Constraining the anomalous Higgs boson coupling in production *

: Higgs boson production in association with a photon ( H + ) 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 + 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 TeV. Constraints on the Wilson coefficients of di-mension-six EFT operators related to the Higgs boson to photon coupling are provided for the first time in the H + final state at the LHC. We present an interpretation of the recent ATLAS resonance search results with 36.1 fb −1 of pp collision data at TeV in view of the search for the Higgs boson anomalous coupling in the final state. We pro-vide constraints on the Wilson coefficients of dimension-six EFT operators for the first time in the final state with pp collision data. These results demonstrate excellent physics potential of the production process. With differential cross sections measured for the process in the future, the constraints can be further improved.


Introduction
After the discovery of the Higgs boson [1,2], measurements of the Higgs boson couplings to the other fundamental particles became 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., and processes. The Higgs-photon coupling has been extensively studied in the various Higgs boson decay channels including and with the LHC data recorded by the ATLAS and CMS experiments [3][4][5][6][7][8][9][10][11].
H+γ H+γ pp → H+γ Apart from the Higgs boson decay channels involving photons, Higgs boson production in association with a photon can also be used to measure the Higgsphoton coupling. The production cross section is predicted to be very small in SM, but anomalous couplings introduced in models beyond SM (BSM) can have significant effects. The process was considered as a promising and clean channel at LEP [12,13], and was 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 pro-H+γ H+γ cess to anomalous Higgs-photon couplings was discussed in Ref. [15]. It is predicted that some Wilson coefficients of dimension-six operators related to Higgsphoton couplings can be probed down to 10 −2 with 300 fb −1 of pp collision data at 14 TeV. There is no particular analysis measuring anomalous Higgs-photon couplings via this channel using the LHC data. The ATLAS and CMS collaborations have reported the results of heavy resonance searches in 13 TeV pp collision data [16,17]. Apart from the resonance models, their results are also sensitive to non-resonant production and to the anomalous coupling between the Higgs boson and photon. However, these results have not been interpreted as limits on the anomalous Higgs-photon coupling.
In this paper, the latest resonance search results from the ATLAS collaboration [16] are reinterpreted within the SM effective field theory (EFT) and are presented as constraints on the Wilson coefficients of dimension-six EFT operators. The study is based on a pp collision dataset of 36.1 fb −1 at TeV. This paper is organized as follows. Section 2 gives a short overview of the EFT framework and a brief description of the signal Monte Carlo generation for the reinterpretation. Section 3 describes the analysis strategy. Sec- In the SM effective field theory approach, the effects of BSM interactions are parametrized using higher-dimension operators in addition to the SM Lagrangian. Leading contributions at collider energies are expected to originate from dimension-six operators. A general effective Lagrangian with dimension-six operators takes the form c i with the Wilson coefficients 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 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 process and lead to a large relative change in its production cross section. Therefore, the process is a sensitive probe for exploring the anomalous Higgs-photon coupling [15].
A public implementation of the SILH Lagrangian is available in the general Higgs Effective Lagrangian (HEL) [19,20]. The HEL model is implemented in Feyn-c γcHWcHB pp → H+γ c γcHWcHB Rules [21], comprising 39 dimension-six operators and their corresponding Wilson coefficients. Its Universal FeynRules Output [22] has been interfaced to the Mad-Graph5_aMC@NLO [23] event generator. In this work, the HEL model is used with all the other Wilson coefficients fixed to 0 except , and . The production cross section is computed for different values of , and , using MadGraph5_aMC@NLO v2.6.2 with NNPDF2.3 [24] parton distribution functions. We then parametrize the signal cross section as a function of the Wilson coefficients that result from the computation. Figure 1 presents a two-dimensional parametrization of the signal cross section parametrized as a function of two of the three Wilson coefficients, with the third coefficient fixed to 0. Monte Carlo event samples are also generated with the same configurations. The ATLAS resonance search [16] is carried out to search for heavy resonances decaying to the SM Higgs boson and a photon, using the 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 in the smooth background of the invariant mass spectrum . As reported in the ATLAS paper, the mass spectrum observed is consistent with the background-only hypothesis and no evidence of new resonances is found. The highly boosted signature is of particular interest for probing the anomalous Higgs-photon coupling, as the BSM signal contribution may show longer tails extending up to the TeV scale in the and photon distributions, while the SM expectation drops more steeply [15]. Instead of performing a bump hunt on the spectrum as in the original ATLAS paper, we perform a counting experiment with the published spectrum to constrain the anomalous coupling of the Higgs boson. According to the ATLAS paper [16], 138 events were observed in the signal region , consistent with the expected number of background events . We reinterpret the ATLAS data as follows.
The expected number of events in the signal region can be expressed as s+b, where s and b are the expected number of signal and background events, respectively. To constrain the Wilson coefficients, 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 . Both b 0 and are obtained from the background fits in the ATLAS paper [16]. The expected number of signal events s depends on the Wilson coefficients . It can be further expressed as: The integrated luminosity L int of the ATLAS data sample is 36.1 fb −1 . The SM branching ratio Br = 58% for the 125 GeV Higgs boson [25] is used. The signal efficiency accounts for the event loss due to detector effects, and to the reconstruction and selection efficiencies in the ATLAS analysis. It is determined by applying the efficiency table published in the ATLAS paper [16] to the simulated spectra in the signal Monte Carlo samples, and allows to evaluate the overall efficiency. The production cross section is computed in terms of the Wilson coefficients , and , as described in Section 2. The Wilson coefficients , and are treated as the parameters of interest (POIs). 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, where is the value of the nuisance parameter b that maximizes the likelihood function for a given set of values of the Wilson coefficients . The denominator is the unconditional maximum-likelihood function, where and are the maximum-likelihood estimates of and b, respectively.

Results and discussion
c γcHWcHB 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 to 0. The constraints on , and are shown in Figure 2. The 68% and 95% confidence intervals are shown in Table 1.
Two-dimensional likelihood scans are also performed and the confidence regions are shown in Figure 3. Apart from the two Wilson coefficients indicated in the plot, the remaining one is fixed to 0 during the scan.

H+γ
We compare the channel results with those ob- tained in the combined and channels based on the same pp dataset collected by the AT-LAS experiment. The 68% C.L. intervals from the combined channels [6] are:  The limits can be further improved by considering the shape information from the differential distributions instead of doing a simple counting experiment. In the channel, the 95% C.L. observed limit for has been improved to −0.057 < < 0.051 after including differential distributions [4], which is four times better than the limit achieved from the channel in our study. In the channel, improvements to the sensitivity are also anticipated by including additional information from the and photon distributions, but we consider the shape analysis beyond the scope of this paper.

H+γ H+γ H+γ
We present an interpretation of the recent ATLAS resonance search results with 36.1 fb −1 of pp collision data at TeV in view of the search for the Higgs boson anomalous coupling in the final state. We provide constraints on the Wilson coefficients of dimensionsix EFT operators for the first time in the final state with pp collision data. These results demonstrate excellent physics potential of the production process. With differential cross sections measured for the process in the future, the constraints can be further improved.