Advances in High Energy Physics

Volume 2018, Article ID 4174602, 7 pages

https://doi.org/10.1155/2018/4174602

## Predictions for the Isolated Diphoton Production through NNLO in QCD and Comparison to the 8 TeV ATLAS Data

Laboratoire de Physique Théorique d’Oran (LPTO), University of Oran1-Ahmed Ben Bella, BP 1524, El M’nouar Oran 31000, Algeria

Correspondence should be addressed to Lahouari Semlala; zd.naro-vinu@irauohal.alalmes

Received 27 March 2018; Revised 18 June 2018; Accepted 18 July 2018; Published 7 August 2018

Academic Editor: Juan José Sanz-Cillero

Copyright © 2018 Bouzid Boussaha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We present cross-section predictions for the isolated diphoton production in next-to-next-to-leading order (NNLO) QCD using the computational framework MATRIX. Both the integrated and the differential fiducial cross-sections are calculated. We found that the arbitrary setup of the isolation procedure introduces uncertainties with a size comparable to the estimation of the theoretical uncertainties obtained with the customary variation of the factorization and renormalization scales. This fact is taken into account in the final result.

#### 1. Introduction

Considerable attention, both experimental and theoretical, has been paid to the study of the diphoton productions. This process is relevant for testing the standard model predictions and is of great importance in Higgs studies. The diphoton final state is also important in new physics researches: the extra-dimensions, the supersymmetry, and the new heavy resonances are three important topics among others.

The theoretical calculations are possible thanks to the codes DIPHOX [1], ResBos [2], 2gRes [3], 2gNNLO [4], MCFM [5], and recently MATRIX [6].

In addition to the* direct* production from the hard subprocess, photons can also result from the fragmentation subprocesses of QCD partons. The complete NLO one- and two-*fragmentation* contributions are implemented in DIPHOX. In ResBos only a simplified one-fragmentation contribution is considered but the resummation of initial-state gluon radiation to NNLL accuracy is included. Both DIPHOX and ResBos implement the gg component, to LO and NLO in QCD, respectively. In the (NLO) MCFM calculations, the fragmentation component is implemented to LO accuracy.

Thanks to the high rate of production of final diphoton pairs (considered as relatively clean), experimentalists make precise measurements, pushing the experimental uncertainties down to the percent level; thus, NLO calculations have become insufficient and therefore more precise investigations are required in order to reproduce the data and to provide a precise modeling of the SM backgrounds.

During the first run of the LHC (Run I), measurements of the production cross-section for two isolated photons at a center-of-mass energy of TeV are performed by ATLAS [7] and CMS [8], based on an integrated luminosity of 4.9 and 5.0 , respectively. This is concluded by ATLAS [9] at TeV using an integrated luminosity of 20.2 which gives a much more accurate result.

In [9], the authors reported that NLO calculations fail to reproduce the data and even if there is improvement of the result with 2gNNLO, it remains insufficient.

Although the NNLO isolated diphoton production cross-sections can be calculated using the 2gNNLO and MCFM public codes, we used the most recent code MATRIX, because, in addition to its NNLO accuracy, it allows us to estimate systematic errors related to the -subtraction procedure in an automatic way (see below).

Our work is organized as follows. In Section 2.1, we give a short description of the MATRIX code. In Section 2.2, we present the two isolation prescriptions used in the analysis. We propose a precise estimation of the uncertainties in NNLO QCD calculations containing at least one photon in the final state. In Section 2.3, the NNLO cross-section results are presented and compared to LHC data. We finish with the conclusion in Section 3.

#### 2. NNLO Cross-Sections

##### 2.1. The MATRIX Code

The parton-level Monte Carlo generator MATRIX performs fully differential computations at the next-to-next-to-leading order (NNLO) QCD; it is based on a number of different computations and tools from various people and groups [6, 10–15]. It achieves NNLO accuracy by using the -subtraction formalism in combination with the Catani–Seymour dipole subtraction method. The systematic uncertainties inherent to the -subtraction procedure may be controlled down to the few per mille level or better for all NNLO predictions. To do this, a dimensionless cut-off is introduced which renders all cross-section pieces separately finite and the power-suppressed contributions vanish in the limit . MATRIX simultaneously computes the cross-section at several values and then the extrapolated result is evaluated, including an estimate of the uncertainty of the extrapolation procedure, in an automatic way.

We can apply realistic fiducial cuts directly on the phase-space. The core of MATRIX framework is MUNICH Monte Carlo program, allowing us to compute both QCD and EW corrections at NLO accuracy. The loop-induced contribution entering at the NNLO is available for the diphoton production process.

##### 2.2. Isolation Parameters

An isolation requirement is necessary to prevent contamination of the photons by hadrons produced during the collision, arising from the decays of , etc. Two prescriptions may be used for this purpose:(i)The standard cone isolation criterion, used by collider experiments: a photon is assumed to be isolated if the amount of deposited hadronic transverse energy is smaller than some value , inside the cone of radius in azimutal and rapidity angle centered around the photon direction: can be either a fixed value or a fraction of the transverse momentum of the photon :

and are chosen by the experiment; ATLAS and CMS use , but differs in their various measurements:(ii)The “smooth” cone or Frixione isolation criterion [16]: in this case is multiplied by a function such thata possible (and largely used) choice isso that

Despite the fact that the Frixione criterion (formally) eliminates all fragmentation contribution, it is not yet included in the experimental studies. On the other hand, the use of this criterion by the theoretical investigations at NNLO is necessary to ensure an Infra-Red (IR) safe definition of the cross-section since no fragmentation functions are included.

In ATLAS measurement [9], the standard criterion is adopted for DIPHOX and ResBos but the “smooth” prescription is used for 2gNNLO, assuming . This is far from the Les Houches accord 2013 recommendations which state that to match experimental conditions to theoretical calculations with reasonable accuracy, the isolation parameters must be tight enough: or (assuming ) [17].

In [18], the authors presented a rather complete study of the impact of the isolation parameters on the diphoton cross-sections. We can lift the following points from this study:(i)The NNLO cross-sections are more sensitive to the variation of the parameters of isolation in comparison with the NLO results.(ii)At fixed , the total NNLO cross-section for the “smooth” isolation increases by in going from to GeV.(iii)Considering the interval , at fixed GeV, the total NNLO cross-section with increases by about with and decreases by about 5% with ; the corresponding scale uncertainty is less than .

We notice that the isolation uncertainties due to the choice of the isolation parameters are comparable to the scale uncertainties; thus, we have to consider the arbitrary choice of these parameters as a major source of the theoretical systematic errors as well as uncertainties related to the choice of the scale. This must be included in the final result.

To evaluate these isolation uncertainties (i.e., to determine both the central value and deviations), we use MATRIX to calculate the NLO integrated cross-sections by varying the parameters = and GeV; then the results are compared to the NLO cross-sections obtained by running the DIPHOX code using the standard isolation prescription with the same and parameters.

The so-called box (NNLO) contribution to the channel is removed from the DIPHOX results to ensure that the comparison holds at the same NLO-order and the fine structure constant is fixed to ; the setup is summarized in Table 1 and results are shown in Figures 1-2.