Enhanced Rates for Diphoton Resonances in the MSSM

We propose a simple mechanism for copiously producing heavy Higgs bosons with enhanced decay rates to two photons at the LHC, within the context of the Minimal Supersymmetric extension of the Standard Model (MSSM). In the CP-conserving limit of the theory, such a diphoton resonance may be identified with the heavier CP-even $H$ boson, whose gluon-fusion production and decay into two photons are enhanced by loops of the lightest supersymmetric partner of the top quark $\tilde{t}_1$ when its mass $m_{\tilde{t}_1}$ happens to be near the $\tilde{t}^*_1\tilde{t}_1$ threshold, i.e.~for $m_{\tilde{t}_1}\!\simeq \!\frac12 M_H$. The scenario requires a relatively low supersymmetry-breaking scale $M_S\stackrel{<}{{}_\sim} 1$ TeV, but large values of the higgsino mass parameter, $\mu \stackrel{>}{{}_\sim} 1$ TeV, that lead to a strong $H \tilde{t}^*_1 \tilde{t}_1$ coupling. Such parameters can accommodate the observed mass and standard-like couplings of the 125 GeV $h$ boson in the MSSM, while satisfying all other constraints from the LHC and dark matter searches. Additional enhancement to the diphoton rate could be provided by Coulombic QCD corrections and, to a lesser extent, by resonant contributions due to $\tilde{t}_1^* \tilde{t}_1$ bound states. To discuss the characteristic features of such a scenario, we consider as an illustrative example the case of a diphoton resonance with a mass of approximately 750 GeV, for which an excess was observed in the early LHC 13 TeV data and which later turned out to be simply a statistical fluctuation.

In December 2015, the ATLAS and CMS collaborations have reported an excess in the 13 TeV LHC data corresponding to a possible resonance Φ with a mass of approximately 750 GeV decaying into two photons [1]. With the collection of more data in 2016, this initial diphoton excess turned out to be simply a statistical fluctuation and faded away [2]. In the meantime, a large number of phenomenological papers were written [3] interpreting the excess in terms of a resonance and attempting to explain the very large initial diphoton rate. Indeed, assuming that the new state Φ is a scalar boson, the production cross section in gluon-fusion σ(gg → Φ) times the two-photon decay branching ratio BR(Φ → γγ) was reported to be of order of a few femtobarns and such rates were very difficult to accommodate in minimal and theoretically well-motivated scenarios beyond the Standard Model (SM) [3]. As we need to stay alert for such unexpected surprises of New Physics at future LHC runs, the study of new mechanisms that lead to enhanced production rates for such diphoton resonances remains an interesting topic on its own right. In this paper, we consider diphoton resonances in one such scenario: the Minimal Supersymmetric extension of the SM (MSSM) [4,5], softly broken at scales M S = O(1 TeV) for phenomenological reasons. We investigate a few possibilities that lead to a large enhancement of the pp → γγ rate which, for instance, could have explained the too large 750 GeV excess in the initial LHC 13 TeV data in terms of New Physics.
In the MSSM, two Higgs doublets are needed to break the electroweak symmetry leading to three neutral and two charged physical states. The Φ resonance could have corresponded to either the heavier CP-even H or the CP-odd A bosons [6], both contributions of which may be added individually at the cross-section level. The heavy neutral H and A bosons are degenerate in mass M H ≈ M A in the so-called decoupling regime M A ≫ M Z in which the lighter CP-even h state, corresponding to the observed 125 GeV Higgs boson, has SM-like couplings as indicated by the LHC data [7]. Nevertheless, it has been shown [6] that in most of the MSSM parameter space, a diphoton rate of O(a few fb) cannot be generated using purely the MSSM particle content. Indeed, although the Φ = H/A Yukawa couplings to top quarks are sizeable for small values of the well-known ratio tan β of the two-Higgs-doublet vacuum expectation values, the only input besides M A that is needed to characterize the MSSM Higgs sector (even when the important radiative corrections are taken into account [8]), the top quark cannot generate sizeable enough loop contributions to the gg → H/A and H/A → γγ processes to accommodate such a diphoton rate. The supersymmetric particles give in general too small loop contributions because their couplings to the Higgs bosons are not proportional to the masses and decouple like ∝ 1/M 2 S for large enough sparticle masses. In this Letter we show that there exists a small but vital area of parameter space, in which large production rates of O(1 fb) for diphoton resonances at the LHC with √ s = 13-14 TeV can be accounted for, entirely within the restricted framework of the MSSM. In the CP-conserving limit of the theory, the CP-even H boson of the MSSM would be produced through the effective Hgg and Hγγ couplings, which are enhanced via loops involving the lightest top squarkt 1 . The statet 1 will have significant loop contribution if its mass mt 1 happens to be near thet * 1t 1 threshold, mt 1 ≃ 1 2 M H . Given that stoponium Σt ≡ (t * 1t 1 ) bound states can be formed in this kinematic region [9], the diphoton rate will be further enhanced by resonant contributions to the amplitude thanks to the Σt states. In addition, assuming a Higgs mass M H < ∼ 1 TeV, large values of the Higgsino mass parameter µ are required, e.g. µ > ∼ 1 TeV, for a stop SUSY-breaking scale M S ∼ 1 2 -1 TeV. Such values enhance the strength of the Ht * 1t 1 coupling, through the so-called F -term contribution from the Higgs doublet superfield H u that couples to up-type quark superfields. Another smaller source of enhancement arises from the stop mixing parameter A t , which can still play a significant role if the ratio tan β is relatively low, i.e. for tan β < ∼ 10.
Besides comfortably allowing O(1 fb) diphoton rate, such parameter scenarios can naturally describe the observed SM-like h state with a mass of 125 GeV, for tan β > ∼ 5 (after allowing for all theoretical uncertainties of a few GeV due to higher order effects), and comply with all present constraints on the supersymmetric particle spectrum [7]. Here, we assume that the top squarkt 1 is the lightest or next-to-lightest visible supersymmetric particle, for which a lower-mass gravitino or a bino nearly degenerate witht 1 can successfully play the role of the dark matter in the Universe, respectively.
For illustration, let us now discuss in detail an example in which the diphoton resonance Φ is the one that could have corresponded to the excess observed in early 13 TeV data and how it could have been explained in the MSSM. The Φ state may be either the CP-even H boson or the CP-odd A scalar which, in the decoupling limit, have both suppressed couplings to W ± and Z gauge bosons, and similar couplings to fermions. The latter are controlled by tan β, with 1 < ∼ tan β < ∼ 60. For values tan β < ∼ 5, the only important Yukawa coupling λ Φf f is the one of the top quark, while for tan β > ∼ 10, the couplings to bottom quarks and τ leptons are enhanced, i.e. λ Φf f = √ 2m f /v ×ĝ Φf f withĝ Φtt = cot β andĝ Φbb =ĝ Φτ τ = tan β at the tree level. Nevertheless, for a mass M Φ ≈ 750 GeV, values tan β > ∼ 20 are excluded by the search of A/H → τ τ resonances [10], while tan β values not too close to unity can be accommodated by the search for H/A → tt resonance [11].
At the LHC, the Φ = H/A states are mainly produced in the gg → Φ fusion mechanism that is mediated by a t-quark loop with cross sections at √ s = 13 TeV of about σ(gg → A) ≈ 1.3 pb and σ(gg → H) = 0.8 pb for M Φ ≈ 750 GeV and tan β ≈ 1 [12]. The H/A states will then mainly decay into top quark pairs with partial (≈ total) widths that are of order Γ Φ ≈ 30 GeV. The two-photon decays of the H and A states are generated by the top quark loop only, and the branching ratio for the relevant inputs are: BR(A → γγ) ≈ 7 × 10 −6 and BR(H → γγ) ≈ 6 × 10 −6 [13,14]. Thus, one has a diphoton production cross section σ(gg → γγ), when the resonant s-channel H-and A-boson exchanges are added, of about σ(gg → Φ) × BR(Φ → γγ) ≈ 10 −2 fb. Evidently, this cross-section value is at least two orders of magnitude too short of what was needed to explain the LHC diphoton excess, if this were due to the presence of new resonance(s). The crucial question is therefore whether contributions of supersymmetric particles can generate such a huge enhancement factor of ∼ 100. The chargino (χ ± 1 ) contributions can be sufficiently large only in a rather contrived scenario, in which the mass m χ ± 1 satisfies the relation m χ ± 1 = 1 2 M A within less than a MeV accuracy, such that a large factor of QEDcorrected threshold effects can occur [15]. In such a case, however, finite-width regulating effects due to (χ + 1 χ − 1 ) bound states might become important and may well invalidate this possibility. Here, we consider a more robust scenario, where the enhancement of the signal is driven mainly by a large Ht * 1t 1 coupling thanks to a large µ parameter, and the impact of possible bound-state effects due to a stoponium resonance Σt is properly assessed.
At leading order, the contributions of the top quark t and its superpartnerst 1 andt 2 to both the Hγγ and Hgg vertices 1 (in our numerical analysis, all fermion and sfermion loops are included) are given by the amplitudes (up to colour and electric charge factors) where the functional dependence of the form factors A H 1/2 (τ i ) and A H 0 (τ i ) for spin-1 2 and spin-0 particles (with τ i = M 2 H /4m 2 i for the ith particle running in the loop) is displayed on the left pannel of Fig. 1. As expected, they are real below the M H = 2m i mass threshold and develop an imaginary part above this. The maxima are attained near the tt andt * 1t 1 -mass thresholds for the loop functions Re(A H 1/2 ) and Re(A H 0 ), respectively. Specifically, for τ i = 1, one has Re(A H 1/2 ) ≈ 2.3 and Re(A H 0 ) ≈ 4 3 , whilst Im(A H 0 ) ≈ 1 for τ i values slightly above the kinematical opening of thet * 1t 1 threshold. Hence, the stop contribution is maximal for mt 1 = 375 GeV and, it is in fact comparable to the top quark one, since for Since the SUSY scale M S ≡ √ mt 1 mt 2 is supposed to be close to 1 TeV from naturalness arguments, one needs a large splitting between the two stops; the contribution of the heaviert 2 state to the loop amplitude is then small. The significant stop-mass splitting is obtained by requiring a large mixing parameter which appears in the stop mass matrix, X t = A t −µ/ tan β. At the same time, a large value of X t ≈ √ 6M S , together with tan β > ∼ 3, maximize the radiative corrections to the mass M h of the observed h-boson 2 and allows it to reach 125 GeV for a SUSY-breaking scale M S ∼ 1 TeV [17,18]. Large values of µ and A t (and of X t ) increase considerably the Ht * 1t 1 coupling that can strongly enhance the Hgg and Hγγ amplitudes. In the decoupling limit and for maximally mixedt i states, the tree-level Ht * 1t 1 -coupling is given by [5] g Ht 1t1 = M 2 In the central pannel of Fig. 1,ĝ Ht 1t1 is plotted as a function of µ for several values of tan β and fixed X t = A t − µ cot β = √ 6 M S , so as to get M h ≈ 125 GeV with a scale M S = 1 TeV. As can be seen from the central pannel,ĝ Ht 1t1 can be very large for µ in the multi-TeV range. In fact, above the value tan β ≈ 3, only the third term of eq. (2) is important and the coupling is enhanced for large values of µ. For instance, if M S ≈ 1 TeV and mt 1 = 375 GeV, thet 1 contribution to the loop amplitudes in eq. (1) is roughlŷ In particular, for µ = −4M S as in the so-called CPX scenario [18,19], the stop effects can be twice as large as the top ones with tan β = 1. This gives a prediction for the diphoton cross section which is about 2 4 = 16 times larger than that obtained for tan β = 1. Finally, one should take into account the size of the resonance width Γ H . Indeed, the diphoton rate is given by the gg → H production cross section times the H → γγ decay branching ratio and the impact of the total width Γ H is important in the latter case. For tan β = 1, the total width is almost exclusively generated by the H → tt partial width, t cot 2 β/v and is about 30 GeV for M H = 750 GeV. In our case, this situation is unacceptable since, as we have increased σ(gg → H) by including the stop contributions and we have BR(H → tt) ≈ 1, σ(gg → H → tt) would be far too large and so is excluded by tt resonance searches [11]. BR(H → tt) needs thus to be suppressed and, at the same time, also the total decay width which leads to an increase of BR(H → γγ). This can be achieved by considering larger tan β values for which For tan β = 10, one then obtains Γ H ≈ 2 GeV and BR(H →tt) ≈ 20% as can be seen in the right-hand side of Fig. 1, where the H fermionic branching ratios and the total width are displayed as a function of tan β. The ratio BR(H → γγ) can be thus increased, in principle, by an order of magnitude compared to the tan β = 1 case. Nevertheless, if a larger decay width is required for the resonance, one can increase the chosen tan β value to, say tan β ≈ 20 (i.e. closer to the limit allowed by H/A → τ τ searches [10]) and enhancing thet 1 contribution by increasing the value of the parameter µ. However, values Γ H > ∼ 30 GeV cannot be achieved in principle 3 . Note that small values of tan β, tan β < ∼ 5, cannot be tolerated, as they do not suppress enough BR(H →tt) to a level to be compatible with tt resonance searches [11].
When all the ingredients discussed above are put together, the cross section σ(gg → H) times the decay branching ratio BR(H → γγ) at the LHC with √ s = 13 TeV is displayed in S /mt 1 > ∼ 800 GeV, the two sbottoms with mb 1,2 ≈ M S (with couplings to the H boson that are not enhanced) and the first/second generations sfermions (assumed to be much heavier than 1 TeV) are included together with the ones of the bottom quark, but they are small compared to that of the lightestt 1 . As can be seen, for tan β = 10 for instance, an enhancement by a factor of about 100 can be obtained for a value |µ| = 3 TeV, i.e. |µ| ≃ 5M S 4 . Hence, one easily arrives at production cross sections of O(1 fb) at the LHC for heavy Higgs resonances well above the tt threshold decaying sizeably into two photons, e.g. comparable to the diphoton cross sections initially observed by ATLAS and CMS in their early 13 TeV data [1].
While the M S and X t values adopted for the figure above lead to sufficiently large radiative corrections to generate a mass for the lighter h state that is close to M h = 125 GeV for tan β > ∼ 5 (in particular if an uncertainty of a few GeV from its determination is taken into account [17]), the required large µ value might be problematic in some cases. Indeed, at high 3 In fact, to obtain a sizeable total width, one option could be to take mt 1 a few GeV below the 1 2 M H threshold: one then opens the H →t 1t1 channel which increases the width Γ H . This channel would suppress BR(H →tt) as required at low tan β but also BR(H → γγ). Nevertheless, in the later case, some compensation can be obtained as the stop loop amplitude can be enhanced relative to the top one. 4 Such large values of |µ| can be obtained, for instance, in the context of the new MSSM [20], in which the tadpole term t S S for the singlet field S has different origin from the soft SUSY-breaking mass m 2 S S * S. For values of t 1/3 S ≫ m S , a large vacuum expectation value for S can be generated of order v S ≡ S ≃ t S /m 2 S ≫ m S ∼ M S , giving rise to a large effective µ parameter: µ eff = λv S ≫ M S , where λ < ∼ 0.6 is the superpotential coupling of the chiral singlet superfield S to the Higgs doublet superfields H u and H d . Hence, in this new MSSM setting, the appearance of potentially dangerous charged-and colour-breaking minima [21] due to a large µ eff can be avoided more naturally than in the MSSM. tan β and µ, there are additional one-loop vertex corrections that modify the Higgs couplings to b-quarks, the dominant components being given by [22] where λ t = √ 2m t /v. Note that in eq. (5), the first and second terms are the dominant gluinosbottom and stop-chargino loop corrections to the Hbb coupling, respectively. For |µ| tan β ≫ M S , as is required here, these corrections become very large and would, for instance, lead to an unacceptable value for the bottom quark mass. Hence, either one should keep |µ| < ∼ 5M S or alternatively, partly or fully cancel the two terms of the equation above. This, for instance, can be achieved by choosing a trilinear coupling A t < 0 and a very heavy gluino with a mass mg such that mg ≈ −4|µ| 2 /A t .
Nevertheless, the leading order discussion held above is not sufficient to address all the issues involved in this context and it would be desirable to provide accurate predictions for a "realistic" MSSM scenario, for which all important higher order effects are consistently implemented as in one of the established public codes. Specifically, using the program SUSY-HIT [13] which calculates the spectrum (through Suspect) and decays (through HDECAY and SDECAY) of the Higgs and SUSY particles, we have identified MSSM benchmark points in which the gg → H → γγ rate is almost entirely explained when NLO QCD corrections to the rate are included as in Ref. [23]. For instance, for tan β = 10, third-generation scalar masses of mt L = mt R = mb R = 0.8 TeV ≈ M S , trilinear couplings A t = A b = 2 TeV, gaugino mass parameters M 1 = 1 2 M 2 = 1 6 M 3 = 350 GeV and a higgsino mass µ = 2.3 TeV, the program Suspect2 (version 2.41) yields mt 1 = 373.75 GeV and mt 2 = 847 GeV. Moreover, fixing the CP-odd A-scalar mass to M A = 756 GeV, one obtains M H = 747.6 GeV, which is somewhat above the 2mt 1 ≈ 747.5 GeV threshold, and M h = 121 GeV, but with an inherent theoretical uncertainty estimated to be ∼ 3-4 GeV. With these inputs, an enhancement factor of at least two orders of magnitude is obtained, when compared to the case in which only the top loop contributes with tan β = 1. In detail, HDECAY 3.4 computes BR(H → γγ) = 9.2×10 −4 , BR(H → gg) = 4.2×10 −2 and a total width Γ H = 2.06 GeV, to be compared with BR(H → γγ) = 6×10 −6 , BR(H → gg) = 1.8×10 −3 and Γ H = 35 GeV without stop loops and tan β = 1. Hence, making the plausible assumption that the QCD corrections vary the same way in both the gg production and decay rates, we get an enhancement factor of ∼ 200, leading to a cross section σ(gg → H → γγ) ≈ 0.83 fb at the LHC with √ s = 13 TeV.
Also, we expect additional contributions to come from other sources, as we will discuss below. Note that besides giving rise to an h boson with a mass M h close to 125 GeV and SM-like couplings, this benchmark point leads to BR(H → τ τ ) = 7% and BR(H → tt) = 15%. Given that only the gg → H production channel gets enhanced thanks tot 1t * 1 -threshold effects, we can thus estimate that σ(gg → H) BR(H → τ τ ) ≈ 62 fb at √ s = 13 TeV, which satisfies the current LHC limits deduced from direct MSSM Higgs searches in the τ τ final state [24], in particular when one takes into account the uncertainty bands reported there. The complete input and output program files for the aforementioned benchmark point are available upon request 5 . Two additional sources of corrections might significantly increase the gg → H → γγ production cross section, as we will briefly outline below, and need to be taken into account.
The first one is that the form factor for the Hγγ and Hgg couplings appearing in eq. (1) and displayed in Fig. 1 (left) does not accurately describe the threshold region, that we are interested in here 6 . This is because when the stop mass lies slightly above threshold, a Coulomb singularity develops signalling the formation of Swave (quasi) bound states [26][27][28]. Following Ref. [15], this can be taken into account, in a non-relativistic approach 7 , by re-writing the form factor close to threshold as [27] where a and b are perturbative calculable coefficients obtained from matching the nonrelativistic theory to the full theory. To leading order, one has a = 1 2 (1 − π 2 4 ) and b = 2π 2 /m 2 t 1 for the real and imaginary parts, respectively. Moreover, Et 1 = M H −2mt 1 is the energy gap from the threshold region and Γ ef t 1 is a regulating effective scattering width for the top squark in the loop which can be of O(1 GeV) or below. If the stop total width Γt happens to be too small, specifically if Γt ≪ 1 GeV, Γ ef t 1 is expected to be then of order the decay width Γ Σt of the stoponium state Σt whose impact on the diphoton excess will be discussed later. Finally, G(0, 0; Ef ) is the S-wave Green's function of the non-relativistic Schrödinger equation in the presence of a Coulomb potential V (r) = −C F α/r [30].
Following Ref. [15], we have estimated the absolute value of the enhancement factor F , defined as F = A H 0 (threshold enhanced)/A H 0 (perturbative), as a function of the effective width Γ ef t 1 , for a resonance mass M H = 750 GeV and an energy gap Et 1 = M H −2mt 1 negative 5 We thank Pietro Slavich for his cooperation on this issue. 6 Our estimates are performed by defining all input parameters in the DR scheme, including the stop masses mt 1,2 and the trilinear Yukawa coupling A t . To accurately address, however, the issue of threshold and stoponium effects, other IR-safe renormalization schemes may be more appropriate, especially for the definition of the colouredt 1 -particle mass mt 1 , similar to the potential-subtracted and 1S renormalization schemes for the t-quark mass m t used in higher-order computations of tt production at threshold [25]. However, such scheme redefinitions for mt 1 and A t do not generally change the predicted values of physical observables, such as decay rates and cross sections, at a given loop order of the perturbation expansion. 7 In the context of QCD, we are dealing with a region in the deep infra-red regime where non-perturbative gluon mass effects that extend up to the GeV region might be needed to be taken into account [29]. In view of the lack of first principle's calculation for the case of quasi-stable top squarks, we perform a conservative estimate by adapting the results of the non-relativistic approach in [27]. and of order 1 GeV. We find 8 that for Γ ef t 1 = Γt 1 = O(1 GeV), one can easily obtain an enhancement factor of 2, while for a smallert 1 decay width, a much larger factor is possible. For instance, for Γt 1 ≈ 200 MeV (which can easily be achieved if the mass difference betweeñ t 1 and the lightest neutralino χ 0 1 is small enough so that only three-or four-body or loop inducedt 1 decay modes can occur), the enhancement factor in the H → γγ amplitude is about 2, 4, 8, for Et 1 = −1.5,−2,−2.5 GeV, respectively. Note that the maximum enhancement of a factor 8 is reached for Et 1 ≈ −2.5 GeV.
Hence, considering that a similar threshold enhancement could be present in the Hgg amplitude, one can achieve at least one order of magnitude enhancement in the gg → H → γγ cross section times branching ratio compared to the leading order result. Together with the initial one loop contribution of the mt 1 ≈ 1 2 M H top squark discussed before, this will be sufficient to increase the diphoton production rate to the level of O(1 fb). In addition, possible QCD threshold enhancements can be sufficiently large so as to avoid considering too high µ or A t values to enhance the coupling g Ht 1t1 , and one can thus obtain sizeable diphoton production cross sections of O(1 fb) at the LHC, even with basic SUSY parameters that can occur in constrained MSSM scenarios, such as the minimal supergravity model with non-universal Higgs mass parameters [4].
A second important issue that needs to be addressed is the formation of the stoponium bound states Σt and their mixing with the CP-even H boson 9 . For our illustrations, we only consider the lowest lying 1S scalar stoponium state Σt, which can mix with the H boson. Our approach is similar to Ref. [9], and we ignore the potential impact of s-dependent effects on the H and Σt masses, their widths and their mixings [32]. In this simplified scenario, the resonant transition amplitude A res (s) = A(gg → H, Σt → γγ) is given by where V g H (V γ H ) and V g Σt (V γ Σt ) are the effective couplings of H and Σt to the gluons g (photons γ), and we neglect non-resonant contributions in our estimates. For the lowest lying state Σt, its mixing δM 2 HΣt with the H boson is purely dispersive and of O(40 GeV)×M Σt , as estimated in the Coulomb approximation, by virtue of eqs. (3.10)-(3.12) of [33]. Moreover, we observe that for tan β ∼ 5-10, the decay widths of the heavy H boson and the stoponium Σt are comparable in size, i.e., Γ H ∼ Γ Σt ∼ O(GeV) [9], but the effective H couplings V g,γ H are QCD-enhanced with respect to the Σt couplings V g,γ Σt by a factor of 2 (or more). Consequently, the amplitude A res (s), with only the H-boson included, is at least a factor of 3 larger than the one with only the stoponium Σt being considered.
At the cross section level, we may naively estimate that ignoring potentially destructive Higgs-stoponium interference effects [34], the inclusion of all stoponium resonances can increase the signal cross section σ(gg → Φ → γγ) by up to a factor of 1.5, especially if one adopts the results for the stoponium wave-function R nS (0) at the origin, from non-relativistic lattice computations [35]. This increase in the signal rate would open a somewhat wider portion of the MSSM parameter space for an enhanced production rate of diphoton resonances.
In summary, in this exploratory Letter we have considered scenarios in the context of the MSSM in which very large diphoton rates can be obtained at the current and future LHC runs. For the sake of illustration, we have taken the example of the excess in the diphoton spectrum observed by ATLAS and CMS in their early 13 TeV data [1] and which turned out to be simply a statistical fluctuation [2]. In the context of the MSSM, this excess of O(fb) could have been explained by the production of the heavier CP-even H boson of a mass M H ≃ 750 GeV, with the large gg → H production cross section times H → γγ decay branching ratio. This enhancement is a combination of three different sources, all related to the fact that the lighter top squark 10 has a mass close to the 1 2 M H threshold, i.e. mt 1 ≈ 375 GeV. The first one is that, at leading order,t 1 contributes maximally to the Hgg and Hγγ amplitudes, especially if the Ht * 1t 1 coupling is strong which can be achieved by allowing large values for the higgsino mass parameter µ. Compared to the case where only the top quark contribution is considered for tan β = 1 for which it is maximal, an enhancement factor of two orders of magnitude for the gg → Φ → γγ signal can be achieved. This alone, might be sufficient to obtain O(fb) diphoton rates. Nevertheless, a second source of enhancement can come from the inclusion of QCD corrections to the H → γγ process near the 1 2 M H threshold which can easily lead to an extra factor of 2 or more enhancement at the amplitude level. Finally, a last ingredient is the formation of stoponium bound states which can mix with the H boson. Their effect might increase the gg → Φ → γγ rate by another factor of about 2.
Hence, the addition of these many enhancement factors will give rise to an enhanced diphoton cross section of O(1 fb) for a heavy diphoton Higgs resonance, having a mass well above the tt threshold, e.g. with M H ≈ 750 GeV, even within the context of the plain MSSM 11 .
The scenario thus features light top and bottom squarks and, hence, a relatively low SUSY scale M S < ∼ 1 TeV as favoured by naturalness arguments. This nevertheless allows for the h-boson mass to be close to 125 GeV, if tan β is relatively large and stop mixing maximal as in our case. In order to cope with constraints from SUSY particle searches at the LHC [7], the gluino and the first/second generation squarks should have masses above the TeV scale. The charginos and neutralinos should also be heavy (in particular the higgsinos as µ is large) except the lightest neutralino χ 0 1 , which could be the lightest stable SUSY-particle (LSP) and must have a mass only slightly lower than mt 1 , as LHC limits on mt 1 are practically non-existent if m χ 0 1 > ∼ 300 GeV [7]. In this case, the first accessible visible SUSY state at the LHC would bet 1 which will mainly decay intot 1 → cχ 0 1 (via loops) andt 1 → bff ′ χ 0 1 (at the three-or four-body level) [38]. The dominant decays of the heavier stop 12 will bet 2 →t 1 Z and to a lesser extentt 2 →t 1 h, while those of two bottom squarks could almost exclusively beb 1,2 →t 1 W . Hence, besides M H ≈ 2mt 1 which is a firm prediction, the present scenario favours a light third generation squark spectrum, as well as the usual MSSM degenerate heavy Higgs spectrum, M A ≈ M H ± ≈ M H , that can be probed at the current LHC run.
Our scenario exhibits a number of other interesting phenomenological features that need 10 A similar mechanism with light bottom squarks can be invoked but it is disfavoured compared to the stop one because: (i) the electric charge e b = − 1 3 forces us to pay a penalty of a factor 4 in the Hγγ vertex and (ii) it is more difficult to enhance the Hb * 1b1 coupling to the required level, sinceĝ Hb1b1 ∝ m b (A b tan β −µ). For the case of τ -sleptons, the situation is even worse as they affect only the Hγγ loop and the relevant couplingĝ Hτ1τ1 is smaller by a factor m b /m τ . 11 To the best of our knowledge, the present Letter and the earlier attempt in Ref. [15] have offered the first interpretations for 750 GeV diphoton resonances with enhanced production rates within the context of the usual MSSM with R-parity conservation and without any additional particle content. Otherwise, other minimal beyond-the-MSSM suggestions include the R-parity violating MSSM [36] and the next-to-MSSM [37]. 12 The rate for pp →t * 2t 2 → ZZχ 0 1 χ 0 1 jj → ℓ + ℓ − +jets+missing energy would be in the right ballpark for mt 2 ≈ 600-800 GeV, so as to explain the apparent 3σ excess in the ATLAS data at √ s = 8 TeV [39].
to be discussed in more detail. On the Higgs side, for instance, one would like to precisely determine the impact of the SUSY particle spectrum on the tree-level and loop-induced decays of the MSSM Higgs states, such as H → Zγ in which similar effects as in H → γγ might occur, as well as quasi-on-shell H ( * ) →t * 1t 1 which offers a direct and falsifiable test of the actual threshold enhancement mechanism under study here. Another interesting issue would be to explore the possibility of resonant CP-violating effects at the Φ resonance which could then be a mixture of the CP-even and CP-odd states [32]. In the case of the supersymmetric spectrum, our scenario leads to relatively light top and bottom squarks as discussed above and it would be interesting to study how they can be detected in the presence of, not only a bino-like LSP that is nearly mass degenerate with thet 1 state, but also a gravitino LSP in both gravity or gauge-mediated SUSY-breaking scenarios. This last aspect can have two important consequences: (i) thet 1 total width would be very small, as only multi-body or loop-generated decays will be allowed [38], and (ii) the relic density of the bino dark matter might be obtained through stop-neutralino co-annihilation [40].
Hence, within the context of the MSSM, diphoton resonances produced with largely enhanced rates at the LHC could lead to an extremely interesting phenomenology both in the Higgs and the superparticle sectors. Some of these aspects have been briefly touched upon in this note and we leave the discussion of many other aspects to a forthcoming study [41].