The 750 GeV excess from photon-photon and quark-quark processes
Tanumoy Mandal, Ulf Danielsson, Rikard Enberg, Gunnar Ingelman
aa r X i v : . [ h e p - ph ] M a y THE 750 GEV EXCESS FROM PHOTON-PHOTON AND QUARK-QUARKPROCESSES
TANUMOY MANDAL, ULF DANIELSSON, RIKARD ENBERG, GUNNAR INGELMAN
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
The observed excess in the diphoton mass spectrum around 750 GeV at the 13 TeV LHCpossibly indicates the presence of a photonphilic resonance. We show that the excess canbe explained by a scalar of the type involved in Bekenstein’s framework for varying electro-magnetic coupling theories. The scalar, in our model, couples dominantly to photons and ismainly produced by the quark-quark fusion at the LHC. In addition, it can also be producedin photon-photon fusion. Our model has only two free parameters, the mass of the scalar andthe scale of the new physics, which are fixed by the LHC excess to 750 GeV and 1.5 - 2 TeV,respectively. The scalar has a large three-body decay to a fermion pair and a photon, whichprovides an interesting search channel with a dilepton-photon resonance around 750 GeV.
Recently both the ATLAS and the CMS collaborations have reported excesses in the diphotoninvariant mass distribution around 750 GeV1 , e and the talk is mainly based on our paper inRef. 3 on this subject. The original concept of space-time varying fine-structure constant wasconstructed by Jacob Bekenstein 4 in context of cosmology. In the Bekenstein model 4, it is assumed that e is not really a constant and varies with space-time. The variation is given by e = e ǫ ( x ), where e is the constant EM coupling and ǫ ( x ) isa scalar field whose kinetic energy is given by Λ ( ∂ µ ǫ ) / (2 ǫ ) where Λ is an energy scale. Thefield strength tensor is given by F µν = [ ∂ µ ( ǫA ν ) − ∂ ν ( ǫA µ )] /ǫ . We define b F µν = ∂ µ A ν − ∂ ν A µ ,and introduce a scalar field ϕ such that ǫ = e ϕ . Assuming small field limit, we write ǫ ≃ ϕ ,and keep only terms linear in ϕ . Finally, we define a new field φ = ϕ Λ, so that all fields haveheir usual mass dimensions. In this way, we find a Lagrangian for standard electromagnetismplus the terms associated with the scalar field as
L ⊃
12 ( ∂ µ φ ) − M φ φ + 12Λ φ b F µν b F µν . (1) We study the LHC phenomenology of our model and derive limits on the scale Λ from therelevant 8 TeV data and also find out the favored values of Λ required to explain the 750 GeVdiphoton excess.
Figure 1 – Sample Feynman diagrams of the two and three body decay modes of φ . The only possible two-body decay of φ is the diphoton mode, which is a tree level decay –not a loop-induced decay through a charged particle. In Fig. 1, we show the Feynman diagramsof all possible two and three body decay modes of φ . In Table 1, we show the partial widthsand branching ratios (BR) of φ into its two, three and four body decay modes for Λ = 1TeV, calculated using MadGraph5 . It is important to note that the branching ratios of φ areindependent of Λ. From Table 1, we can see that φ → γγ is the dominant decay mode andthis mode has a branching ratio of about 70%. Due to the large branching in the diphotonmode, φ might be a good candidate to explain the recent 750 GeV diphoton excess at the LHC.Moreover, the nonobservation of any excess expected in other channels from a SM-like scalarcan also be explained as other decays of φ are not SM-like.Decay Mode φ → γγ φ → γf f ( jj ) φ → γγf f φ → γW W φ → γγW W TotalWidth (GeV) 8.393 2.672 (1.505) 0.610 0.447 0.022 12.14BR (%) 69.12 22.00 (12.39) 5.02 3.68 0.18 -
Table 1: The partial widths and branching ratios of φ for M φ = 750 GeV. The widths are proportional to Λ − andare here given for Λ = 1 TeV, whereas the BRs are independent of Λ. Here, f includes all SM charged fermionsand j denotes jets of “light” quarks, including b .Figure 2 – Sample Feynman diagrams of the production of φ at the LHC. In Fig. 2, we show a few sample Feynman diagrams of the two main production channels of φ at the LHC. Unlike the gg initiated SM-like Higgs boson production, these channels are inducedby a qq initial state. In Table 2, we present the partonic cross sections of various productionmodes of φ for the 8 and 13 TeV LHC for Λ = 1 TeV.roduction mode φγ φγj φγjj φjj γγ → φ φℓℓ φγW φγW W φγγ CS@8TeV (fb) 2.339 1.161 0.513 4.622 30.84 0.017 0.064 0.176 0.026CS@13TeV (fb) 10.63 6.486 3.439 15.15 77.59 0.081 0.577 4.847 0.140
Table 2: Partonic cross sections of various production channels of φ for Λ = 1 TeV computed at renormalization( µ R ) and factorization ( µ F ) scales µ R = µ F = M φ = 750 GeV for LHC at 8 and 13 TeV. These cross sectionsare computed using CTEQ6L1 PDFs by applying some basic generation level cuts. Here, j denotes light jetsincluding b -jet and ℓ includes e ± and µ ± . In the γγ → φ mode, the two initial photons come from proton. The experimental searches for a high mass diphoton resonance, where the signal is an s -channel spin-0 or spin-2 resonance decaying to diphoton generally demand exactly two selectedphotons with no selected jet, whereas for inclusive diphoton resonance searches, one keeps eventswith at least two selected photons and any number of selected jets. The two important pro-duction channels of φ viz. inclusive pp → φγ → γ and pp → φjj → γγjj contribute most tothe ATLAS 1 and CMS 2 analyses. Now, we want to investigate how selection cut efficienciesdepend on the different selection criteria imposed on the number of photons and jets. In Ta-ble 3, we show cut efficiencies for different selection criteria on the number of photons and jetsfor the inclusive pp → φγ → γ and pp → φjj → γγjj channels at the 13 TeV LHC by roughlyemploying the selection cuts used by ATLAS 1 and CMS 2 for their 13 TeV analyses.Category 2 γ + 0 j ≥ γ + 0 j γ + ≥ j γ + 1 j γ + 2 j γ + ≥ j ≥ γ + ≥ j ATLAS ( φγ ) 0.008 0.278 0.142 0.057 0.042 0.641 0.788ATLAS ( φjj ) 0.0009 0.001 0.546 0.030 0.219 0.010 0.556CMS ( φγ ) 0.036 0.323 0.247 0.086 0.063 0.704 0.957CMS ( φjj ) 0.0009 0.001 0.750 0.035 0.291 0.013 0.763 Table 3: Cut efficiencies for different selection criteria on the number of selected photons and jets for the 13 TeVATLAS and CMS diphoton resonance searches. Here, “ φγ ” and “ φjj ” mean inclusive (up to 2-jets) pp → φγ → γ and pp → φjj → γγjj processes respectively. In order to derive a limit on Λ by recasting the σ × BR upper limit from an experiment,we need to properly take care of the cut efficiencies. This can be done by using the followingrelation: N s = σ s × ǫ s × L = X i σ i × ǫ i ! × L , (2)where N s is the number of events for the signal considered and σ s is the corresponding signalcross section for luminosity L . The corresponding signal cut efficiency is denoted by ǫ s . Whendifferent types of signal topology and/or final state contribute to any experimental observable, N s can be expressed by the sum ( P i σ i × ǫ i ) × L . Here, i runs over all contributing signalprocesses to any observable. In our case, the following two processes contribute the most to the s -channel diphoton resonance searches at the LHC:Process I ( p ) : pp → φγ → γ + jets; Process II ( p ) : pp → φjj → γγjj. (3)Therefore, in our case N s = Λ − × ( σ p × ǫ p + σ p × ǫ p ) Λ=1 TeV × L . Here, σ p i is the signalcross section for the i -th process and the corresponding signal efficiency is ǫ p i .The LHC Run-I data of ATLAS and CMS set an upper limit of the cross section in the range1-2 fb. Using this we can extract a lower limit of Λ for our model. For 2 γ +0 j category, we obtaina lower limit of Λ in the range 0.2-0.6 TeV. Choosing instead 2 γ + ≥ j would, however, give alower limit Λ in the range 1.2-1.8 TeV. From the 13 TeV data, where a more pronounced hintfor an excess can give more precise information regarding our model. We obtain the essentialresults shown in Table 4, resulting in values of Λ that can explain the 750 GeV diphoton excessesobserved by both ATLAS 1 and CMS 2. As we mentioned earlier, the extraction of Λ depends onxperiment σ s ǫ s σ p ǫ p ǫ p σ p ǫ p ǫ p Λ (C1) Λ (C2)(fb) (fb) (C1) (C2) (fb) (C1) (C2) (TeV) (TeV)ATLAS@13TeV 10.5 0.4 9.9 0.14 0.79 9.7 0.55 0.56 1.3 1.8CMS@13TeV 17.0 0.3 9.9 0.25 0.96 9.7 0.75 0.76 1.4 1.8
Table 4: The observed upper limit on cross sections, σ s and corresponding efficiencies, ǫ s for mass around 750GeV. In the last two columns we show the derived value of Λ for M φ = 750 GeV for the selection categories C1:2 γ + ≥ j and C2: ≥ γ + ≥ j . what selection category is used. For the category of 2 γ + 0 j (C1) selection for ATLAS analysis,we get Λ ≈ . ≈ . ≥ γ + ≥ j (C2). The corresponding CMS values on Λare 1.4 TeV and 1.8 TeV for C1 and C2 respectively. We have proposed that the diphoton excess is due to a 750 GeV scalar associated with variationsof the fine-structure constant. Our model has only two new parameters, the mass of the scalar M φ and the energy scale Λ. Both are fixed by the LHC excess, with M φ ∼
750 GeV andΛ ∼ . − φ → γq ¯ q ) ∼
13% forquarks and BR( φ → γℓ + ℓ − ) ∼
10% for leptons. This gives the main additional prediction ofour model: events with a lepton-lepton-photon resonance at 750 GeV. The scalar resonance isdominantly produced together with an additional real or virtual photon, which, if virtual, givesrise to a pair of jets or leptons. This gives another prediction: the existence of an additionalphoton and/or jets in the events, which are not part of the resonance. These predictions shouldbe looked for in future LHC analyses.The scalar can be produced through photon-photon fusion where the initial photons arecoming from proton and this production can be very large due to the infra-red enhancementin the collinear limit. Due to the limited knowledge of proton form factors, the photon fusioncontribution inherits large uncertainties 5. Therefore, it is very important to understand thephoton PDF in proton for robust predictions. Currently, we are working on this direction tounderstand various issues in the photon-flux to improve our model predictions.
Acknowledgments
TM would like to thank the organizers of the Moriond QCD 2016 for giving the opportunity topresent this result. This work is supported by the Swedish Research Council under contracts 621-2011-5107 and 2015-04814. T.M. is supported by the Carl Trygger Foundation under contractCTS-14:206.
References
1. The ATLAS collaboration, ATLAS-CONF-2015-081.2. CMS Collaboration [CMS Collaboration], collisions at 13TeV,” CMS-PAS-EXO-15-004.3. U. Danielsson, R. Enberg, G. Ingelman and T. Mandal, arXiv:1601.00624 [hep-ph].4. J. D. Bekenstein, Phys. Rev. D , 1527 (1982). doi:10.1103/PhysRevD.25.15275. L. A. Harland-Lang, V. A. Khoze and M. G. Ryskin, JHEP1603