The 750 Gev Diphoton Excess As a First Light on Supersymmetry Breaking

Physics Letters B 759 (2016) 159–165

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Physics Letters B

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The 750 GeV diphoton excess as a ﬁrst light on supersymmetry breaking ∗ J.A. Casas a, J.R. Espinosa b,c, , J.M. Moreno a a Instituto de Física Teórica, IFT-UAM/CSIC, Nicolás Cabrera 13, UAM Cantoblanco, 28049 Madrid, Spain b Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193, Bellaterra (Barcelona), Spain c ICREA, Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain a r t i c l e i n f o a b s t r a c t

Article history: One of the most exciting explanations advanced for the recent diphoton excess found by ATLAS and Received 15 February 2016 CMS is in terms of sgoldstino decays: a signal of low-energy supersymmetry-breaking scenarios. The Received in revised form 27 April 2016 sgoldstino, a scalar, couples directly to gluons and photons, with strength related to gaugino masses, that Accepted 21 May 2016 can be of the right magnitude to explain the excess. However, fitting the suggested resonance width, Available online 25 May 2016 45 GeV, is not so easy. In this paper we explore efficient possibilities to enhance the sgoldstino Editor: G.F. Giudice width, via the decay into two Higgses, two Higgsinos and through mixing between the sgoldstino and the Higgs boson. In addition, we present an alternative and more efficient mechanism to generate a mass splitting between the scalar and pseudoscalar components of the sgoldstino, which has been suggested as an interesting alternative explanation to the apparent width of the resonance. © 2016 The Author(s). 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.

1. Introduction an scalar field φ (the sgoldstino) coupled to gluons and photons in a direct way, so that an effective production via gluon fusion and The ATLAS and CMS Collaborations√ have recently reported an the subsequent decay into photons are possible. Beside reproduc- excess in diphoton searches at s = 13 TeV for a ∼ 750 GeV ing the observed cross section, any good explanation of the data diphoton invariant mass [1–3]. The local significance is 3.9σ (AT- should account for the apparent sizeable width of the resonance, LAS) and 2.6σ (CMS), although it gets smaller once the look- φ/Mφ 0.06, although the data are not yet conclusive and the elsewhere effect is taken into account. However, the fact than both significance of such a large width is not too large. For this rea- experiments see the signal in the same place has created in the son, in the following, scenarios that are able to explain at least a community the expectation that it could be the long expected sig- significant fraction of that apparent large width are considered fa- nal of new physics. vorably. The authors of ref. [6] discussed a simple explanation for Once the accumulated statistics at ATLAS and CMS grow large the apparent width: a mass splitting (as advocated in [4]) between enough, we will see finally whether or not this excess is an statisti- the scalar and pseudoscalar degrees of freedom of the sgoldstino. cal fluctuation. In the meantime, it is tempting to try and interpret In this paper we review the explanation of the diphoton sig- the data as a signal of new physics as the flood of papers studying nal (sect. 3) based on this type of scenarios (sect. 2), exploring different BSM scenarios that could accommodate the excess testify. mechanisms for a broad φ , potentially consistent with the data. Those most relevant to our discussion are [4–10]. In our opinion, We present other mechanisms for the mentioned sgoldstino mass probably the most exciting theoretical possibility to accommodate splitting, which are more efficient than those considered up to this resonance is the one pursued by the authors of [5,6,8], who now (sect. 4). In our analysis we discuss some subtleties not pre- have contemplated scenarios with a scale of SUSY breaking not viously considered that can constrain and affect substantially the far from the TeV scale (low-scale SUSY breaking) [11–14]. Poten- results. We also discuss the possibility that sgoldstinos decay effi- tially, these models contain the main ingredient to fit the signal: ciently into Higgses (sect. 5), as the partial width into that channel is naively parametrically enhanced with respect to other channels; into Higgs decay channels through sgoldstino-Higgs mixing * Corresponding author. (sect. 6); and into Higgsinos (sect. 7), as there is more freedom to E-mail address: jose.espinosa@cern.ch (J.R. Espinosa). enhance this width without clashing with previous LHC searches. http://dx.doi.org/10.1016/j.physletb.2016.05.070 0370-2693/© 2016 The Author(s). 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. 160 J.A. Casas et al. / Physics Letters B 759 (2016) 159–165

2. The low-scale SUSY-breaking scenario Similarly, from Eqs. (1) and (2), the scalar potential V = V F + V D for the two supersymmetric Higgs doublets plus the complex singlet field , is1: The low-scale SUSY-breaking (LSSB) scenario√ [11–14] is a framework in which the scale of SUSY breaking, F , and its medi- 1 = 2 + ˜ 2| |2 + ˜ 2 2 + ation, M, are not far from the TeV scale. The main differences with V F αφm (ρφm h.c.) 2 respect to more conventional supersymmetric models, where the 2 2 2 2 2 + m |Hu| + m |H | + m Hu · H + h.c. latter scales are large, are the following: i) the low-energy effec- Hu Hd d 12 d tive theory includes the chiral superfield, , responsible for SUSY ∗ ∗ 2 ∗ ∗ 2 + (mX + m )|Hu| + (mX + m )|Hd| breaking, in particular its fermionic (goldstino) and scalar (sgold- 1 X1 2 X2 + + ∗ · + stino) degrees of freedom; ii) besides the ordinary SUSY-soft break- (mX3 mX4 )Hu Hd h.c. ing terms, the effective theory contains additional hard-breaking 1 1 + | |4 + | |4 + | |2| |2 + | · |2 operators, e.g. quartic Higgs couplings. The latter make the Higgs λ1 Hu λ2 Hd λ3 Hu Hd λ4 Hu Hd 2 2 sector resemble a two-Higgs doublet model with an additional 1 2 2 2 (complex) singlet. LSSB models present a much milder electroweak + λ5 (Hu · Hd) + λ6|Hu| Hu · Hd + λ7|Hd| Hu · Hd + h.c. fine-tuning than usual MSSMs [12,13] and a rich phenomenology 2 [11–14]. As discussed in refs. [5,6,8], the LSSB scenario can nicely + ... (7) explain the diphoton excess at 750 GeV observed at the LHC. where the dots stand for higher order terms in and nonrenor- Let us summarize the main ingredients of LSSB scenarios. Ex- malizable terms suppressed by powers of M. The various mass panding in inverse powers of M, superpotential, W , Kähler poten- parameters and quartic couplings in (7) are explicit combinations tial, K , and the gauge kinetic function, fab, read [11] of the parameters in W and K (see ref. [11] for explicit formulae). As a summary, denoting by μ the typical scale of the supersym- ρφ 3 metric mass parameters [μ, μ , ··· in Eq. (1)] and m˜ = F /M, the W = W MSSM + F + +··· 6M2 2 ˜ 2 mass terms in the potential have contributions of order μ , m , μ m˜ μ. We assume μ m˜ , so that all these squared mass terms are + + +··· · 2 μ Hu Hd expected to be m˜ . Analogously, trilinear terms, m , have con- M Xi tributions of order μ2/M, m˜ 2/M, m˜ μ/M. Finally, the Higgs quartic 1 2 couplings have supersymmetric D-term and F -term contributions, + + +··· (Hu · Hd) + ··· , (1) 2M M where the latter include supersymmetry breaking contributions as (D) (F ) (D) well: λi = λ + λ . The λ are as in the MSSM: αφ αu i i i K =||2 1 − ||2 +··· +|H |2 1 + ||2 +··· 2 u 2 1 1 4M M (D) = (D) = 2 + 2 (D) = 2 − 2 λ1 λ2 (g g ), λ3 (g g ), 2 αd 2 4 4 +|Hd| 1 + || +··· M2 (D) 1 2 λ =− g , (8) 4 2 + · αud ¯ 2 +··· + + ··· Hu Hd h.c. , (2) (D) (D) (D) (F ) 2M2 and λ = λ = λ = 0. Besides, typically λ ∼ m˜ 2/M2, 5 6 7 i ˜ 2 2 2 δab mμ/M , μ /M , although some of these couplings can receive f = 1 + c + ··· . (3) (F ) (F ) ab 2 a contributions at a lower order, λ ∼ m˜ /M, λ ∼ μ/M. Whether ga M 5 i=6,7 the effective theory expansion starts at order m˜ /M or m˜ 2/M2 is Here all the parameters are dimensionless, except the μ, μ ··· pa- a model-dependent question. In what follows we will generically rameters in the superpotential, which have dimensions of mass. (F ) ∼ ˜ 2 2 assume λi m /M but the reader should keep in mind this ex- Replacing by its auxiliary field, F , one gets the soft breaking ception, which might be important in some cases. The effective terms of the theory. In particular, from Eq. (3), one gets masses for quartic self-coupling of the light (SM-like) Higgs, λ|H|4, reads gluinos, M , winos, M , and the bino, M , e.g. M = c F /M. Like- 3 2 1 1 1 = (D) + (F ) + wise, replacing by its scalar component, a complex singlet field, λ λ λ δradλ, (9) that we also denote by , where 1 1 λ = λ c2 + λ s2 + (λ + λ + λ ) sin2 2β = √1 + 1 β 2 β 3 4 5 (φS iφP ) (4) 2 4 2 + 2 + 2 λ6cβ λ7sβ sin 2β, (10) (where φ is the scalar component and φ the pseudoscalar one), S P = ≡ one obtains couplings of the φ’s with the MSSM fields. In par- with tan β Hu / Hd vu/vd. This quartic coupling determines the Higgs mass as in the SM, i.e. m2 = 2λv2, with v2 = v2 + v2 = ticular, the coupling to gluons and photons is directly related to h u d 2 gaugino masses as: (246 GeV) . The sizes of the various contributions are ˜ 2 (D) 2 2 2 (F ) 2 m 2 M 2λ v = m cos (2β) , 2λ v ∼ v , L ⊃ √ 3 a aμν − ˜ aμν Z 2 tr Gμν(φS G φP G ) M 2 2F 2 3 m4 m˜ 2 ∼ t t M ˜ 2δradλv log , (11) γ μν ˜ μν 2π 2 v2 m2 + √ tr Fμν(φS F − φP F ), (5) t 2 2F where mt˜ is the stop mass scale. where Mγ˜ is the photino mass,

1 A linear term in can always be removed by a ﬁeld redeﬁnition. For more 2 2 Mγ˜ = M1 cos θW + M2 sin θW . (6) details, see [11]. J.A. Casas et al. / Physics Letters B 759 (2016) 159–165 161

the total width calculated summing gg + γγ plus other contributions (see e.g. [15]) from the decay into WW, ZZ, Zγ (choosing M1 = M2), which can be comparable to γγ, while φ-decays into tops or goldstinos give only a small contribution. The region consistent with the data corresponds to the area between these two bands. However, one should keep in mind that in the region with small M3 the production mechanism is dominantly photon-fusion, which is in tension with 8TeV data. Finally the gray region is excluded by LHC dijet searches [16] (with the boundary value of M3 scaling as F ). This exclusion limit has been calculated assuming that the φ width is determined by φ decays to SM gauge bosons only and therefore applies only to the blue band. Playing only with the decay channels discussed above one cannot explain = 0.06Mφ , as is clear from the ﬁgure: the band intersection is excluded by dijet searches. Therefore, in order to get closer to the apparently favored green band, there are two possibilities (apart from the possibility that the evidence for the broad width eventually disappears, even if the resonance is there): → that the experimental data correspond in fact to two unresolved Fig. 1. Regions of the M3, Mγ˜ plane√ in which the observed cross section σ (pp resonances, mimicking a broad width; or that other decays of φ φ → γγ) is reproduced, assuming F = 4TeVand M1 = M2. The green and blue bands correspond to = 0.06Mφ and the actual from decays into SM gauge enhance its width by the right amount. We explore these possibil- bosons, respectively. Thin (broad) bands correspond to 1σ (2σ ). The gray region ities in the following sections. is excluded by LHC dijet searches (but applies only to the blue band). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.) 4. Two unresolved resonances

The λ(F ) contributions to the Higgs quartic coupling play a cru- Although the mass resolution in the diphoton channel is very cial role in this kind of scenario: moderate values of the ratio m˜ /M good, with the current statistics, two narrow resonances close in or m˜ 2/M2 (as small as ∼ 0.1–0.2for large tan β) can push up the mass could well be responsible for the apparently wide resonance Higgs mass significantly, so that the measured value mh 125 GeV that ATLAS reports. In the sgoldstino scenario we consider, such can be achieved alleviating the naturalness tension of supersym- double resonance is a natural possibility, as the complex singlet metric models [12]. field has two real components, as explicitly shown in Eq. (4), In this paper we are interested in the decoupling regime with and generic scalar potentials give different masses to φS and φP . a single light Higgs doublet. The singlet should have a 750 GeV Indeed, such mass splitting has been proposed in [4,6] as a resolu- mass while a linear combination of H1 and H2 will have mass tion to the puzzle of the large width of the 750 GeV resonance. In around the TeV scale. this section we go beyond that analysis in several respects, point- ing out that other sources of sgoldstino mass splitting, different 3. The diphoton excess from the one considered in [6], are possible and interesting. After electroweak symmetry breaking (EWSB), the mass matrix The total cross section, σ (pp → φ → γγ), where φ generically for the neutral scalars generically mixes the two sgoldstino fields 0 denotes either φS or φP , is dominated by gluon fusion, and can φS,P with three Higgs fields: the light Higgs h , and the two heavy 0 0 be expressed in terms of the partial widths, gg, γγ and total ones, H and A . In first approximation, neglecting effects from width , as EWSB, as v Mφ , one simply gets from (7) the two sgoldstino ˜ 2 ± squared-mass eigenvalues m (αφ ρφ). A small√ mass splitting re- 1 quires ρ α , in which case M m˜ ρ / α M ρ /α . So, σ (pp → φ → γγ) (C gggg + Cγγγγ)γγ, (12) φ φ φ φ φ φ φ φ sMφ Mφ ∼ 30 GeV requires the mild hierarchy ρφ/αφ ∼ 0.04 between ρ and α , the Wilson coefficients of the first nonrenormalizable with C 2137, C 54 at 13 TeV (see e.g. [4]). We include in φ φ gg γγ terms of in the Kähler potential and superpotential, see Eqs. (1) the production mechanism photon-fusion, which can also be rele- and (2). This source of sgoldstino mass splitting, not considered in vant, as discussed in [9]. From Eq. (5), one can extract the partial [6], is potentially the largest one. widths of φ into gluons and photons: Additional, or alternative, sources of sgoldstino mass splitting 2 3 2 3 from EWSB effects can have two different origins: (i) the trilinear M M M ˜ M 3 φ γ φ couplings that connect the singlet and the Higgs doublets H gg = ,γγ = . (13) i 2 2 2 4π F 32π F in Eq. (7), and (ii) mixed quartic couplings, of the type (λa + ∗ ∗ λ 2)[a |H |2 +(b H · H +h.c.)], that we did not write explicitly Fig. 1 shows the regions in the {M3, Mγ˜ } plane where σ (pp → a i i u d in (7). We consider them in turn. φ → γγ) (summing the contributions from both φS and φP ) is consistent with the combined experimental value,√ which we Type (i) splitting occurs through contributions to the off- − ≡ 0 0 0 naively estimate as σ ∼ 8 ± 2.1fb, for a typical value F = 4 TeV.2 diagonal entries, hi φS,P (with hi h , H , A ), in the Higgs- The green band corresponds to the assumption (favored by ATLAS) sgoldstino mass matrix, that are different for φS and φP and are ∼ ˜ 2 3 that the total width is = 0.06 Mφ . The blue band corresponds to of order mX v, with mX m /M. The size of the φ mass splitting depends on the kind of Higgs that mixes with the sgoldstinos.

√ 2 If we impose Mi < F as an absolute limit required for the EFT √expansion to 3 make sense, explaining the observed diphoton cross-section implies F 8TeV. The trilinear couplings also induce a small vacuum expectation value φ ∼ ∝ 2 2 The allowed values of M3, Mγ˜ simply scale as M F . mX v /Mφ that plays a subdominant role in the discussion that follows. 162 J.A. Casas et al. / Physics Letters B 759 (2016) 159–165

= 1 2 First, if sgoldstinos mix with the light Higgs via a δV 2 mX φh term in the potential, there are two potentially dangerous side- effects. The mixing leads, via eigenvalue repulsion, to a reduction 2 ∼ 2 2 2 of the light Higgs mass by δmh mX v /Mφ (which should be 2 bounded to be naturally smaller than κmh , with κ of order a few), and an upward shift of M2 and M2 of the same order δm2 but φS φP h 2 not necessarily equal for φS and φP , resulting in a Mφ that is a 2 ∼ ˜ 2 ∼ ˜ fraction of δmh . Noting that mX m /M, and Mφ m, one gets 2 2 Mφ ∼ m˜ (v /M ). This is the kind of mass splitting discussed in 2 2 [6]. Using the above-mentioned natural constraint δmh κmh , we 2 ∼ get Mφ mh/(2Mφ) 10κ GeV. Second, since the light Higgs picks up a small sgoldstino component, this mixing reduces uni- versally the Higgs couplings (up to the small couplings of the sgoldstino to different SM particle species). This reduction of Higgs couplings, which has an effect similar to an invisible Higgs width, is bounded by LHC Higgs data to sin2 α 0.2at 95% C.L. [18], where α is the sgoldstino-Higgs mixing angle, given by 2m v Fig. 2. Partial width of sgoldstino decay into two light Higgses (induced by a trilin- X 2 sin 2α = . (14) ear coupling mX φh /2) as a function of the sgoldstino-Higgs mixing angle α. The 2 − 2 Mφ mh gray region is excluded by the LHC limit on the Higgs invisible width. This bound roughly translates into a bound on the splitting, channel for the sgoldstinos into two light Higgses, φ → hh, with M (M /2) sin2 α. In general, splittings M ∼ few × 10 GeV φ φ φ a partial width that is parametrically large and can play a central imply sin2 0.1, which could be visible in the future. However, α role in determining the total φ-width. as we show in section 6, the mixing angle is strongly constrained Let us write schematically the relevant trilinear couplings as by other physical effects, which calls into question the viability of this option. 1 2 δV = mX φh , (15) If the sgoldstinos mix instead with the heavy Higgs doublet, 2 of mass M H , the sgoldstino mass splitting depends on the rela- 2 ∼ 2 2 2 where we generically denote the (real) sgoldstinos as φ and mX ∼ tive size of Mφ and M H . If M H Mφ , one gets Mφ mX v /M H , m˜ 2/M as usual. Through this coupling, φ can decay to two light smaller than the splitting in the previous case. The case M H Mφ 4 would lead to mass splittings similar to those already consid- Higgs bosons. Naively, using a large enough mX , one can get a ∼ = ered but is difficult to realize due to constrains from heavy Higgs sizeable partial width (e.g. mX 1.9TeVto get φ/Mφ 0.06). 2 ∼ However, there is an obstruction to how large mX can be: as searches. Finally, if M H Mφ , one gets instead Mφ mX v, and then M ∼ m v/M ∼ m˜ (v/M), parametrically larger than pre- we saw in the previous section, this coupling also induces an φ X φ = vious splittings. Notice that in this latter case the mixing between sgoldstino-Higgs mixing with angle α given by Eq. (14), sin 2α 2m v/(M2 − m2). This imposes the upper bound m ≤ (M2 − the sgoldstino(s) and the heavy Higgs doublets can be significant, X φ h X φ 2 with potentially important implications for the sgoldstino decays: mh)/(2v) 1.1TeV, which becomes mX 0.9 TeV once the LHC the total width of the sgoldstino would be affected by the large upper bound sin2 α 0.2is imposed. This will limit how large the fermionic width of the heavy Higgses, which can be of order hh can be. In addition, in order to calculate hh, we have to re- ∼ 10 GeV in that mass range. write Eq. (15) in terms of mass eigenstates, and this introduces In the type (ii) case, there are EWSB contributions to the φS − mixing-angle factors. Then the coupling relevant for the sgoldstino 2 ∼ ˜ 2 2 3 − 2 = φP entries of the mass matrix, of order λX v , with λX m /M . decay is not mX but mX (cα 2cαsα), with sα sin α, etc., so the The sgoldstino mass splitting results either from contributions to partial width reads off-diagonal squared-mass entries or from different contributions 2 + ∗ ∗2 [ | |2 + 2 to the diagonal entries. More precisely, (λa λa ) ai Hi 1 3 2 2 mX 2 2 2 2 = (c − 2c s ) 1 − 4m /M . (16) (b H · H + h.c.)] leads to M 2|λ |(a v + 2bv v ), with hh α α α h φ u d φ a i i u d 32π Mφ Reλa (Imλa) contributing to the (off-)diagonal splitting. The generic 2 ∼ 2 result is Mφ λX v and somewhat sizeable values of λX are As mX is related to the mixing angle by Eq. (14), the partial width required for an sgoldstino mass splitting of the right size: e.g. is uniquely determined by α. This is shown in Fig. 2, which makes λX ∼ 0.5for Mφ ∼ 20 GeV. We see there is tension between clear that the naive expectations are not fullfilled, and the maximal ∼ ∼ achieving a large mass splitting (which requires large λX ) and the partial width is 2.5 GeV (corresponding to mX 700 GeV), too validity of the effective theory expansion (which requires small small to explain the large value of φ suggested by ATLAS. λX ), but somewhat sizeable values of the mass splitting should On the other hand, the mixing between the original Higgs and still be possible. the sgoldstino enables a new contribution to the φ → hh decay. Namely, a term in the superpotential 5. A large φ-width via hh decay?

4 In addition to (15), nonrenormalizable operators that one expects to appear in In the previous section we have discussed several ways to gen- ←→ L = μ † + μ | |2 + erate naturally an sgoldstino mass splitting that can explain the the effective theory [11], like δ 5 κi ∂ (Hi Dμ Hi )/M κi ∂ ∂μ Hi /M → large width of the 750 GeV diphoton resonance. In particular, we h.c., could potentially contribute to the decay φ hh. However, the ﬁrst operator in δL does not contribute to the decay of into two on-shell Higgses and the presented several options beyond the one discussed in [6], which 5 second one can be rewritten, by integration by parts and use of the equations of was based on a trilinear coupling between the sgoldstinos and ∼ 2 motion of , as an operator of the same form as (15) with a coeﬃcient Mφ /M, the light Higgs. In fact, such trilinear couplings open a new decay which is of the same order as mX . J.A. Casas et al. / Physics Letters B 759 (2016) 159–165 163

Therefore the contribution to the total width of the sgoldstino is

δ( → WW, ZZ, tt) (247.5GeV) sin2 α (20) which is quite sizeable, even for mild mixing angles (it gives δ 50 GeV for sin2 α 0.2). In the last equation we have not considered the interference effects with the direct decays → WW, ZZ, tt, which are typically subdominant. There are two potentially dangerous drawbacks of this φ − h mixing. The first is that these enhanced decays, particularly the one into ZZ, can be in conflict with LHC limits. Namely, one should respect the bound ZZ 13γγ [7]. Using Eq. (13) we get a bound on sin2 α5: 2 2 Mγ˜ 1TeV sin2 α 0.7 √ √ . (21) F F Note that this bound restricts severely the possibility of a sgoldstino splitting due to mixing√ with the Higgs if the photino mass is substantially smaller that F . Fig. 3. Same as Fig. 1 but including an additional contribution to the sgoldstino The second drawback is that the φ admixture in the Higgs will partial width, δφ /Mφ = 0.025 (blue band). The light (dark) gray region is excluded by LHC hh (monojet) searches (if the additional partial widths is due to φ → hh also affect the coupling of Higgs to gluons and photons (which (invisible) decays). (The limit from dijet searches is displaced to the right of the are loop suppressed in the SM). Normalizing these couplings as plot in comparison with Fig. 1). (For interpretation of the references to color in this μν μν cggh/(4v)Gμν G and cγγh/(4v)Fμν F , fits to LHC Higgs data figure legend, the reader is referred to the web version of this article.) −3 put constraints on cγγ and cgg roughly of order 10 , see e.g. [18]. The bound on cγγ can be used to set the constraint c F 4 δW = , (17) 4! M3 √ 2 √ 2 − F F induces a term in the scalar potential sin2 α 8 × 10 6 . (22) Mγ˜ 1TeV ˜ 2 c m 3 δV = + h.c. (18) 2 3! M A similar bound on sin α, involving M3 instead of Mγ˜ , follows from the bound on cgg. Putting together Eq. (21) and (22) sets 2 This gives a new contribution to the φh coupling involved in 2 × −3 2 2 an upper limit sin α 2 10 , and using this in Eq. (20) gives φ → hh decay, of size ∼ cm˜ cαs /M once mixing angle effects α δφ 0.5GeV, atiny shift, so this h −φ mixing mechanism cannot are taken into account. Although in principle this is parametrically explain the large sgoldstino width.6 smaller than the initial coupling in Eq. (15), there is no mixing- 2 Notice also that the previous upper bound on sin α restricts angle obstruction to how large this new trilinear can be, so it can dramatically the possibility of a sizeable mass splitting between φS be substantially larger than mX . Consequently the effective φhh and φP due to a trilinear coupling between sgoldstinos and Higgs, coupling, and thus the total width into Higgses, can be notably as in Eq. (15); i.e. the mechanism proposed in ref. [6]. Namely, larger, eventually as large as suggested by ATLAS. However, having 2 from the discussion after Eq. (14) the bound on sin α translates a large hh can be in conflict with LHC hh searches and one should into a bound Mφ 0.75 GeV. further impose the limit 20( ) [4,17]. Fig. 3 shows how hh γγ obs The arguments used in this section are of more general appli- this constraint can ruin this as a solution to the large width prob- cability and can constrain scenarios that mix the light Higgs and lem. In this figure, the region excluded by hh searches assumes the scalar at 750 GeV (for work in this direction see [10]). δφ,hh/Mφ = 0.025. 7. Sgoldstino decay into Higgsinos 6. Larger width from sgoldstino-Higgs mixing? Besides the sgoldstino decay in two Higgs bosons, discussed in As we have seen in the two previous sections, a trilinear cou- the previous section, the decay in two Higgsinos is an additional pling between sgoldstinos and Higgs, as in Eq. (15), has two conse- channel that could be naturally open and can be important. quences: a splitting between the scalar and pseudoscalar compo- From the superpotential in Eq. (1) one gets the interaction term nents of the sgoldstino and a decay of sgoldstino into two Higgses. Both effects can contribute to the apparent width of the 750 GeV μ ˜ ˜ δL = Hu Hd + h.c. , (23) resonance, as favored by ATLAS data. M Here we discuss an additional effect of that mixing that en- → ˜ ˜ hances the sgoldstino width, but is potentially dangerous. Since the between the sgoldstino and the Higgsinos, which allows H H ≤ physical sgoldstino has a sin α component of Higgs, the former can decay if mH˜ μ Mφ/2. Provided the Higgsino is the LSP, this decay through the usual decay channels of the Higgs boson, with decay contributes to the invisible width of the sgoldstino. LHC a rate suppressed by sin2 α. Now, for a 750 GeV SM Higgs the de- monojet searches constrain also such invisible decays, with the cay is dominated by WW, ZZ and tt, with the following partial widths [19]: 5 Given the interplay between the photino and gluino masses to accommodate the observed diphoton excess, this bound can be re-written as an upper bound on (H(750 GeV) → WW) = 145 GeV , the gluino mass. 6 − SM (H(750 GeV) → ZZ) = 71.9GeV, The bound on cγγ might be substantially weaker if cγγ √2cγγ (admit- tedly this would be a big coincidence). However, this requires Mγ˜ / F 1, casting (H(750 GeV) → tt) = 30.6GeV. (19) doubts on the EFT expansion. 164 J.A. Casas et al. / Physics Letters B 759 (2016) 159–165

limit translating into inv 400(γγ)obs [4,20]. The impact of this In this paper we also have explored other possibilities to en- limit is shown in Fig. 3. The contribution to the width is hance the sgoldstino width, namely the decay into two Higgses, 3/2 two Higgsinos and the contribution from mixing between the 2 4m2 Mφ μ H˜ sgoldstino and the Higgs boson. The decay into Higgses arises from ˜ ˜ = 1 − . (24) H H 2 2 the above-mentioned trilinear couplings. The maximal value of this 4π M Mφ partial width is extremely constrained by (sgoldstino-Higgs) mix- Parametrically, using μ m˜ , this width is of order m˜ 3/M2 like ing effects. Typically, it turns out to be too small, although it is those discussed in section 3 but, being independent of gaugino enhanced by the presence of trilinear sgoldstino operators, that are = masses, there is more freedom to increase it. Getting H˜ H˜ /Mφ normal in LSSB. The mixing has other side effects, in particular it 2 enables the decay of the sgoldstino through its Higgs-component, 0.06 requires (μ /M) 0.84 for mH˜ 100 GeV (its lower limit from LEP), a value that is too large to justify the effective the- which enhances notably the total width. However, one must be ory expansion in powers of m˜ /M. However, if we choose instead careful not to violate the present bounds on ZZ, as well as on 2 = Higgs couplings, particularly those from h → data. The com- (μ /M) 0.5we get H˜ H˜ 27 GeV, for the same value of mH˜ ; γγ a large value close enough to the ATLAS indication. Moreover, this bination of these two types of constraints imposes severe bounds is just a partial contribution to the width that should be added to on the scenario and, in particular, on the value of the mixing an- others that could potentially be large, like that from the hh decay gle. studied in section 5. In addition, using this particular channel to Finally, the sgoldstino width into Higgsinos can be large if the enhance the sgoldstino width we do not run into the problem of latter are light enough. Although accounting for the full width sug- clashing with LHC searches, as was the case for hh. In fact, Fig. 3 gested by ATLAS is not possible within the regime of validity of the holds also if δφ is due to Higgsino decays, but now the excluded effective theory expansion, Higgsino decays can certainly make it gray area (due to hh searches) would not apply, and this leaves a easier to fit ATLAS data. In summary, there are potentially inter- region (overlap between blue and green bands) that can success- esting mechanisms to enlarge the sgoldstino width which, besides, fully explain the diphoton rate and the large width. lead to relevant predictions for LHC. Finally, let us remark that the same operator that is responsible We find tantalizing that this (hint of a) signal could correspond for the above sgoldstino coupling to Higgsinos also gives a (pos- to an sgoldstino, a particle that lies at the very heart of supersym- itive) contribution to the light Higgs mass through a λ(F ) quartic metry breaking, similar in a sense to the central role of the Higgs coupling as discussed in section 1, with for electroweak symmetry breaking. If nature is kind to us, this could represent a huge step forward in our understanding of the 1 μ 2 2 = 2 2 origin of electroweak symmetry breaking and the role that super- δmh v sin 2β. (25) 2 M2 symmetry presumably plays in it. 2 ∼ 2 ∼ 2 2 For (μ /M) 0.5one gets δmh mh sin 2β. This can be very useful to reproduce the observed Higgs mass with less finetuning, Acknowledgements one of the crucial virtues of this type of scenario [12]. J.R.E. thanks Joan Elias-Miró and Mario Martínez for interest- 8. Conclusions ing discussions and acknowledges support by the Spanish Ministry MINECO under grants FPA2014-55613-P, FPA2013-44773-P, by the We have re-examined the diphoton excess observed by ATLAS Generalitat de Catalunya grant 2014-SGR-1450 and by the Severo and CMS [1–3] as a possible supersymmetric signal of low-scale Ochoa excellence program of MINECO (grant SEV-2012-0234). J.R.E. SUSY breaking (LSSB) scenarios [11–14]. These models contain an and J.A.C. thank Hanna Jarzabek and Resu del Pozo for support excellent candidate to fit the signal: an scalar field (the sgoldstino) during a very unusual Christmas. J.A.C. and J.M.M. are partially coupled to gluons and photons in a direct way, so that an effective supported by the MINECO, Spain, under contract FPA2013-44773-P, production via gluon fusion and the subsequent decay into photons Consolider-Ingenio CPAN CSD2007-00042, as well as MultiDark is possible. The partial widths into gluons (photons)√ depends on CSD2009-00064. We also thank the Spanish MINECO Severo Ochoa the ratio of the gluino (photino) mass over F , i.e. the scale of excellence program under grant SEV-2012-0249. SUSY breaking. The possibility of accommodating the diphoton excess as a sig- References nal of LSSB has been proposed in [5,6,8]. However, although the observed cross section is not difficult to fit, the typical width of [1] LHC seminar, ATLAS and CMS physics results from Run 2, talks by Jim Olsen the sgoldstino is much smaller than the value suggested by the and Marumi Kado, CERN, 15 Dec. 2015; ATLAS results, φ/Mφ 0.06. The authors of Ref. 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In this paper we have presented nances in pp collisions at s 8TeVwith the CMS detector. [4] R. Franceschini, et al., What is the gamma gamma resonance at 750 GeV?, alternative mechanisms to generate the sgoldstino splitting. The arXiv:1512.04933 [hep-ph]. first relies on mixed sgoldstino-Higgs quartic couplings (somewhat [5] B. Bellazzini, R. Franceschini, F. Sala, J. Serra, Goldstones in diphotons, arXiv: sizeable) and, although the mechanism falls short of explaining the 1512.05330 [hep-ph]. full mass splitting, it can still give some sizeable contribution to it [6] C. Petersson, R. Torre, The 750 GeV diphoton excess from the goldstino super- that might be good enough to accommodate the data. The second partner, arXiv:1512.05333 [hep-ph]. [7] J. Ellis, S.A.R. Ellis, J. Quevillon, V. Sanz, T. You, On the interpretation of a pos- and most efficient mechanism relies on self-couplings of the Gold- sible ∼ 750 GeV particle decaying into γγ, arXiv:1512.05327 [hep-ph]. stino superfield in the superpotential, naturally expected to appear [8] S.V. Demidov, D.S. Gorbunov, On sgoldstino interpretation of the diphoton ex- after supersymmetry breaking. cess, arXiv:1512.05723 [hep-ph]. J.A. Casas et al. / Physics Letters B 759 (2016) 159–165 165

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