Collider Signatures of Low Scale Supersymmetry Breaking: a Snowmass 2013 White Paper

CPHT-RR085.0913, DFPD-2013/TH/17, LPN13-058

Collider signatures of low scale supersymmetry breaking: A Snowmass 2013 White Paper

Emilian Dudas,1, ∗ Christoffer Petersson,2, 3, 4, † and Riccardo Torre5, 6, ‡ 1Centre de Physique Théorique, Ecole´ Polytechnique, CNRS, Palaiseau, France 2Physique Théorique et Mathématique,UniversitéLibre de Bruxelles, C.P. 231, 1050 Bruxelles, Belgium 3International Solvay Institutes, Brussels, Belgium 4Department of Fundamental Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden 5Dipartimento di Fisica e Astronomia, Universitàdi Padova, and INFN Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy 6SISSA, Via Bonomea 265, I-34136 Trieste, Italy

We consider the possibility that supersymmetry is broken at a low scale, within one order of magnitude above the TeV scale. In such a case, the degrees of freedom associated with the spontaneous breaking of supersymmetry, the goldstino fermion and its scalar superpartner (the sgoldstino), can have signiﬁcant interactions with the Standard Model particles and their superpartners. We discuss some characteristic processes, involving the goldstino and the sgoldstino, and the collider signatures they give rise to. These signatures involve scalar resonances in the di-photon, di-jet, di-boson and di-tau channels, the possible relation between these resonances and deviations in the Higgs couplings

as well as exotic Higgs decays in the monophoton +E/ T and the four photon channels.

I. INTRODUCTION gauge singlet chiral superfield √ 2 X = x + 2θGe + θ FX , (1) If supersymmetry (SUSY) is a feature of Nature it must where the auxiliary component F acquires a non- be in a broken phase at low energies. A model-independent X vanishing vacuum expectation value ( ), hF i = f, that consequence of the spontaneous breaking of (global) SUSY vev X breaks SUSY.1 For linearly realized (but spontaneously is the existence of a Goldstone Weyl fermion, the goldstino. broken) SUSY, the goldstino has a complex scalar super- The existence of gravity implies that SUSY is a local sym- partner, the sgoldstino x.2 In contrast to the goldstino, the metry, that the spin 1/2 goldstino is eaten by the spin 3/2 sgoldstino is not protected by the Goldstone shift symme- gravitino, becoming its longitudinal component, and that √ try and it generically acquires a mass upon integrating out the gravitino acquires a mass m3/2 = f/( 3MP), where √ 18 some heavy states in the SUSY breaking sector. The pre- f is the SUSY breaking scale and MP = 2.4 · 10 GeV. √ cise value of its mass depends on the details of that sector, Treating f (or, equivalently, m3/2) as a free parame- such as the symmetries (e.g. R-symmetry) and the loop ter one can categorize different scenarios of SUSY breaking level at which its mass is generated. If the sgoldstino mass and mediation. Gravity and anomaly mediation are rele- √ is much larger than the energy scale under consideration, it vant for high scale SUSY breaking, with f of the order of can be integrated out and as a consequence, SUSY is non- 1011 GeV, while gauge mediation is relevant for lower val- √ linearly realized in the resulting low energy effective theory. ues of f, down to around 50 TeV (below which one typi- In the case where the SUSY breaking sector is strongly cou- cally encounters tachyonic scalars in the messenger sector). √ pled and no energy scale exists at which SUSY is linearly However, the lower experimental bound on f is at or be- √ realized, the elementary scalar component in Eq. (1) is re- low 1 TeV, which leaves the possibility of having f within placed by a goldstino bilinear, x → GG/(2F ), such that arXiv:1309.1179v1 [hep-ph] 4 Sep 2013 e e X an order of magnitude above the TeV scale, which is the √ the corresponding non-linear superfield XNL satisfies the 2 case we discuss in this note. When f is of this order, the constraint XNL = 0 [29]. gravitino is approximately massless and, due to the super- Being a Goldstone mode, the goldstino couples deriva- symmetric equivalence theorem [1,2], the gravitino can be tively to the supercurrent, or, upon using the equations replaced by its goldstino components. For different aspects and discussions on models with a low SUSY breaking scale see, for example, Refs. [3–28]. 1 In general the goldstino is a linear combination of all the neutral We consider the case where the goldstino G resides in a fermions whose associated auxiliary F or D component acquires a e 2 non-vanishing vev. Here we assume that |hFX i| provides the dom- inant contribution to the vacuum energy and that the goldstino, to a good approximation, is aligned with the fermion component of X. ∗Electronic address: [email protected] 2 Since the sgoldstino is complex it gives rise to two real scalars, one †Electronic address: christoff[email protected] CP -even and one CP -odd. In terms of R-parity, the goldstino is ‡Electronic address: [email protected] odd while the sgoldstino is even. 2 of motion, non-derivatively to the divergence of the su- the L3 Collaboration [30], where a conservative bound of √ percurrent. A simple way to incorporate the interactions f > 238 GeV was obtained. The CDF Collaboration at of the goldstino, and its sgoldstino superpartner, with the the Tevatron has looked both for the γ + E/ T [31] and the Standard Model (SM) fields and their superpartners is to j + E/ [32] signatures and the resulting bounds are com- T √ √ promote all soft terms to SUSY operators containing the parable to the LEP one: f > 221 GeV and f > 214 goldstino superfield of Eq. (1), GeV, respectively. Z m2 The LHC experiments have also performed searches for φ m2 φe†φe → d4θ e X†XΦ†Φ , (2) both γ + E/ and j + E/ , but with focus mainly on large φe f 2 T T extra dimension and dark matter models.3 So far only one Z m m λαλ → d2θ λ XW αW , (3) analysis, done by the ATLAS Collaboration, has presented λ α f α √ their results in terms of bounds on f [33]. In this analysis where Φ/W α are generic matter/gauge superfields and the superpartners are not integrated out and different rela- 2 tions between the squark and gluino masses are considered. m /mλ are the corresponding scalar/gaugino soft masses. φe The most conservative bound that can be extracted from In addition to the soft mass terms, which are recovered √ Ref. [33] is f > 650 GeV for heavy squarks and gluinos from the SUSY operators by taking the auxiliary compo- √ but bounds as strong as f 1.1 TeV are obtained for nents of the X’s and inserting their vev’s, the SUSY op- & erators in Eqs. (2) and (3) also give rise to goldstino and particular relations between the squark and gluino masses. sgoldstino interactions with the component fields of the matter/gauge supermultiplets. The coefficients of these in- III. SIGNATURES OF LOW SCALE SUSY teractions are proportional to the ratio of the correspond- BREAKING MODELS ing soft parameter over the SUSY breaking scale. Hence, in √ the scenario where the f is not far above the scale of the In this section we briefly review some of the charac- soft parameters, the goldstino and sgoldstino interactions teristic signatures of models with a low SUSY breaking can be significant. scale, arising from processes involving the goldstino and the sgoldstino. Note that the auxiliary component FX of the goldstino superfield of Eq. (1) is treated dynamically and upon integrating it out, it gives rise to a tree level F -term scalar A. Sgoldstino production and decay potential. As can be seen from Eq. (2) in the case where By taking the scalar sgoldstino component from the gold- Φ is a Higgs superfield, F couples to the Higgs scalars, µν X stino superfield X and the gauge kinetic term Fµν F from which gives rise to new quartic Higgs couplings in the F - α W Wα in (3) we see that the sgoldstino couples to (the term scalar potential, beyond those proportional to gauge transverse components of) the SM gauge bosons. The coupling constants in the usual D-term scalar potential. strengths of these interactions are given by the correspond- These new interactions can help to raise the mass of the ing gaugino soft mass over f. For example, the sgoldstino lightest neutral CP-even Higgs scalar to 125 GeV already coupling to gluons is proportional to the gluino mass and at the tree level [13, 19]. the coupling to photons is given by a linear combination (with weak mixing angles) of the bino and wino masses. II. BOUNDS ON THE SUSY BREAKING SCALE At a hadron collider the sgoldstino is resonantly produced via gluon-gluon fusion. The production cross-section can Model-independent bounds on the SUSY breaking be found in Ref. [22]. Since the sgoldstino can couple scale/gravitino mass can be derived by means of an effec- strongly to gauge bosons, relevant searches for sgoldsti- tive approach in which all the SM superpartners are taken nos involve direct searches for a scalar resonance into the to be heavy and integrated out from the spectrum. In this di-photon (x → γγ), di-jet (x → gg) or di-boson (x → ZZ, case, effective higher dimensional operators give rise to the x → WW ) final states. Due to the very high background processes e+e− → GGγ at e+e− colliders and pp → GGγ e e e e in the di-jet final state at the LHC, we expect the di-boson and pp → GGj at hadron colliders [5,6]. These effective e e searches to be more efficient in the low mass region ( 1 operators are suppressed by powers of the SUSY breaking . TeV). Searches in the aforementioned final states are of- scale and therefore these processes can be used to set a √ lower bound on f. Several experimental searches have been performed for these signatures, referred to respectively as monophoton 3 See Ref. [26] for a discussion concerning LHC bounds on four- plus missing energy (γ + E/ ) and monojet plus missing fermion contact interactions and how they can be translated into T bounds on higher-dimensional operators, present in low scale SUSY energy (j + E/ T ), at LEP, Tevatron and LHC. The most breaking models, with coefficients involving the SUSY breaking updated bound from the LEP experiments comes from scale. B Implications for Higgs Couplings 3 ten performed by the experimental collaborations having the Yukawa couplings depend on the separate soft A-term in mind different kind of resonances, such as graviton exci- for the corresponding fermion, this allows for the freedom tations in models with extra dimensions or sequential SM to break the usual relations between the different Higgs Z0 and W 0 (see, e.g., Refs. [34, 35]). However, it would couplings to fermions. If, for example, the Higgs coupling be very useful if the experimental efficiencies and the kine- to tau leptons is shown to deviate from the SM expecta- matic acceptances were given also for scalar particles in tion, but not the Higgs coupling to bottom quarks, and if a these searches. Moreover, while in the WW and ZZ fi- sgoldstino mixing correction would be responsible for this nal states the whole region starting from mh and up to a deviation, it would imply that the sgoldstino itself couples few TeV seems to be covered by the experimental analy- strongly to taus. In this case, a search for a scalar reso- ses (Higgs searches plus Exotics searches), there appears nance in the di-tau channel would be well-motivated. The to be a gap in the searches in the di-photon channel for most relevant searches in the di-tau channel are given by resonances with a mass between 150 GeV (the upper end Refs. [36, 37] which, however, focus on Z0 resonances and of the reach in the Higgs search in the di-photon channel) do not not provide the efficiency times acceptance for a and 500 GeV (the lower end in the search for Kaluza-Klein scalar particle. As it was already pointed out for the di- gravitons [34]). boson case, it would be very useful to have these quantities for a scalar particle from the experimental collaborations B. Implications for Higgs Couplings in order to be able to interpret the analyses in terms of a As was discussed above, the sgoldstino scalar can couple low scale SUSY breaking model with a sgoldstino scalar in strongly to the SM gauge bosons. Moreover, the CP-even the low energy spectrum. sgoldstino will in general mix with the scalar state corresponding to the SM-like Higgs at 125 GeV. Therefore, C. Exotic Higgs decays through mixing with sgoldstino, the SM-like Higgs can have In this section we discuss exotic Higgs decays, involving modified couplings to gauge bosons. In Ref. [22] it was the goldstino and the sgoldstino, for which we would like shown that, through a tree-level sgoldstino mixing correc- to encourage experimental searches. tion, it is possible to enhance the Higgs coupling to photons without significantly modifying any of the other Higgs cou- • h → γ + E/ T plings. If the Higgs coupling to photons would turn out to This Higgs decay into a monophoton plus missing trans- be enhanced with respect to the SM expectation, in the 0 verse energy arises from the process h → χe1Ge → γGeGe context of this scenario, it would suggest that the sgold- which is kinematically allowed when the lightest neutralino stino couples strongly to photons and that a scalar reso- 0 is lighter than the Higgs. The coupling hχe1Ge arises from, nance in the di-photon channel below the TeV scale would for instance, Eq. (2) (with Φ being a Higgs superfield), by be well-motivated to search for. Note that the sgoldstino taking the auxiliary field (and inserting its vev) from one mixing is uniquely determined by the soft parameters, see of the X’s and the goldstino component from the other X, Refs. [24, 26] for the explicit mixing corrections to all the while taking a Higgs scalar and a higgsino component, re- couplings of the SM-like Higgs scalar. 0 spectively, from the two Higgs superfields. The χe1γGe cou- In Ref. [24] it was studied the possibility of using sgold- pling arises from Eq. (3) by taking the goldstino component stino mixing to disentangle the usual relations between the from X, while taking a gaugino and a gauge field strength 4 different Higgs couplings to SM fermions. In the mini- α 5 component from W Wα. Since the kinematic distribution mal SUSY SM (MSSM), the Higgs couplings to the down- of the transverse momentum of the photon has an endpoint type quarks and the leptons, normalized with respect to at half the Higgs mass, the relevant phase space regime is their corresponding SM value, coincide at the tree-level γ pT 6 mh/2 ≈ 63 GeV. This process, as well as the relevant and this degeneracy is typically only slightly broken at the backgrounds, were studied in Ref. [20]. quantum level. The sgoldstino couples to the SM fermions c via superpotential operators such as (Ad/f)XQHdD and • h → 4γ/2γ2j/4j c (Ae/f)XLHdE , which also give rise to the tri-linear scalar These Higgs decays arise from the processes soft A-terms. Since the sgoldstino mixing corrections to h → xx → (γγ)(γγ)/(γγ)(jj)/(jj)(jj), which are present when the sgoldstino mass is below half the Higgs mass.6

4 In addition to the sgoldstino mixing corrections, modifications of the Higgs couplings to fermions arise from, for instance, 5 If kinematically allowed, also the (subleading) process “wrong Yukawa couplings”, e.g. X†H†QU c in the Kahler poten- d h → χ0G → ZGG occurs [20]. tial, which can be generated and significant in models with a e e e e 6 The 4 jet final state is expected to be swamped by the QCD back- low SUSY breaking scale [26]. ground at a hadron collider. However, if one or both of the sgold- 4

In the particular case where the sgoldstinos are very light stino/sgoldstino to the SUSY SM are proportional to (100-400 MeV) the analysis of Ref. [39] is sensitive since the soft parameters and masses of the SM superpartners. it searches for Higgs decays into two pseudo-scalars, each Hence, these couplings contain information about the su- of which decays to two photons. Due to the strong boost, perpartner spectrum that can be used to relate seemingly each of the two pairs of photons are so collimated that disconnected experimental analyses, such as searches for most of them are misidentified with single photons and superpartners, new scalar resonances, exotic Higgs decays hence this decay contributes to the usual di-photon chan- and modified Higgs couplings. nel. However, in the case where the sgoldstino is heavier Some of the distinctive signatures described in this note than that it should be possible to isolate and reconstruct have analogous signatures in other models, for which anal- all the 4 photons. The decays of the Higgs into 4γ/2γ2j yses are already available. In this case it would be very use- via two pseudo-scalars in the context of a non-SUSY ful if the experimental collaborations could provide the ef- model with a pseudo-scalar and heavy vector-like fermions ficiencies and acceptances for all the different spin/Lorentz were considered in Refs. [40, 41]. structures that could give rise to a given signature. In conclusion, we would like to encourage experimental • h → E/ T searches for models with a low SUSY breaking scale. This invisible Higgs decay can arise from the process Moreover we think that a systematic experimental pro- h → GeGe, see for instance Ref. [13]. gram for this framework should be established.

IV. CONCLUSIONS Acknowledgements Bounds on the scale of SUSY breaking are currently at or below 1 TeV. With no theoretical bias, and motivated The work of E.D. was supported in part by the European by the negative results of the SUSY searches in the first ERC Advanced Grant 226371 MassTeV, the French ANR run of the LHC, we point out that models where SUSY is TAPDMS ANR-09-JCJC-0146 and the contract PITN- broken around the TeV scale can have non-standard and GA-2009-237920 UNILHC. The work of C.P. was sup- distinctive phenomenology. New processes and modifica- ported in part by IISN-Belgium (conventions 4.4511.06, tions to the SM ones arise in this framework, depending 4.4505.86 and 4.4514.08), by the “CommunautéFran¸caise only on the soft parameters and the SUSY breaking scale. de Belgique” through the ARC program and by a “Mandat The characteristic processes we have discussed involve d’Impulsion Scientifique” of the F.R.S.-FNRS. The work the degrees of freedom associated with the spontaneous of R. T. was supported by the ERC Advanced Grant no. breaking of SUSY, i.e. the goldstino and the sgoldstino. 267985 DaMeSyFla. R.T. also acknowledges the Grant In contrast to other neutral fermions and scalars present Agreement number PITN-GA-2010-264564 LHCPhenoNet in other extensions of the SM, the couplings of the gold- of the Research Executive Agency (REA) of the European Union.

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