294. The leptonic Higgs as a messenger of dark matter

This is a guest post by Piyush Kumar from U. of California, Berkeley. Dmitry.

I would like to thank Dmitry for inviting me to post a guest blog on my recent paper “The leptonic Higgs as a messenger of dark matter” with Lawrence Hall and Hock-seng Goh on Dark Matter (DM).

The story begins with some data reported in the summer and fall of 2008. The PAMELA experiment reported an excess of positrons in the few GeV to 100 GeV range, providing further support to the earlier results of HEAT and AMS. In addition, results from the ATIC balloon experiment suggests an excess of electrons and positrons in the 300 GeV to 600 GeV range roughly consistent with earlier observations of PPB-BETS. Of course, these observations are still preliminary and need to be corroborated with more data. Moreover, even if confirmed, the data may have reasonable astrophysical explanations. While that remains a logical possibility, nonetheless, these observations have generated tremendous interest in the particle physics community, as they might provide the first non-gravitational evidence for Dark Matter (DM).

There are two interesting challenges faced by any model trying to explain the excesses in the above experiments. First, for annihilating DM these signals require that the annihilation cross-section for DM particles is typically two to three orders of magnitude larger than that expected from the thermal freezeout of WIMP DM. On the other hand, for decaying DM, the life-time of the DM particles must be extremely large, of seconds. Second, the signals apparently require annihilations or decays dominantly into leptons rather than hadrons, since there is no reported excess in anti-proton cosmic rays.

In our paper, we have explored a general framework for DM based on our current understanding of particle interactions and taking into account the challenges mentioned above. In addition to the known physics of quarks and leptons interacting via gauge interactions, we expect new physics to include both a Higgs sector, responsible for symmetry breaking, and a dark matter sector. The idea of a WIMP DM sector is particularly interesting as it ties in with general ideas about electroweak symmetry breaking. We are thus led to the three sectors in the figure below.

The interactions between the higgs sector and the Standard Model sector are well known; the interactions of the WIMP DM sector with the other two sectors are more speculative on the other hand. However, if we think about it, the WIMP idea is that the mass scales of the dark matter and Higgs sectors are both related to the weak scale, and this strongly suggests some connection between these two sectors. In our work, we explore the possibility that any direct couplings between the WIMP sector and the visible sector are subdominant; thus the Higgs sector is seen to be the messenger that makes the WIMP visible to us, as shown in the Figure. The question now arises as to what constraints the cosmic ray data imposes on the Higgs sector. It turns out that the Higgs sector in the SM or in the MSSM does not give rise to a good fit to the data as in these cases the higgs decays predominantly to pairs of bosons, bottom quarks or top quarks (if heavy enough). This gives rise typically to too many anti-protons than actually observed by PAMELA. Also, the signal in is smooth, and does not give the peak shown by balloon experiments like ATIC. Thus, from the data we are quite generally led to a framework in which the Higgs couples dominantly to leptons, hence the title of our paper.

Since the Higgs couples via Yukawa couplings, the leptonic Higgs will dominantly decay to pairs of tau leptons which will subsequently cascade to electrons and positrons. A straightforward consequence of this is that the ATIC peak is broader and fitting the PAMELA data requires a larger DM mass than in models where the WIMP cascades directly to electrons or muons. Also, the signal for the positron fraction in PAMELA is expected to continue to energies larger than 100 GeV, and not to show a very sharp peak. Another very interesting feature of the framework results from the production of tau leptons. Since decays of taus give rise to an fraction of photons (mostly from s coming from tau decays) and neutrinos (from three-body tau decays), there is the possibility of energetic gamma rays and neutrinos in the energy range 100-1000 GeV. However, these signals depend on whether the taus originate from DM annihilations or decays.

The main focus of the paper was to emphasize the general nature of the Higgs sector through which the WIMP DM sector couples to the visible sector, and not to specialize to a particular DM sector. Therefore, both annhilation and decay modes of the DM particles were studied and simple models giving rise to both modes were provided. Also, depending on whether DM is a scalar or fermion, the leptonic cosmic ray signals could arise from a variety of channels: DM annihilation to , or DM decay to , , , via intermediate Higgs states. Good fits to both PAMELA and ATIC data could be typically obtained for around 4 TeV. If the ATIC data is ignored, then around a TeV can explain the PAMELA data. Regarding constraints from energetic gamma rays and neutrinos coming from the direction of the Galactic Center, it turns out that annihilations provide much more stringent bounds on the parameter space of models compared to decays. But at the same time, they also lead to better detection possibilities for future experiments. The primary reason for this difference is the fact that flux of gamma rays and neutrinos depends on for annihilations in contrast to for decays, and because , the mass-density of DM particles in the Galactic Center, is expected to be quite large (although there are large theoretical uncertainties).

One of the most interesting aspects of this framework, at least in my opinion, is the fact that the cosmic-ray signals are necessarily correlated with LHC Higgs signals! Let me explain. Since the DM masses typically turn out to be a TeV or higher, it is hard to produce the DM particles directly at the LHC. However, the leptonic (and hadronic) Higgs states could be produced at the LHC (since they are ) GeV) subsequently decaying to tau leptons. In order to provide concrete predictions, we studied a two-Higgs doublet model in which a (softly broken) discrete symmetry (parity) forces one of the Higgs to couple dominantly to leptons and the other to quarks. This gives rise to extremely interesting 4 signals at the LHC from Drell-Yan production (-channel exchange) of the leptonic Higgs and its pseudoscalar partner, followed by their decays to tau pairs. The same process also gives rise to production of charged higgs pairs which dominantly decay to . This channel therefore provides a new search strategy for the Higgs which has not been well studied so far, and could provide a discovery channel for modest luminosities around 30 . In addition, we find that the signal from single Higgs (both leptonic and hadronic) production by vector boson fusion followed by decay to tau pairs can be naturally enhanced compared to that for the Standard Model Higgs, and hence could also provide a discovery channel at modest luminosities. So, Higgs physics seems to be extremely promising.

Finally, I would like to comment on the general compatibility of DM models trying to explain cosmic ray signals, with the observed upper bound on the DM relic abundance. For annihilating DM, there is a mismatch in general in the cross-section required to explain the cosmic-ray signals and the cross-section required to obtain the correct relic abundance from a “standard” thermal freeze-out computation. Many models in the literature try to explain the required large annihilation cross-section for cosmic ray signals by a Sommerfeld enhancement which is operative at non-relativistic velocities () in the galactic halo, while still having a standard thermal relic abundance during thermal freeze-out. Although an interesting idea, this requires the presence of very light states ( GeV) whose mass scale has to be explained. In addition, these light particles have to survive existing constraints from low-energy particle physics experiments as well as astrophysics. Since there do not naturally exist any such light states within our framework, the mismatch between the two cross-sections has to be explained by a different mechanism. It turns out that the correct relic abundance can be obtained even for a larger cross-section compared to the thermal one, if one assumes the existence of late-decaying light () scalar fields (also known as “moduli”) because in this case the relic abundance is determined by the reheat temperature of the modulus rather than the freezeout temperature of DM. This gives rise to non-thermal production of Dark Matter. In fact, such light moduli fields automatically occur within “realistic” string theory compactifications, and hence non-thermal production of DM is quite natural. All this may sound a bit cryptic, but if you are interested, see some of my papers on this subject – “Non-thermal Dark Matter and the Moduli Problem in String Frameworks” and “Neutrino Masses, Baryon Asymmetry, Dark Matter and the Moduli Problem – A Complete Framework“. People always rave about the thermal WIMP ”miracle”, but there is always two-to-three orders of magnitude slop in the “miracle” in terms of the relic abundances. Indeed, the wino, one of the best motivated WIMPs, has a relic abundance about two orders of magnitude lower than the observed one for a weak scale mass ( GeV). It seems to me that with some reasonable assumptions, it is possible to obtain the same parametrics for the relic abundance with a similar “slop” in the non-thermal case as well.

On the other hand, if the DM decay modes are relevant for cosmic-ray signals, then one has to explain the extremely long lifetime (s) required for the cosmic ray data. It turns out that if the lepton parity (for a leptonic Higgs) and dark parity (the parity which keeps the DM stable) are spontaneously broken by , then a lifetime of the correct magnitude can be naturally obtained. Note that signals for LHC Higgs physics are the same for both annihilation and decay modes since the parity breaking effects are extremely small.