Dark Matter versus h → γγ and h → γZ with supersymmetric triplets

The Triplet extension of the MSSM (TMSSM) alleviates the little hierarchy problem and provides a significant enhancement of the loop-induced diphoton rate of the lightest CP-even Higgs h. In this paper we pursue the analysis of the TMSSM Higgs phenomenology by computing for the first time the h → Zγ decay. Interestingly we find that the rates of loop-induced decays are correlated and their signal strengths can rise up to 40% – 60% depending on the channel. We furthermore study the dark matter phenomenology of the TMSSM. The lightest neutralino is a good dark matter candidate in two regions. The first one is related to the Higgs and Z resonances and the LSP is mostly Bino. The second one is achieved for a mass larger than 90 GeV and the LSP behaves as the well-tempered neutralino. An advantage of the triplet contribution is that the well-tempered neutralino can be a Bino-Triplino mixture, relieving the problem of achieving M2 ∼ M1 in unified scenarios. The dark matter constraints strongly affect the Higgs phenomenology, reducing the potential enhancements of the diphoton and of the Zγ channels by 20% at most. These enhancements are however larger than the MSSM ones. In the near future, complementarity of dark matter direct searches and collider experiments will be crucial to probe most of the parameter space where the neutralino is the dark matter candidate.


Introduction
The discovery of the Higgs boson [1,2] has closed a long era: its mass is no more a free parameter. Its value m h 126 GeV is in agreement with the mass range predicted in supersymmetric scenarios [3]. Nevertheless, the minimal version of these models, the socalled Minimal Supersymmetric Standard Model (MSSM), turns out to be ailing by the LHC discovery. The value m h 126 GeV is indeed well above the one that the MSSM naturally predicts, and heavy third generation squarks and large stop mixing are required to reproduce the measured mass [4][5][6][7]. The MSSM electroweak sector therefore needs an unpleasant amount of fine tuning and a little hierarchy problem plagues the model.
In non-minimal supersymmetric scenarios this problem can be alleviated. They can indeed involve new contributions (absent in the MSSM) that rise the tree-level prediction of the Higgs mass. For this reason smaller radiative corrections and less tuning in the electroweak sector are required. The drawback of this important achievement is (partial) loss of predictivity since extra free parameters have been introduced. A compromise between naturalness and predictivity is thus to consider scenarios extending the MSSM as little as possible.
If one does not enlarge the gauge symmetry group of the Standard Model (SM), the only extension boosting the tree-level Higgs mass is to couple new chiral superfields to the Higgs sector of the superpotential. To this aim only singlets and SU (2) L triplets with hypercharges Y = 0, ±1 are allowed by gauge invariance [8]. Whereas the former option has been deeply studied, see e.g. [9] and references therein, the latter is less known and has received special attention only after ATLAS and CMS initially measured sizeable deviations in the diphoton Higgs rate [10,11]. Indeed, the triplet superfield involves extra charginos that can largely enhance the diphoton channel [12][13][14] without requiring peculiar features such as large deviations in the main Higgs decay rates, huge stop masses, ultra light charginos or very heavy Higgsinos as it occurs in other scenarios [5,[15][16][17]. In particular, such an enhancement can be achieved in both decoupling and non-decoupling regime (i.e. with large and small CP-odd Higgs mass m A ) while resembling the dominant SM Higgs couplings [18].
Although the observed Higgs signal strengths [1,2] might appear SM-like because of an accidental compensation between production and decay rates that per se differ from the SM predictions, it is still worth to analyze scenarios where each Higgs decay but the loop-induced ones, and Higgs production is SM-like. In this simplified approach, indeed, it is easier to highlight the origin of a potential deviation (in loop-induced channels) that lies on the top of the global suppression/enhancement present in all channels. Such a deviation is somehow expected since loop-induced processes are particularly sensitive to new physics that can not perturb the dominant Higgs channels. This method has been applied in ref. [12] to show that charginos can provide up to 45% diphoton enhancement in the Y = 0 Triplet extension of the MSSM (TMSSM).
The same approach is applied in the present paper. We extend the analysis of ref. [12] to a broader parameter space and we find that a slightly larger enhancement of about 60% can be achieved via chargino contributions. More interestingly, we show that this departure from the SM prediction is tightly correlated to the deviation in the h → Zγ channel. In any case, the Γ(h → Zγ) rate can never be larger than about 1.4 times its SM value 1 .
These upper bounds are obtained without imposing any Dark Matter (DM) constraint on the TMSSM field content. Nevertheless they are compatible with the DM observables if the Higgs phenomenology is somehow disentangled from the DM puzzle. This is achieved for instance by invoking gravitinos, axions and axinos as DM candidates [20][21][22][23], or by postulating cosmological scenarios with non-standard DM production [24]. On the contrary, if the DM candidate is required to be the Lightest Supersymmetric Particle (LSP) of the TMSSM within the traditional cosmological assumptions, the above bounds should be revisited. To this aim we pursue the analysis of the Higgs phenomenology for the case having the lightest neutralino as DM particle. In order to capture the most stringent features related to the h → Zγ and h → γγ enhancements, we require the relic density to rely only on the chargino, neutralino and SM fields. In other words, besides analyzing the DM annihilation via Higgs and Z boson resonances, we study a kind of well-tempered neutralino in the TMSSM.
By definition the well-tempered neutralino in the MSSM is a tuned mixture of gaugino and Higgsino that achieves the correct relic density away from resonances and coannihilations with other supersymmetric particles [25]. The successful parameter space consists of either the Bino and Higgsinos, or the Bino and Wino having almost degenerate mass terms. Other issues however jeopardize these two scenarios: the former is strongly constrained by limits on the DM Spin-Independent (SI) elastic scattering, and the latter seems unnatural since supersymmetry breaking mechanisms unlikely lead to degenerate Bino and Wino soft masses.
Introducing the TMSSM fermionic triplet, hereafter dubbed Triplino, provides new features to the DM phenomenology. In fact, the Triplino can play the role of the Wino component, making the tuning between Bino, Wino and Higgsinos masses unnecessary and opening up a new viable DM parameter space for the well-tempered neutralino. Moreover, the Triplino mass parameter is a superpotential term that in principle can be produced by supersymmetry breaking sources different from those generating the gaugino masses 2 .
Interestingly, we find that in the TMSSM the DM constraints strongly impact the loop-induced Higgs processes. Independently on the regions where the LSP achieves the observed relic density the h → γγ and h → Zγ enhancements cannot be larger than 20%. This mostly occurs because larger enhancements need light Higgsino and Triplino mass parameters, which tend to push the SI elastic scattering off nuclei of the lightest neutralino above the LUX exclusion limit [26].
The rest of the paper is organized as follows. In section 2 we review the basic features of the TMSSM and its most natural parameter space. We also present some improvements in the determination of the lightest Higgs mass m h . Section 3 describes the Higgs signatures in the TMSSM, with emphasis to the Higgs invisible width and loop-induced decay channels. In particular, the first calculation of the Γ(h → Zγ) width in the TMSSM is presented here. Section 4 is dedicated to set up the method of our numerical analysis, as well as the parameter choice. Section 5 studies in detail the signal strengths of loop-induced Higgs decays and their correlation. We then move to discuss the DM phenomenology and its impact on the Higgs signatures in section 6. Section 7 is finally devoted to summarize our findings.

Generic Features
In the TMSSM the matter content of the MSSM is extended by a Y = 0 SU (2) L -triplet superfield In comparison with the MSSM, the TMSSM superpotential and soft-breaking Lagrangian contain respectively two and three extra renormalizable terms [8,27]: where A · B ≡ ij A i B j with 21 = − 12 = 1 and 22 = 11 = 0. For sake of simplicity we assume no sources of CP violation and consequently all parameters are taken as real.
In general the neutral scalar component ξ 0 acquires a VEV ξ 0 . Electroweak precision observables impose ξ 0 4 GeV at 95% CL [18,28] which, unless of a tuning on the parameters, corresponds to the hierarchy For A λ , µ and µ Σ at the electroweak scale, such a hierarchy requires m Σ 2 TeV [18] 3 . As a consequence, the mixing between the MSSM Higgs sector and the scalar triplet is rather small and it can be safely neglected for m Σ 5 TeV [12]. These values of m Σ as well as the hierarchy in eq. (2.4) will be assumed in the following. This in particular allows to take ξ 0 ≈ 0.
As the Σ scalar components decouple from the Higgs fields H 1 and H 2 , which interact with the down and up right-handed quarks respectively, the Higgs sector at the electroweak scale looks like the one of the MSSM with some O(λ 2 v 2 ) shifts in the tree-level mass spectrum. By imposing the minimization conditions for the electroweak symmetry breaking, it turns out [18] GeV, m Z and m W are the Z and W vector boson masses, and m 2 1 , m 2 2 and m 2 3 are the usual MSSM soft parameters of the Higgs fields 3 For discussions on the naturalness of such a hierarchical scenario see refs. [12,18].
H 1,2 whose neutral components are decomposed as H 0 Moreover, the CP-even squared mass matrix in the basis (h 2 , h 1 ) is given by The contributions O(λ 2 v 2 ) lift the lightest eigenvalue m 2 h and the little hierarchy problem can be then alleviated with respect to the MSSM. This can be easily seen in the limit The O(λ 2 v 2 ) term can provide a sizeable boost to m h . In particular, no large radiative corrections are required to catch m h 126 GeV for large λ and small tan β 4 . On the other hand, some rather large radiative corrections to the Higgs sector are unavoidable due to the lack of experimental evidence of stops and gluinos. Within the specific assumptions the experimental analyses are based on [29], stop and gluino bounds in the presence of any lightest neutralino mass are quite stringent, namely m t 650 GeV and M 3 1.4 TeV [30][31][32] (for loopholes see e.g. refs. [33,34]). Their radiative corrections to the Higgs sector are then sizeable and need to be stabilized at the expense of a certain amount of fine tuning in the model (for details see e.g. ref. [35]).
A further important source of tuning comes from the triplet if m Σ is large. We require this to be subdominant to the gluino and stop ones in order to alleviate the little hierarchy problem as much as possible. Notice that this condition does not prevent from m Σ > m t since triplets have less degrees of freedom and (typically) smaller coupling to H u,d than stops. In this respect, the parameter choice m Σ 5 TeV, m t 650 GeV and λ 1 is allowed [12,18].
In order to simplify our analysis, we will restrict the parameter space to a subset where all the above issues are taken into account. We will focus on the parameter region with m = m U = m D = m Q . This choice indeed (i) alleviates the little hierarchy problem as it boosts m h with subdominant Σ radiative corrections. Moreover, as far as µ Σ and µ are not too large, it (ii) naturally satisfies the hierarchy (2.4) and (iii) allows to neglect the mixing between the Σ scalars and the low energy sector. All sleptons are considered heavy enough not to interact with the relevant SUSY spectrum; numerically they have been taken to be 3 TeV. The precise parameter space we consider is defined in section 4, together with all observational constraints used in this analysis.

The Higgs Mass
Nowadays the LHC measurement of the Higgs mass is very accurate. The most recent analyses present 2-σ uncertainties of about 1% on the central value m h 125.6 GeV [1,36].
Such accuracy goes much further than the typical precision that beyond-the-SM theoretical papers achieve. These works indeed are more aimed to capture the qualitative features of new frameworks than to accurately evaluate their predictions. In this spirit, seminal works on the TMSSM have analyzed the Higgs sector at treelevel approximation [3,8,27]. Dominant one-loop corrections coming from stops and scalar triplets, as well as one-loop contributions from heavy Higgsinos and Triplinos, have been included only recently [12,18,37]. Despite these efforts, the theoretical uncertainties on the TMSSM Higgs mass spectrum is far from being comparable with the experimental one.
A pragmatic approach to this problem is to absorb the (potentially large) theoretical error on m h into an effective uncertainty on the high energy parameters, especially on the m U , m Q and m Σ soft-breaking terms (and on the trilinear parameters if they are allowed to be large). It is however problematic to quantify the latter uncertainty and how it propagates to the physical observables. For instance, big effects can arise in the DM relic density in the neutralino-stop coannihilation region, or in the SI cross-section when stop mediation dominates the interaction. On the other hand, less dramatic effects arise when the parameters absorbing the Higgs theoretical uncertainty provide sub-leading corrections to the observables. In order to reduce these uncertainties, here we improve the recent TMSSM Higgs mass calculations [12,18,37] and consider loop effects in the whole mass spectrum.
For this purpose we use the SARAH-3.3.0 program [38,39] to obtain the full two-loop Renormalization Group Equations (RGEs). The code, which works in the DR renormalization scheme, also provides the full one-loop ElectroWeak-Symmetry Breaking (EWSB) conditions and full one-loop spectrum to which we include some O(h 2 t g 2 3 ) and O(h 4 t ) twoloop contributions.
The RGEs are solved numerically by the SPheno-3.2.4 [40,41] code. The solution fulfills the above EWSB conditions at the electroweak scale m Z , as well as some experimental constraints (e.g. the quark mass spectrum; for details see refs. [40,41]). It is univocally determined once we choose the values of the residual free parameters of the theory 5 . These inputs are given (and we will quote them) at the SUSY renormalization scale, Q.
Once the RGEs are solved, all running parameters and couplings at the scale Q are known. These are used to determine the pole mass spectrum. In this way, we determine the pole mass m h at full one-loop plus O(h 2 t g 2 3 ) + O(h 4 t ) two-loop order on top of the two-loop RGE resummation 6 .
The renormalization scale dependence m h (Q) highlights the improvement in the Higgs mass calculation and it is presented in figure 1 for several values of λ and the parameter setting in eq.   A last comment concerns the chargino and neutralino parameters. As shown in the figure, if (part of) the chargino spectrum is heavy, relevant negative corrections to m h can arise [37]. For instance, depending on the value of λ, m h is lowered by about 1-: 4 GeV by moving µ = M 2 from 300 GeV to 1 TeV when m = 700 GeV and µ Σ = M 1 = 150 GeV (c.f. dotted and solid curves of figure 1). Of course, this decrement can be compensated by modifying either (λ, tan β) and/or by increasing m, as the dotted-dotted-dashed lines highlight. 7 Notice that the lines with very small λ reproduce the MSSM result except of modifications due to the extra SU (2)L-charged content provided by the triplet.

Higgs signatures
Since our aim is to explore the qualitative capabilities of the TMSSM, in particular those related to DM features, we do not look for interplay of Higgs production and decay widths to overcome the LHC bounds. We instead try to work well within the ballpark allowed by data, that is, we attempt to reproduce a SM-like Higgs sector.
The first step in this direction is to fix the tree-level Higgs couplings to SM fields. They are SM-like if, on the top of our assumption m Σ m h , it occurs either (i) m A is much larger that m h or (ii) tan β and λ have values within the so-called alignment region [18]. Here we focus on the first possibility. In this case results are independent of the specific choice of m A and we can thus fix m A = 1.5 TeV without lack of generality.
The second step is to check the radiative corrections to the Higgs couplings coming from non-SM particles. For our parameter choice, given in eqs. (2.11) and (2.12), loop corrections to tree-level interactions are negligible. They may instead be responsible of important deviations from the SM in loop-induced processes. For gluon fusion, which is the main Higgs production mechanism at LHC, no relevant deviation arises in our analysis since squarks are assumed rather heavy and tan β is small. Therefore, the total Higgs production is SM-like. On the contrary, charginos may be light and eventually the Γ(h → γγ) and Γ(h → Zγ) widths may depart from their SM values. However, these two processes are not yet well measured due to lack of statistics and of indirect impact on other processes: in practice Γ(h → γγ) and Γ(h → Zγ) are so small that they play no role in the branching ratios of other Higgs decays. For this reason we do not force them to be SM-like, as we aim to do with the dominant Higgs channels.
Finally, one has to guarantee that no new relevant Higgs decay process is open. This typically occurs when the mass of the lightest neutralino is sufficiently small to allow for the h → χ 0 1 χ 0 1 channel. In such a case, any signal strength R XY ≡ BR(h → XY )/BR SM (h → XY ) calculated by disregarding the invisible width, should be corrected by the factor 1 − BR(h → χ 0 χ 0 ) 8 . As the branching ratio BR(h → χ 0 χ 0 ) is bounded by ATLAS and CMS analyses [43,44], it is worth to estimate it.

The
The Higgs decay channel into a pair of lightest neutralinos is open for m χ 0 1 < m h /2. Its width is given by Here the quantities N 1i are the components of the lightest (unitary) eigenvector of the neutralino mass matrix M χ 0 which is determined at one-loop after the RGEs flow achieved via SPheno and SARAH as explained in section 2.2. The quantity m χ 0 1 is the pole mass of the lightest eigenstate of M χ 0 . At tree level M χ 0 reduces to Notice that due to the LEP chargino mass constraint m χ + 1 100 GeV, a lightest neutralino with mass m χ 0 1 < m h /2 must be predominantly Bino. The coupling g hχ 0 1 χ 0 1 is then dominated by the Higgsino and Bino mixings, namely N 11 N 13 and N 11 N 14 . Consequently, for a given set of parameters, the experimental constraint on BR(h → χ 0 1 χ 0 1 ) turns out to be a lower bound on µ.
When m χ 0 1 is even smaller, namely lighter than m Z /2, also the LEP bound Γ(Z → χ 0 1 χ 0 1 ) 2 MeV [45] has to be taken into account. As the constraint on BR(h → χ 0 1 χ 0 1 ), it imposes a lower bound on µ once the other parameters are fixed. We quantify it by the expression Moreover, when Higgsinos are extremely heavy and the lightest (Bino-like) neutralino is below the threshold of about 20 GeV, the further channel h → χ 0 2 χ 0 1 may be kinematically open without any dangerous enhancement to the invisible width of the Higgs or Z bosons. However, being µ very large, the chargino χ ± 1 and the neutralino χ 0 2 are almost degenerate. The LHC analysis on three leptons plus missing energy [30] excludes the parameter region of this scenario where χ 0 2 mostly decays into Z ( * ) χ 0 1 . In the remaining region where the channel χ 0 2 → h ( * ) χ 0 1 competes, it is instead unclear what the experimental limits are. Determining them would require a specific analysis that goes beyond the scope of this study and we then conservatively focus on the region with BR(h → χ 0 χ 0 ) = BR(h → χ 0 1 χ 0 1 ).

The h → γγ channel
Since the Higgs production is SM-like, the diphoton signal strength R γγ depends only on BR(h → γγ). For our setting in eqs. (2.11) and (2.12) only charginos can induce deviations from the SM prediction of Γ(h → γγ). Their contributions to R γγ have been already calculated by means of the low-energy approximation [12,18] or in the M 2 decoupling limit [27], starting from the tree-level chargino mass matrix It has been observed that maximal diphoton enhancement occurs when all chargino mass parameters are light (compatibly with the chargino mass bound) and moreover, in the regime of very small tan β and large λ (linked one to each other by the Higgs mass constraint), when Triplino and Higgsino mass parameters are degenerate [18].
In the present analysis we improve the previous estimate by including loop-corrections in M χ ± . In many cases these radiative contributions increase the lightest chargino mass by about 10% with respect to its tree-level value. They can hence be important when one cuts the allowed parameter space due to the LEP bound m χ ± i 100 GeV. When only charginos provide new (sizeable) contributions to the diphoton channel and the Higgs production is SM-like, R γγ is given by where A 1/2 is the spin-1/2 scalar function (see e.g. ref. [46] for its explicit expression) with argument is the lightest Higgs effective coupling to charginos.
The quantities A γγ W and A γγ t are the W -boson and top-quark contributions whose values are respectively -8.3 and 1.9 for m h 126 GeV.
In the procedure we apply, which corresponds to the one SPheno and SARAH employ, R γγ is calculated by plugging the chargino pole masses into where U and V are the unitary matrices diagonalizing the one-loop chargino mass matrix ).

The h → Zγ channel
LHC constraints on R Zγ are still very weak [47,48]. Nevertheless, the h → Zγ channel, likewise the h → γγ decay, is worth to analyze since it is particularly sensitive to new colorless electrically-charged particles which do not change the Higgs production. At the best of our knowledge, in the TMSSM the R Zγ signal strength has never been calculated.
Similarly to the case of R γγ , for our setting (2.11) and (2.12) only charginos can move Γ(h → Zγ) from its SM value. This leads to (3.10) -10 - The contributions A Zγ W and A Zγ t have been first obtained in refs. [49,50]. They can be expressed in term of Passarino-Veltman three-point functions and turn out to be A Zγ W = −12 and A Zγ t = 0.6 for m h 126 GeV [51]. In the TMSSM the chargino contribution comes from triangular loops where all three chargino mass-eigenstates run in and can be flipped from one to another at the vertices (both clockwise and anti-clockwise helicity directions must be taken into account). No flipping however occurs at the vertex involving the photon. For this reason only up to two chargino mass-eigenstates run inside a given loop and each diagram involves a loop integration that is formally similar to those arising in the MSSM calculation (where only two charginos exist). Consequently the study of the Γ(h → Zγ) is a straightforward generalization to three charginos of the MSSM expression given in ref. [51].
In the view of the above considerations, we can generalize the procedure of ref.
[51] and we obtain in which: f is a linear combination of Passarino-Veltman functions defined in ref. [51]; (3.13)

Numerical analysis setup
The TMSSM involves several free parameters. Some of them have to be fixed for practical purposes but play no role in our analysis. This is the case for the whole slepton sector whose masses are assumed above the TeV scale not to interfere with the chargino and neutralino phenomenology we analyze. Other parameters have a minor impact, and their choice given in eq. (2.11) is motivated in section 2.1. Some have to satisfy the EWSB conditions (as explained in section 2.2), and finally only the followings are still undetermined: To accomplish an efficient sampling on these seven parameters, we adopt an approach based on Bayes' theorem where d are the data under consideration, L(d|θ i ) is the likelihood function and p(θ i |d) is the posterior Probability Distribution Function (PDF). The function π(θ i ) is the prior PDF, it is independent of data and describes our belief on the values of the theoretical parameter, before the confrontation with experimental results. NS parameters Prior range All priors π(θ i ) used in the analysis and their ranges of variation are summarized in table 1. A flat prior is assumed for the stop parameter m, with an upper bound at 2 TeV in order not to introduce a large electroweak fine-tuning. For gaugino, Higgsino and Triplino masses, we instead consider logarithm priors and values below the TeV scale. Such a choice is aimed to improve the statistics in the parameter space where charginos tend to be close to their LEP mass bound, may enhance R γγ and R Zγ , and may open the window of the lightest neutralino DM particle. For the same purpose, and in order not to barely reproduce a MSSM-like phenomenology, we also impose tan β smaller than 10. A similar reasoning applies for the chosen range for λ. Within such values we expect to fully cover the TMSSM parameter region where the little hierarchy problem is alleviated (with respect to the MSSM) and perturbation theory does not break down before the GUT scale [12]. On the other hand, we neither exclude a priori scenarios with Landau poles at the PeV scale because these may be avoided in ultraviolet completions of the TMSSM.
The likelihood function is the conditional probability of the data given the theoretical parameters. The data d used in L(d|θ i ), which are the observables and constraints summarized in table 2, are as follows.
Collider data: We require the lightest CP-even Higgs mass m h to be compatible with the ATLAS and CMS measurements [1,2], which we (indicatively) combine by a statistical mean. Its uncertainty is dominated by the theoretical error, which is estimated to be around 3 GeV [42]. We also assume chargino and stop masses that fulfill the bounds m χ ± 1 > 101 GeV [28] and m t 1 > 650 GeV [30]. Finally, we require the invisible decay width of the Z boson to be smaller than 2 MeV [45].
DM data: We impose the lightest neutralino relic abundance to match Ω DM h 2 measured by Plank [52], as we are interested only in single-component DM. Notice that the experimental error on this observable has become incredibly smaller than the theoretical one, hence we consider an additional 20% of theoretical uncertainty [53]. Furthermore, we enforce the neutralino SI cross-section off nuclei, σ SI n , to be compatible with the LUX direct detection exclusion bound [26] at 90% CL. For the theoretical prediction of the SI cross-section mediated by the Higgs boson, we do not introduce uncertainties related to the strange quark content of the nucleon: we fix the ratio of nucleon mass and strange quark mass to be f s = 0.053 MeV, accordingly to ref. [54] (for effects due to different choices of  [26] f s and similar quantities such as σ πn see e.g. refs. [55][56][57][58][59]). For either the relic density and the Higgs mass we use a Gaussian likelihood function whose peak corresponds to the measured central value and whose width reproduces the standard deviation of the measurement (explicit quantities are quoted in table 2). For the σ SI n constraint we instead implement a Heaviside likelihood function. The DM constraints are implemented in the likelihood function L DM (d|θ i ), the collider constraints are implemented in the likelihood function L Coll (d|θ i ) and the full likelihood is simply the product of every individual likelihood associated to an experimental result. Finally, the above stop and chargino mass limits as well as the constraint on the Z-boson invisible width are absorbed into the prior PDFs: each parameter point generating a TMSSM mass spectrum that violates these bounds is discarded.
For some given values of the theoretical inputs θ i the collider and DM observables are computed by means of some public codes. We briefly summarize the programming procedure. We employ SARAH-3.3.0 and SPheno-3.2.4 to calculate the TMSSM mass spectrum (where radiative corrections are taken into account as described in section 2.2). Also Γ(Z → χ 0 1 χ 0 1 ), BR(h → χ 0 1 χ 0 1 ), R γγ and R Zγ are determined by dint of SPheno-3.2.4 along the lines of section 3 (for R Zγ we also use the Passarino-Veltman functions that are implemented in the CPsuperH2.3 libraries [60]). Afterward, the SPheno-3.2.4 output is elaborated by micrOMEGAs 2.4.5 [61]. In this way we compute the DM observables listed in table 2.
To explore the parameter space we link SPheno and micrOMEGAs 2.4.5 to the nested sampling algorithm MultiNest v3.2 [62] (with specifications of 4000 live points and tolerance parameter set to 0.5). This algorithm produces the posterior samples from distributions with a large number of parameters and with multi-modal likelihoods more efficiently than Markov Chain Monte Carlo. At practical level we run two samples: for analyzing the Higgs phenomenology we use only L Coll (d|θ i ) (sample 1), whereas when exploring the DM constraints as well, we use the full likelihood (sample 2). MultiNest v3.2 might however populate with an insufficient number of points regions where the likelihood is flat. This is relevant for the R γγ and R Zγ observables, as we do not impose constraints on their values in the likelihood function. To address this issue we run two additional samples with L(d|θ i ) 3 = L Coll (d|θ i )×L γγ (d|θ i ) and L(d|θ i ) 4 = L Coll (d|θ i )×L DM (d|θ i )×L γγ (d|θ i ) (for the case without and with the DM constraints respectively, sample 3 and sample 4). These two likelihood functions include a fake information associated to an extra Gaussian likelihood function L γγ (d|θ i ) with R γγ = 1.6 ± 0.2 to ensure a efficient exploration of region with large h → γγ and h → γZ signal strengths 9 . We do not provide a statistical analysis of the samples but show the result for points drawn randomly from the posterior PDF, which are provided in the * post equal weight.dat file constructed by MultiNest v3.2, hence we can safely combine the samples originating from different run with different likelihood functions. Before discussing our findings, let us mention some experimental bounds that we do not enforce in the sampling phase.
Different bounds on BR(h → χ 0 1 χ 0 1 ) exist in the literature [43,44,[63][64][65][66]. Imposing any of them would make our results of difficult interpretation if a different bound should be considered. We thus prefer not imposing any cut on BR(h → χ 0 1 χ 0 1 ) and just presenting its value in the results we present.
We are also aware of the bounds on the chargino and neutralino masses based on simplified models: in scenarios with m χ 0 1 100 GeV and m χ ± 1 m χ 0 2 , data analyses impose m χ ± 1 350 GeV at 95% CL if χ 0 2 decays 100% into Z boson, or m χ ± 1 170 GeV if χ 0 2 decays 100% into h boson [67,68]. However, due to its not straightfoward intepretation in the generic TMSSM parameter space, we do not impose such constraints. Instead, in the post processing phase of the samples we verify that these bounds do not apply in the interesting ballpark of our analysis. Indeed, in particular when we achieve a relevant diphoton enhancement, the fields χ 0 2 and χ ± 2 are mixed states and consequently (i) their masses are not degenerate and (ii) the neutralino decay channels into Z and h bosons can compete especially due the Triplino component and its potentially sizeable coupling λ.
Finally, we also consider the B s → µ + µ − and B → X s γ observables and the neutralino Spin-Dependent (SD) cross-section off protons and neutrons. We use SPheno-3.2.4 and micrOMEGAs 2.4.5 respectively to calculate them. As expected in scenarios with low tan β, these B-meson signatures are in full agreement with experiments [69,70]. We will compare the results for SD cross-section with COUPP and XENON100 limits [71,72] on proton and neutron respectively and comment them in section 6.

R Zγ and R γγ without DM contraints
Within the TMSSM, the possibility of achieving sizeable enhancements in R γγ has been previously highlighted in refs. [12,18]. These analyses were performed by considering treelevel chargino masses and low-energy limit approximations. They were moreover carried out for some illustrative parameter regions. In this section we extend the previous analysis focused on the m A m h regime [12]. In particular, we explore a broader parameter space (but still keeping large m A ) and we include the radiative effects discussed in section 3.2. We also present our findings for R Zγ in eq. (3.10).
Before reporting the result of the full parameter sampling, it is educative to understand the role of some inputs. The essential parameter dependence of R γγ and R Zγ is shown in For the parameter choice considered in the figure, the enhancement in h → γγ is always larger than the one in h → Zγ. Moreover, R γγ and R Zγ are strongly correlated and a sizeable enhancement in R γγ requires a departure from the SM also in the h → Zγ channel. These behaviors will be confirmed in the results of the full parameter sampling.
As figure 3 shows, in each scenario the largest R γγ and R Zγ are achieved by reducing tan β and increasing λ, which also corresponds to requiring less tuning in the electroweak sector (cf. eq. (2.10)). The enhancement is mostly due to the decrease of m χ ± 150 GeV but quite different R γγ . These observations are in agreement with previous results obtained for R γγ [12,15,16].
A last remark concerns the parameter range of figure 2. We do not enter the regime of tan β 1 and λ 1 to achieve larger enhancements. Besides the reasons previously provided, there is a further issue that imposes such a restriction: the more the tree-level Higgs mass is boosted, the smaller the radiative corrections have to be not to overstep the m h 126 GeV constraint. In particular, this may require stop masses below the bound of table 2, as it happens in scenario C at λ 0.85 with tan β 1.1. Of course, slightly bigger enhancements would exist by allowing for m t 650 GeV and/or m Σ 5 TeV. However, since prooving the experimental suitability of such modifications would require specific collider analyses, and lowering m Σ may also increase the electroweak fine tuning, we do not further discuss this possibility.
The two samples obtained with L Coll (d|θ i ) are presented in figure 3. The amount of diphoton enhancement is encoded in the color of the points: R γγ < 1.1 in gray, 1.1 < R γγ < 1.2 in blue, 1.2 < R γγ < 1.3 in green, 1.3 < R γγ < 1.4 in brown, and R γγ > 1.4 in yellow (this color code will be maintained in the rest of the paper). The bottom left panel of the figure proves that the presence of the Triplino is fundamental to achieve R γγ 1.3. Indeed, if the Triplino component of the lightest chargino is negligible, R γγ falls to MSSMlike values, i.e. R γγ 1.2 [16] 10 . However, in some extreme cases, Triplino effects may be still present even when µ Σ is quite large and the Triplino component of the lightest chargino is subdominant (but not negligible), as the case µ Σ 900 GeV and R γγ 1.4 shows.
The features of the parameter regions where the yellow points accumulate can be explained as follows. As observed in figure 2, large diphoton enhancements are allowed for small tan β and rather large λ (cf. bottom right panel). In such a case, the relation if the Wino mixing is sizeable. Therefore, also M 2 has to be small to achieve maximal enhancements (cf. top left plot). In particular, in order to minimally suppress the loop function A 1/2 (τ χ ± i ), the parameters have to be correlated in such a way that m χ ± 1 ≈ 101 GeV. The effect of the Higgs and stop mass constraints is pointed out in the bottom right panel of the figure. The region with small λ and small tan β is not populated because the tree-level Higgs mass (2.10) is very small. In such a case, only large stop loop corrections to m h could push it up to 126 GeV, but such corrections are not allowed due to the m range of table 1. On the contrary, in the upper empty area with small tan β, the tree-level Higgs mass is too large. In this case stop loop corrections have to be small not to overstep the Higgs mass constraint, but they are incompatible with the bound m t 1 > 650 GeV. Curiously, the mass bound cuts off most of the parameter space where the TMSSM exhibits a Landau pole at a scale Q 10 8 GeV (see ref. [12] for estimates of the Landau pole scale). We stress however that the border of this empty region could be mildly moved by considering larger values of M 2 , µ, and µ Σ than those in table 1. Heavier charginos would indeed provide bigger (negative) radiative correction to m h that should be compensated by slightly larger stop masses to keep m h ≈ 126 GeV [37].
Although figure 3 presents only R γγ results, the above considerations apply also to R Zγ . Indeed, in the TMSSM R γγ and R Zγ are tightly correlated. This is proven in figure 4, which displays the values of R γγ and R Zγ arising in the samples 1 and 2. Since the sampling also explores the region with small M 1 , the h → χ 0 1 χ 0 1 channel can be open. Depending on the value of BR(h → χ 0 1 χ 0 1 ), the points in the figure are colored as follows: BR(h → χ 0 1 χ 0 1 ) < 1% in light blue, 1% ≤ BR(h → χ 0 1 χ 0 1 ) < 20% in violet, 20% ≤ BR(h → χ 0 1 χ 0 1 ) < 50% in dark yellow and BR(h → χ 0 1 χ 0 1 ) ≥ 50% in red (this color code will be followed in the rest of the paper).
In the left panel of the figure, the light blue area is not aligned with the remaining region. We have investigated the origin of this feature and it seems related to the different kinds of configurations of chargino parameters in that region. In fact, in the upper-left part of the light blue area, the typical chargino configuration yields to very large g L,R h χ 0 1 χ 0 1 (for M 1 100 GeV). Therefore, only when m χ 0 1 is tuned just below the m h /2 threshold, BR(h → χ 0 1 χ 0 1 ) is small. Unless of this rare accident, BR(h → χ 0 1 χ 0 1 ) is either huge or zero. Consequently, for the configurations of chargino parameters that populate the upper-left part of the light blue area, R γγ and R Zγ are typically either larger or much smaller than one, and an empty region at R γγ ≈ 1 and R Zγ ≈ 0.9 is thus produced.
The opposite effect instead occurs in the lower part of the light blue region: the typical chargino parameters yield tiny g L,R h χ 0 1 χ 0 1 and hence BR(h → χ 0 1 χ 0 1 ) is small for very most of the values that M 1 can assume. For these configurations of chargino parameters, therefore, R γγ and R Zγ do not jump from one value to a very different one at the threshold m χ 0 1 ∼ m h /2 but slowly change as function of M 1 . For this reason the violet region is abundantly populated by such chargino configurations.
Finally, let us summarize the most striking result of this section. From our analysis we obtain the following TMSSM bounds (see figure 3): and we stress the tight degree of correlation between the two loop-induced processes.We will comments on the future experimental implications of these bounds in the conclusions (section 7).

DM phenomenology and constraints on R γγ and R Zγ
In this section we present the TMSSM phenomenology in the presence of a neutralino DM candidate. As previously motivated, we require that no supersymmetric particle but neutralinos and charginos interferes during freeze-out, to achieve the correct relic density.
To understand the relevant consequences of introducing the Triplino component, we first analyze the Wino decoupling limit. In figure 5 (left panel) the behaviors of the lightest-neutralino relic density and SI cross-section (black and red lines, respectively) for the limit M 2 1 TeV are depicted as a function of M 1 . The corresponding masses m χ 0 1 , m χ 0 2 , m χ ± 1 (left panel) and the lightest neutralino compositions (right panel) are also displayed by the mark code reported in the legends. The choice µ = 500 GeV, µ Σ = 180 GeV, tan β = 2.9 and λ = 0.88 is assumed. The SI cross-section is normalized to 10 −9 pb, which is close to the maximum of LUX sensitivity given by σ SI 8 × 10 −10 pb at m χ 0 1 ∼ 50 GeV [26]. It results that at low M 1 the lightest neutralino, which is almost pure Bino, overcloses the Universe until it reaches the Higgs resonance. In this region the lightest neutralino can provide the correct relic density and, moreover, its SI cross-section is below the LUX upper bound (i.e. the red curve is below 0.8). This occurs because the Higgsino components in the coupling g hχ 0 1 χ 0 1 is enough suppressed to be compatible with LUX results. The Higgs pole region is only mildly sensitive to the presence of the Triplino. For different parameter configurations, the correct relic density is achieved also at the Z boson resonance. We will discuss these two poles more in detail in section 6.2. . The lightest chargino is degenerate with the next-to-lightest neutralino. Right: Component of LSP as a function of M 1 : in red is the Bino fraction, in brown the Triplino, in yellow and green the two Higgsino components and in blue the Wino fraction (as labelled in the caption). In both panels µ = 500 GeV, M 2 = 1.5 TeV, µ Σ = 180 GeV, tan β = 2.9 and λ = 0.88.
Above the Higgs resonance, the relic density increases until it reaches the opening of the W + W − annihilation channel and then decreases. It reaches the experimental value when the coannihilation with the lightest chargino χ ± 1 (and marginally with χ 0 2 ) becomes efficient enough. Since the field χ ± 1 is dominantly Triplino (we are assuming µ µ Σ ), the coannihilation cross section strictly depends on the tuning between µ Σ and M 1 . In particular, the correct relic density occurs for M 1 < µ Σ and the LSP is Bino-like (cf. right panel). Since in this region also the LUX constraint is fulfilled, it results that in the TMSSM a well-tempered Bino-Triplino neutralino can be a good DM candidate.
The behaviors of the relic density and SI cross section shown in the figure is then a proof of concept for the DM in the TMSSM. Indeed we find two qualitatively-different regions where the LSP satisfies the DM constraints. In the next two sections we discuss them in detail, still in the M 2 decoupling limit.

Well-tempered 'Bino-Triplino' neutralino
As it is well known, in MSSM scenarios with well-tempered neutralinos the correct relic density is achieved by a tuning of the Bino and Wino (or Higgsino) mass parameters to get an opportune balance between the large annihilation cross-sections of the Bino and the small ones of the Wino (or Higgsino) [25]. In the TMSSM with M 2 above the TeV scale, the role of the Wino is replaced by the Triplino, which still has gauge interactions with the W bosons. The channels contributing to the relic density are the chargino annihilation into W + W − , ZZ followed by the coannihilations χ 0 1 χ ± 1 → ZW ± , qq . The relevance of the former processes with respect to the latter ones depends on the exact hierarchy between M 1 and µ Σ . The µ parameter is instead constrained by LUX. Indeed, due to the LUX bound the Higgsino components of the LSP have to be small in order to suppress the g h χ 0 1 χ 0 1 coupling that is the main responsible for the SI cross section via Higgs exchange. This is illustrated in figure 6, where the SI cross section is plotted as a function of µ Σ .
In all panels of the figure we fix tan β = 2.9, λ = 0.88 and M 2 = 1.5 TeV. Besides the quantities shown in figure 5, also the values of R γγ are displayed (for the color code of each quantity see the legend). At each point the parameter M 1 is adjusted just below µ Σ to reproduce the observed relic density. For µ = 300 GeV (top panels), the LSP is mostly Bino but the amount of its subdominant components vary at different µ Σ . For light LSPs, the Triplino mixing is comparable to the Higgsino ones and the SI cross section is below the LUX limit. As soon as both Higgsino components reach the Triplino one, the SI crosssection is excluded by the LUX bound. By increasing µ to 500 GeV (bottom panels), the Higgsino mixings at a given µ Σ become smaller than in the µ = 300 GeV case, and the SI remains below the LUX bound in a wider range: χ 0 1 satisfies all DM constraints in the mass range of 90÷200 GeV. The Higgsino components tend to be always larger than the Triplino one, as the Triplino connects with the Bino only via the Higgsino mixing (see eq. (3.3)). The figure confirms as well that the mechanism that provides the relic density is a balance between annihilation and coannihilation with the lightest chargino, as both particles are close in mass. The contribution of χ 0 2 in coannihilation is marginal and depends strongly on the exact mixing.
Of course, the minimal µ value that LUX allows depends on the parameters that we have kept fixed in the figure. In particular, the LUX bound on µ becomes stronger at small tan β (see eq.(3.2)). This anti-correlation is discussed more in detail in section 6.4. However, we can anticipate that it affects negatively the enhancements of both γγ and Zγ Higgs signals. Indeed, as previously discussed, large R γγ and R Zγ require either tan β and µ to be small. This is confirmed by the brown line in the left panel of figure 6: for the considered parameter set, the maximal R γγ drops as µ goes from 300 GeV to 500 GeV.

DM at the Higgs and Z resonances
The Higgs and Z boson resonances are fine-tuned regions as they rely on the fact that for M 1 ∼ m h /2 and M 1 ∼ m Z /2 the annihilation cross-section gets enhanced, hence decreasing the relic density. We first comment on the Higgs pole.
The case of the Higgs resonance is peculiar because the phenomenology of the LSP can be reconducted to one coupling only. The vertex Bino-Higgsino-Higgs is responsible for both the annihilation ( χ 0 1 χ 0 1 → h → qq) and the SI scattering cross-section since the neutralino is mostly pure Bino. Hence the key parameters are M 1 and µ, whereas there is a minor dependence on both µ Σ and M 2 . Similarly to the case of the well-tempered neutralino, the µ parameter is constrained by the LUX bound, as illustrated in figure 7 where at each point M 1 is tuned at the Higgs resonance to achieve the observed relic density. (The plotted quantities and their color code are as in figure 6). Indeed for µ = 300 GeV (top panels), the SI cross-section is only marginally compatible with the LUX constraint at large µ Σ and clearly a small decrease in µ will exclude these points (cf. top and bottom left panels). The behavior of the SI cross-section is only mildly dependent on µ Σ , as it is almost flat over all µ Σ range. This is even more manifest for µ = 500 GeV (lower panels). For such a µ value the SI cross section is well below the experimental bound. From the right panels it is clear that the LSP is almost pure Bino and that the the dominant annihilation channels is a Higgs exchange on s-channel. Indeed, due to the large mass gap between the lightest neutralino and the other charginos and neutralinos (left panel), coannihilation is completely irrelevant.
In the Higgs resonance region one might expect to have large R γγ and R Zγ signal strengths because the DM phenomenology is not tightly bounded to the Triplino component. In other words the µ Σ parameter is not correlated to σ SI Xe or Ω DM h 2 , and therefore can take low values such that the lightest chargino mass is close to the LEP bound. However, the anti-correlation between tan β and µ mentioned in section 6.1, is present in this region as well. Therefore, the enhancement in the R γγ turns out to be at most ∼ 10% for µ = 300 GeV and negligible for µ = 500 GeV, as indicated by the brown line in the left panel of figure 7. We will discuss this issue in detail in section 6.4.
A similar reasoning applies to the Z resonance region, with the difference that in that region the process that fixes the relic density, which is proportional to the Z-Higgsino coupling of the LSP (given in eq. (3.4)), is uncorrelated from the SI elastic cross-section.

DM in the TMSSM: global survey
In this section we present the results of a comprehensive sampling of the TMSSM parameter space, using the likelihood L DM (d|θ i ) and the prior ranges described in section 4. Figure 8 (left panel) shows the mass value for which the LSP is a viable DM candidate compatible with LUX (blue solid). As discussed above, there are two separate regions: one with the resonances at 40 GeV m χ 0 1 70 GeV, and one with a well-tempered neutralino at m χ 0 1 90 GeV. The apparent upper limit at about 600 GeV is an artifact of the prior range choice for the mass parameters. Notice that almost all the parameter space is in the sensitivity range of XENON1T [73] (black dotted line), so an effective TMSSM might be probed by DM direct searches in 5-7 years time 11 . In our sample the minimal values of σ SI Xe correspond to the contribution to the SI cross-section due to squarks exchange, when the Higgsino component start to be negligible. The value is similar in all the sample as the squark sector is kept heavy. More interestingly, the requirement of having the LSP as good DM candidate sets as well an upper bound on the Higgs invisible branching ratio BR(h → χ 0 1 χ 0 1 ) < 20% (violet points), which is comparable to current LHC bounds [63][64][65][66] (indeed there are the very few dark yellow points with BR(h → χ 0 1 χ 0 1 ) > 20%). This illustrates the complementarity between DM direct searches and colliders: significant values of the Higgs invisible width can be fully probed by XENON1T.
In the right panel of figure 8 we show the σ SI Xe versus the SD cross-section on neutron (which is equivalent to the one on proton). As in the previous figures, violet points represent parameter configurations with BR(h → χ 0 1 χ 0 1 ) > 1%, whereas brown points correspond to SD cross-section values at odds with the XENON100 exclusion bound, whose strongest limit σ SD n 3 × 10 −4 pb is at m χ 0 1 ∼ 50 GeV. We do not remove the brown points from our samples as the nuclear uncertainties on the structure functions for the nucleons are large and can affect the predicted number of events by a factor of 3-4 [72,75,76]. In addition the predictions for the SD on proton give the same value, however these values are below the COUPP sensitivity, which reaches the maximum at σ SD p ∼ 5 × 10 −3 pb for m χ 0 1 ∼ 40 GeV. These points with large σ SD p,n are associated to the t-channel Z boson exchange and arise when Higgsino components are sizable. They correspond to the Z resonance region, where the coupling g Z χ 0 1 χ 0 1 is large. In the case of SD scattering there is a one-to-one correspondence with the annihilation cross-section mediated by the Z boson. The main bulk of the sample is however below the current SD bounds, because the coupling to the Z boson tends to be suppressed for most of the LSP composition, being predominantly Binolike. The sharp cut on the upper values of SD and SI when the Higgs channel into invisible is open is due to the LUX bounds. XENON1T will be less sensitive to SD interaction (perhaps ∼ 10 −6 pb), hence the model is more likely to be tested with the SI cross-section and the brown points will all be probed, independently of the nuclear uncertainties.
When M 2 is decreased to the same scale as the other chargino parameters, the phenomenology of the DM is wider and the tight bound on the lower limit of µ described above (sections 6.1 and 6.2) is relaxed by the additional admixture with the Wino component. This is illustrated in figure 9, where we display the LSP mass versus the neutralino and chargino parameters as labelled. From the top left panel, it is clear that the LSP is mostly Bino, as m χ 0 1 and M 1 follow each other over all the allowed range. From the other three panels it is striking that the Higgs and Z resonances are mostly independent from M 2 and µ Σ as they can acquire approximately any allowed value.
The case of the well-tempered neutralino, where all possible combinations of compositions for the are available, is more interesting. Indeed the LSP can be mixed Bino-Triplino, as discussed above, but it can never be Triplino dominated because the LSP would be the corresponding chargino. Successful DM candidates can also show up as MSSM-like states, that is Bino-Wino, in which case the relic density is achieved by neutralino annihilation into W + W − and coannihilation with the lightest chargino producing qq . These MSSM-like scenarios are however less appealing because the condition M 1 ∼ M 2 is not recovered by the usual supersymmetry-breaking mechanisms. Of course, a large portion of the parameter space presents mixed Bino-Triplino-Wino LSP, for which the dominant annihilation and coannihilation channels are χ 0 1 χ 0 1,2 → W + W − and χ 0 1 χ ± 1 → qq . Due to the LUX bound only µ larger than about 300 GeV is allowed. Moreover, the relic density is achieved by a mixture of annihilation and coannihilation. More specifically the main processes are χ 0 1 χ 0 1 → hZ, qq and χ 0 1 χ ± 1 → ZW ± . Instead, when all components (Bino-Triplino-Wino-Higgsino) in the LSP are sizable, the main annihilation channels are the following: χ ± 1 χ ± 1 → W ± W ± , χ 0 1 χ ± 1 → hW ± and χ 0 1 χ 0 1 → hZ.  Figure 10 shows the γγ signal strength versus the Zγ one, similarly to figure 4. The possible R γγ and R Zγ that can be achieved in the TMSSM where the DM constraints are satisfied, are displayed in cyan. They are superposed to the points of figure 4 where no DM observable is imposed (here displayed in green). The DM constraints alleviate the change in slope that arises in the correlation plot without DM constraints (cf. left panel of figure 4): the cyan points follow a smooth pattern with respect to the dark green ones. As previously discussed, the missing dark green zone in the upper part of that plot is due to a Higgs branching ratio varying very fast as soon as it is kinematically open. There, to get small reduction in the signal strength, M 1 should lie exactly on the threshold value, which is a very infrequent situation. On the contrary, with the LSP being DM, the relic density constraint requires M 1 ∼ m h,Z /2 (or the well-tempered neutralino conditions) and therefore a large portion of the sampled parameter space is concentrated in the pole regions.

DM implications on R γγ and R Zγ
On the other hand, on general basis, the DM constraints are not encouraging about the collider Higgs phenomenology. Indeed, our analysis leads to R γγ 1.25 , R Zγ 1.2 (with DM obs.) . (6.1) The most stringent constraint on the parameter space where large R γγ and R γγ are achieved, is the LUX bound on SI cross-section, which rules out the configurations where either µ and tan β are simultaneously small: the anti-correlation between these two variables is striking from the right panel of figure 10 12 . In particular, for tan β 1 the LSP is a viable DM candidate only for µ > 500 GeV, i.e. it is incompatible with the ballpark that provides the largest possible enhancements (see figure 4). The possibility of achieving sizeable loop-induced decays of the Higgs and at the same time a successful neutralino DM particle, starts arising at tan β 3 and µ 300 GeV: this is exactly the region that saturates the bounds in eq. (6.1), as shown by the green points in the right panel (these points have R γγ > 20%). The mild enhancement of 10% is viable in all tan β range, as it is due to small values of µ Σ . This is illustrated in figure 11. In the left panel we show the projection of the R γγ values as a function of λ and tan β: the range of the Triplino coupling λ that provides the enhancements is limited with respect to figure 4, being scattered at around 0.8÷0.9. Signal strengths larger than one can only be achieved for small values of µ Σ (central panel); they are however only marginally sensitive to M 2 . The same points are instead concentrated to both small values of µ and µ Σ (right panel) and they mostly correspond to the Higgs and Z resonance regions. This is confirmed by looking at the

Conclusions
We are entering the era of precision Higgs physics: the measurements of the Higgs mass, couplings and decay modes have already started to be highly sensitive to new physics beyond the SM. In this paper we have considered the Higgs phenomenology of the Y = 0 triplet extension of the MSSM, dubbed TMSSM, in which the new coupling between the triplet and the MSSM Higgses can alleviate the little hierarchy problem and modify the chargino and neutralino sector.
We have first accurately determined the couplings and pole masses of the stops, charginos, neutralinos and lightest CP-even Higgs h. Then, we have tackled the subtle effects of the Triplino in the h → γγ and h → Zγ loop-induced processes. We have shown that the additional Triplino component in the chargino sector provides a maximal enhancement of 60% in the R γγ signal strength, which is slightly larger than previously estimated (i.e. R γγ 1.45) [12]. An enhancement up to 40% can be achieved in the R Zγ signal strength, which we find to be highly correlated with the diphoton channel, even though it is always smaller than R γγ . The parameter region leading to the largest R γγ and R Zγ is characterized by tan β 2 and µ ∼ µ Σ ∼ M 2 ∼ 250 GeV, and in particular by light charginos close to the LEP bound. The enhancement in the TMSSM is significantly larger than the one achievable in the MSSM (∼ 20% for R γγ ) for the same chargino lower mass bound [16]. The measurements of these processes are likely to improve in the next years. LHC is indeed expected to probe the SM prediction of Γ(h → Zγ) once O(100 fb −1 ) data is collected [78], and to measure the g hγγ effective coupling within a 10% accuracy after a high luminosity 3000 fb −1 run [79]. With these further data the Higgs diphoton signal strength will plausibly converge to the SM value. In such a case, sizeable deviations in h → Zγ would not be compatible with the TMSSM. On the contrary, if data will still exhibit a positive deviation from the SM, there would be a clear indication of physics beyond the SM. The above predictions and the tight correlation between R γγ and R Zγ could be thus crucial to rule out or provide hints for the scenario considered here.
Besides the Higgs decays, we have investigated the DM phenomenology in the TMSSM, focusing on the interplay of the neutralino and chargino sectors enlarged by the triplet components. Similarly to the MSSM, the LSP is a viable DM candidate in the Higgs or Z pole region, and in the so-called well-tempered regime. The Higgs and Z pole regions are characterized by a Bino DM and are poorly sensitive to the Triplino, as the Higgs-Higgsino-Bino is the only relevant coupling. However, the well-tempered neutralino, where the LSP achieves the correct relic density via coannihilation with the lightest chargino, presents a new feature. Indeed the Triplino component of the LSP can substitute the Wino in the well-tempered neutralino and can solve the problem of having M 1 ∼ M 2 from grand unified model perspective. Indeed the requirement of DM comes at the expenses of satisfying the LUX exclusion limit for SI elastic cross-section on nuclei. The dominant contribution is due to Higgs exchange, which imposes a lower bound on µ. Interestingly we found that this has an impact for the R γγ and R Zγ enhancements: the Higgs-chargino coupling is reduced as well suppressing the signal strengths to at most 20%. Notice that these values are once again larger than the ones provided by the MSSM with DM constraints [16], when the Higgs production is SM-like.
The scenario considered here nicely illustrates the complementarity of DM direct searches with LHC. For instance the next generation of direct detection experiments, such as XENON1T, will probe a consistent portion of the neutralino TMSSM parameter space. Moreover it will be capable of constraining the Higgs invisible decay branching ratio up to 1%, in a time scale comparable to the LHC one. In general the TMSSM is less constrained by current LHC bounds on simplified models or supersymmetric searches. Indeed the presence of the Triplino can modify the couplings and the decay modes. This has been already observed for stops in the TMSSM [80] even though a precise estimate of their current mass bound is still missing. On the other hand no study exists for the chargino and neutralino mass bounds. Although we have checked that the present constraints [67,68] do not apply to our analysis ballpark, a dedicated investigation would be required in order to accurately determine the allowed parameter region. Present data should primarily affect the chargino parameter region with light lightest-neutralino and with small h → Zγ and h → γγ enhancements. With more LHC data strongest bounds are expected, in particular for the DM mass close to the Z or h resonance. On the other hand, in order to probe the coannihilation region (where the spectrum is compressed), ILC data and analyses similar to that proposed in ref. [81] would be crucial.