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Light charged Higgs at the beginning of the LHC era

The terascale will be explored with the start of the LHC. One of the most fundamental questions which we expect to be answered is the root of electroweak symmetry breaking and whether the Higgs mechanism is realized in nature or not. In this context we pose the question if existing experimental data still allow for a light non-minimal Higgs sector. We tackle this question first in the context of the two Higgs doublet model and then we concentrate in two supersymmetric models, the constrained MSSM and the MSSM with non-universal Higgs masses. In both supersymmetric scearios, light pseudoscalar and light charged-Higgs bosons are still viable provided tan beta is large. In this regime, we emphasize the importance of the constraints provided by the decay B to tau nu mediated by the charged-Higgs at tree-level. In addition we comment on generic predictions for hadronic colliders and indirect searches in such scenarios.


I. INTRODUCTION
The presence of a non-standard Higgs boson with a "small" mass, below 200 GeV, would be a very interesting possibility in the first years of LHC operation. In fact, the interest on this possibility has been recently increased with the small differences from Standard Model (SM) expectations found at CDF and D0 [1,2] and has motivated several analysis in the context of the minimal supersymmetric standard model (MSSM) [3,4]. Even though the results are completely compatible with the absence of non-SM Higgs bosons at the 2 σ level these small discrepancies have motivated the question whether it is possible to have a light non-SM Higgs consistent with the present experimental constraints. In this letter we intend to answer this question in models with 2 Higgs doublets and specially in the framework of the MSSM. During the first years of LHC operation and with the new measurements at Tevatron, top quark physics will receive a big boost with a significantly improved understanding of its physics and perhaps find a first clue of physics beyond the SM. Perhaps the best possible situation to obtain sizeable beyond-the-SM effects in top-quark physics corresponds to the existence of a charged Higgs boson of mass close to the top quark mass. In this work we will explore the possibility of having such a light Higgs sector in different models and how this affects phenomenology.
Clearly, the presence of a charged Higgs implies necessarily an extended Higgs sector. Therefore the simplest model we can explore and our first option is a two Higgs doublet model (2HDM). In a generic type II 2HDM we see that the charged-Higgs is constrained to be heavier than 295 GeV by BR(b → sγ), although a pseudoscalar mass in the range 150-200 GeV is still allowed. As a second option we consider supersymmetric models, where we find that a light charged-Higgs below 200 GeV is still possible both in the Constrained MSSM (CMSSM) and in an MSSM with non-universal Higgs masses. However, in these models the decay B → τ ν is a very strong constraint in the light m H + -large tan β region and, in particular, in the CMSSM sets a strict lower limit of 180 GeV for the charged-Higgs mass.
In the next section we explore in detail a generic type II two Higgs doublet model. Section III analyzes the CMSSM and a MSSM with non-universal Higgs masses and comments about models with mediation mechanisms other than gravity. In section IV we present the signatures of the light charged-Higgs scenario in collider and indirect search experiments.
Finally in section V we present our conclusions.

II. TWO HIGGS DOUBLET MODELS
The two Higgs doublet model is the simplest extension of the SM obtained with the only addition of a second Higgs doublet. A 2HDM with generic Yukawa couplings has severe Flavour Changing Neutral Currents (FCNC) problems and, for this reason, the Higgs couplings are restricted by an ad hoc discrete symmetry to forbid FCNC at tree-level. The two main options are the type-I and the type-II 2HDMs, depending on whether the up-type and down-type fermions are coupled to the same or different Higgs doublets respectively. In our analysis, we will assume a type-II 2HDM with a Higgs potential given by [5] where Φ i are the Higgs iso-doublets with hypercharge 1 2 . Being a type-II 2HDM, this potential satisfies a (softly-broken) discrete symmetry under the transformation Φ 1 → Φ 1 and Φ 2 → −Φ 2 . A nonzero value of m 2 3 indicates that the discrete symmetry is broken softly and would correspond to a Bµ coupling in supersymmetric models. The eight free parameters (m 2 1 -m 2 3 and λ 1 -λ 5 ) can be rewritten in terms of eight "physical" parameters, i.e. four Higgs mass parameters m h , m H , m A , m H ± , two mixing angles α, β, the vacuum expectation value v, and the soft-breaking scale of the discrete symmetry M. The two physical CP-even fields h and H are such that m 0 h ≤ m 0 H . In particular, the masses of the CP-odd, A (CP-odd) and the charged Higgs, H ± , are related by the following expression with v = v 2 1 + v 2 2 , where v 1 and v 2 are the vacuum expectation values of Φ 1 and Φ 2 , respectively. Imposing the vacuum conditions we can replace m 2 1 and m 2 2 by v 1 and v 2 . Then the masses of the heavier bosons (H, H ± and A) take the form m 2 Φ = m 2 3 /(sin β cos β) 2 +λ i v 2 , where λ i is a linear combination of λ 1 -λ 5 . When m 2 3 /(sin β cos β) 2 ≫ λ i v 2 , the mass m 2 Φ is determined by the soft-breaking scale of the discrete symmetry m 2 3 , and is independent of λ i . This corresponds to the so-called decoupling limit. On the contrary, when M 2 is limited to be at the weak scale (M 2 < ∼ λ i v 2 ) a large value of m Φ is realized by taking λ i to be large; i.e., the strong coupling regime. However, too large λ i leads to the breakdown of perturbation theory [6,7,8]. Furthermore, low energy precision data also impose important constraints on the model parameters [9]. We take into account the following bounds to constrain the 2HDM parameters 1 : i) Perturbative unitarity [6], corresponding to |a 0 (ϕ A ϕ B → ϕ C ϕ D )| < ξ (we take ξ = 1/2 in our analysis), where a 0 (ϕ A ϕ B → ϕ C ϕ D ) is the S-wave amplitude for the elastic scattering process ϕ A ϕ B → ϕ C ϕ D of the longitudinally polarized gauge bosons (and Higgs bosons). These conditions translate into constraints on the couplings λ i (i = 1−5) [7,8].
ii) Vacuum stability [11] iii) Constraints on oblique-corrections from LEP with the S, T and U parameters [9]. In particular, the T parameter is such that T ≃ α −1 EM ∆ρ, with ∆ρ ≤ 10 −3 . The above constraint can be satisfied if a custodial SU(2) V [12] is approximately conserved and [12,13] iv) B-physics constraints, in particularB → X s γ and B → τ ν. RegardingB → X s γ, the present experimental world average performed by HFAG [14] is while the theoretical estimate performed at the NNLO level [15,16] (for the reference value E cut = 1.6 GeV) is The NNLO SM prediction for B(B → X s γ) SM is lower than B(B → X s γ) exp by more than 1σ. This fact allows sizable NP contributions with the same sign as the SM ones like charged-Higgs boson contributions in 2HDMs. In the numerics we utilize the 1 For comparison, see the recent analysis of Ref. [10]. Even if our results qualitatively agree with those of Ref. [10], our numerical analysis was still necessary to understand whether the specific scenario studied in the present work is possible within a 2HDM.
formulae presented in Ref. [17] and updated in Ref. [18] that take into account the NNLO contributions for the SM [15,16].
Combining the SM prediction and the experimental results for B(B → X s γ), we impose the constraint at the 2σ level.
Combining the recent B-factory results [19,20] , with the SM expectation , whose numerical value suffers from sizable parametrical uncertainties induced by f B and V ub , it is found that where we have assumed f B = 0.216 ± 0.022 and V ub = (4.00 ± 0.26) × 10 −3 (from the average of inclusive and exclusive semileptonic B decay modes) by HFAG [14]. The decay B u → τ ν represents a very powerful probe of the scenario of light charged Higgs [21,22,23] because it is a tree-level process and we have that In the case of the decay A 0 that is obtained in SUSY models (see next section). Therefore B s → µ + µ − does not provide a further constraint on the 2HDM parameter space once the previous constraints are satisfied.
Applying these constraints we have numerically found the allowed range for m H + requiring a pseudoscalar mass m A in a narrow region, 150 < m A /GeV < 200, while all the other parameters of the model including tan β are left free. The upper bound on the m H + mass (for the imposed range of m A ) is found to be ∼ 400 GeV for any tan β value by the unitarity and ∆ρ constraints. The lower bound on M H ± is set by the constraints arising fromB → X s γ (M H ± > 295 GeV at 95% confidence level independently of tan β [16]). This bound is improved for large tan β values (tan β ∼ 45-65) by the B → τ ν constraints. In fact, as discussed in the next section, the tree-level decay B → τ ν sets a bound on tan β/M H + that roughly allows charged-Higgs masses higher than 295 GeV for tan β = 45 and higher than 420 GeV for tan β = 65 2 . Therefore a generic 2HDM of type II can still be compatible with a range between 150 and 200 GeV for the mass of the light pseudoscalar Higgs boson, although the charged Higgs is always constrained to be above 295 GeV byB → X s γ.
However, we have to recall that it is very difficult to accommodate the present discrepancy for the muon anomalous magnetic moment in a 2HDM scenario.
Notice that a scenario with a light pseudoscalar Higgs boson with mass M A ≤ 200GeV and a charged Higgs with mass M H ± ≥ 300GeV is not compatible with minimal SUSY frameworks.

III. SUPERSYMMETRIC MODELS
The Higgs sector of the MSSM is a special case of Eq. (1). The MSSM has been extensively studied in the literature (see e.g. [26,27] and references therein) and the presence of the different supersymmetric partners of the SM particles increases the phenomenological constraints to satisfy [28]. Therefore, the first question we have to answer is whether it is possible or not to obtain a pseudoscalar Higgs boson of a mass below 200 GeV in the MSSM satisfying simultaneously all the different constraints. We will answer this question basically in two versions of the MSSM: the Constrained MSSM (CMSSM) and the nonuniversal Higgs mass (NUHM) MSSM [29,30,31,32,33,34,35,36]. Then we comment about other SUSY-breaking mediation mechanisms such as gauge mediation and anomaly mediation models.

A. CMSSM and NUHM
The CMSSM is fixed by 4 initial parameters : m 0 , M 1/2 , A 0 and tan β plus the sign of the µ parameter. However, the sign of the µ parameter is bound to be positive by the requirement of a correct prediction to the muon anomalous magnetic moment and the B → X s γ branching ratio. Before considering in detail the different indirect constraints it is useful to identify the possible regions of CMSSM parameter space that can accommodate 2 In fact, lighter charged Higgs masses than these values, although never lighter than 295 GeV, can be allowed for larger tan β values if the SM contribution is canceled by a charged Higgs contribution as large as twice the SM one with opposite sign. a pseudoscalar mass below 200 GeV.
In order to establish the m 2 H + , m 2 A dependence on the input parameters of the CMSSM, let us consider the following tree-level expressions and their approximate values at medium to large values of tan β: The mass of the charged Higgs and the pseudoscalar 3 are very similar in the MSSM, as at tree-level they satisfy the relation: These masses are then obtained from the electroweak values m 2 Hu (m t ) and m 2 H d (m t ) which are determined through the RGEs As it is well known, m 2 Hu (m t ) < 0 in the entire SUSY parameter space due to the large RGE effects proportional to y 2 t . The approximate numerical solution for m 2 Hu (m t ), valid for any tan β value, is [30] clearly showing that m 2 Hu (m t ) < 0. On the contrary, m 2 H d (m t ) crucially depends on tan β. For instance, if we assume low/moderate tan β, i.e. tan β ≤ 10, we can neglect to first approximation X b,τ in Eq. (12) and the LO solution for In this regime, m 2 H d (m t ) > 0 and thus both m 2 H d (m t ) and m 2 Hu (m t ) provide positive contributions to m 2 A in Eq. (9). For larger tan β values, negative RGE effects proportional to In this large tan β regime, m 2 H d and m 2 Hu provide opposite contributions to m 2 A in Eq. (9) that, indeed, can result strongly reduced. As we will see below, our numerical analysis confirms that we find light pseudoscalar masses, m A ≤ 200 GeV, only for tan β > 50.
At large tan β, the requirement of correct EW symmetry breaking and a neutral LSP sets important constraints on the allowed (m 0 , M 1/2 , tan β) values. In particular in CMSSM models, the lightest stau mass is M 2 GeV. However, the m 2 0 dependence of m 2 A is quite mild, as a result of the large negative RGE effects driven by y 2 t , y 2 b ∼ 1. So, at large tan β, the m 2 A mass is almost determined by the M 2 1/2 contribution while a relatively large m 0 affects the Higgs mass only marginally. On the other hand, the allowed values for the trilinear parameter A 0 are also constrained by the requirement of absence of charge and colour breaking minima and it turns out typically that −3 < A 0 /m 0 < 3. In the analysis of the flavour physics observables the value of A t (together with the value of µ) plays a particularly important role. The RGE equation for A t is: where t = log(Q/M GUT ). The LO solution of Eq. (14) provides the approximate result Similarly to the CMSSM case, the value of m 2 H d (m t ) depends strongly on tan β. However, given that the bottom and tau Yukawa couplings are smaller than the top Yukawa up to values of tan β > ∼ 50, it is clear that we can expect the coefficient of m H d,0 to be positive. GeV, 900 < m 0 < 2500 GeV, tan β > 30 and −3m 0 < A 0 < 3m 0 . In the NUHM (right), in addition 25. Green (light grey) points satisfy all direct bounds on scalar and gaugino masses. Black points satisfy also the main indirect constraints and Ω χ < 0.14 as explained in the text and red circles are points that in addition predict a BR(B → τ ν) within the experimental range. Crossed red circles satisfy 0.08 < Ω χ < 0.14.
Then replacing these values in Eq. (9), we can see that the contribution of m H u,0 to m 2 A is negative while the contribution of m H d,0 is positive (see for instance Table III in [30]).
Therefore we can reduce m 2 A in the NUHM with respect to the CMSSM for m H d < m Hu . Our numerical analysis below is done using RGE at two loop order [39] taking into account the complete flavour structure and the masses calculated at one-loop order [40] using SPheno [41]. In particular for the µ parameter and the neutral Higgs masses two-loop corrections are added [42]. We always impose the direct constraints on sfermion, gaugino and chargino masses from LEP and Tevatron [43]. In Figure 1 we show the values of m H + as a function of tan β for tan β > 30 in a scatter plot with M 1/2 ≤ 600 GeV and 900 < m 0 < 2500 GeV in the CMSSM and NUHM. All the points in these figures, including green points satisfy all direct bounds on scalar and gaugino masses. Ignoring indirect constraints for the moment, the most interesting feature here is the strong dependence of the mass with tan β. We see that, indeed as discussed above, we can obtain charged Higgs masses below 200 GeV in the CMSSM only for very large values of tan β, tan β ≥ 53. Therefore, before imposing the dark matter and indirect constraints, it is possible to obtain charged Higgs masses below 200 GeV in the CMSSM for µ > 0, tan β ≥ 54, m 0 ≥ 900 GeV and M 1/2 ≤ 400 GeV. In the NUHM case, we have allowed a small departure from universality for the Higgs masses that can be 25% lighter or heavier that the common soft-mass m 0 at the GUT scale. In Figure 2 we can see the effect of a small non-universality in the GUT Higgs masses in the mass of the charged Higgs at M W . As expected, the difference in the initial values of Higgs masses has a strong impact on the mass of the charged Higgs although we allow only a 25% departure for m Hu and m H d from m 0 . This becomes more pronounced if we allow for a larger breaking of universality. In the right-hand side plot of figure 1 we see that this small departure from universality is enough to obtain charged Higgs masses smaller than 200 GeV for values of tan β as low as 30 before imposing the indirect constraints.
Next, we must check that in this region of the parameter space it is possible to satisfy all the indirect constraints, specially those arising from processes enhanced by powers of tan β, namely BR(B → τ ν), BR(B → X s γ), B s → µ + µ − and the muon anomalous magnetic moment (g − 2). The behaviour of these observables in the large tan β regime was discussed in detail in Refs. [22,23,44,45,46,47,48,49,50,51,52,53,54,55], 4 which provides a good approximation to the full one-loop result [59] when the chargino masses are substantially lighter then the slepton masses, as it happens in our case.
The SUSY contributions to BR(B s → µ + µ − ) can be summarized by the following approximate formula where ǫ Y is defined through the flavor violating Yukawa interactions It receives contributions both from charginos and gluinos 5 thus, we can write ǫ Y = ǫχ with A 0 values and moderate/small M 1/2 ; in this same region, the coefficient c in (δ d LL ) 23 is large, and this makes the cancellation mechanism more effective. In the region of parameter space we explore, this is exactly the situation: we have both m 0 and A 0 large and M 1/2 small. Then A t (and also µ) are relatively small when compared to the heavy sfermion masses. The arguments of the loop functions, specially y q R,L , are large and then H 2 (x >> 1, y = x) ≃ −1/x also reducing the chargino contribution.
Finally let us consider the B → τ ν decay. As shown in Eq. (6), the ratio between the experimentally measured branching ratio and the SM expectation is given by R exp Bτ ν = 1.07 ± 0.42. On the other hand, in SUSY, the charged-Higgs exchange contribution is [21,22,23,24] where non-holomorphic corrections to the down-type Yukawa coupling have been included.
As evident from Eq. (20), B u → τ ν represents a very powerful probe of the scenario we are exploring [21,22,23]. In contrast to B s → µ + µ − , B u → τ ν is a tree-level process, thus, in this last case, there is no way to reduce the size of the NP contribution when tan β is large and the heavy Higgs is light. In fact, as we show below, we find that charged Higgs masses below 200 GeV are only possible when the observed branching ration is obtained through a SUSY contribution twice the SM one (with opposite sign).
Similarly, charged scalar currents mediated by the charged Higgs affect also the process K → lν with l = e, µ. The new physics effect in the ratio R Kµν = B SUSY (K → µν)/B SM (K → µν) would be obtained from Eq. (20) with the replacement m 2 B → m 2 K . Although the charged Higgs contributions are now suppressed by a factor m 2 K /m 2 B ≃ 1/100, this is well compensated by the excellent experimental resolution [60,61] and the good theoretical control. However, given that these new physics effects are at the % level, we would need a theoretical prediction for the SM contribution at the same level to use this decay as an effective constraint. We would then need an independent determination both of f K (possibly from lattice QCD) and V us . At present unquenched lattice calculations of f K are not well established and precise enough. The above argument for K → lν does not apply to B → ℓν. In fact, even if the f B and V ub uncertainties are much larger that the f K and V us ones, they cannot hide in any way the huge NP effects in B → ℓν arising in our scenario. Therefore, although it may play an important role in the future, we do not include the constraints from K → lν in the following.
In Fig. 1 we can see the effect of these indirect constraints. Here, green (light grey) points satisfy only direct bounds while black points satisfy also the constraints from BR(B → X s γ), BR(B s → µ + µ − ), the anomalous magnetic moment of the muon (g −2) µ and the upper limit on the dark matter abundance Ω χ < 0.14. Both in the CMSSM and the NUHM we see that it is rather easy to satisfy these indirect constraints due to the relatively heavy sfermions and small µ and A t . As expected, the main constraint here comes from the process B u → τ ν that corresponds to the red circles in this figure. In the case of the CMSSM, we are bound to values of tan β > 53 for m H + < 200 GeV. Therefore, B u → τ ν sets the lowest allowed value of m H + to 180 GeV. We have to emphasize again the importance of this tree-level constraint in this scenario. In the absence of this constraint, all black points would be allowed and hence charged Higgs masses as low as 120 GeV would be possible in the CMSSM.
In the case of the NUHM, smaller values of tan β can still produce light charged Higgs masses as seen in Fig. 2. In the plot on the right-hand side of Fig. 1 we can clearly see the Finally in Figure 3 we analyze the dark matter constraints on these points. The requirement of a correct dark matter abundance sets important restrictions on the allowed parameter space [33,34,35,36,62,63,64]. However, in this region of large m 0 and small M 1/2 this constraint is relatively easy to satisfy. We can see that both in the CMSSM and the NUHM all our points cluster in the funnel region on both sides of the line m H + = 2m χ .
In fact in the NUHM we can see that there are points (not allowed by indirect constraints but satisfying the dark matter bound) much closer than expected to this central line. This is possible due to the fact that the annihilation cross section is proportional to tan 2 β and for lower values of tan β the allowed region is much closer to the resonance. Therefore we conclude that these points correspond basically to the funnel region, although significant contributions from other annihilation processes also occur.
To conclude this section, we would like to comment on the differences between our analysis and the analysis presented in Ref. [3]. While on general grounds we agree with the conclusion of Ref. [3], there are some relevant differences that we would like to emphasize. First, the authors of Ref. [3] state that it is not possible in the CMSSM to find a light pseudoscalar reproducing the small CDF discrepancy consistently with all the constraints. In contrast, we have shown that a CMSSM can still accommodate such a scenario. Moreover, the authors of Ref. [3] also claim that there exists a lower bound for BR(B s → µµ) of BR(B s → µµ) > 2 × 10 −8 in the region compatible with all the constraints. We disagree with this statement and we find no lower bound for BR(B s → µµ). Finally, in contrast to Ref. [3], we emphasize the fundamental impact of B → τ + ν − . As we have discussed in detail, B → τ + ν − represents probably the most important constraint/probe of this scenario.

B. Other mediation mechanisms
In gauge-mediated SUSY breaking scenarios [65], the SUSY breaking is transmitted to the MSSM sector through gauge interactions. In the minimal gauge-mediation (MGM) model, the messenger fields get fermionic masses M M = λ S and scalar masses m 2 = |λ S | 2 ± |λ F S | through their Yukawa couplings to a singlet field S. Supersymmetry breaking is then transmitted to the MSSM gauginos and scalars through one-loop and twoloop diagrams respectively and we obtain: where from Eq. (22) GeV would require a strong cancellation between the two Yukawadependent coefficients at a level of C g u −C g d ∼ 10 −2 . This can be compared with the situation in the CMSSM where we can take M 1/2 of order 200 GeV and we only need C g u − C g d ∼ 1. This estimate is confirmed by our numerical analysis, performed by means of a scanning over the MGM parameter space with SPheno [41]. In particular, we have not been able to find points with m A < 300GeV. Given that in the present analysis we are interested in scenarios allowing a light-heavy Higgs sector with m A < ∼ 200GeV, the phenomenology of MGM models will be not analyzed.
In Anomaly Mediation the SUSY breaking is transmitted from the hidden sector by the the superconformal anomaly [66,67]. All the soft-breaking parameters are determined in a renormalization group invariant way by a single parameter, the gravitino mass. The soft-breaking parameters are given by: where β a and β Y i are the beta functions of gauge and Yukawa couplings, γ i the anomalous dimension of the corresponding matter superfield and m 3/2 the gravitino mass. Unfortunately, pure anomaly mediation is not acceptable because it leads to tachyonic sleptons.
The different approaches to solve this problem make the analysis highly model dependent.
A simple solution to this problem maintaining also the renormalization group invariance is to add a (or several) Fayet-Iliopoulos D-term contribution(s) to the scalar masses [68,69].
In this way the scalar masses in Eq. (25) are replaced by m 2 i = 1 2γ i m 2 3/2 + m 2 0 Y i , where m 0 is the D-term contribution and Y i the charge corresponding to the new broken U(1) symmetry. The spectrum depends then on the charges of the SM particles under the new U(1) groups. Although we do not make a full analysis, following Ref. [69], we can see that the requirement of m A > 90 GeV sets one of the limits on the allowed region of the parameter space. Therefore in these particular models it is relatively easy to have pseudoscalar masses below 200 GeV. However, a correct electroweak symmetry breaking is obtained only for values of tan β < 27 making most of the phenomenology and specially indirect searches less interesting [69]. In Ref. [57] a different solution to the tachyonic problem is analyzed with similar results. A complete analysis of more general anomaly mediation models is indeed interesting and will be discussed elsewhere.

IV. GENERIC SIGNALS OF THE LIGHT CHARGED-HIGGS SCENARIO
As we have seen in the previous section, it is still possible to have a light charged Higgs both in CMSSM and in NUHM models consistent with all the phenomenological constraints.
At this point we can ask what would be the signatures of this scenario. We will discus the possible signals both at high-energy colliders (LHC, Tevatron) and at low-energy flavour changing experiments.

A. Direct searches at colliders
The expected spectrum in the light charged-Higgs scenario is somewhat peculiar. In Table I we present the allowed range of input parameters in the CMSSM for points with a charged-Higgs below 200 GeV satisfying all direct constraints and indirect constraints and a dark matter abundance in the range 0.08 < Ω χ < 0.14. As we can see, the main features of this region of parameter space are M 1/2 << m 0 and tan β > 55. As a consequence, we can expect relatively light gauginos and heavy sfermions. This is confirmed in Table II where we show the obtained mass ranges with these input parameters. In this table we see that sfermions of the first two generations are roughly above 1 TeV. Only sfermions of the third generation can be relatively light due to the effect of the large Yukawa couplings.   In the NUHM the allowed range of input parameters is shown in Table III  SUSY contribution to BR(B → sγ). However in the NUHM scenario, this can be compensated by selecting lower tan β values. The particle mass ranges in NUHM models are shown in Table IV. The comments made for the CMSSM apply also here. Notice that the CMSSM is a particular case of the NUHM, so all the allowed points in the CMSSM are also allowed in the NUHM.
Let us first discus the Higgs sector in this scenario. As can be seen in Tables II and IV    As discussed above, our scenario predicts relatively light gaugino masses. In particular the gluino mass turns out to be usually lighter than the squarks. This has important phenomenological consequences at hadronic colliders. In fact from Tables II and IV we can see that the gluino is always lighter than squarks of the first two generations thus the decaỹ g → q 1,2q1,2 is never allowed. In general this is not always true for squarks of the third generation as can be seen in the tables. However, in our numerical analysis we find that the decayg → tt 1 is never kinematically allowed. On the contrary,g → bb 1 is possible for < ∼ 10% of the allowed points. Notice that this fact is only due to the small bottom mass compared to the top mass. If none of these decays is kinematically allowed, gluino has either three body decays into two quarks and either a neutralino or a chargino or the loop induced two-body decay into gχ 0 i . In the scenarios discussed above tan β is relatively large implying that final states containing quarks of the 3rd generations are strongly preferred [71]. The branching ratios of the final states bbχ 0 i are enhanced compared to ttχ 0 i due to obvious kinematical reasons.Therefore, independent of kinematics we expect in gluino decays an enhancement of final states containing b-quarks.

B. Indirect FCNC searches
The main features of our scenario are large tan β and light Higgs masses. Therefore we can expect sizeable SUSY contributions to tan β-enhanced decays, specially in B s → µ + µ − and B → τ + ν − . Even though we find very large contributions to the above observables in most of the points of our numerical analysis, we must stress that it is not guaranteed that an experimental/theoretical improvement in these decays would find a departure from the SM expectations. In fact, in the B s → µ + µ − case we can always find regions where the smallness of A t and/or gluino-chargino cancellations can reduce SUSY contributions to the level of the SM. With respect to the B → τ + ν − decay we stress that the light-Higgs scenario with large tan β values can accommodate the present experimental determination only when the SUSY contribution is roughly twice the SM one (note that the charged-Higgs contribution has always opposite sign compared to the SM one). Therefore, even if tuned, it is always possible to find a (tan β, m H + ) combination reproducing the SM prediction for this branching ratio. However we must emphasize that both decays are probably the most promising indirect channels to look for the light charged-Higgs scenario.
In addition to these hadronic observables, lepton flavour violating (LFV) transitions, as ℓ i → ℓ j γ, are also very sensitive probes of the large tan β scenario. Unfortunately these decays require an additional source of LFV. However, LFV couplings naturally appear in the MSSM once we extend it to accommodate the non-vanishing neutrino masses and mixing angles by means of a supersymmetric seesaw mechanism [72,73]. In this case, LFV entries in the slepton mass matrix (m 2 L ) ij are radiatively induced [72]: where Y ν are the neutrino Yukawa couplings (the potentially large sources of LFV) and M X and M R are the GUT and the heavy right handed neutrino masses, respectively. In our analysis, we consider a rather conservative situation where the mixing angles in the neutrino Yukawa matrix are small, CKM-like [74], and the largest neutrino Yukawa eigenvalue is O (1) similarly to the top Yukawa.
In Fig. 5 on the left-(right-)hand side, we report the predictions of the CKM-like scenario for µ → e (τ → µ) transitions as a function of ∆a µ employing the ranges for the input parameters listed in Table I Table I. CMSSM and NUHM models (with RH neutrinos) have very similar predictions. Given that both ℓ i → ℓ j γ and ∆a µ = (g µ − g SM µ )/2 are generated by dipole operators, it is natural to expect that their amplitudes are closely connected [23,75]. In particular, assuming a CMSSM spectrum, it is found that B(ℓ i → ℓ j γ) ≈ ∆a µ 30 × 10 −10 where δ ij LL has been evaluated by means of Eq. (26) for A 0 = 1. As we can see, the correlation is not exactly a line as one would expect from Eq. (27), since i) the loop functions for the two processes are not identical, ii) while BR(ℓ i → ℓ j γ) strongly depends on A 0 through δ ij LL (see Eq. (26)), ∆a µ is almost insensitive to A 0 . From Fig. 5 we see that, although model dependent, both µ → eγ and τ → µγ branching ratios could naturally reach the experimentally projected sensitivities in MEG and SuperB factories. This is specially true in the interesting region of the SUSY parameter space where also the (g − 2) µ anomaly, i.e. ∆a µ = a exp µ − a SM µ ≈ (3 ± 1) × 10 −9 , can find a natural explanation. Furthermore, we note that, although our scenario has a very light heavy Higgs sector m A < ∼ 200 GeV and large tan β values, tan β > ∼ 40, Higgs mediated LFV transitions [76,77,78,79,80,81] are not particularly enhanced, as could be expected. The reason for this is that Higgs mediated lepton flavour violating couplings are quite suppressed because of the large mass splitting between the gaugino and sfermion masses. In particular, as we can see from Fig. 5, both BR(τ → µη) and BR(B → τ µ) (that are purely Higgs mediated processes [76]), never exceed the level of few 10 −12 . Higgs mediated contributions to τ → µµµ are completely subdominant compared to the dipole (τ → µγ * ) effects.
As it concerns the µ → e transitions, scalar current effects contribute quite sizably only to BR(µ + Al → e + Al). However, for the parameter space relevant in our analysis, both BR(µ + Al → e + Al) and BR(µ → eee) lie below the 10 −14 level, well far from their current experimental resolutions.
Finally, the predictions for τ → e transitions are simply obtained from those for the τ → µ transitions by BR(τ → eX) = |V td /V ts | 2 BR(τ → eX) (with X = γ, η, µµ, ee) and BR(B → τ e) = |V td /V ts | 2 BR(B → τ µ). These models, in the light m H + -large tan β region have to face strong restrictions from the B → τ ν decay, that turns out to be the strongest constraint of our scenario. In particular, in the CMSSM tan β is always larger than 50 when we want m H + < 200 GeV and then the B → τ ν decay sets a strict lower limit of 180 GeV for the charged-Higgs mass. This lower limit from B → τ ν is relaxed in NUHM models where we can obtain light charged Higgses with smaller values of tan β. Moreover, we have analyzed the generic predictions of our light charged-Higgs scenario for hadronic colliders and indirect searches. Finally, we have addressed the question whether the above scenario can be tested through LFV processes.
To this purpose, we have considered a rather conservative ansatz for the source of LFV, the so-called CKM-like [74] case, and we have evaluated the predictions for the most relevant low-energy LFV processes. Interestingly enough, both µ → eγ and τ → µγ branching ratios naturally reach the experimentally projected sensitivities in MEG and SuperB factories, specially in the region where the (g − 2) µ anomaly can find a natural explanation.