Scholarly article on topic 'Enhanced rates for diphoton resonances in the MSSM'

Enhanced rates for diphoton resonances in the MSSM Academic research paper on "Physical sciences"

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Abstract of research paper on Physical sciences, author of scientific article — Abdelhak Djouadi, Apostolos Pilaftsis

Abstract 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 t ˜ 1 when its mass m t ˜ 1 happens to be near the t ˜ 1 ⁎ t ˜ 1 threshold, i.e. for m t ˜ 1 ≃ 1 2 M H . The scenario requires a relatively low supersymmetry-breaking scale M S ≲ 1  TeV , but large values of the higgsino mass parameter, μ ≳ 1  TeV , that lead to a strong H t ˜ 1 ⁎ 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 t ˜ 1 ⁎ 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.

Academic research paper on topic "Enhanced rates for diphoton resonances in the MSSM"

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Physics Letters B

www.elsevier.com/locate/physletb

Enhanced rates for diphoton resonances in the MSSM

Abdelhak Djouadiab, Apostolos Pilaftsisb c *

a Laboratoire de Physique Théorique, CNRS and Université Paris-Sud, Bât. 210, F-91405 Orsay Cedex, France b Theory Department, CERN, CH 1211 Geneva 23, Switzerland

c Consortium for Fundamental Physics, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, United Kingdom

CrossMark

A R T I C L E I N F 0

Article history:

Received 13 May 2016

Received in revised form 9 November 2016

Accepted 6 December 2016

Available online 12 December 2016

Editor: A. Ringwald

A B S T R A C T

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 t-i when its mass m-t1 happens to be near the tjt-i threshold, i.e. for m-t1 ~ 2 MH. The scenario requires a relatively low supersymmetry-breaking scale MS < 1 TeV, but large values of the higgsino mass parameter, ¡i > 1 TeV, that lead to a strong Htjti 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 tjti 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.

© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

In December 2015, the ATLAS and CMS collaborations have reported an excess in the 13 TeV LHC data corresponding to a possible resonance $ 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 $ is a scalar boson, the production cross section in gluon-fusion ff(gg ^ $) times the two-photon decay branching ratio BR($ ^ yy) 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 dipho-

* Corresponding author.

E-mail address: apostolos.pilaftsis@manchester.ac.uk (A. Pilaftsis).

ton resonances in one such scenario: the Minimal Supersymmetric extension of the SM (MSSM) [4,5], softly broken at scales MS = O(1 TeV) for phenomenological reasons. We investigate a few possibilities that lead to a large enhancement of the pp ^ yy 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 elec-troweak symmetry leading to three neutral and two charged physical states. The $ 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 MH & MA in the so-called decoupling regime MA ^ MZ 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 $ = H/A Yukawa couplings to top quarks are sizeable for small values of the well-known ratio tan /) 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

http://dx.doi.org/10.1016/j.physletb.2016.12.011

0370-2693/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

radiative corrections are taken into account [8]), the top quark cannot generate sizeable enough loop contributions to the gg — H/A and H/A — yy 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 a 1/MS 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 «fs = 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 Hyy couplings, which are enhanced via loops involving the lightest top squark t1. The state t1 will have significant loop contribution if its mass mt1 happens to be near the t^t1 threshold, m^ ~ 2 MH. Given that stoponium = (t^t1) 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 h~t states. In addition, assuming a Higgs mass MH < 1 TeV, large values of the Higgsino mass parameter i are required, e.g. i > 1 TeV, for a stop SUSY-breaking scale Ms ~ 2-1 TeV. Such values enhance the strength of the Ht^ti coupling, through the so-called F-term contribution from the Higgs doublet superfield Hu that couples to up-type quark superfields. Another smaller source of enhancement arises from the stop mixing parameter At, which can still play a significant role if the ratio tan fi is relatively low, i.e. for tan fi < 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 fi > 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 squark t1 is the lightest or next-to-lightest visible supersymmetric particle, for which a lower-mass gravitino or a bino nearly degenerate with t1 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 $ 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 $ 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 fi, with 1 < tan fi < 60. For values tan fi < 5, the only important Yukawa coupling ff is the one of the top quark, while for tan fi > 10, the couplings to bottom quarks and t lep-tons are enhanced, i.e. ff = 42m f/v x g $ ff with g $tt = cot fi and g$bb = g$xx = tan fi at the tree level. Nevertheless, for a mass M$ & 750 GeV, values tan fi > 20 are excluded by the search of A/H — tt resonances [10], while tan fi values not too close to unity can be accommodated by the search for H/A — tt resonance [11].

At the LHC, the $ = H/ A states are mainly produced in the gg — $ fusion mechanism that is mediated by a t-quark loop with cross sections at Vs = 13 TeV of about a(gg — A) & 1.3 pb and a(gg — H) = 0.8 pb for M$ & 750 GeV and tan fi & 1 [12]. The H/A states will then mainly decay into top quark pairs with partial (& total) widths that are of order r$ & 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 — YY) & 7 x 10-6 and BR(H — yy) & 6 x 10-6 [13,14]. Thus, one has a diphoton production cross section ff(gg — YY), when the resonant s-channel H- and A-boson exchanges are added, of about ff(gg — $) x BR($ — yy) & 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 su-persymmetric particles can generate such a huge enhancement factor of ~ 100. The chargino (x±) contributions can be sufficiently large only in a rather contrived scenario, in which the mass mx±

satisfies the relation mx± = 2MA within less than a MeV accuracy,

such that a large factor of QED-corrected threshold effects can occur [15]. In such a case, however, finite-width regulating effects due to (x+X-) 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 Htjt1 coupling thanks to a large i parameter, and the impact of possible bound-state effects due to a stoponium resonance is properly assessed.

At leading order, the contributions of the top quark t and its superpartners t1 and t2 to both the Hyy and Hgg vertices1 (in our numerical analysis, all fermion and sfermion loops are included) are given by the amplitudes (up to colour and electric charge factors)

A(Hyy) & A(Hgg)

& AH/2(tt) x cotp + £ gm/m\ x AH(vt¡), (1) i=1,2

where the functional dependence of the form factors Ay2(Tj) and

AH(T) for spin-1 and spin-0 particles (with r¡ = MH/4m2 for the ith particle running in the loop) is displayed on the left panel of Fig. 1. As expected, they are real below the MH = 2m¡ mass threshold and develop an imaginary part above this. The maxima are attained near the tt and t|t1-mass thresholds for the loop functions Re(AH/2) and Re(AH), respectively. Specifically, for t¡ = 1, one has Re(AH/2) ^ 2.3 and Re(AH) ^ f, whilst Im(AH) ^ 1 for t values slightly above the kinematical opening of the tjt1 threshold. Hence, the stop contribution is maximal for m^ = 375 GeV and, it is in fact comparable to the top quark one, since for t¡ = MH/4m2 ^ 4.75, one has |AH/2(Tt)\ & 1.57 to be contrasted with |AH(1)| & 1.33. Since the SUSY scale MS m~t1 m~t2 is supposed to be close to 1 TeV from naturalness arguments, one needs a large splitting between the two stops; the contribution of the heavier t2 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, Xt = At — \x/ tan p. At the same time, a large value of Xt together with tan p > 3,

maximize the radiative corrections to the mass Mh of the observed h-boson2 and allows it to reach 125 GeV for a SUSY-breaking scale Ms ~ 1 TeV [17,18].

Large values of ¡i and At (and of Xt) increase considerably the Htjt1 coupling that can strongly enhance the Hgg and Hyy am-

1 Because of CP invariance, the CP-odd boson A does not couple to identical sfermions, so their quantum effects on Agg and Ayy vertices appear first at two loops and are therefore small. Note that the contributions of the first and second generation sfermions are tiny while those of third generation sbottoms and staus are important only at very high tan fi values; they will all be included in the numerical analysis. The chargino loops in $ — YY can be neglected if there is no threshold enhancement [15].

2 This scenario is reminiscent of the "gluophobic" one discussed in Ref. [16] for the light h boson but, here, the squark t1 is rather heavy compared to Mh and will have only a limited impact on the loop induced gg — h production and h — YY decay processes.

0.3 0.5 1 2 3 4 5 r = M|/4mf

__^___

0.2 0.3 0.5 0.7 1 2 3 -fi/M s

BR(tt) "X — BR(bb)

BR(tt) i

HI rH [TeV] / /

3 5 10 20 30 60 tan/3

Fig. 1. Left: The real and imaginary parts of the form factors AH/2 with fermion loops and A{j with scalar loops as functions of the variable t = MH/4mi. Center: the coupling (in units of eMZ/ cos6W sin6W) vs squared mass ratio gHt1t1 /m| as a function of the higgsino mass i [in TeV] for At = V6ms (with MS = 1 TeV) and several tanp values. Right: the tt, bb, tt branching fractions and the total width [in TeV] of the H state (when only decays into fermions occurs) for MH = 750 GeV as a function of tanp.

plitudes. In the decoupling limit and for maximally mixed ti states, the tree-level Htjt1-coupling is given by [5]

M2? 2 2 1

?Hhh = 4 sin2£ + cot2 p m2 + ^mt(At cotp — ¡i).

In the central panel of Fig. 1, g^^ is plotted as a function of i for several values of tan p and fixed Xt = At — ¡i cot p = V6 ms , so as to get Mh & 125 GeV with a scale MS = 1 TeV. As can be seen from the central panel, g^^ can be very large for i in the multi-TeV range. In fact, above the value tanp & 3, only the third term of eq. (2) is important and the coupling is enhanced for large values of For instance, if MS & 1 TeV and m^ = 375 GeV, the t1 contribution to the loop amplitudes in eq. (1) is roughly

2 mt i

gHt ~t /m2 x AH (r~t ) &----—— & —0.8 — .

t1 ' t1 0 ( t1) 3 mt1 mt1 M

In particular, for i = -4MS as in the so-called CPX scenario [18,19], the stop effects can be twice as large as the top ones with tan p = 1. This gives a prediction for the diphoton cross section which is about 24 = 16 times larger than that obtained for tan p = 1.

Finally, one should take into account the size of the resonance width rH. Indeed, the diphoton rate is given by the gg — H production cross section times the H — yy decay branching ratio and the impact of the total width rH is important in the latter case. For tan p = 1, the total width is almost exclusively generated by the H — tt partial width, rH & T(H — tt) a m^cot2 p/v and is about 30 GeV for MH = 750 GeV. In our case, this situation is unacceptable since, as we have increased a(gg — H) by including the stop contributions and we have BR(H — tt) & 1, a(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 — yy). This can be achieved by considering larger tan p values for which

m;2 2 mi: 2 m? 2 Fh a— cot2 p + — tan2 p + — tan2 p. (4)

For tan p = 10, one then obtains rH & 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 tanp. The ratio BR(H ^ yy) can be thus increased, in principle, by an order of magnitude compared to the tan p = 1

case. Nevertheless, if a larger decay width is required for the resonance, one can increase the chosen tan p value to, say tan p & 20 (i.e. closer to the limit allowed by H/A tt searches [10]) and enhancing the t1 contribution by increasing the value of the parameter ¡i. However, values rH > 30 GeV cannot be achieved in principle.3 Note that small values of tanp, tan p < 5, cannot be tolerated, as they do not suppress enough BR(H — tt) to a level to be compatible with ttt resonance searches [11].

When all the ingredients discussed above are put together, the cross section ff(gg — H) times the decay branching ratio BR(H — yy) at the LHC with «fs = 13 TeV is displayed in Fig. 2 as a function of the parameter i for the representative values tanp = 3, 5, 10, 20 and MH = 750 GeV. The rate is normalised to the case where only top quark loops are present with tan p = 1. The scenario features a light stop with m^ & 1MH & 375 GeV, which is obtained for a SUSY scale Ms & 600 GeV and a stop mixing parameter Xt = V6Ms, respectively. The contributions of the other states, the heavier stop with mj2 ~ M2S/m~t1 > 800 GeV, the

two sbottoms with m

: MS (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 lightest t1 . As can be seen, for tan p = 10 for instance, an enhancement by a factor of about 100 can be obtained for a value \i\ = 3 TeV, i.e. \i\ ~ 5MS.4 Hence, one easily arrives at production cross sections of O(1 fb) at the LHC for heavy Higgs resonances well above the ttt 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].

3 In fact, to obtain a sizeable total width, one option could be to take m~t1 a few GeV below the 2MH threshold: one then opens the H — t1t1 channel which increases the width rH. This channel would suppress BR(H — tt) as required at low tanp but also BR(H — yy). 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 \i\ can be obtained, for instance, in the context of the new MSSM [20], in which the tadpole term tSS for the singlet field S has different origin from the soft SUSY-breaking mass m2SS* S. For values of t]/3 > mS, a large vacuum expectation value for S can be generated of order vS = (S) ~ tS/m2S > mS ~ MS, giving rise to a large effective i parameter: ¡eff = XvS > MS, where X < 0.6 is the superpotential coupling of the chiral singlet superfield S to the Higgs doublet superfields Hu and Hd. Hence, in this new MSSM setting, the appearance of potentially dangerous charged- and colour-breaking minima [21] due to a large ¡eff can be avoided more naturally than in the MSSM.

-1 0 f! [TeV]

Fig. 2. The enhancement factor of the diphoton cross section a(gg ^ H) x BR(H ^ yy) at the 13 TeV LHC as a function of i [in TeV] for several values of tan p. It is obtained when including in the Hgg and Hyy vertices third generation fermion f and all sfermion f loops, in particular that of the lightest top squark i1 with m^ = 1MH & 375 GeV, and is normalised to the rate when only the top quark loop is present with tanp = 1.

While the MS and Xt 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 Mh = 125 GeV for tanp > 5 (in particular if an uncertainty of a few GeV from its determination is taken into account [17]), the required large i value might be problematic in some cases. Indeed, at high tan p and there are additional one-loop vertex corrections that modify the Higgs couplings to b-quarks, the dominant components being given by [22]

^b J ^

V 3n max(m?

, m? , m? ) bi b?

16n? max(i?, m? , m? )

i tan p,

where Xt = V2mt/v. Note that in eq. (5), the first and second terms are the dominant gluino-sbottom and stop-chargino loop corrections to the Hbb coupling, respectively. For |i| tanp ^ MS, 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 |i| < 5MS or alternatively, partly or fully cancel the two terms of the equation above. This, for instance, can be achieved by choosing a trilinear coupling At < 0 and a very heavy gluino with a mass mg such that mg & -4|l|2/At.

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 ^ YY rate is almost entirely explained when NLO QCD corrections to the rate are included as in Ref. [23]. For instance, for tan p = 10, third-generation scalar masses of m~tL = m~tR = mbR = 0.8 TeV & MS, trilinear couplings At = Ab = 2 TeV, gaug-ino mass parameters M1 = 1M2 = 1M3 = 350 GeV and a higgsino mass i = 2.3 TeV, the program Suspect2 (version 2.41) yields mt1 = 373.75 GeV and mt2 = 847 GeV. Moreover, fixing the CP-odd A-scalar mass to MA = 756 GeV, one obtains MH = 747.6 GeV, which is somewhat above the 2mt1 & 747.5 GeV threshold, and

Mh = 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 p = 1. In detail, HDECAY 3.4 computes BR(H ^ yy) = 9.2 x 10-4, BR(H ^ gg) = 4.2 x 10—2 and a total width rH = 2.06 GeV, to be compared with BR(H ^ yy) = 6x 10—6, BR(H ^ gg) = 1.8x 10—3 and TH = 35 GeV without stop loops and tanp = 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 ff(gg ^ H ^ YY) & 0.83 fb at the LHC with V? = 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 Mh close to 125 GeV and SM-like couplings, this benchmark point leads to BR(H ^ tt) = 7% and BR(H ^ tt) = 15%. Given that only the gg ^ H production channel gets enhanced thanks to t1tj -threshold effects, we can thus estimate that a(gg ^ H) BR(H ^ tt) & 62 fb at V? = 13 TeV, which satisfies the current LHC limits deduced from direct MSSM Higgs searches in the tt 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 ^ YY 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 Hyy and Hgg couplings appearing in eq. (1) and displayed in Fig. 1 (left) does not accurately describe the threshold region, m^ & 2MH [23] 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 S-wave (quasi) bound states [26-28]. Following Ref. [15], this can be taken into account, in a non-relativistic ap-proach,7 by re-writing the form factor close to threshold as [27]

A0H = a + b x G(0, 0; Eti + irfen),

where a and b are perturbative calculable coefficients obtained from matching the non-relativistic theory to the full theory. To leading order, one has a = 1 (1 — ) and b = 2n 2/m2 for the real and imaginary parts, respectively. Moreover, E~t1 = MH — 2m~t1 is the energy gap from the threshold region and reff 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 Tf happens to be too small, specifically if Tj ^ 1 GeV, reff is expected to be then of order the decay width T^ of the stoponium state whose impact on the diphoton excess will be discussed later. Finally, G (0, 0; Ef) is the S-wave Green's function of the

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 m^ ? and the trilinear Yukawa coupling At. To accurately address, however, the issue of threshold and stoponium effects, other IR-safe renor-malization schemes may be more appropriate, especially for the definition of the coloured t1-particle mass m^, similar to the potential-subtracted and 1S renor-malization schemes for the t-quark mass mt used in higher-order computations of ti production at threshold [?5]. However, such scheme redefinitions for m^ and At 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 [?9]. In view of the lack of first principle's calcu-

lation for the case of quasi-stable top squarks, we perform a conservative estimate by adapting the results of the non-relativistic approach in [?7].

non-relativistic Schrodinger equation in the presence of a Coulomb potential V(r) = —CFa/r [30].

Following Ref. [15], we have estimated the absolute value of the enhancement factor F, defined as F = Aff(threshold enhanced)/ A¡H (perturbative), as a function of the effective width reff, for a resonance mass MH = 750 GeV and an energy gap E~t1 = MH — 2m~tl negative and of order 1 GeV. We find8 that for r~ff = r^ = O(1 GeV), one can easily obtain an enhancement factor of 2, while for a smaller t1 decay width, a much larger factor is possible. For instance, for r^ & 200 MeV (which can easily be achieved if the mass difference between t1 and the lightest neutralino x0 is small enough so that only three- or four-body or loop induced t1 decay modes can occur), the enhancement factor in the H ^ yy amplitude is about 2, 4, 8, for E-tl = —1.5, —2, —2.5 GeV, respectively. Note that the maximum enhancement of a factor 8 is reached for Et1 & —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 ^ yy cross section times branching ratio compared to the leading order result. Together with the initial one loop contribution of the m~t1 & 1MH 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 ¡ or At values to enhance the coupling gHt1t1, 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 £ and their mixing with the CP-even H boson.9 For our illustrations, we only consider the lowest lying 1S scalar stoponium state £~t, 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 £ masses, their widths and their mixings [32]. In this simplified scenario, the resonant transition amplitude Ares(s) = A(gg ^ H, £ ^ yy) is given by

Aes (s) = (VH , Vg)

s - MH + iMHrH

*H S M H g

S M H g,

s - Mg + iM*t r*

where VH (VH) and Vg. (Vg) are the effective couplings of H and g~t to the gluons g (photons y ), and we neglect non-resonant contributions in our estimates. For the lowest lying state g-t, its mixing S MH g with the H boson is purely dispersive and of 0(40 GeV) x M g, as estimated in the Coulomb approximation, by virtue of eqs. (3.10)-(3.12) of [33]. Moreover, we observe that for tan/) ~ 5-10, the decay widths of the heavy H boson and the stoponium g-t are comparable in size, i.e., rH ~ rgt ~ O(GeV) [9], but the effective H couplings VHY are QCD-enhanced with respect to the g~t couplings Vg^ by a factor of 2 (or more). Consequently, the amplitude ^res(s), with only the H -boson included, is at least

8 We thank Aoife Bharucha for her help in this issue.

9 As this work was being finalized for submission, Ref. [31] appeared in which the stoponium bound state was put forward as the only source for an enhanced diphoton rate of the size reported in [1]. There is some partial overlap with our discussion here but the mixing with the H boson, and more generally all issues related to this Higgs state (which is almost entirely responsible of the diphoton excess in our case), have not been considered in Ref. [31].

a factor of 3 larger than the one with only the stoponium g~t 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 ff(gg ^ $ ^ yy) by up to a factor of 1.5, especially if one adopts the results for the stoponium wave-function RnS(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 MH ~ 750 GeV, with the large gg ^ H production cross section times H ^ yy decay branching ratio. This enhancement is a combination of three different sources, all related to the fact that the lighter top squark10 has a mass close to the 1MH threshold, i.e. m-t1 & 375 GeV. The first one is that, at leading order, t1 contributes maximally to the Hgg and Hyy amplitudes, especially if the H^^ coupling is strong which can be achieved by allowing large values for the higgsino mass parameter ¡. Compared to the case where only the top quark contribution is considered for tan ft = 1 for which it is maximal, an enhancement factor of two orders of magnitude for the gg ^ $ ^ yy 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 ^ yy process near the 1MH 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 ^ $ ^ yy 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 MH & 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 MS < 1 TeV as favoured by naturalness arguments. This nevertheless allows for the h -boson mass to be close to 125 GeV, if tan ft 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 ¡i is large) except the lightest neutralino X\, which could be the lightest stable SUSY-particle (LSP) and must

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 eb = — 3 forces us to pay a penalty of a factor 4 in the Hyy vertex and (ii) it is more difficult to enhance the Hbjb] coupling to the required level, since gHb g a mb (Ab tan ft — ¡). For the case of t-sleptons, the situation is even worse as they affect only the H yy loop and the relevant coupling ¡¡h t1t1 is smaller by a factor mb /mT.

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].

have a mass only slightly lower than m~t1, as LHC limits on m~t1 are practically non-existent if mx0 > 300 GeV [7]. In this case, the

first accessible visible SUSY state at the LHC would be t1 which will mainly decay into t1 — cx0 (via loops) and t1 — bf f'x? (at the three- or four-body level) [38]. The dominant decays of the heavier stop12 will be t2 — t1 Z and to a lesser extent t2 — t1h, while those of two bottom squarks could almost exclusively be b 1,2 — t1 W. Hence, besides MH & 2m-t1 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, MA & MH± & MH, that can be probed at the current LHC run.

Our scenario exhibits a number of other interesting phe-nomenological features that need 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 — Zy in which similar effects as in H — YY might occur, as well as quasi-on-shell H(2) — tjt1 which offers a direct and falsi-fiable 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 $ 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 the t1 state, but also a gravitino LSP in both gravity or gauge-mediated SUSY-breaking scenarios. This last aspect can have two important consequences: (i) the t1 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].

Acknowledgements

We would like to thank Aoife Bharucha for collaboration at the early stages of this work. Discussions with Manuel Drees, Michael Spira and Pietro Slavich are gratefully acknowledged. AD is supported by the ERC advanced grant Higgs@LHC (with 321133) and AP by the Lancaster-Manchester-Sheffield Consortium for Fundamental Physics, under STFC research grant: ST/L000520/1.

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