Centrality dependence of electroweak boson production in PbPb collisions at the CERN Large Hadron Collider

Recent data on the nuclear modification of $W$ and $Z$ boson production measured by the ATLAS collaboration in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ show an enhancement in peripheral collisions, seemingly contradicting predictions of the Glauber model. The data were previously explained by arguing that the nucleon-nucleon cross section may be shadowed in nucleus-nucleus collisions and hence suppressed compared with the proton-proton cross section at the same collision energy. This interpretation has quite significant consequences for the understanding of heavy-ion data, in particular in the context of the Glauber model. Instead, we provide an alternative explanation of the data by assuming that there is a mild bias present in the centrality determination of the measurement; on the size of the related systematic uncertainty. Using this assumption, we show that the data is in agreement with theoretical calculations using nuclear parton distribution functions. Finally, we speculate that the centrality dependence of the $W^{-}/W^{+}$ ratio may point to the relevance of a larger skin thickness of the Pb nucleus, which, if present, would result in a few percent larger PbPb cross section than currently accounted for in the Glauber model and may hence be the root of the centrality bias.

Figure 1

Ratio of shadowed over standard inelastic cross section in $p\mathrm{Pb}$ and PbPb collisions as function of $\sqrt{s_{\mathrm{NN}}}$ calculated with hijing [11]. The results from Eskola et al. [10], i.e., the fit to the boson data as well as the computed cross sections at 5.02 TeV with their minijet model, normalized by 70 mb, are also shown. The reported central values were slightly shifted to assign symmetric uncertainties. For the calculations, the results for different factorization scales were combined assuming they were independent of each other.

Figure 2

Illustration of the combined bias (black) resulting from an AP bias of 2%–4% and the multiplicity bias. The effect of the AP bias (red) is expressed as the ratio of $T_{AA}$ computed with and without the bias for PbPb collisions at 5.02 TeV using tglaubermc [12] with ${\sigma }_{NN}=67.6\mathrm{mb}$. The multiplicity bias (blue) from the centrality determination is estimated from hg-pythia [22].

Figure 3

Measured $W^{+}$, $W^{-}$, or $Z$ boson $R_{AA}$ [1, 2] as a function of centrality compared with various calculations. The solid lines show the expected value for $R_{AA}$ without nuclear modification, $R_{AA}^{\mathrm{ref}}$ from Eq. (2), using the NNPDF3.1 [27], a NLO cross-section calculations with the centrality-dependent weights from Glauber to describe the isospin dependence and an anchor bias of 3%, as explained in the text. The dashed lines with the shaded band denote the $R_{AA}^{\mathrm{th}}$ obtained from NLO calculations incorporating nuclear effects via the use of the nNNPDF2.0 [28] and EPPS16 [13] PDFs given in Table 1.

Figure 4

Measured $W^{+}$, $W^{-}$, or $Z$ boson $R_{AA}$ [1, 2] normalized by $R_{AA}^{i,\mathrm{ref}}$, from Eq. (2), as a function of centrality. The central value was obtained assuming an AP bias of 3% The band around unity denotes the change of the ratio if 2% (upper value) or 4% (lower value) had been assumed instead. The dashed lines with the shaded band denote the $R_{AA}^{i,\mathrm{th}}$ using the nNNPDF2.0 [28] and EPPS16 [13] PDFs normalized by $R_{AA}^{i,\mathrm{iso}}$, given in Table 1.

Figure 5

$R_{AA}^{W^{-}}/R_{AA}^{W^{+}}$ ratio using the ATLAS data [1] as a function of centrality compared with the same $W^{-}/W^{-}$ ratio computed with $R_{AA}^{\mathrm{ref}}$. The $y$ scale on the right denotes the relative change of the model relative to the baseline (no neutron skin) given by the respective $R_{AA}^{\mathrm{iso}}$ ratio, shown as a constant line. In the Glauber model the parameters for the proton and neutron distributions of Pb were modified by one and two standard deviations of their respective uncertainties, as described in the text.