750 GeV diphotons from closed string states

We show that low-mass-scale string compactifications, with a generic D-brane configuration that realizes the standard model by open strings, can explain the relatively broad peak in the diphoton invariant mass spectrum at 750 GeV recently reported by the ATLAS and CMS collaborations. Under reasonable assumptions, we demonstrate that the excess could originate from a closed string (possibly axionic) excitation \varphi that has a coupling with gauge kinetic terms. We estimate the \varphi production rate from photon-photon fusion in elastic pp scattering, using the effective photon and narrow width approximations. For string scales above todays lower limit M_s \approx 7 TeV, we can accommodate the diphoton rate observed at Run II while maintaining consistency with Run I data.

We show that low-mass-scale string compactifications, with a generic D-brane configuration that realizes the standard model by open strings, can explain the relatively broad peak in the diphoton invariant mass spectrum at 750 GeV recently reported by the ATLAS and CMS Collaborations. Under reasonable assumptions, we demonstrate that the excess could originate from a closed string (possibly axionic) excitation ϕ that has a coupling with gauge kinetic terms. We estimate the ϕ production rate from photon-photon fusion in elastic pp scattering, using the effective photon and narrow width approximations. For string scales above today's lower limit M s ≈ 7 TeV, we can accommodate the diphoton rate observed at Run II while maintaining consistency with Run I data. Very recently, ATLAS [1] and CMS [2] announced preliminary results on inclusive diphoton searches using (respectively) 3.2 fb −1 and 2.6 fb −1 of data recorded at a center-of-mass energy √ s = 13 TeV. The two experiments observed an excess of events over expectations from standard model (SM) processes in the invariant mass spectrum at ≈ 750 GeV. This could be interpreted as decays of new massive particle ϕ. For  Even though the excess is not statistical significant yet, it is interesting to entertain the possibility that it corresponds to a real signal of new physics. A plethora of models have been proposed to explain the data including some string inspired scenarios [6,7]. Actually in [6]

Table 1
Chiral spectrum of SM fields in the 4 stack D-brane model. We have added the right handed neutrino stretching between the lepton brane and the right brane.

Fields
Sector (F is the photon field strength.) Herein we put forward an alternative solution from string theory, namely that ϕ corresponds to a closed string state. Namely we consider extensions of the SM based on D-brane string compactifications with large extra dimensions [8]. The basic unit of gauge invariance for D-brane constructions is a U (1) field, so that a stack of N identical D-branes eventually generates a U (N) theory with the associated U (N) gauge group; for N = 2, the gauge group can be Sp(1) ∼ = SU(2) rather than U (2) [9,10]. In the presence of many D-brane types, the gauge group becomes a product form where N i reflects the number of D-branes in each stack. In the perturbative regime, gauge interactions emerge as excitations of open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Our explanation of the peak in the diphoton invariant mass spectrum is independent of the structure of the D-brane model. Nevertheless, to motivate the discussion we adopt a minimal model containing 4 stacks of D-branes. The basic setting of the gauge theory is given by [11][12][13].
In the bosonic sector the open strings terminating on the QCD stack contain, in addition to the SU(3) C octet of gluons g a μ , an is anomaly free. However, the Q B (gauged baryon number) is not anomaly free and we expect this anomaly to be canceled via a Green-Schwarz mechanism involving the exchange of twisted Ramond-Ramond (RR) closed string states [14][15][16][17][18]. There is an explicit mass term in the Lagrangian for the new gauge μ whose scale comes from the compactification scheme. The scalar that gets eaten up to give the longitudinal polarization of the Y is a closed string field and there is no extra Higgs particle [19]. In addition to the intermediate RR field, which is absorbed by the Y in the anomaly cancellation, there is a closed string mode ϕ which couples to the anomaly free combination of the hypercharge (1). It can be either a scalar field from the Neveu-Schwarz sector that is complexified with the RR state absorbed by Y , or another RR pseudo-scalar (axion) coupled to FF . In this Letter we propose that the observed diphoton excess originates from the closed string excitation ϕ. There are two properties of the scalar ϕ that are necessary for explaining the 750 GeV signal. It should be a special closed string state with dilaton-like or axion-like coupling to F 2 (respectively to FF ) of the electromagnetic field, but decoupled from F 2 of color SU(3). The couplings of closed string states to gauge fields do indeed distinguish between different D-brane stacks, depending on the localization properties of D-branes with respect to ϕ in the compact dimensions. More specifically, it is quite natural to assume that ϕ is a closed string mode that is associated to the wrapped cycles of the U (1) L and U (1) I R stack of D-branes, however is not or only weakly attached to the wrapped cycle of Sp(1) L or the color SU(3) stack of D-branes. In this way, we can avoid unwanted dijet signals 1 . Furthermore, since the string mass scale is now known to be larger than M s ≈ 7 TeV [20], the mass M ϕ ≈ 750 GeV must be suppressed with respect to the string scale by some anomalous loop corrections. Because ϕ is a twisted closed string localized at an orbifold singularity, its coupling to γ γ should be suppressed by M −1 s , provided the bulk is large [21]. With this in mind, we parametrize the coupling of ϕ to the photon by the following ver- where v ∼ M s . To remain in the perturbative range, we also require c γ γ to be reasonably small. The partial decay width of ϕ to diphotons then follows as The diphoton signal is produced via photon-photon fusion with ϕ as the resonance state [22,23]. The simplest way to get a reliable estimate of σ (pp → γ γ ) is provided by the equivalent photon approximation (originally due to Fermi [24] and later on developed by Weizsäcker [25] and Williams [26]). Under the narrow width approximation, the cross section is found to be where f γ s (x 1 ) is the photon distribution function, which for small x takes the following approximate form where α ≈ 1/129, m p is the proton mass, and q * is the inverse of the minimum impact parameter for elastic scattering [27,28].
Following [23] we consider the range 130 MeV < q * < 170 MeV, which accommodates the LHC two photon Higgs production cross section. The total cross sections are σ √ s=13 TeV = 162 fb total 45 GeV 1 We may note in passing that if an excess of dijet events is observed in future LHC data, this can be easily accommodated by coupling ϕ to F 2 of SU(3) C changing the localization properties of D-branes with respect to ϕ in the internal space. GeV for q * = 130 MeV. With the observed total decay width of total = 45 GeV, the branching fraction is given by where v GeV ≡ v/GeV. We perform a scan in the parameter space (c γ γ , v). As one can see in Fig The assumed coupling of ϕ to the hypercharge field strength yields additional decay channels in the visible sector, namely ϕ → γ Z and ϕ → Z Z , with γ Z γ γ = 2 tan 2 θ W ≈ 0.6 and Z Z γ γ = tan 4 θ W ≈ 0.08 . (9) The precise branching fraction into γ Z and Z Z is one of the hallmark predictions of our model. In general one would expect a coupling to hypercharge and a coupling to SU(2) bosons with a parameter controlling their relative strength. This would appear in the emergent couplings to Z Z , γ γ , and γ Z . This would be the generic situation even in other effective field theory models.
One may wonder whether the missing fraction of the decay width can be explained through the coupling of ϕ to gravitons.
However, as we show in the Appendix, the KK tower of gravitons gives a negligible contribution to the total width. On the other hand, the missing fraction of the decay width could arise from the coupling of ϕ to other bulk fields, such as fermions, which has less number of derivatives. These hidden fermions could make a contribution to the dark matter content of the universe [29,30]. For collisions at when q * = 170 MeV and σ √ s=8 TeV = 6.5 fb total 45 GeV when q * = 130 MeV [23]. Although both agree with LHC8 data [3,4], we see that smaller values of q * correspond to a much larger increase in going from 8 TeV to 13 TeV.
In closing, we comment on other anomalies observed by the LHC experiments. As noted elsewhere [13] the new Abelian gauge bosons of the D-brane structure (which suffer a mixed anomaly with the SM but are made self-consistent by the Green-Schwarz mechanism) can also accommodate the diboson [31,32]