Light Signals from a Lighter Higgs

With the Higgs search program already quite mature, there is the exciting possibility of discovering a new particle with rates near that of the SM Higgs. We consider models with a signal in $\gamma \gamma$ below the SM Higgs mass, taking the recent $2.9\, \sigma$ (local) CMS excess at 95 GeV as a target. We discuss singlet models with additional vectorlike matter, but argue that a Type-I two Higgs doublet model provides a more economical scenario. In such a setup, going into regions of moderate-to-strong fermiophobia, the enhanced $\gamma \gamma$ branching ratio allows signals from $VH$+VBF production to yield $\sigma \times BR_{\gamma\gamma} $ comparable to total SM rates. Light $H$ production can be dominated via rare top decays $t \rightarrow b H^+ \rightarrow b W^{*} H$, which provides an alternate explanation of the excess. We consider this in the context of other Higgs anomalies, namely the LEP Higgs excess near the same mass, and excesses in $t\bar{t}h$ searches at Tevatron and LHC. We find that with $140\, \mathrm{GeV}<m_{H^+}<160\, \mathrm{GeV}$, $\tan \beta \sim 5$ and a coupling to gauge bosons of $\sin^2 \delta \sim 0.1$, such a scenario can produce all the excesses simultanously, where $tth$ arise from contamination from the rare top decays, as previously proposed. An implication of the Type-I scenario is that any $\gamma \gamma$ excess should be associated with additional elements that could reduce background, including $b$-jets, forward jets or signs of vector boson production.


I. INTRODUCTION
The search for the Higgs boson was a tremendous undertaking. Not just at the LHC, but in the decades and experiments that preceded it. Results from LEP and the Tevatron provided the basis on which the multi-channel searches at the LHC proceeded. With the Higgs now discovered, and the LHC awaiting more luminosity -but little more energy -it is worth turning some attention to understanding what sorts of particles might still lie hidden in these data.
The simplest reason to pursue this is straightforward -at the LHC, one expects a massive increase in luminosity, and thus sensitivity, to new states, even with couplings well below O(1). The second reason is that throughout the search for the Higgs, there have been a variety of tantalizing bumps and excesses, many of which have lingered as open questions on the myriad exclusion plots presented over the years. For many, it is impossible not to at least consider whether these bumps might tell a consistent story of some new physics beyond the standard model.
Amongst these bumps comes the most recent result from CMS [1], which shows a small excess near 95 GeV in the diphoton channel. We begin our discussion, in Section II, describing ways to explain this excess and then show, in Section III how some of these approaches may also explain historical excesses from LEP and the Tevatron, as well as excesses in other channels at the LHC. We conclude in Section IV.

A. Higgs signals from singlets
A simple example is that of a singlet scalar, φ, which has been extensively discussed (see e.g., [5][6][7][8][9][10][11][12]). To allow for production from gluon fusion at the LHC the singlet must couple to extra vectorlike colored matter, yφΨΨ, necessitating the introduction of many new degrees of freedom. If that matter is also electrically charged, then the decay to photons is automatic. Such particles that can appear at near-SM rates -but are easily distinguished from a SM Higgs -have been referred to previously as Higgs friends [12]. In another context, in a higher mass regime around 700-800 GeV, this has been referred to as the "everybody's model" [13].
The production cross section for such a particle can be related to its gluon decay width, and these quantities for a SM Higgs of the same mass, Where we assume N Ψ copies of a vectorlike Dirac color triplet fermion, with mass m Ψ .
The overall cross section times branching ratio is then: for N Ψ fermions with charged Q Ψ . A 95 GeV SM-like Higgs boson has a gluon fusion production cross section of 76.3 pb and a width into gluons of 0.15 MeV. Thus, Thus, a signal at the size seen at CMS is still possible, but it requires new light colored particles. Even a new colored fermion as light as 200 GeV could have escaped detection so far at the LHC, if it decays predominantly into three jets [14]. However, while it appears one can evade LHC bounds on colored particles and still have a sizable signal, it is certainly not economical to add new states both to observe and explain the production. Moreover, although we have not yet discussed them, such a model cannot hope to easily explain the other Higgs related anomalies present in the data.
An alternative approach to adding a singlet and new colored fermions is instead to mix the singlet, s, with the Higgs boson. In such a case, the light mass eigenstate's couplings to SM fields will be proportional to some mixing angle sin δ (hereafter s δ ). The dominant production of s will be through gluon fusion, but will occur at a rate suppressed by s 2 δ . Furthermore, as the dominant branching ratio (s → bb) is also proportional to the fermion coupling, the rate to γγ is independent of this mixing, Thus, the rate to produce s in the diphoton channel is directly proportional to the γγ width of s. Achieving a rate comparable to the SM Higgs then requires s having a diphoton width comparable to the SM Higgs (i.e. Γ(γγ) ≈ 0.5 keV), which is not possible through mixing alone. As we can see from (4), this is possible, if s has O(1) couplings to additional light fermions which have O(1) electric charge.

B. Type I Two Higgs Doublet Models
Perhaps the most economical model is the Type I two Higgs Doublet model (see discussion in [15]). This model consists of two SU (2) scalar doublets, Φ 1,2 which have opposite charge under a discrete Z 2 symmetry, we take both to have hypercharge Y = 1/2. All right-handed SM fermions are even under the Z 2 which means that one doublet, Φ 1 , is fermiophobic. Such a model provides some additional freedom in its couplings to gauge bosons and fermions, and containing already a charged scalar which can mediate new processes.
We parametrize the two doublets as With h corresponding to the Higgs observed at 125 GeV, and H its CP-even partner. The tree-level couplings of the Higgs mass eigenstates to fermions, relative to the coupling of a SM Higgs are Where we have introduced the angle δ = β − α − π/2 to parametrize the deviation of the Higgs couplings from SM values [16]. Similarly the couplings to gauge bosons are The cross sections and widths of the new Higgs boson vary differently depending on these angles. Normalizing to a m H = 95 GeV, there are first those that scale with (s α /s β ) 2 , and also those that are proportional to s 2 δ , Finally, the diphoton partial width is The couplings of the 125 GeV Higgs boson are constrained to lie close to SM values [17] which means that |s δ | < ∼ 0.4. We will consider regions of mild fermiophobia, where the coupling of H to fermions is suppressed. Thus, for the remainder of this paper we will consider the region s δ < 0, the region s δ > 0 is the region of (mild) fermiophilia. We define the ratio f 2 F P = s 2 δ /(s 2 α /s 2 β ) as the "factor of fermiophobia" and consider fermiophobic regions to be those where f 2 F P 1. In these regions, the branching ratio to diphotons is enhanced fermiophobic regime the branching ratio to diphoton is BR H→γγ 3f 2 F P × 10 −3 . The approximate relationship above assumes the bb decay still dominates the total width.
Using the results above, we see that, in the fermiophobic limit, the rate for H → γγ through gluon fusion production scales as With various bounds limiting s 2 δ 0.1, this is a small fraction of the needed rate. In contrast, VBF/VH production processes scale as For f 2 F P > ∼ 7, the fermiophobic regime, gluon fusion will no longer be the dominant production channel for H → γγ. This discussion has so far focused on tree-level changes to the Higgs BR to photons.
However, the light Higgs also couples to the charged Higgs. One expects a loop of charged There is another production possibility, again involving a light charged Higgs, that was recently emphasized by [18]. Namely, that that light scalar production can occur in cascades from a heavier charged Higgs [19][20][21][22][23][24]. In a type-I model, in the presence of a charged Higgs below the top mass, m H + < m t , [18] showed that the production of the light Higgs via  Fig 1, and again there is a region at moderate tan β where the rate fits the CMS excess. If this channel is available it will dominate production and one would expect additional signals in the LHC events.
There are several constraints on new light Higgs bosons that limit the available parameter space. These constraints are weaker for a Type-I 2HDM than for Type-II. Due to mass splittings among components of the Higgs doublets there are contributions to the precision electroweak observables S and T , however these constraints are weak. There are indirect constraints from B-physics observables e.g. ∆M s , B 0 s → µ + µ − , b → sγ, etc [25]. The strongest constraint over most of the parameter space we are interested in comes from

III. GLOBAL PERSPECTIVE OF OTHER ANOMALIES
With so many Higgs searches, it is perhaps not surprising that a number of anomalies have arisen. Here we provide a brief discussion of a few of them and how one might attempt to explain them simultaneously.

LEP anomaly
Using approximately 2.5 fb −1 of data taken across a range of energies, 189 GeV < √ s < production ttH V h, and VBF production mechanisms in addition to gluon fusion, but did not break out separate analyses for them, setting limits based on their expected relative rate and efficiencies in the SM.

A. Explaining the Excesses with a Type-I 2HDM
It is clear that one can explain any one of the excesses, for instance with a new singlet coupled to vectorlike fermions, but an intriguing question is whether one can explain most or even all of the excesses in a compact model. As discussed in Section II B it is possible to explain the CMS γγ bump at 95 GeV in a Type-I 2HDM in the region of fermiophobia. We shall argue that such a Type-I 2HDM provides a simple explanation for all excesses, while being consistent with null results.
The LEP results [4] are most simply understood as a type of scalar mixing with the Higgs boson at a level s 2 δ ∼ 0.1. However, this could be a SU (2) singlet or doublet scalar field. Producing a γγ signal at the LHC comparable to the SM with such a small mixing is a challenge, however. Absent new colored particles, one must boost the production cross section via mixing with the SM Higgs. Since such rates are necessarily below the SM, we must in turn resort to enhancing the γγ width of the new state.
As shown earlier (13), going to the fermiophobic regime, f F P 1, increases BR H→γγ .
With the requirement from LEP that s 2 δ ∼ 0.1, we must go into the strongly fermiophobic regime, where f 2 f p ≈ 20 − 40. Then we find a signal at the LHC of σ HV +HV BF × BR H→γγ ∼ 0.1 pb, while the rate from gluon fusion is considerably smaller, (14,15). That is, the CMS γγ excess can be explained not by ggF but instead by the combination of VBF and associated production, which all lead to events with additional activity and other signals.
We show the consistent region of parameter space in Fig.3 (left).
If the charged Higgs present in 2HDM's is lighter than the top mass there is an even more exciting possibility. This scenario, first discussed in [18], has the dominant light Higgs production via t → H + b → HW * b. It was argued in [18] that this process, involving a final state very similar to tth, would be a natural contaminant of those searches, and, indeed, could provide the explanation of the excesses seen. For a charged Higgs mass in the range 140 GeV < m H + < 160 GeV, one needs tan β ≈ 5 to explain the tth signals. Unfortunately, with m H + = 140 GeV. For the right plot, the approximate range (hashed) to explain the leptonic tth excesses is 4 < ∼ tan β < ∼ 6 [18]. For s δ > 0, the Higgs is fermiophilic (i.e., f 2 f p < 1) and the γγ rates are suppressed.
to explain the LEP excess in this tan β regime, one is naturally in the moderately fermiophobic regime, and is a non-trivial consistency check of this scenario. While it was noted by [18] that one could explain the LEP and tth signals simultaneously, the near-inevitable boosted γγ signal was not recognized at the time. The global consistency of all three anomalies is shown in Fig.3 (right), for m H + = 140 GeV. Note that increasing the charged Higgs mass shifts the required region for both CMS γγ and tth to smaller tan β. This is compatible with the constraints on the tan β coming from rare top decays and indirect constraints from Because the BR(H → γγ) is so much larger than in the SM, the expected rate is an order of magnitude -or more -beyond what is expected from the SM. Assuming the efficiency to pass the analysis cuts for a 95 GeV Higgs is comparable to the SM one expects a considerable number of signal events just below the existing analysis range. The resolution of the diphoton invariant mass is ∼ 1.5 GeV so a small fraction of the events centered around 95 GeV will leak into the analysis window, but this is too small to have been observed. It almost defies belief, but the natural implication of this scenario is that there is an enormous signal lying just outside the currently searched mass window. While this seems unlikely, we cannot find any published paper or note that precludes this exciting possibility.

IV. DISCUSSION
With the increasing sensitivity of Higgs searches, we confront the prospect of the discovery of new particles with Higgs-like properties. Simple models can provide signals into diphotons at rates comparable to the SM. Singlets can still provide high rates, but need additional light fields to provide production and/or widths to γγ. In contrast, a doublet mixing with the SM Higgs in the form of a Type-I 2HDM provides an economical model that provides a boosted γγ signal in the fermiophobic regime of parameters. In the simplest case, the signal is generated not by ggF but by V BF + V H production, and thus would offer additional tags to improve separation of signal and background.
This last possibility is particularly exciting when viewed through the lens of a series of anomalies in Higgs searches. LEP (ZH, H → bb), CDF (ttH, H → bb), ATLAS (ttH, multilepton searches) and CMS (H → γγ) have all seen excesses consistent with a particle near m H = 95 GeV. The production follows the scenario proposed by [18], where the light Higgs is produced in a cascade t → H + b → bW + * H, which naturally contaminates the ttH searches. Interestingly, if one attempts to explain LEP along with ttH anomalies, one is inevitably forced into a region where the light Higgs is somewhat to very fermiophobic, and the γγ rate is enhanced. In such case, lowering the mass threshold for ttH, H → γγ searches, or looking for additional tags in conventional H → γγ searches should yield dramatic signals well above SM rates.
In summary, it is clear the prospect for discovery of new states in Higgs searches is significant. Moreover, if any of the anomalies above survice after further scrutiny and data, it may be that Higgs searches are not only the searches that completed the Standard Model, but may be the ones that find the first physics beyond it, as well.