the total number of pseudo-experiments) is indicated in the plot. The $p\mbox{-value}$ is expressed in terms of the significance in units of the standard deviation of a Gaussian ($a\cdot\sigma$) by solving $2 \int_{a}^{\infty} N_{0,1}(x) \, \mathrm{d} x = p\mbox{-value}$ for $a$ (two-tailed test)