Constraining the anomalous Higgs boson coupling in $H$+$\gamma$ production

Higgs boson production in association with a photon ($H$+$\gamma$) offers a promising channel to test the Higgs boson to photon coupling at various energy scales. Its potential sensitivity to anomalous couplings of the Higgs boson has not been explored with the proton-proton collision data. In this paper, we reinterpret the latest ATLAS $H$+$\gamma$ resonance search results within the Standard Model effective field theory (EFT) framework, using 36.1 fb$^{-1}$ of proton-proton collision data recorded with the ATLAS detector at $\sqrt{s}=13$ TeV. Constraints on the Wilson coefficients of dimension-six EFT operators related to the Higgs boson to photon coupling are provided for the first time in the $H$+$\gamma$ final state at the LHC.


I. INTRODUCTION
After the discovery of the Higgs boson [1, 2], measurements of the Higgs boson couplings to the other fundamental particles become crucial tests of the nature of the Higgs boson. In the Standard Model (SM), coupling of the Higgs boson to photon is forbidden at the tree level, and is induced by heavy particle loops in, e.g., H → γγ and H → Zγ processes. The Higgs-photon coupling has been extensively studied in various Higgs boson decay channels including H → γγ and H → ZZ * /Zγ * /γ * γ * → 4 with LHC data recorded by the ATLAS and CMS experiments [3][4][5][6][7][8][9][10][11].
Apart from the Higgs boson decay channels involving photons, Higgs boson production in association with a photon can also be used to measure the Higgs-photon coupling. The H+γ production cross section is predicted to be very small in the SM, but anomalous couplings introduced by models beyond the SM (BSM) can have significant effects on it.
The H+γ process was considered as a promising and clean channel at LEP [12,13], and has been used by the DELPHI collaboration to search for anomalous couplings of the Higgs boson to vector bosons [14]. At the LHC, potential sensitivity of the pp → H+γ process to anomalous Higgs-photon couplings has been discussed in Ref. [15]. It is predicted that some Wilson coefficients of dimension-six operators related to Higgs-photon couplings can be probed down to 10 −2 with 300 fb −1 pp collision data at 14 TeV. There is no particular analysis measuring the anomalous Higgs-photon couplings via this channel using the LHC data. ATLAS and CMS collaborations have reported the results on heavy H+γ resonance searches in 13 TeV pp collision data [16,17]. Besides the resonance models, their results are also sensitive to non-resonant H+γ production and to the anomalous coupling between Higgs boson and photon. However, these results have not been interpreted as limits on the anomalous Higgs-photon coupling.
In this paper, the latest H+γ resonance search results from the ATLAS collaboration [16] are reinterpreted within the SM effective field theory (EFT) framework, and are presented as constraints on Wilson coefficients of dimension-six EFT operators. The study is based on a pp collision dataset of 36.1 fb −1 at √ s = 13 TeV.
This paper is organized as follows. Section II gives a short overview of the EFT framework, and a brief description of the signal Monte Carlo generation for the reinterpretation.
with Wilson coefficientsc i describing the strengths of the BSM interactions.
We focus on a set of dimension-six operators known as the strongly-interacting light Higgs (SILH) Lagrangian [18]. It is written as where W k µν , B µν and G a µν are the gauge field strength tensors, and Φ is the Higgs doublet. Among all the Wilson coefficients in the SILH Lagrangian,c γ ,c HW andc HB are related to the anomalous Higgs-photon coupling through a direct HZγ or Hγγ vertex. With the presence of these BSM vertices, additional tree level diagrams, in particular an s-channel diagram via a virtual photon or Z boson as the mediator, can contribute to the pp → H+γ process and lead to a large relative change in its production cross section. Therefore, the H+γ process is a sensitive probe to explore the anomalous Higgs-photon coupling [15].
A public implementation of the SILH Lagrangian is available in a general Higgs Effective Lagrangian (HEL) [19,20]. The HEL model is implemented in FeynRules [21], comprising 39 dimension-six operators and their corresponding Wilson coefficients. Its Universal FeynRules Output [22] has been interfaced to the MadGraph5 aMC@NLO [23] event generator. In this work, the HEL model is used with all the other Wilson coefficients fixed at 0 exceptc γ ,c HW andc HB . The pp → H+γ production cross section is computed at different values ofc γ ,c HW andc HB , using MadGraph5 aMC@NLO v2.6.2 with NNPDF2.3 [24] parton distribution functions. We then parametrize the signal cross section as functions of the Wilson coefficients according to the computation. Figure 1 presents a two-dimensional parametrization of the signal cross section parametrized as functions of every two of the three Wilson coefficients with the third coefficient fixed at 0. Monte Carlo event samples are also generated with the same configurations.

III. ANALYSIS STRATEGY
The ATLAS H+γ resonance search [16] is carried out to search for heavy resonances decaying to a SM Higgs boson and a photon, using the bb decay of the Higgs boson. In its signal region, both the selected photon and the Higgs boson are highly boosted (with large momenta). The search is performed by looking for a bump on a smooth background of the H+γ invariant mass spectrum m Hγ . As reported by the ATLAS paper, the mass spectrum observed is consistent with the background-only hypothesis and no evidence of new resonances is found.
This highly boosted signature is of particular interest for probing the anomalous Higgsphoton coupling, as the BSM signal contribution may show longer tails extending up to TeV scale in the m Hγ and photon p T distributions, while the SM expectation drops more 4 steeply [15]. Instead of performing a bump hunt on the m Hγ spectrum as in the original ATLAS paper, we perform a counting experiment with the published m Hγ spectrum to constrain anomalous coupling of the Higgs boson. According to the ATLAS paper [16], 138 events have been observed in signal region 800 GeV < m Hγ < 3.2 TeV, consistent with the expected number of background events 138 ± 12. We reinterpret the ATLAS data as follows.
The expected number of events in signal region can be expressed as s + b, with s and b being the expected number of signal and background events, respectively. To constrain the Wilson coefficients parameters, we construct a likelihood function assuming that the number of observed events n follows a Poisson distribution with an expectation value s + b: Here b is treated as a nuisance parameter. It is constrained by a Gaussian term with a mean value b 0 and a standard deviation σ b . Both b 0 and σ b are obtained from the background fit results in the ATLAS H+γ paper [16]. The expected number of signal events s depends on the Wilson coefficientsc i . It can be further expressed as: The integrated luminosity L int of the ATLAS data sample is 36. Constraints on the Wilson coefficients are obtained by evaluating the profiled likelihood ratio assuming the asymptotic approximation [26]: Here the numerator is the conditional maximum-likelihood function, withb being the value of nuisance parameter b that maximize the likelihood function for a given set of values of the Wilson coefficientsc i . The denominator is the unconditional maximum-likelihood function withĉ i andb being the maximum-likelihood estimates ofc i and b, respectively.

IV. RESULTS AND DISCUSSIONS
A one-dimensional likelihood scan is performed to obtain constraints on each of the three Wilson coefficients in the EFT framework with the other two fixed at 0. Constraints onc γ , c HW andc HB are shown in Figure 2. The 68% and 95% confidence intervals are shown in Table I.  The limits onc γ is much stringent, but the limits onc HW andc HB are in the same order of magnitude compared to the H+γ channel results. These results demonstrate excellent sensitivity of the H+γ production process to some of the Wilson coefficients in the EFT framework. Combination of the H+γ channel with other channels will further improve the sensitivity on the Higgs boson anomalous couplings.
Limits can be further improved by considering shape information from differential distributions instead of doing a simple counting experiment. In the H → γγ channel, the 95% C.L. observed limit ofc HW has been improved to −0.057 <c HW < 0.051 after including differential distributions [4], which is four times better than the limit achieved from the H+γ channel in our study. In the H+γ channel, improvements to the sensitivity are also anticipated by including additional information from the m Hγ and photon p T distributions, but we consider a shape analysis beyond the scope of this paper. [8] ATLAS and CMS Collaborations. Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at √ s = 7 and 8 TeV. JHEP, 08:045, 2016.