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Published for SISSA by Springer

Received: March 21, 2016

Accepted: May 2, 2016 Published: May 23, 2016

J er emy Bernon,a Andreas Goudelis,b Sabine Kraml,a Kentarou Mawataria,c and Dipan Senguptaa

aLaboratoire de Physique Subatomique et de Cosmologie, Universit e Grenoble-Alpes, CNRS/IN2P3,53 Avenue des Martyrs, Grenoble, F-38026 France

bInstitute of High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, Vienna, 1050 Austria

cTheoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel, and International Solvay Institutes, Pleinlaan 2, Brussels, B-1050 Belgium

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: We study kinematic distributions that may help characterise the recently ob-served excess in diphoton events at 750 GeV at the LHC Run 2. Several scenarios are considered, including spin-0 and spin-2 750 GeV resonances that decay directly into photon pairs as well as heavier parent resonances that undergo three-body or cascade decays. We nd that combinations of the distributions of the diphoton system and the leading photon can distinguish the topology and mass spectra of the di erent scenarios, while patterns of QCD radiation can help di erentiate the production mechanisms. Moreover, missing energy is a powerful discriminator for the heavy parent scenarios if they involve (e ectively) invisible particles. While our study concentrates on the current excess at 750 GeV, the analysis is general and can also be useful for characterising other potential diphoton signals in the future.

Keywords: Phenomenological Models, Phenomenology of Field Theories in Higher Dimensions

ArXiv ePrint: 1603.03421

Open Access, c

[circlecopyrt] The Authors.

Article funded by SCOAP3. doi:http://dx.doi.org/10.1007/JHEP05(2016)128

Web End =10.1007/JHEP05(2016)128

Characterising the 750 GeV diphoton excess

JHEP05(2016)128

Contents

1 Introduction 1

2 Scenarios for the 750 GeV diphoton excess 32.1 750 GeV resonance 42.2 Heavier parent resonance 5

3 Event simulations 7

4 Results 84.1 750 GeV resonance 84.2 Heavier parent resonance 11

5 Conclusions 12

A Sequential resonance with S1 = S2 14

B Mass and width e ects for the antler topology 15

1 Introduction

The excess in the diphoton invariant mass spectrum around 750 GeV observed by ATLAS [1] and CMS [2] in the rst LHC Run 2 data led to a sheer ood of theory papers trying to explain the alleged signal.1 The interpretations put forward span a wide spectrum, including extra Higgs bosons, axions, sgoldstinos, radions, gravitons, hidden glue-balls, hidden- or techni-pions and so on. Typically, the existence of additional new particles and/or new (strong) dynamics is invoked, in order to account for the increase in cross section from ps = 8 to 13 TeV and to evade the often stringent bounds from null results in dijets, monojets and other search channels both at ps = 8 and 13 TeV. The rst theory papers discussing various ways to reproduce the observed diphoton rate as well as possibly a large width while avoiding existing constraints from Run 1 appeared on the arXiv already on the day after the announcement of the excess [4{11]. More than 200 papers followed to date.

Whatever one may think of this \ambulance chasing" [12], an interesting question that arises is how to experimentally di erentiate between this variety of possible interpretations. Needless to say this question will be of imminent importance should the observed excess turn into a discovery with the accumulation of more data. One approach consists of observing the new state in di erent decay modes, as the predictions for the (ratios of) rates

1The ATLAS excess consists of 14 events in 3.2 fb1 of data; it has a local (global) signi cance of 3.6 (2.0 ) and seems to favour a large width of about 45 GeV (see however [3]). The CMS excess consists of 10 events in 2.6 fb1 of data; it has a local (global) signi cance of 2.6 (1.2 ) and is consistent with a narrow width.

{ 1 {

JHEP05(2016)128

of speci c nal states vary between di erent concrete models. Another, complementary approach is to rely on the diphoton signal itself and attempt its detailed characterisation in terms of kinematic distributions. As a preparatory step in the latter direction, in this paper we study the expectations for di erential distributions from various signal hypotheses and discuss ways to discriminate between them. We note in passing that both approaches | inclusive measurements in di erent nal states and kinematic distributions | have been pursued successfully to scrutinise the 125 GeV Higgs signal in Run 1 [13{25].

Irrespective of the underlying model, the interpretations put forward generically fall in just a few classes. First, if we are dealing with a new particle with mass of 750 GeV which undergoes a two-body decay into two photons, the classi cation is by spin and production mechanism. The most straightforward option is a 750 GeV spin-0 (singlet scalar or pseudoscalar) particle produced in gluon fusion and decaying to photons e.g. via loops of new vector-like quarks. Bottom-quark (b b) initiated production could also provide the necessary increase in cross section from ps = 8 to 13 TeV of about a factor ve [10]. If it has electroweak couplings, a scalar resonance can also be produced in vector boson fusion and vector-boson associated production. Photon-initiated production has also been discussed [26{29].

Another option is a spin-2 resonance, like the Kaluza-Klein (KK) graviton in Randall-Sundrum (RS)-type models [30], which might be produced from gg or q

q initial states.

A spin-1 particle would not decay into photons,2 and higher spins are not considered because they are disfavoured theoretically. In order to explain a large width, as seemingly favoured by ATLAS, the resonance should couple not only to gluons and photons (and perhaps quarks) but also to non-standard states such as dark matter or light hidden-valley particles. Invisible decays are, however, fairly constrained (although not excluded) by the8 TeV mono-X searches as discussed e.g. in [33].

Alternatively, the new particle can be (much) heavier than 750 GeV and undergo a three-body [34, 35] or a cascade decay [10, 36{41] into two photons along with one or more light new particle(s). These light new particles would then need to be soft or invisible so as to avoid detection. Such a scenario could \naturally" explain the apparent broadness of the diphoton invariant mass peak, as well as soften the tension with the 8 TeV data. Note that in this case the new states can in principle be scalars, vectors or fermions.

Kinematic distributions for characterising the 750 GeV diphoton excess have been considered previously in the literature. For example, [42] discussed gg versus q

q initiated

production of a spin-0 resonance, while [28, 43{45] discussed kinematic distributions arising from spin-2 resonances (in part comparing them to the spin-0 case). Reference [28] also discussed how to di erentiate gluon- from photon-induced production for both spin-0 and spin-2 particles, while the authors of [46] performed a spin-parity analysis for photo-production including PDF uncertainties. For the case of a heavier parent resonance, [38] considered EmissT and E distributions for various cascade-decay topologies.

2See however [31] for a scenario where a vector resonance decays to a photon and a light scalar, followed by a decay of the scalar into two highly collimated photons, Z[prime] ! + s ! 3 , which might appear as a

diphoton nal state. A 750 GeV vector resonance is also considered in [32], where the resonance decays into a photon and a massive dark photon, V (750) ! [prime], followed by a displaced dark photon decay [prime] ! e+e

which can be misidenti ed as a photon.

{ 2 {

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In this work we study the kinematic distributions arising from 750 GeV spin-0 and spin-2 resonances and compare them to those obtained from the production of heavier parent particle(s) that undergo two- or three-body decays. We go beyond the previous investigations listed above by analysing a consistent set of kinematic distributions for all these di erent cases. Moreover, we employ more realistic simulations including initial-state QCD radiation and parton shower matching.

We note that the results of our analysis hold regardless of the fate of the 750 GeV diphoton excess and should provide useful guidelines for the discrimination of other potential diphoton excesses that could appear during the 13 TeV LHC Run.

The paper is organised as follows: in section 2 we brie y present the scenarios we will consider and our choices for the parametrisation of the relevant interactions. Section 3 describes the computational tools we employ for our analysis as well as some important technical features. Our main results on the kinematic distributions that could be used to discriminate among di erent explanations of the diphoton signal are presented in section 4. We conclude in section 5. Appendices A and B contain supplementary considerations on two of the heavy parent scenarios discussed in the main part of the paper.

2 Scenarios for the 750 GeV diphoton excess

As brie y discussed in the Introduction, the various scenarios for the diphoton excess can be quite generically classi ed according to the number and the nature of the nal state particles as well as according to the initial state producing them in the rst place. A full survey of all types of models that have been proposed in the literature is not the scope of our study. Instead, our approach is mostly driven by the di erent types of topologies that could generate the excess at 750 GeV.

Even so, a choice is to be made for the parametrisation of the relevant interactions. It has already been argued that the relatively large, O(5{10) fb, cross section seemingly

favoured by the ATLAS and CMS data [47] would either require fairly light weakly coupled new physics, mostly likely in tension with observations, or might be pointing towards some type of strong dynamics or to some relatively singular threshold e ect [48, 49]. In this case, a complete description of the underlying physics is likely to involve some momentum-dependent form factors the form of which depends on the speci c setup being invoked.

A simpler approach, yet powerful enough to capture the main e ects of interest for our work, is to parametrise the couplings of the new state(s) to the SM ones in terms of e ective operators suppressed by appropriate powers of some e ective eld theory (EFT) scale .3 Note that the scale does not correspond to the cuto scale of the theory: the two are rather typically related to each other, but the relation depends on the speci c UV-completion. We also note that in everything that follows we will ignore Lagrangian terms that are not directly relevant to our analysis, whereas we will remain agnostic to whether the new states introduced in the e ective Lagrangian description are fundamental or composite.

3A discussion and motivation can be found, e.g. in the introduction of [50].

{ 3 {

JHEP05(2016)128

Figure 1. Diagrams of the 750 GeV resonance scenario for spin-0 (left) and spin-2 (right).

2.1 750 GeV resonance

The simplest way to accommodate the 750 GeV diphoton excess is by invoking a particle Xs with a mass of 750 GeV that decays into a pair of photons.4 The Landau-Yang theorem [52, 53] then guarantees that Xs can be a spin-0 particle X0 or a spin-2 particle X2. In either case it can be produced via gluon, q

q, photon or vector boson fusion, or in association with a vector boson or a pair of top quarks.

Out of these cases, we consider gg and b b production of a spin-0 resonance, and gg and q

q production of a spin-2 one, as depicted in gure 1. Note that gg and b b production are particularly interesting because they yield the highest gain in parton luminosities when going from ps = 8 to 13 TeV, being enhanced by factors of 4.7 and 5.4 respectively as

opposed to valence quarks for which the corresponding factors are of the order of 2.5 [10]. Similarly, in the case of vector boson fusion, naively assuming that the parton luminosities scale with the quark ones, one expects an enhancement of roughly a factor 2.7, well below the corresponding values for b quarks and gluons. Besides, in the spin-0 case, if the new state is somehow involved in electroweak symmetry breaking, it is expected to couple to the SM fermions proportionally to their mass and should, hence, interact more with the third generation than with light- avor quarks. For a spin-2 resonance, the prime example is the KK graviton, which has universal couplings to gluons and quarks. We thus consider gg and q

q production for the spin-2 case.

Spin-0. In the spin-0 case, gluon fusion production followed by decay into a pair of photons can be parametrized by the e ective Lagrangian

Lg0 =

1 4

JHEP05(2016)128

X0 , (2.1)

where Ga and A are the SU(3)C and U(1)EM eld strength tensors respectively,a =

2 [epsilon1] Ga, and[notdef] = 12[epsilon1] A are their duals, and

()

g and

()

g Ga ()

G a, +()

A ()A

are the CP-even (odd) couplings of X0 to gluons and photons. This Lagrangian leads to gg ! X0 ! /gg at

the leading order (LO).

To study the case of X0 production from b b annihilation, we write an e ective Lagragian as

Lb0 =

()

b b(i 5)bX0 + 1

()

A X0 , (2.2)

4For the reader who wants to dive into a plethora of realizations within concrete models, [51] provides an extensive overview together with the actual model implementations.

{ 4 {

where

stood as

X 2 , (2.3)

where X 2 is the spin-2 resonance and T g,q, are the energy-momentum tensors; see the explicit formulae, e.g., in [55, 56]. While conventional graviton excitations have a universal coupling strength 1, we adopt a more general parametrisation by introducing the coupling parameters g, q and without assuming any speci c UV model [57, 58]. We consider three cases:

R q/ g = [notdef]0.1, 1, 10[notdef] , (2.4) corresponding to the gluon-dominant, universal coupling, and quark-dominant scenarios, respectively. These scenarios amount to 99%, 87% and 7% gluon fusion contributions to the total 750 GeV spin-2 resonance production cross section at the 13 TeV LHC respectively [44].

2.2 Heavier parent resonance

Another way to induce a peak in the diphoton invariant mass distribution is by invoking more complicated decays or decay chains of a heavier parent particle, leading to three (or more)-body nal states. In this case, one can envisage a number of di erent topologies. In our study, we consider the following possibilities:

I) A process of the type pp ! S3 ! S2 + S1, S2 ! with S1 being invisible or leading

to soft decay products. Such a scenario could e.g. be motivated by considering dark matter or \hidden valley" [59] models. In principle S3 can be a fundamental scalar or vector [10] or a composite particle (Q

Q bound state) [4].

II) A 3-body decay scenario with single production of the heavier resonance: pp ! S3 ! S1 [34], where S1 is again invisible or decays softly. This scenario is equivalent to the previous one in the limit that S2 is heavy (virtual).

III) A 3-body decay scenario as above but with associated production of S3 and S1: pp ! S3S1, S3 ! S1 [34]. Such a scenario has the advantage of allowing for the

{ 5 {

()

b parametrises the CP-even (odd) coupling of the X0 to a pair of b-quarks. This Lagrangian leads to b b ! X0 ! /b

()

b should generically be under-

b. The coe cients

b cbmb/ where the value of cb/ can vary from one model to another. As

an example, if X0 is taken to be the (heavy) pseudoscalar of a type-II two Higgs doublet model, one would expect v = 246 GeV and cb tan (although in this case one

should also include the corresponding coupling to the top quark with ct cot , which

would contribute to gluon-induced production).

Spin-2. As an alternative possibility, we also consider a massive spin-2 particle which couples to the SM gauge and matter elds through their energy-momentum tensors [54, 55]. As argued above, we only consider the interactions with gluons, light quarks and photons [44]:

L2 =

()

JHEP05(2016)128

g T g + q T q + T

~ ~

Figure 2. Diagrams for the heavier resonance scenarios I{IV.

existence of a new conserved quantum number under which S1 and S3 are charged, and which would stabilize S1, the lightest state of the new sector.

IV) The \antler" topology from a process of the type pp ! S3 ! [notdef]2[notdef]2, [notdef]2 ! [notdef]1 + as proposed in [38].5 While it is rather di cult to envisage a realistic scenario, this topology is reminiscent of general gauge-mediated supersymmetry breaking scenarios [60] with a su ciently short-lived neutralino NLSP, see e.g. [61].

For concreteness, we concentrate on gluon-initiated production of a CP-even spin-0 parent resonance. The relevant diagrams are shown in gure 2. These scenarios can be described by the Lagrangians

LgH =Xi,j=1,2,3

[bracketleftbigg]

1 4 ggSiGa Ga, Si +

14 2 ggSSijGa Ga, SiSj[bracketrightbigg]

, (2.5)

JHEP05(2016)128

LS,~H =

Xi,j,k=1,2,3

Xl,m=1,2

h SSSijkm3SiSjSk + S~~ilmSi

[notdef]l[notdef]m[bracketrightBig]

, (2.6)

L H =

Xi,j=1,2,3

1 4 SiA A Si +

14 2 SSijA A SiSj

+ 1

~~ij (A

[notdef]l [notdef]m + h.c.)

Xl,m=1,2

[bracketleftbigg]

[bracketrightbigg]

, (2.7)

where in the last (magnetic-type) operator, = i

2 [ , ]. The couplings relevant for each of the scenarios I{IV are summarised in table 1, together with the mass combinations that we consider as benchmarks. For simplicity, and regardless of naturalness arguments, all other couplings are taken to be zero throughout the subsequent analyses.

In [36] a scenario similar to our scenario I was considered, namely production of a heavier (pseudo)scalar resonance which decays into a pair of new pseudoscalars with mass of 750 GeV, which decay further into photons. This would correspond to scenario I with m2 = m1 and is discussed in appendix A.

For the antler topology, scenario IV, we note that one has to nely adjust the masses of S3 and [notdef]2, and even more so their decay widths, in order to obtain the desired diphoton invariant mass spectrum. For our simulations, we use (S3) = 0.1 and ([notdef]2) = 0.05 GeV for the antler topology. The sensitivity on the masses and widths will be commented upon

5Note that in this scenario we take the ~is to be fermions, as the scalar case cannot be rendered gauge invariant at the leading operator order unless ~1,2 are mass degenerate.

{ 6 {

scenarios relevant couplings m3 m2 m1

I Sequential resonance ggS3, SSS321, S2 1200/1200 750/750 440/40

II 3-body decay (single) ggS3, SS31 900/1800 heavy 43/977

III 3-body decay (assoc.) ggSS31, SS31 900/1800 heavy 43/977

IV Antler ggS3, S~~322, ~~21 1700/1600 849/798 175/10

Table 1. Coupling assignments and benchmark mass combinations for scenarios I{IV; single and assoc. mean single and associated production as illustrated by the second and third diagram of gure 2, respectively.

in appendix B. For scenarios I{III, we use (S3) = 10 GeV, which does not signi cantly a ect the relevant distributions.

We note that these cases do by no means exhaust all the possibilities for reproducing the 750 GeV excess. For instance, we do not consider scenarios with very light states decaying into pairs of highly boosted photons which would be misidenti ed as individual photons. Examples for this are pp ! Z[prime] ! s ! 3 [31] or pp ! S ! aa, a ! [7, 62{67].

Exhausting all these possibilities is beyond the scope of this work.

3 Event simulations

While we employ the Higgs Characterisation (HC) [50] model for the 750 GeV resonance scenarios,6 we implemented the Lagrangians for heavier parent resonances in Feyn-Rules [69] to generate the model les which can be interfaced [70, 71] to event generators.

We generate inclusive signal samples by using the tree-level matrix-element plus parton-shower (ME+PS) merging procedure. In practice, we make use of the shower-kT scheme [72], implemeted in MadGraph5 aMC@NLO [73] with Pythia6 [74], and generate signal events with parton multiplicity from zero to two, e.g. pp ! X0,2 + 0, 1, 2 partons. The merging separation parameter is set to Qcut = 200 GeV for the 750 GeV

resonance scenarios and to Qcut = 200, 250, 300 GeV for the heavier parent scenarios with

m3 = 900, 1200, 1600{1800 GeV, respectively. Hadron-level events are analyzed in Mad-Analysis5 [75], where we de ne jets by using the anti-kT algorithm [76] as implemented in FastJet [77] with the jet cone radius R = 0.5.

At the analysis level, we require for the transverse momentum pT and pseudorapidity of the photons and jets

pT ( ) > 25 GeV , [notdef] ( )[notdef] < 2.5 , (3.1)

pT (j) > 25 GeV , [notdef] (j)[notdef] < 5 (3.2) respectively. Moreover, we assume 100% reconstruction e ciency for photons and, when relevant, for b-jets. This is justi ed because we are only comparing shapes of distributions,

6The model le is publicly available at the FeynRules repository [68]. Although the HC model is designed to study the spin-parity nature of the 125 GeV Higgs boson, one can easily change its mass mX0,2

as a parameter.

{ 7 {

JHEP05(2016)128

0.12

Spin-0 (gg):

= 45 GeV

= 1 GeV

Spin-0 (gg):

0.1

0.08

0.06

0.04

0.02

0 0 100 200 300 400 500 600 700 800

(

) [GeV]

0.12

Spin-0 (gg):

= 45 GeV

= 1 GeV

Spin-0 (gg):

0.1

0.08

0.06

0.04

0.02

0 0 100 200 300 400 500 600 700 800

(

) [GeV]

Figure 3. Normalised transverse momentum distributions of the leading and subleading photons, pT ( 1) (left) and pT ( 2) (right), for diphoton events produced from a gluon-induced 750 GeV spin-0 resonance at the 13 TeV LHC, comparing the narrow resonance ( = 1 GeV) and the broad resonance ( = 45 GeV) cases.

not overall rates. The mild pT and dependence of the e ciencies can be neglected for

our purpose.

4 Results

4.1 750 GeV resonance

We begin by considering the e ect of a narrow vs. broad nature of a 750 GeV resonance on kinematic distributions. It turns out that there is very little sensitivity to the width, the largest e ect occurring for the transverse momentum distributions of the photons illustrated in gure 3 for the case of a 750 GeV spin-0 resonance. In particular, for the leading photon pT ( 1) is more peaked for a smaller width. An analogous behaviour is observed for the second photon, where for a narrow width, the pT ( 2) distribution has a sharp cut-o near mX0/2 = 375 GeV, while for a broad width there is a larger tail towards higher pT values. All other distributions that we will consider, including the transverse momentum of the diphoton system, pT ( 1 2), show very little sensitivity to the width. The picture is essentially the same for a spin-2 resonance. In the following we will therefore consider only the = 45 GeV case for 750 GeV resonances and contrast it to the distributions obtained for heavier parents.

Next, gure 4 compares transverse momentum and pseudo-rapidity distributions of the diphoton system and the leading jet and photon as well as rapidity separation ( ) distributions of jets and photons for a spin-0 resonance produced in either gg (red lines) or b b (blue lines) fusion. The blue dashed lines depict the case of associated production with a b b pair, pp ! X0b

JHEP05(2016)128

b with 2 b-tagged jets. We also show the number of jets N(j) (or b-jets N(b)). We observe that QCD radiation leads to a rather hard pT spectrum of the diphoton system, which is zero at the LO, especially in the gg fusion production case. Moreover, a gluon-induced diphoton resonance tends to be produced more towards the central region than a b b one and involves a higher jet activity. The distinction between gg and b b initiated production can be further enhanced by requiring 2 b-tagged jets, which

{ 8 {

0.12

0.1

Spin-0 (gg) )

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

0.08

0.06

0.04

0.02

0 6

0 2 4 6 8

(

)

0.2

Spin-0 (gg) )

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

10 0 100 200 300 400 500 600 700 800

(

) [GeV]

Spin-0 (gg) )

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

0.15

0.1

0.05

0 -8 -6 -4 -2 0 2 4 6 8

(

)

0.15

Spin-0 (gg) )

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

0.1

0.05

0 4

0 1 2 3 4 5

)

0.12

Spin-0 (gg) )

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

0.1

0.08

0.06

0.04

0.02

0 6

0 2 4 6 8

, j

)

Spin-0 (gg) )

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

10 0 100 200 300 400 500 600 700 800

) [GeV]

JHEP05(2016)128

0.5

Spin-0 (gg)

)

Spin-0 (b

): N(b)

Spin-0 (b

0.4

0.3

0.2

0.1

0 0 1 2 3 4 5 6 7 8

N (j)

0.25

Spin-0 (gg)

)

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

0.2

0.15

0.1

0.05

0 4

0 1 2 3 4 5

(

)

Spin-0 (gg)

)

Spin-0 (b

) w/ 2 b-jets

Spin-0 (b

10 0 100 200 300 400 500 600 700 800 900 1000

(

) [GeV]

Figure 4. Normalised distributions in pT and of the diphoton system and the leading jet and photon as well as in of the photons and jets for the 750 GeV spin-0 scenario at the 13 TeV LHC. The number of (b-)jets is also presented. The gluon-induced and b-quark-induced cases are shown by red and blue solid lines, respectively. The diphoton events with two b-jets for the b-induced case are also shown by blue dashed lines.

changes the distributions for the b b case in a distinct way (for gg production most events would be rejected). It is clear that the extra jet activity a ects the higher tail of the pT of

the leading photon. The dependence of transverse momentum and rapidity distributions on the gg and di erent avour q

q initial states was discussed in detail in [42].

The distributions in gure 4 are insensitive to the CP nature of X0. To distinguish a

CP-even from a CP-odd X0 from the diphoton nal state, one would need to exploit the azimuthal angle correlation of extra jets in 2 +2 jets events with a vector boson fusion-like cut on m(jj) and/or (j, j), analogous to Higgs studies [58, 78{81]. This is illustrated in gure 5 but will require high luminosity to be potentially measurable. We note that a heavier X0 leads to a smaller jj oscillation [81], i.e. for the 750 GeV case it will be more di cult to measure CP e ects than for the 125 GeV Higgs.

Let us now turn to the spin-2 case. As pointed out in [50], and depicted in gure 6, the non-universal coupling scenario (R q/ g [negationslash]= 1) gives rise to a unitarity-violating

behaviour at higher order in QCD.7 To avoid such behaviours, or to show results with

7We note that, unlike the R = 10 (quark-dominant) case, the distributions for R = 0.1 (gluon-dominant) is very similar to the R = 1 case since the gluon-initiated process is dominant for the universal coupling case, as mentioned before.

{ 9 {

0.1

0.08

0.06

0.04

0.02

Spin-0 (gg): CP-even

Spin-0 (gg): CP-odd

0 0 0.5 1 1.5 2 2.5 3

)

, j

JHEP05(2016)128

Figure 5. Normalised distribution of the azimuthal angle between the two tagging jets in X0+2 jets events for the CP-even (red) and -odd (blue) X0 cases, requiring [notdef] (j1, j2)[notdef] > 4.

) [GeV]

0.1

0.08

Spin-0 (gg)

Spin-2 : R = 1 Spin-2 : R = 10

0.06

0.04

0.02

0 6

0 2 4 6 8

(

)

Spin-0 (gg)

Spin-2 : R = 1 Spin-2 : R = 10

Spin-0 (gg)

Spin-2 : R = 1 Spin-2 : R = 10

10 0 100 200 300 400 500 600 700 800

) [GeV]

10 0 100 200 300 400 500 600

(

Figure 6. Normalised distributions in pT ( 1 2), ( 1 2) and pT (j1) for the 750 GeV spin-2 scenario at the 13 TeV LHC. The red and green lines show the R = 1 and 10 cases, respectively. For reference, the gluon-initiated spin-0 case is shown as black dashed line. Note the unitarity-violating behaviour for the R = 10 case.

respect to any UV completion of the spin-2 model, in the following spin-2 analysis we require the tagging jets to ful ll [58]

pT (j) < pmaxT(j) = 200 GeV . (4.1)

In gure 7 we present the same set of distributions as in gure 4 for the case of a spin-2 resonance with mass of 750 GeV (and width of 45 GeV). Here, we compare R = 1 (red), 0.1 (blue) and 10 (green). The gluon-initiated spin-0 case is also shown by black dotted lines as a reference, for easier comparison with gure 4. Note that here we require the above pmaxT(j) cut even for the spin-0 case in order to perform a meaningful comparison. We see that while q

q dominated production di ers from gg dominated production in several of the distributions, most notably the jet activity, distinction of the gg initiated spin-0 and spin-2 cases is less obvious. This was also observed for the case of the 125 GeV Higgs characterisation in [50]. There are, however, some di erences in the heavy resonance decay; indeed most promising for di erentiating spin-0 from spin-2 are the rapidity separation between the two photons, ( 1, 2), and to some extent the leading photon pT and

distributions [43, 44], simply due to the di erent decay distributions between the spin-0 and spin-2 resonances.

{ 10 {

0.12

0.2

Spin-0 (gg)

Spin-2 : R = 1 Spin-2 : R = 0.1 Spin-2 : R = 10

0.15

0.1

0.05

0 6

0 2 4 6 8

(

)

Spin-0 (gg)

Spin-2 : R = 1 Spin-2 : R = 0.1 Spin-2 : R = 10

Spin-0 (gg)

Spin-2 : R = 1 Spin-2 : R = 0.1 Spin-2 : R = 10

0.1

0.08

0.06

0.04

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10 0 50 100 150 200 250 300 350 400 450 500

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(

) [GeV]

(

)

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Spin-2 : R = 1 Spin-2 : R = 0.1 Spin-2 : R = 10

0.1

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0 1 2 3 4 5

)

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Spin-2 : R = 1 Spin-2 : R = 0.1 Spin-2 : R = 10

10 0 50 100 150 200 250

) [GeV]

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0.1

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, j

)

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0.3

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0.15

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)

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10 0 100 200 300 400 500 600 700 800 900 1000

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) [GeV]

Figure 7. Normalised distributions in pT and of the diphoton system and the leading jet and photon as well as in of the photons and jets for the 750 GeV spin-2 scenario at the 13 TeV LHC. The red, blue and green lines show the R = 1, 0.1 and 10 cases, respectively. For reference, the gluon-initiated spin-0 case is shown as black dashed line. A cut of pT (j) < 200 GeV is imposed as explained in the text.

4.2 Heavier parent resonance

We next contrast the above results to the di erent cases of a heavier parent resonance described in section 2.2. To begin with, we show in gure 8 (left) the diphoton invariant mass distributions for the di erent benchmark scenarios from table 1. We see that with a precise lineshape analysis one should be able to discriminate the three-body decay and antler scenarios (II{IV) from the cases where the two photons originate from a two-body decay of a 750 GeV particle. Even for the diphoton coming from the 750 GeV resonance (with a 45 GeV width) in scenario I, the lineshape can di er from the one for direct resonance production (black dashed) depending on m1.

If S1 or [notdef]1 are invisible, an observable that can be more readily exploited with less data to discriminate the heavier parent from the direct 750 GeV resonance case is the amount of missing transverse energy, EmissT, shown in the right panel in gure 8. Depending on the precise mass pattern, the EmissT distribution may also help to discriminate between scenarios I{IV. We note that scenarios III and IV as well as scenarios I with a light S1 and the 3-body decay scenario II with a very heavy parent all lead to very high EmissT.

{ 11 {

Spin-0 (gg)

= 440 GeV

I: m

= 40 GeV

I: m

= 900 GeV

II: m

= 1800 GeV

II: m

= 900 GeV

III: m

= 1800 GeV

III: m

= 1700 GeV

IV: m

= 1600 GeV

IV: m

10 4 100 200 300 400 500 600 700 800 900 1000

miss [GeV]

Spin-0 (gg)

= 440 GeV

I: m

= 40 GeV

I: m

= 900 GeV

II: m

= 1800 GeV

II: m

= 900 GeV

III: m

= 1800 GeV

III: m

= 1700 GeV

IV: m

= 1600 GeV

IV: m

10 300 400 500 600 700 800 900 1000 1100 1200

JHEP05(2016)128

m (

) [GeV]

Figure 8. Normalised distributions of diphoton invariant mass (left) and missing transverse energy (right) for the heavier parent scenarios I{IV. For reference, the gluon-initiated spin-0 case is shown as black dashed line.

While so far ATLAS and CMS have not provided any details on the event structure of the diphoton excess, such high EmissT would have been a striking feature and di cult to miss. In this respect scenarios I and II with masses that minimize the amount of EmissT (red and blue solid lines) seem most interesting. Nonetheless for these cases the missing energy still peaks around 100 GeV, which would be a powerful discriminator against the direct 750 GeV resonance production discussed in section 4.1.

To obtain complementary information to the above and/or if S1 or [notdef]1 are not invisible but lead to soft decay products because of, e.g., a hidden valley cascade, one can make use of the conventional kinematic distributions that we already considered for the 750 GeV spin-0 and spin-2 resonance cases. These are shown in gure 9 for the heavier parent scenarios. While the distributions involving jets o er little discriminating power, the diphoton pT and distributions are rather distinct. Concretely the diphoton system is harder and more central depending on the scenario. Additional information can be obtained from the pT ( 1)

spectrum. Putting everything together it seems feasible to distinguish not only between the 750 GeV and heavier resonance cases but also among the heavier parent scenarios I{IV, although distinguishing between scenarios I and II is somewhat more involved. Here note that in the sequential resonance case there are two free parameters, m3 and m1, while in the 3-body decay case m3 and m1 are tightly related once the m spectrum is xed. Comparing scenario I with (m3, m1) = (1200, 440) GeV to scenario II with m3 = 900 GeV we see that the former leads to a somewhat softer pT ( 1 2) spectrum, and pT ( 1) exhibits a notch (on log scale) around 375 GeV.

5 Conclusions

Should the observed excess in diphoton events at 750 GeV turn into a discovery with the accumulation of more data, the next step will be to elucidate its precise nature. An immediate question in this context will be whether we are dealing with the direct production of a new 750 GeV spin-0 or spin-2 particle that decays into a pair of photons, or with a

{ 12 {

0.2

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Spin-0 (gg) IIIIIIIV

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0 2 4 6 8

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)

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0 2 4 6 8

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)

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III

10 0 100 200 300 400 500 600 700 800 900 1000

(

) [GeV]

0.15

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III

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0 4

0 1 2 3 4 5

)

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III

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III

0.1

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JHEP05(2016)128

0.06

0.04

0.02

10 0 100 200 300 400 500 600 700 800 900 1000

0 -8 -6 -4 -2 0 2 4 6 8

) [GeV]

, j

)

0.5

Spin-0 (gg)

III

0.4

0.3

0.2

0.1

0 0 1 2 3 4 5 6 7 8

N(j)

0.25

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Spin-0 (gg) IIIIIIIV

0.15

0.1

0.05

0 4

0 1 2 3 4 5

(

)

Spin-0 (gg)

III

10 0 100 200 300 400 500 600 700 800 900 1000

(

) [GeV]

Figure 9. Normalised distributions for the heavier parent scenarios I{IV. For each scenario, the full (dashed) lines are for the rst (second) mass combination, cf. table 1 and gure 8. For reference, the gluon-initiated spin-0 case is shown as black dashed line.

heavier particle that follows a more complicated decay pattern with the masses of the involved particles conspiring to give two photons with an invariant mass spectrum peaking around 750 GeV. The characteristics of additional activity present in the events, such as the amount of missing energy, the jet multiplicity, or the presence of b-jets or other particles accompanying the two photons constitute an important piece of information to this end. On a longer timescale, one can envisage a detailed characterisation of the diphoton signal in terms of kinematic distributions.

As a preliminary step towards such a program, in this work we studied kinematic distributions that may help determine the nature of the putative 750 GeV excess. Using a simple parametrisation of the underlying interactions, we analysed the pT , and

distributions of photons and jets and the overall jet activity expected for a 750 GeV spin-0 resonance produced through gg or b b fusion, a 750 GeV spin-2 resonance produced in gg or q

q fusion, and four di erent scenarios for a heavier spin-0 parent produced in gg fusion and undergoing 3-body or cascade decays. We found that combinations of the distributions of the diphoton system and the leading photon can help distinguish the topology and mass spectra of the di erent scenarios, while patterns of QCD radiation can help di erentiate the production mechanisms. Moreover, the presence of missing energy can help disentangle

{ 13 {

the direct resonance scenario from the heavy parent one if the latter involves (e ectively) invisible particles. In this spirit, the study of such distributions constitutes a powerful complementary approach to both, the search for other decay modes of the new state(s) responsible for the diphoton signal and standard direct searches for additional particles that could accompany the new state(s).

While our conclusions about the prospects of distinguishing between di erent topologies are generally optimistic, one has to bear in mind the limitations of the EFT approach8 that we employed in our analysis. For example, the presence of relatively light new particles in loops (for weakly coupled models) or form factors (for strongly coupled ones) could bring about some momentum-dependence of the underlying interactions, which would distort some of the distributions we have considered. In this case there should however also be other observable e ects, most notably the eventual detection of additional new particles as the sensitivity of the LHC searches improves with more data.

The future of the 750 GeV excess remains, of course, unknown. Our results can, however, also be of relevance for other potential excesses that might be observed during the LHC Run 2. In any case, we are eagerly looking forward to the next round of data-taking that might (hopefully) turn the present excess into a discovery and thus open the door to a plethora of exciting new physics explorations.

Acknowledgments

This work was supported in part by the \Investissements davenir, Labex ENIGMASS", the ANR project DMASTROLHC grant no. ANR-12-BS05-0006, the Theory-LHC-France initiative of the CNRS (INP/IN2P3) and the Research Executive Agency (REA) of the European Union under the Grant Agreement PITN-GA2012-316704 (HiggsTools). AG is supported by the \New Frontiers" program of the Austrian Academy of Sciences.

A Sequential resonance with S1 = S2

A special case of the sequential resonance, i.e. our scenario I given by the leftmost diagram in gure 2, is when S3 decays into two identical particles S2 = S1. This was considered in [36], where the authors studied the production of a heavier (pseudo)scalar resonance decaying into a pair of lighter pseudoscalars with mass of 750 GeV, which decay further into electroweak SM gauge bosons via the Wess-Zumino-Witten anomaly. While this case is distinct from the other heavier parent cases we considered | the events would contain additional hard particles from the decay of the second S2 (e.g., pp ! S3 ! S2S2 !

+ZZ) which should be observable | it is interesting to compare the resulting di erential distributions of the diphoton signal to those of our scenario I benchmark points. This is exempli ed in gure 10, where the dotted red line shows the case m3 = 1700 GeV, m2 = m1 = 750 GeV. Note that we assume exactly two photons; the possibility of the second S2 also decaying into is ignored. Interestingly, most of the distributions look

8See e.g. [82] for a recent discussion in the context of Higgs EFTs.

{ 14 {

JHEP05(2016)128

Spin-0 (gg)

= 440 GeV

Spin-0 (gg)

= 440 GeV

I: m

1 = 40 GeV

I: m

1 = 750 GeV

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10 4 0 100 200 300 400 500 600 700 800 900 1000

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) [GeV]

I: m

1 = 40 GeV

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1 = 750 GeV

I: m

10 300 400 500 600 700 800 900 1000 1100 1200

JHEP05(2016)128

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) [GeV]

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= 440 GeV

I: m

1 = 40 GeV

I: m

1 = 750 GeV

I: m

0.1

0.05

0 6

0 2 4 6 8

(

)

Spin-0 (gg)

= 440 GeV

I: m

1 = 40 GeV

I: m

1 = 750 GeV

I: m

10 4 0 100 200 300 400 500 600 700 800 900 1000

(

) [GeV]

Figure 10. Normalised distributions for di erent mass combinations for the heavier parent resonance scenario I. For reference, the gluon-initiated spin-0 case is shown as black dashed lines.

very similar to those of the m3 = 1200 GeV, m2 = 750 GeV, m1 = 40 GeV case. The exception is ( 1 2), which is more central and does not exhibit any dip at = 0.

B Mass and width e ects for the antler topology

While the heavier resonance scenarios I{III can reproduce the observed diphoton excess in a rather generic manner, scenario IV (the so-called antler topology) is subject to some ne-tuning. First of all, as already noted in [38], obtaining the desired diphoton invariant mass spectrum requires a ne adjustment of m1, m2 and m3. The interrelation between the three masses to obtain the correct endpoint is illustrated in gure 11 (left). While a priori this does not look too constraining, the additional requirement that the cut-o in m be steep enough is a very severe constraint, pushing m2 extremely close to m3/2: the 1 range from the t in [38] is above the blue line in gure 11 (left).

Related to this, we observe moreover a strong sensitivity to the decay widths. This is illustrated in gure 11 (right), where we compare the m spectrum of the benchmark point (m3, m2, m1) = (1700, 849, 175) GeV obtained with 3 = 2 2 = 0.1 GeV (as used in gures 8 and 9) to that obtained with somewhat larger but still narrow widths of

3 = 2 2 = 1 GeV. We see that m quickly attens out. Also shown for comparison is the resulting m spectrum when changing m2 from 849 GeV to 845 GeV (i.e. m2/m3 = 0.497

{ 15 {

0.500

m1=10

m1=175

= 849 GeV,

= 0.1 GeV

2 = 849 GeV,

3 = 1 GeV

2 = 845 GeV,

3 = 0.1 GeV

2 = 845 GeV,

3 = 1 GeV

10 300 400 500 600 700 800 900 1000 1100 1200

m (

) [GeV]

0.498

0.496

m 2/m 3

0.494

0.492

m1=300

0.490

1500 1600 1700 1800 1900 2000

JHEP05(2016)128

m3 [GeV]

Figure 11. Left: solutions for the antler topology that produce an endpoint in the diphoton invariant mass spectrum of E = 827+30.336.9 GeV [38] in the plane of m3 versus m2/m3 for three di erent choices of m1 = 10, 175 and 300 GeV (in light red, yellow and light blue, respectively). The 1 limit = 0.0322+0.02960.0317 [38] is satis ed between the two horizontal blue lines. Right: sensitivity

of the diphoton invariant mass spectrum to m2/m3 and the S3 decay width, for m3 = 1700 GeV and m1 = 75 GeV.

instead of 0.499). Here the dependence on the width is less dramatic, as we are a bit further away from the threshold. However, m is already too at to provide a good explanation for the observed excess.

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

Web End =CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Abstract

We study kinematic distributions that may help characterise the recently observed excess in diphoton events at 750 GeV at the LHC Run 2. Several scenarios are considered, including spin-0 and spin-2 750 GeV resonances that decay directly into photon pairs as well as heavier parent resonances that undergo three-body or cascade decays. We find that combinations of the distributions of the diphoton system and the leading photon can distinguish the topology and mass spectra of the different scenarios, while patterns of QCD radiation can help differentiate the production mechanisms. Moreover, missing energy is a powerful discriminator for the heavy parent scenarios if they involve (effectively) invisible particles. While our study concentrates on the current excess at 750 GeV, the analysis is general and can also be useful for characterising other potential diphoton signals in the future.

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Title

Characterising the 750 GeV diphoton excess

Author

Bernon, Jérémy; Goudelis, Andreas; Kraml, Sabine; Mawatari, Kentarou; Sengupta, Dipan

Pages

1-21

Publication year

2016

Publication date

May 2016

Publisher

Springer Nature B.V.

e-ISSN

10298479

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/JHEP05(2016)128

ProQuest document ID

1790886663

SISSA, Trieste, Italy 2016

Characterising the 750 GeV diphoton excess

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