Scale and isolation sensitivity of diphoton distributions at the LHC

TL;DR

This paper addresses tensions between NNLO QCD predictions for diphoton distributions at the LHC and experimental data by re-evaluating theoretical uncertainties from photon isolation and scale choices. It introduces matched-hybrid isolation, analyzes its infrared sensitivity, and contrasts it with the conventional smooth-cone prescription, finding substantial, region-dependent effects on cross-sections and distributions. It also compares central scale choices, particularly $\mu_0 = M_{\gamma\gamma}$ versus $\mu_0 = \langle p_T^{\gamma} \rangle$, showing that dynamic scales can improve mutual agreement and that the combination of hybrid isolation with $\mu_0 = \langle p_T^{\gamma} \rangle$ yields noticeably better agreement with ATLAS 8 TeV data across several observables. The work highlights that scale and isolation prescriptions are non-negligible sources of theoretical uncertainty and emphasizes the need for including these effects in precision phenomenology and in future NNLO studies with alternative subtraction and resummation approaches.

Abstract

Precision measurements of diphoton distributions at the LHC display some tension with theory predictions, obtained at next-to-next-to-leading order (NNLO) in QCD. We revisit the theoretical uncertainties arising from the approximation of the experimental photon isolation by smooth-cone isolation, and from the choice of functional form for the renormalisation and factorisation scales. We find that the resulting variations are substantial overall, and enhanced in certain regions. We discuss the infrared sensitivity at the cone boundaries in cone-based isolation in related distributions. Finally, we compare predictions made with alternative choices of dynamical scale and isolation prescriptions to experimental data from ATLAS at 8 TeV, observing improved agreement. This contrasts with previous results, highlighting that scale choice and isolation prescription are potential sources of theoretical uncertainty that were previously underestimated.

Figures (17)

• Figure 1: The matched-hybrid isolation profile function $\chi^\text{hyb}$ for $n\in \left\{\frac{1}{2}, 1, 2 \right\}$ and several choices of the inner cone radius, $R_d$ (dashed). As $R_d \to 0$ (dotted), the smooth-cone (solid) suppression of the collinear singularity is retained, but the numerical deviation from the constant profile function of fixed-cone isolation is diminished. For all values of $R_d$, exactly-collinear radiation is vetoed.
• Figure 2: The variation $\Delta\sigma \left(R_d\right) = \sigma_\text{hybrid} - \sigma_\text{smooth}$ at NLO as a function of the inner-cone radius $R_d$, for $R=0.4$. All other parameters are kept constant. As expected, the gluon splitting gives rise to a quadratic dependence, whilst the quark splitting gives rise to a logarithmic divergence arising from the integrated collinear singularity.
• Figure 3: Isolation cone effects at NLO, showing the difference between matched-hybrid and smooth-cone isolation $\Delta\sigma$. The $\mathrm{d}\xspace \Delta\sigma / \mathrm{d}\xspace\Delta R_{\gamma j}$ distribution has regions of highly-local sensitivity to $R_d$, whilst the $\mathrm{d}\xspace \Delta\sigma / \mathrm{d}\xspace\Delta y_{\gamma\gamma}$ distribution is sensitive only through a small global normalisation. In the first plot the jet cut is 1 GeV; at this order all jets comprise a single parton. Higher values of the jet cut increase the minimal value of $\Delta R_{\gamma j}$ at which partons of that $p_\mathrm{T}\xspace\xspace$ can be emitted and not vetoed, with the minimum approximately $R \sqrt{p_{\mathrm{T}\xspace}^{j_{}}\xspace / E_{\mathrm{T}\xspace}^{\text{iso}}\xspace}$, leading to steeper slopes to the left of the peak.
• Figure 4: Detailed isolation cone effects at NLO, showing the difference between matched-hybrid and smooth-cone isolation $\Delta\sigma$. The absolute predictions for smooth-cone isolation are shown for reference. At this order, isolation criteria only apply at all in the limited region of phase-space defined by $p_{\mathrm{T}\xspace}^{\gamma\gamma}\xspace \leqslant E_{\mathrm{T}\xspace}^{\text{iso}}\xspace$. Here, as for the ATLAS 8 TeV data considered throughout, $E_{\mathrm{T}\xspace}^{\text{iso}}\xspace=11~\mathrm{GeV}\xspace\xspace$.
• Figure 5: The variation $\Delta\sigma \left(R_d\right) = \sigma_\text{hybrid} - \sigma_\text{smooth}$ at NNLO as a function of the inner-cone radius $R_d$, for $R=0.4$. All other parameters are kept constant. The two channels not shown, ${q}\xspace{\bar{q}}\xspace$ and ${g}\xspace{g}\xspace$, have comparable shape (but smaller magnitude) to ${q}\xspace{g}\xspace$ and ${q}\xspace{q}\xspace$ respectively.