The 130 GeV gamma-ray line and the 125 GeV Higgs

[mitchell porter]

In blog discussions of the possible gamma-ray signal at 130 GeV (which is being interpreted as resulting from annihilation of dark matter particles), it's often asked whether this could have anything to do with a 125 GeV Higgs. And now I'm wondering: is it possible that the mass-splitting effects of supersymmetry-breaking are weakest in the Higgs sector, and that the signal results from annihilation of a 130 GeV higgsino? There's actually prior work on the possibility of a gamma-ray line from higgsino annihilation...!

 

[lpetrich]

There's a simpler hypothesis: both particles' masses are associated with electroweak symmetry breaking, and that gives them similar masses.

 

[fzero]

There's a simpler hypothesis: both particles' masses are associated with electroweak symmetry breaking, and that gives them similar masses.

Well the electron and top quark both get masses from EWSB but their masses are not similar at all.

In any case, it can only be for a small region of MSSM parameter space that the higgsino has a mass comparable to the lightest Higgs, or for the higgsino to even be the lightest superpartner (LSP). Martin, http://arxiv.org/abs/hep-ph/9709356, is a very nice review of the MSSM and contains details that I'll leave out.

First of all, the lightest Higgs has a tree-level mass

$$ m_{h^0} \sim m_Z \cos (2\beta) + \mathcal{O}(m_Z/|\mu|), $$

where $m_Z$ is the mass of the Z, $\beta$ is the angle defined by the Higgs vevs, and $\mu$ is the mass term in the MSSM superpotential. This formula also gets corrections from Higgs masses in the soft-breaking potential, as well as a significantly large 1-loop contribution from top and stop loops.

The approximation used above was that $m_Z \ll |\mu|$ and the soft-breaking mass parameters. This is a reasonable assumption given our biases about the SUSY breaking scale and current detection limits.

The neutralinos mix to give mass eigenstates that are linear combinations of the bino, zino, and higginos. The tree-level mass matrix is described by the chargino masses $M_{1,2}$, $\mu$, $m_Z$, and the angles $\beta,\theta_W$. The chargino masses come from soft-breaking terms, while as before $\mu$ comes from the superpotential.

Once again it's useful to expand for $m_Z \ll |\mu|,M_{1,2}$, in which case the mass eigenvalues are

$$\begin{split}
& m_1 \sim M_1 - \frac{m_Z^2}{|\mu|} C_1, \\
& m_2 \sim M_2 - \frac{m_Z^2}{|\mu|} C_2, \\
& m_{3,4} \sim |\mu| - \frac{m_Z^2}{|\mu|} C_{3,4}, \\
\end{split}$$

where the $C_i$ are of order one in most of the parameter space, though they can get large when there are coincidences like $M_{1,2}\sim |\mu|$. Away from these special points, these have been ordered so that the corresponding eigenvectors are in order: "mostly bino", "mostly zino", and two "mostly higgsino" states.

The first thing we should note is that the lightest higgsino-like mass eigenstate has a mass that has little in common with that of the lightest Higgs. To find them to be close in value would probably be a complete coincidence given the arbitrariness of the MSSM parameters.

It's also very unlikely that a higgsino-like particle could be the LSP, or even as light as the lightest Higgs boson. Recall that $\mu$ has it's own fine-tuning/hierarchy problem: since it is protected from corrections above the SUSY breaking scale, there's no good reason for it to be so much smaller than the GUT or Planck scales.

It is more reasonable to assume that the soft-breaking masses $M_{1,2}$ are naturally of order the SUSY breaking scale. In models with gauge coupling unification at some higher GUT scale, $M_1 \sim 0.5 M_2$, so it's typically assumed that $M_1 < M_2 \ll |\mu|$, which is consistent with the labeling of states we made above. Such a hierarchy also suggests that the bino is usually the LSP.

It's possible to say more, but nothing less speculative. I think from the above it's clear that, while not impossible, a higgsino-like LSP with a mass similar to that of the lightest Higgs would be quite unusual.

 

[mitchell porter]

The first thing we should note is that the lightest higgsino-like mass eigenstate has a mass that has little in common with that of the lightest Higgs. To find them to be close in value would probably be a complete coincidence given the arbitrariness of the MSSM parameters.

This would be the key observation. To take the original idea seriously, one should view the postulated higgs/higgsino near-degeneracy as a clue to how supersymmetry is broken and/or as the locus of any deliberate finetuning in the model. If you're going to postulate a coincidence, don't waste it!

 

[Vanadium 50]

Since Fermi/GLAST has not claimed a 130 GeV line, and ATLAS and CMS have not claimed a 125 GeV Higgs, I would say that the two do in fact have a common source: overexcited theorists.

 

[mitchell porter]

I'm not at all committed to the hypothesis in this thread, but I want to mention the existence of a paper claiming that, in the MSSM plus one new beyond-MSSM operator, you can get a higgsino LSP with a mass of order 100 GeV without breaking anything. It was written before we had a 125 GeV higgs and a possible 130 GeV signal of dark-matter annihilation, so it ought to be interesting to check whether its framework is compatible with both of these...

 

[lpetrich]

The case for a 125-GeV Higgs particle is getting stronger - both ATLAS and CMS observe evidence of it with at least 5 stdevs.
[1207.7214] Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
[1207.7235] Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC

The LEP's Higgs-mass lower-limit is about 114.4 GeV, and the putative Higgs particle's mass is 9% greater - it's within the limits of that paper for some parameter values.

 

[mitchell porter]

The major constraints come from DM physics and observation... The simplest idea seems to be, suppose that the LSP is a neutralino that is mostly higgsino, and also suppose that the lightest chargino is almost at the same mass and is also mostly higgsino (this in addition to the lightest higgs being around that mass as well). Having neutralino and chargino at almost the same mass will increase the amplitude for neutralino annihilation into gamma rays, and since we're supposing that everything with "higgs" in it is mysteriously at the same mass scale (see fzero's comment for why this is not expected), the simplest way to get the chargino degenerate with the neutralino is to suppose that it is mostly higgsino, too. :-)

Having optimistically begun with this hypothesis, one could then go to the MSSM mass matrices, and see what sort of relations among mu, m_Z, etc would give you the desired situation, and then one could try to think about MSSM extensions and ways of SUSY-breaking that would produce these relations. Also, you'd need to do something about other ways that the higgsino LSPs can annihilate, which ought to produce a gamma-ray continuum. If it's there, it's quite weak, and in fact a pure higgsino source for the 130 GeV line is already thought to be ruled out for this reason.