On the challenge of estimating diphoton backgrounds at large invariant mass

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

We examine, using the analyses of the 750 GeV diphoton resonance as a case study, the methodology for estimating the dominant backgrounds to diphoton resonance searches. We show that close to the high energy tails of the distributions, where background estimates rely on functional extrapolations or Monte Carlo predictions, large uncertainties are introduced, in particular by the challenging photon-jet background. Analyses with loose photon and low photon ...... cuts and those susceptible to high photon rapidity regions are especially affected. Given that diphoton-based searches beyond 1 TeV are highly motivated as discovery modes, these considerations are relevant for future analyses. We first consider a physics-driven deformation of the photon-jet spectrum by next-to-leading order effects and a phase space dependent fake rate and show that this reduces the local significance of the excess. Using a simple but more general ansatz, we demonstrate that the originally reported local significances of the 750 GeV excess could have been overestimated by more than one standard deviation. We furthermore cross-check our analysis by comparing fit results based on the 2015 and 2016 LHC data sets. Finally we employ our methodology on the available 13 TeV LHC data set assessing the systematics involved in the current diphoton searches beyond the TeV region.

Eur. Phys. J. C (2017) 77:126DOI 10.1140/epjc/s10052-017-4687-y

Regular Article - Theoretical Physics

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Web End = On the challenge of estimating diphoton backgrounds at large invariant mass

J. F. Kamenik1,2, G. Perez3, M. Schlaffer3,a, A. Weiler4

1 Joef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

2 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia

3 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 7610001 Rehovot, Israel

4 Physik Department T75, Technische Universitt Mnchen, James-Franck-Strasse 1, 85748 Garching, Germany

Received: 7 December 2016 / Accepted: 8 February 2017 / Published online: 24 February 2017 The Author(s) 2017. This article is published with open access at Springerlink.com

Abstract We examine, using the analyses of the 750GeV diphoton resonance as a case study, the methodology for estimating the dominant backgrounds to diphoton resonance searches. We show that close to the high energy tails of the distributions, where background estimates rely on functional extrapolations or Monte Carlo predictions, large uncertainties are introduced, in particular by the challenging photon jet background. Analyses with loose photon and low photon pT cuts and those susceptible to high photon rapidity regions are especially affected. Given that diphoton-based searches beyond 1TeV are highly motivated as discovery modes, these considerations are relevant for future analyses. We rst consider a physics-driven deformation of the photon jet spectrum by next-to-leading order effects and a phase space dependent fake rate and show that this reduces the local signicance of the excess. Using a simple but more general ansatz, we demonstrate that the originally reported local signicances of the 750GeV excess could have been overestimated by more than one standard deviation. We furthermore cross-check our analysis by comparing t results based on the 2015 and 2016 LHC data sets. Finally we employ our methodology on the available 13TeV LHC data set assessing the systematics involved in the current diphoton searches beyond the TeV region.

1 Introduction

Searches for new physics at the energy frontier often look for new phenomena at the edge of distributions. In this kinematical region the knowledge of the standard model (SM) background is typically limited and the challenge is to look for a new resonance where only partial knowledge on the SM

a e-mail: mailto:[email protected]

Web End [email protected]

background is available. In this paper we focus in particular on new physics probes based on the high diphoton invariant mass spectrum. We examine, using the analyses of the 750GeV diphoton resonance as a case study, the strategy currently used by the experimental collaborations in estimating the dominant SM backgrounds. We employ our methodology on the 13TeV LHC data set to asses the systematics involved in the current diphoton searches beyond the TeV region.

In their 2015 data sets, both ATLAS and CMS observed an excess in the diphoton spectrum near m = 750 GeV .

The relevant details of the ATLAS and CMS analyses are described in [1,2]. At face value the local signicances for a broad resonance were given by

pATLAS = 4 105,

ATLAS = 3.9,

pCMS = 5 103,

CMS = 2.6,

pcomb = 1 106,

comb = 4.7, (1.1) where pATLAS, CMS, comb (ATLAS, CMS, comb) correspond to the local p value (condence level) of ATLAS, CMS, and their naive combination.1

The local results quoted in Eq. (1.1) are quite signicant and captured the attention of the high energy community. Interpreting them naively, one would be lead to one of the following conclusions:

(i) this excess is a result of a rare statistical uctuation;(ii) this excess implies a discovery of non-Standard Model dynamics.

1 We do not discuss here the global signicance as it strongly depends on the lower value of m dened for the search region. ATLAS (CMS)

chose it to be about 200GeV (400GeV). Furthermore, as discussed below, the region below 500GeV is dominating the t to the functional form which is used to estimate the background. Thus, it is not clear whether one should consider this region as a control region or as the region of interest for the search itself.

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As both conclusions are quite extraordinary (certainly the second one), they motivate an investigation into their robustness. In particular, we raise a third option, to be considered in conjunction with (i), namely, we ask how unlikely is the possibility that(iii) the signicance of the excess is overestimated due to underestimating fake-based backgrounds.

With the inclusion of more data in the analyses the excess eventually vanished [3,4], ruling out the new physics hypothesis (ii). However, the possibility of claim (iii) remains unclear, affecting all analyses which rely on a precise knowledge of the photon faking background and use the same techniques to estimate it.

While our conclusion is independent of the 750GeV resonance we use it as an example case to scrutinize the hypothesis of the underestimated background and its implications.First, the main rationale behind our hypothesis is presented in Sect. 2, followed by a detailed description of our approach to background estimation (Sect. 3) and the statistical treatment of the data (Sect. 4). The comparison with the full 2016 data set is presented in Sect. 5. Our main conclusions are summarized in Sect. 6. For other relevant work, see Refs. [5,6].

2 The rationale

Supercially, the experimental situation related to the diphoton excess was fairly straightforward. The experiments had reported a relatively narrow bump, /m [lessorsimilar] 6% 1. Such

a bump implies a rise in the differential distribution while, due to the rapidly falling parton luminosity functions, it is expected that any reasonable background-related distribution should be a monotonically decreasing function of the invariant mass. Consequently, the presence of a non-Standard Model feature seemed to have been indicated by the measurements. While this was qualitatively correct the challenge is to quantify the signicance of the excess. To endow the bump with a signicance, one needs to control and quantify the background.

The following approaches can be used to constrain the form of the background:I. Data-driven approach Assuming /m 1 and a fea

tureless monotonic background, a robust way to constrain it is through interpolation via a two-sided side band analysis.However, this requires one to have enough measured events at invariant masses both below the resonance and above it. In the case of the 750GeV excess, there were less than 40 events in all of the analyses measured with invariant masses above 850GeV. Such a small number of events does not allow one to use this method reliably.II. First-principle/Monte-Carlo approach There is a rather narrow class of observables for which the theory has

reached an advanced enough level such that we can fully trust our ability to correctly predict the shape of the background distributions. We believe that the invariant mass distribution of experimentally measured diphoton events does not (yet) belong to this selected class of observables. Namely, the continuous diphoton distribution consist of an admixture of two dominant components: (i) The rst is made of two real isolated hard photons. This diphoton distribution is currently known to next-to-next-to-leading order (NNLO) accuracy [7,8] in perturbative QCD and imposing cuts similar to the ATLAS spin-0 analysis suggests an overall uncertainty of about 5% for the invariant mass distribution [8]. (ii) An additional important background component is due to fakes coming mostly from processes involving a hard photon and a jet that passes the various photon quality and isolation cuts [9]. In addition, depending on these cuts, also the dijet background could play an important role. The prompt photonjet cross section is currently known at next-to-leading order (NLO) in QCD, and several codes are available to produce the relevant distributions, including JetPhox [10] and PeTeR [11]. In addition, QCD threshold resummation at next-to-next-to-next-to-leading logarithmic (N3LL) order [12,13] as well as electroweak Sudakov effects are being included [14], resulting in theory uncertainties of about 1020% [9,14,15]. However, a comparison with the 8TeV ATLAS measurement [9] shows that at low photon pT 50 GeV the data exhibits some level of deviations

from the theoretical predictions (a larger uncertainty is found for the invariant mass distribution; see [16]). In addition, it is important to note that the fake rate strongly depends on the quark/gluon avor of the tagged jet (for some discussion of jet avor denitions, see [1720]): intuitively one can understand the difference through the quark and gluon fragmentation functions to pions. At large x, as required to be able to pass photon isolation criteria, gluon fragmentation to few pions is much more suppressed (see e.g. Chapter 20 in Ref. [21]). Accordingly, a dedicated ATLAS study [22] found that there is a probability of about 1 : 2 103 for a

quark jet to fake a photon, and only 1 : 2104 for a gluon jet

to fake a photon, for jets with ET > 40 GeV. Applying this to the photonjet background, we also note that subleading jets might become an important source of fakes if the leading jet is predominantly gluon-initiated.

In order to theoretically predict the purity of the diphoton mass distribution, an appropriate admixture of the diphoton and the photonjet(s) components needs to be constructed [23]. Furthermore, for the latter component, one is required to convolve the photonjet distribution with the relevant fragmentation functions or at least tag the avor of the jet(s). It is also important to note that the purity is a highly phase space dependent quantity. Not only does it depend on the ratio of the differential jetphoton and photonphoton production but also on the jet-to-photon fake rate. The fake

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Eur. Phys. J. C (2017) 77 :126 Page 3 of 13 126

rate may exhibit a strong dependence on the differential quantities such as pT and (pseudo)rapidity . For instance, as discussed below, in the CMS analyses purity is estimated to be better than 90% in the (central-central) EBEB event category but only better than 80% in the (forward-central) EBEE one. Both experiments consider the purity in an inclusive way. However, in the relevant kinematical region the data is not sufcient to constrain possibly large deviations from the inclusive purity estimation (see Fig. 4).III. Functional-t approach Given the present practical limitations of the methods I and II, one is lead to a more phenomenological approach in which the background estimate is obtained by tting an universal function to control regions in the data and then extrapolating into the signal regions using the tted functional form. This allows one to predict the background at relatively high invariant masses in a straightforward manner. Consequently, both experiments are essentially following this approach in most of their analyses,2 although the functional forms used by ATLAS in the spin-0 analysis and by CMS are slightly different. Thus, the signicance of the excess is mostly determined by comparing measured events to a background estimate predicted by a tting function.

While method III is very transparent and makes the search for bumps easy to analyze, it is also rather susceptible to systematic effects, in particular a lack of understanding of the physics modifying the tails of the distributions, as we argue below. The tting functions used by ATLAS and CMS are well suited for describing rapidly falling distributions and are tted to the available data. With the amount of data in the 2015 data sets, the differentially measured number of events is abundant in the low invariant mass region and is spare in the high mass region. The extraction of the functions parameters is thus dominantly controlled by the low m region and hardly affected by modications of the invariant mass distribution at diphoton masses of above roughly 500GeV.However, the signicance of the excess with respect to the tting function is very much affected by such deformations.As it is hard to directly test or predict the correct form of the diphoton mass distribution, this raises the following questions:

I. Is the experimental signal over background estimation robust against the presence of deviations from the tting function predictions at large invariant masses?

II. If this is not the case, can one produce smoking-gun

predictions to show that indeed the signicance of the excess is being overestimated?

Let us rst focus on point I. To examine the sensitivity of

the signicance of the excess to the variation of the tails of

2 An exception is the ATLAS spin-2 analysis which employs a Monte Carlo approach (II) with a data-driven estimate of the photonjet and jet-jet background; see Sect. 4.

the distributions. We consider a family of background shapes that are formed by an admixture of the diphoton and photon jet distributions. We keep the overall inclusive purity of the samples at 90 and 80%, respectively, in accordance with the measured data at low invariant masses. More specically, we use two classes of deformations. The rst is derived from a modication of the photonjet spectrum due to NLO and showering effects combined with an increased fake rate for larger transverse momenta and pseudo-rapidities of the jets.

We then consider a simpler ansatz where we allow the distribution of the pp j component to be reweighted

at invariant masses above 500GeV such that the purity of events with large invariant masses is reduced leading to a controlled deviation from the functional t. In the following section we provide a detailed description of our approach. We also provide some tests of our procedure to check that our method complies with public data (below and above the resonance region) and is passing the relevant statistical tests. We then report how the signicance is affected by the amount of rescaling of the distributions of fakes. Finally we can use our ansatz to address item II and provide smoking guns to

test our hypothesis on overestimating the excess signicance. With the full statistics of the 2016 data sets at hand it would be fairly easy to eliminate our hypothesis.

3 Reducible and irreducible backgrounds

The main background to the diphoton signal is the irreducible pp background. We consider in the follow

ing: ATLAS spin-0 and spin-2, and CMS 13 TeV EBEB and EBEE categories with magnets on. We generate the diphoton invariant mass spectrum at NNLO with MCFM version 8.0 [8,2427] applying the cuts as described in the respective analyses; see Table 1. The main contribution to the reducible background is the pp j production where the hard jet is

a quark jet that is wrongly reconstructed as a photon. We generate this background at leading order (LO) with MadGraph5 version 5.2 [28]. We note that at LO the pp j sample is

dominated by quark jets, which, as already mentioned, lead to a much larger fake rate than gluon jets.

The reconstructed diphoton distribution is a mixture of pp and pp j invariant mass distributions. Let

us dene a short-hand notation for the normalized invariant mass distribution

w X

1 X

d X

dm X , (3.1)

with X = , j. The mixed distribution wmix is a function of

the normalization Nmix and a parameter R, that controls the

shape modication of w j and will be dened Eq. (3.4). We write wmix as

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Table 1 Cuts of the analyses where the subscript refers to the hardest and second hardest photon candidate, the cross section of the pp

sample passing these cuts (calculated at NNLO with MCFM) and of the pp j sample at hadron level (before applying any photon mistag

rate), calculated at NLO with MadGraph5_aMC@NLO, showered with Pythia [29] and the jets clustered with anti-kT , R = 0.4 algorithm using

FastJet [30]. In the last line the ratios of the two distributions in the invariant mass region above 500GeV are given

Analysis ATLAS spin-0 ATLAS spin-2 CMS EBEB CMS EBEE

m >150 GeV >200 GeV >230 GeV >330 GeV pT,1 >0.4 m >55 GeV >75 GeV >75 GeV pT,2 >0.3 m >55 GeV >75 GeV >75 GeV

|1| <2.37 <2.37 <1.44 <1.44

|2| <2.37 <2.37 <1.44 1.57 < 2 < 2.5

|| excluded 1.37 < 1,2 < 1.52 1.37 < 1,2 < 1.52 n.a. n.a. [pb] (NNLO) 2.7 1.9 0.52 0.23 j [pb] (NLO) 1400 1000 250 130 j / m>500 GeV 510 670 470 640

wmix(Nmix) = Nmix

Pw + (1 P)w j

, (3.2)

where P is the inclusive purity of the sample. We set P =

90% (80%) for the ATLAS and CMS EBEB (EBEE) analyses, which is within the reported error bands. We will assume, that w is obtained by normalizing the MCFM diphoton invariant mass distribution. As for w j , following the rationale described in Sect. 2, we modify things in two different ways as we now describe in detail.

3.1 QCD and jet-fake dependence of the diphoton shape

First, we calculate a photonjet mass dependent K-factor using MadGraph5_aMC@NLO, showered and hadronized with Pythia [29] and jets clustered with an anti-kT , R = 0.4

algorithm [31] using FastJet [30]. We note that in the NLO distribution we only consider the hardest jet of the event and we do not record its avor. This step may be potentially improved by the use of an IR-safe jet avor denition, see [1720]. Next, in order to model the dependence of the fake rate on the pseudo rapidity and the transverse momentum we use the following simplied ansatz for the jet rejection r(pT , ):

r(pT , ) = max

r01 + pT /p0T + /0

, (3.3)

where the functional form is motivated by the kinematical dependence of the jet-rejection rates as estimated by ATLAS [22] and the parameter values p0T = 30 GeV, 0 = 4

are chosen to reproduce the rejection rate ratios between the lowest and highest lying and pT bins within uncertainties. Finally, r0/rmin is fairly uncertain as estimates of rejection rates at very high pT and are not publicly available, but reproducing experimental purity estimates in the forward region [2] leads to values in the wide range r0/rmin

[3, 12]. The resulting reweighting factors compared to the

LO partonic m j distribution obtained from MadGraph5, wMGj, at both steps applied successively (wNLOj/wMGj and wNLOfakesj/wMGj) are shown in Fig. 1. We observe that with our choice of fake rate parameters, the largest reweighting factors close to 3 are obtained above m j > 800 GeV for the

ATLAS spin-2 cuts. However, all experimental categories are affected by a reweighting factor which is a combination of NLO, hadronization and faking effects, and which increases with the photonjet invariant mass until it saturates at some point. This suggests a simple functional form for the effective photonjet spectrum deformation which we discuss next.

3.2 Effective shape deformation

In our effective ansatz for the deformation of the photon jet spectrum, we focus on the invariant mass region above m > 500 GeV below which the experiments have sufcient statistics to control the mass distributions and calibrate their analyses and choose a simple, linear form,

w j (R) =

wMGj N(R)

, rmin

,

1 + R

0 m j < 500 GeV

wMGj

m j =500 GeV

wMGj 1 500 GeV m j 760 GeV

wMGj

m j =500 GeV wMGj

m j =760 GeV

1 760 GeV < m j

(3.4)

to roughly account for an overall kinematic dependence of the fake rate, hadronization and higher order effects N(R)

is an R-dependent normalization factor. We dene w j (R)

such that w j (R = 0) corresponds to the partonic LO dis

tribution. Choosing R = 1, the shape of w j is unmodi

ed for m j < 500 GeV, then at up to m j = 760 GeV,

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3.0

Reweightingfactor

4

2.5

Reweightingfactor

3

2.0

NLO

NLO

NLO fakes

spin0

spin2

1.5

NLO fakes

EBEB

EBEE

2

1.0

1

0.5

0

0.0

200 400 600 800 1000 1200

400 600 800 1000 1200

Fig. 1 Reweighting factor for w j with respect to the LO Monte Carlo distribution as a function of the invariant mass for ATLAS (left) and CMS (right). The dashed lines show the reweighting factor to modify

the LO parton distribution wMGj to the NLO shape, including the effects of hadronization. The solid lines include in addition the reweighting due to a phase space dependent fake rate

(a) (b)

Fig. 2 Left Normalized invariant mass distributions after the ATLAS spin-0 cuts for the pp j background with several choices for the

interpolating parameter R. Right Corresponding reweighting factor

just above the observed peak of the apparent excess, and nally it is rescaled by the ratio of the differential cross sections at m j = 500 GeV and m j = 760 GeV for

m j > 760 GeV. The R-dependence of N(R) is chosen

such that the integral over w j is always 1, independent of

the value of R. For the ATLAS spin-2 and the two CMS

analyses, the intervals in the above equation are shifted by10 GeV to larger values due to the different binning in these searches.

In the left panel of Fig. 2, we show the normalized differential pp j cross section for the ATLAS spin-0 analysis

as a function of the invariant mass for several choices of

R. In the right panel, the R-dependent reweighting factor

of Eq. (3.4) is shown. Since the spin-0 analysis applies the strongest cuts on the transverse momenta of the photon candidates (0.4 m and 0.3 m , respectively) its distribution is the steepest. Thus the reweighting factor of this analysis is the largest being almost 7 above 770GeV. The maximal reweighting factors for the other analyses are just above 6.We veried that increasing the at region by 20GeV has only a small impact on the reported results.

In Fig. 3a, c, we show the resulting invariant mass distributions wmix for the ATLAS spin-0 and CMS EBEB analysis,

respectively, on top of the normalized distribution as mea

sured in the 2015 data set.

In addition to the average purity of the full sample, ATLAS and CMS try to estimate the purity as a function of the diphoton invariant mass. This local purity is given by

Pi = P

wi

Pwi + (1 P)wi j

(3.5)

for the ith bin. It can deviate signicantly from the average purity P of the full sample. In Fig. 4, we show the binned

purities for the mixed samples with several choices of R

compared to the purity determined by ATLAS with the 2 2

sideband [32] and the matrix method [33] and by CMS with a method described in [34], respectively. We choose the same binning of the purity as is used in the respective analysis.

While the local purity is within the error band in most of the considered mass range (even for R = 1), it does decrease

for large invariant masses and our ansatz predicts a deviation from the experimental value. Given the low statistics in this range, we consider this as a way to falsify our proposal in the future rather than a contradiction with the currently available data.

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Fig. 3 Top left Combined distributions wmix for the ATLAS spin-0 cuts, all with an overall purity of 90%. The distribution obtained from the 2015 data sets is shown in blue. Bottom left Corresponding distribution for the CMS EBEB analysis. Top right 2 of t to the ATLAS

spin-0 distribution as a function of R. The 1- and 2- regions are indi

cated by the thin lines. Bottom right corresponding plot for the combined CMS EBEB and EBEE analyses

Fig. 4 Purity of the combined distribution as a function of m for several choices of R. The dashed lines show the central value for the purity

as determined by the experiments and shaded the areas show the corresponding error

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4 Statistical treatment

The experimental analyses estimate the background shape by tting a function f (x) with x = m /s to the measured

data. In the ATLAS spin-0 analysis, the following ansatz is used:

f (x) = N

1 x1/3

b

description of the statistical uncertainties; see e.g. [35]. In both t methods, the overow of the experimental histograms is treated as one single bin. The best-t parameters determine the number of expected events Ne in the signal region (SR).

Since we are mostly interested in the local signicance of the 750GeV excess, the SR is chosen by eye from the measured distribution with the aim to capture the excess. We obtain a p-value by comparing the number of measured events in the SR Nm with Ne (more precisely: calculating the

Poisson probability to measure at least Nm events):

p =

n=Nm

x kj=0 a j (log x)j (4.1)

where k = 0 was chosen. For the CMS analyses as well as

the ATLAS spin-2, we use

f (x) = N xa+b log x. (4.2)

Note that the ATLAS spin-2 analysis uses a mixture of Monte Carlo (for the pp background) and data-driven dis

tributions (for the pp j and pp j j background),

leading to similar results as the t function approach. In the data-driven method, the shape of the different backgrounds is obtained by extracting the corresponding events from control samples and tting their distribution with a function. The relative contribution to the observed pp sam

ple is extracted from the data between 200 GeV < m < 500 GeV. For more details on this method see [1]. Given the small statistics in the large invariant mass bins this approach roughly corresponds to our LO MG distribution.

In order to see how the signicance of the 750GeV excess changes with our ansatz, we t the distribution wmix, dened in Eq. (3.2), once with wMGj corresponding to R = 0, and

then with w j as estimated at NLO with showering and hadronization, including fakes and nally with R as a free

t parameter (as well as the appropriate t function f (x)) to the measured data. As an additional template, one could extend the t function f (x) by a modication similar to the one described in Eq. (3.4), which we will, however, not do for the sake of simplicity. The ts are performed with two methods, which yield similar results.

Firstly, we maximize the likelihood

L =

Nbins

Nne n!

eNe. (4.5)

Clearly this simple approach which does not use any signal modeling and relies on a discrete width and position of the SR is far from perfect. Consequently, it is not surprising that the obtained signicances of the excess are smaller than the ones reported by the experiments, even when we use the same t functions. Instead of focusing on absolute values one should therefore rather consider the reduction of the signicance that results from modifying the background. The results of the ts are shown in Table 2.

Finally, an F test is performed to determine if the generalization of our mixed distribution with wMGj to the one with w j (R) given in Eq. (3.4) is needed to describe the data. This

test investigates the improvement of a t when the t function is extended by an additional parameter. For this purpose, a test statistic

F =

(21 22)/(n1 n2)

22/n2

(4.6)

is calculated, where 21,2 are the minimized 2 of the two t functions, n1,2 are the numbers of bins (27 for the ATLAS spin-0) minus the number of input parameters (3 vs. 4 for the tting function and 1 vs. 2 for our distribution), and the subscripts refer to the two t functions with 2 signifying the extended function. Eventually the p-value is determined as

pF-test =

F

e (Nim) (4.3)

where the product goes over all bins and PNe(Nm) is the Poisson probability to measure Nm events when Ne events are expected.

Secondly, we minimize

2 =

Nbins

PNi

[Digamma](x; n1 n2, n2)dx, (4.7)

with [Digamma] being the Fisher distribution. An additional t parameter is warranted if pF-test < 5%; see [1].

We nd that, for the ATLAS searches, the F-test suggests that R should be included as a tting parameter. The probabil

ity of an accidental improvement due to R > 0 is only 2.1%

(ATLAS spin-0) and 0.27% (ATLAS spin-2). On the other hand, the CMS categories do not prefer a signicant nonzero R; see Table 2. Furthermore, as a consistency check,

we apply the F-test on the ATLAS tting function for spin-0, Eq. (4.1), and nd that adding a k = 1 component to the

(Nim Nie)2/Nie (4.4)

where we rebin the data such that each bin contains at least 10 events in order for the 2 distribution to provide a reasonable

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Table 2 Results of the ts to the data of all four analyses. In the rst block from the top the signal region is dened and the number of measured events in this region Nm is given. The results of a likelihood- and a 2 t of the t function (value of the maximal likelihood and minimal 2, respectively, and the local signicance of the 750 GeV excess) are given in the second block. Finally, the third block contains the results of a likelihood and 2 t of the background distributions described in Sect. 3 to the data. When R was tted its best-t value and the corre-

sponding local signicance of the excess are given, otherwise just the signicance. In the last line the result of the F-test, testing whether R

should be used as t parameter, is given. For the minimized 2 the parameter n is the difference of number of bins and t parameters. The errors indicate the 1- interval of the systematic uncertainty of the t.Note that the results of the spin-0 analysis with 3.2 fb1 are based on the analysis with looser photon identication as described in [1]

Analysis ATLAS spin-0 ATLAS spin-2 CMS EBEB CMS EBEE

Measurement

SR 730770GeV 720760GeV 720780GeV 710770GeV 710770GeV

L dt 3.2 fb1 15.4 fb1 3.2 fb1 2.7 fb1 12.9 fb1 2.7 fb1 12.9 fb1

Nm 15 33 40 12 24 21 53

Fitfunction

2 log L 270 330 200 200

3.4 2.9 1.9 1.7

2/n 1.6 0.75 1.2 0.80 1.0 1.2 0.98

3.1+0.20.2 1.2+0.20.2 2.9+0.30.3 1.8+0.30.2 1.5+0.20.3 1.6+0.30.3 1.3+0.20.2

Distribution

R

2 log L 270 360 330 210 310 210 300

R 0.86 0.11 0.97 0.048 0.7 0.24 0.12

2.2 0.0 2.0 1.5 1.2 1.4 0.23

MG

2/n 1.5 0.76 1.3 0.78 1.6 1.1 1.1

3.0+0.00.0 0.2+0.00.0 3.4+0.10.1 1.4+0.10.1 2.6+0.10.1 1.9+0.20.2 0.86+0.140.14 NLO

2/n 1.5 0.76 1.2 0.80 1.6 1.2 1.0

3.0+0.00.0 0.3+0.00.0 3.2+0.10.1 1.4+0.10.1 2.6+0.10.1 1.7+0.20.2 1.2+0.10.1 NLOfakes2/n 1.5 1.4 1.1 0.92 2.0 1.2 1.2

2.7+0.00.0 0.3+0.00.0 2.9+0.10.1 1.2+0.10.1 3.0+0.10.1 1.4+0.20.2 1.7+0.10.1 R

2/n 1.2 0.75 1.0 0.81 1.3 1.1 1.1

R 1.2+0.60.5 0.2+0.20.2 1.1+0.40.4 0.15+0.510.39 0.6+0.20.2 0.30+0.290.22 0.091+0.0840.074 2.0+0.40.4 0.2+0.40.4 1.9+0.50.5 1.5+0.40.4 1.3+0.40.4 1.2+0.40.4 0.40+0.420.42 pF-test 0.021 0.20 0.0027 0.73 0.014 0.19 0.30

function does not pass the test. Hence, as mentioned in [1] only the leading term of the function with k = 0 is retained.

The above in conjunction with the results collected in Table 2 suggest that it is possible that the basis of functions used in Eq. (4.1) is not sufcient to accommodate the deformation of the distribution proposed by us (or at least not the rst term in the functional form).

In the 2 t of the constructed distribution with wMGj we nd similar results for the local signicance as with the 2 t of the functional approach. However, in particular in the two ATLAS analyses, using R as an additional t parameter

reduces the local signicance of the 750GeV excess by 11.5 units. The fact that the reduction is stronger in the spin-2 analysis corroborates our working assumption that the background description deteriorates in the forward region. This is further supported by the observation that in the CMS EBEB analysis, which collects only events with both photon candidates in the central region, no reduction in signicance is observed and the best-t value for R is even slightly neg

ative. Only in the CMS EBEE analysis where one photon candidate is in the forward region the signicance is reduced by tting R, albeit less than in the ATLAS analyses.

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Fig. 5 Upper plots and lower right plot Comparison of the measured and tted distributions with the small and the full data sets. In addition, the pure digamma spectrum as obtained from MCFM is shown. In the upper left plot the comparison is between the smaller Moriond 2016 data set with the old photon isolation method and the full ICHEP

2016 data set. The distributions and functions are normalized to have the same value at the low m end of the histograms.The lower left plot shows the ratios of the normalized t functions fX tted to the ATLAS spin-0 data set X with the year 2015 (2016) in the brackets indicating the old Moriond (updated ICHEP) photon isolation criteria

Since R > 0 attens the distribution one might worry

that the reduction in the local signicance is obtained by overshooting the measured distribution in the high invariant mass region. By verifying that both the minimal 2 and the maximal likelihood hardly change between the functional and the distribution t we show that this is not the case.

As a nal exercise, we try to obtain a combined signicance from the analyses of the 2015 data set. Clearly a proper statistical combination cannot be done, since we neglect correlations between the various analyses and also t for a single universal value of R. Realistically, R is expected to be some

what different for the different analyses since they cover different regions of phase space. Nevertheless, since the naive combination in Eq. (1.1) suffers from similar issues we set them aside and proceed as follows. We sum the 2 of the analyses included in the combination and t for a common

Rwhile keeping the normalizations as separate variables. By combining the two CMS analyses we obtain = 2.4 (1.9)

for wMGj (with w j (R), best-t R = 0.22) and = 1.9

with wNLOfakesj. A combination of the ATLAS analyses is impossible since they are not independent. However, we can combine each of them with the two CMS analyses and obtain for ATLAS spin-0 combined with CMS = 3.6 (2.6

with w j (R), best-t R = 0.46; 3.1 with wNLOfakesj) and

for ATLAS spin-2 combined with CMS = 4.2 (2.8 with

w j (R), best-t R = 0.53; 3.4 with wNLOfakesj), where the

signicance numbers before the brackets are obtained for wMGj.

5 The new energy frontier: searches beyond 1 TeV

Around ICHEP 2016, ATLAS and CMS updated their analyses, now based on 15.4fb1 and 12.9fb1, respectively. In the updated ATLAS spin-0 analysis [3] and the CMS EBEB and EBEE analyses [4] the large excess around 750 GeV vanished and no other signicant excesses were found. An update of the ATLAS spin-2 analysis has not been presented. While CMS processed the data exactly as before, ATLAS made some adjustments, perhaps most importantly, using a tighter photon isolation. We repeat the ts and the statistical treatment of the reported results with the same methods as described above and report the results for the larger data set in Table 2. Note that there is a downwards uctuation in the signal region in the full CMS data set which even leads to a slightly negative signicance.

Comparing the new t functions to the ones based on the previous small data sets presented at Moriond 2016 we nd a steeper functional t in all three analyses; see Fig. 5. While

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Fig. 6 Best-t point of the 2 t of the appropriate function to the Moriond 2016 data set in red with the 1- and 2- contours. The best-t point for the t to the full ICHEP 2016 data set is shown in blue and

in the left plot the best-t point for the ATLAS spin-0 3.2 fb1 data set with the new photon isolation is shown in green

Fig. 7 Plot of the normalized distributions with several choices of R

and normalized t functions to the old and new data sets, all divided by the distribution for R = 0. In the plot for the ATLAS spin-0 analysis

the dashed lines show the results obtained using the old data set with the new photon isolation criteria

the new best-t parameters are within one standard deviation for the two CMS ts, the ones for the ATLAS t deviate by almost two standard deviations after marginalizing over the normalization; see Fig. 6. This might, however, be an effect of the changed photon isolation as the t to the 3.2 fb1 data set with the updated photon identication also deviates by more than one standard deviation from the previous best-t point. A better understanding of the effect of the fake photons could be obtained by investigating the result of changing the isolation criteria with the full 15.4 fb1 data set. The tighter isolation criteria are also reected in the better agreement between the tted distributions and the MCFM generated digamma spectrum.

In order to show the changes in the ts, the ratio of the normalized t functions for the ATLAS spin-0 analysis is shown in the lower left plot of Fig. 5. A direct comparison of the data and the un-normalized t functions, even for the ts to the two different 3.2 fb1 sets, is difcult since the binning of data has changed. The large change in the t parameters is reected in the deviation of more than 5% for the comparison of the ts to the two 3.2 fb1 data sets and the even greater deviation compared with the t function to the full 15.4 fb1 data set. While in the previous signal region near 750GeV the change is of the order of 10% it is greater than 30% near1.6TeV. This shows that the actual shape of the digamma spectrum at high invariant masses is hard to predict precisely

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by an extrapolation and is therefore very much subject to systematic uncertainties.

Finally in Fig. 7 the ratios of several normalized distributions and t functions to the normalized distribution with

R = 0 are shown. These include the distributions with the

best-t value for R based on the Moriond 2016 data set and

the ICHEP 2016 data set and also the NLO distributions and the t functions to the old and new data sets. In the case of the ATLAS spin-0 analysis also the distribution and t function to the 2015 data set with the new photon isolation is shown.By comparing the curves we nd that a sizable systematic uncertainty can be inferred from the differences between the t functions.

6 Conclusions

This paper deals with a problem that often arises in searches for new physics at the energy frontier. In this context the challenge is to look for a new resonance at the upper end of a distribution where only limited knowledge on the SM background is available. As a case study we focus on the 750GeV anomaly where we examine in particular the implications of the possibility that the excess in the 2015 data set is not only due to a (malicious) statistical uctuation but also a result of a physical effect. We discuss possible issues with the background: how much photonjet contamination is still allowed in the region of interest? How could it affect the signicance of the excess?

We study these questions using currently available theoretical tools for computing the photonjet mass distributions and apply them to the small set of publicly available data. However, this approach is limited by our ability to thoroughly disentangle the effects of the (pT , )-dependent jet-fake rate and the theoretical uncertainty of the shape of the photonjets background. We therefore choose to model these combined effects by an m j dependent reweighting of the invariant mass distribution, keeping the overall purity within the quoted ranges. We rst study a physics-driven reweighting procedure: we convolve a mass dependent K-factor with a rapidity and transverse momentum dependent photon fake rate for the jets. The K-factor is extracted comparing the NLO leading-jetphoton to the LO quarkphoton spectrum, and the phase space dependence of the fake rate is estimated from the experimental literature [22]. Both correction factors are approximate, based on incomplete information, and should be taken with a grain of salt. Motivated by this result, we then consider a more phenomenological deformation of the pp j spectrum. It allows us to study

the sensitivity of the signicances on a single continuous quantity R (see Eq. (3.4)) which parametrizes an effective

deformation.

To summarize our results for the 750GeV case study based on the 2015 data we focus on the simpler effective ansatz where we nd the following:

For the ATLAS spin-0 analysis, the signicance of the

excess can be reduced by 1.1 when comparing

the tting function dened in (4.1) with our best t to the R-modied distribution. A comparable reduction is

found for the ATLAS spin-2 measurement. Here however, it is less straightforward to determine the reduction, since the estimation of the background shape in our ansatz differs from that of the ATLAS analysis, which is not reproducible since the required data is not publicly available. Strictly speaking, wMGj does therefore not correspond to the ATLAS approach but is the best approximation we can get. Since, however, ATLAS claims to nd comparable results with the corresponding tting function dened in (4.2), we can reduce the signicance with the R-modied distribution with respect to the t

ting function by 1.0 as well as with respect to the

distribution with wMGj by 1.5.

The effect is smaller for the CMS 13TeV analyses with

0.3 0.4, depending on the category. In a combined t to independent ATLAS and CMS

data sets, the signicance can be reduced by as much as 1.0 (1.4) for the ATLAS spin-0 (spin-2) combined

with CMS.

The larger preference for an enhanced photonjet contribution in the spin-2 sample could point to its higher sensitivity to the large rapidity region where jet fakes are more difcult to reject. Finally, an F-test shows that the ATLAS data support using a more complex distribution.

To summarize our results for the 750GeV case study based on the 2016 data we nd the following:

For the ATLAS spin-0 analysis, we nd that the new

data prefers R in the range 0.2 0.2, eliminating the

remaining signicance of 1.2 in the full data set. As for the spin-2 case no data is currently available.

The updated CMS analyses based on 12.9 fb1 even have

a downwards uctuation with respect to the t function near 750GeV leading to negative signicances. Correspondingly the best-t values for R are negative and

ameliorate the situation.

We emphasize that our simplied ansatz for the effective modication of the photonjet background with R is not

meant to necessarily represent a new background source nor the exact shape of the background contamination in the signal region. Rather its envelope (corresponding to the shaded area in Fig. 2a) is expected to reect a possible combination of higher order QCD contributions, fragmentation, isolation and

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detector effects, which are outside of theoretical control and, in the high invariant mass signal region, also beyond direct experimental probes with currently available data. We further note that a quark avor tagged dijet sample might provide a high-statistics measurement of the relevant photon fake rates (see for instance [36]).

We have also employed our analysis to compare the difference between the tting functions used by ATLAS (with the new isolation criteria) given the 2015 and 2016 data sets.The tting functions where extrapolated to invariant masses beyond the TeV region. In summary we have found that:

A variation of about 30% in the extrapolated background

near m = 1.6 TeV is obtained.

To conclude, we have extensively examined the status of LHC diphoton searches. We have compared the analyses performed on both 2015 and 2016 data sets in order to scrutinize the current state of the art measurements for systematic effects. Using our approach we have reevaluated the current experimental sensitivity to beyond standard model physics, especially in the tails of the diphoton invariant mass distributions, beyond the TeV range. We found that the extrapolation of background shapes is subject to sizable uncertainties, potentially affecting the signicance of possible future excesses near the edge of the measured distributions. Furthermore, our analysis motivates further Monte Carlo studies of the dominant diphoton backgrounds, based on jet avor tagging algorithms. Knowledge of whether a jet is of quark or gluon origin would improve our estimation for the jet-photon faking backgrounds to next-to-leading order QCD accuracy. It is important to note that diphoton-based searches at even larger invariant masses, which are highly motivated, are being performed at present and will continue to be an integral part of the LHC experimental physics program at the high energy frontier.

Acknowledgements We would like to thank Rikkert Frederix for useful discussions. J.F.K. would like to thank CERN for hospitality while this work was being completed and acknowledges the nancial support from the Slovenian Research Agency (research core funding No. P1-0035). The work of GP is supported by grants from the BSF, ISF and ERC and the Weizmann-UK Making Connections Programme. AW is supported by the DFG cluster of excellence Origin and Structure of the Universe and the European Commission (AMVA4NewPhysics, 2020-MSCA-ITN-2015).

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

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Web End =ons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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