## Thursday, 23 April 2009

### Inelastic

As for today, only the DAMA experiment in Gran Sasso claims to have detected dark matter particles. The claim is based on observing the annual modulation of the number of scattering events in DAMA's sodium-iodine detector. Such an effect could arise due the motion of the Earth around the Sun that implies the annual variation of the Earth's velocity with respect to the sea of dark matter pervading our galaxy.

The experimental community is divided about DAMA. One half considers them ignorants who have no idea what they're doing, whereas the other half thinks that they deliberately rigged their results. Theorists, on the other hand, are by construction more open-minded (or maybe just bored) and they sometimes entertain the possibility that the DAMA signal might actually be dark matter. The challenge is then to explain why other, in principle more sensitive detection techniques have yielded null results. There has been several, less or more contrived proposals to reconcile DAMA with the stringent limits from other direct detection experiments like CDMS, XENON, CRESST, ZEPLIN and KIMS. The DAMA signal can be explained by the standard WIMP dark mater scattering on the sodium atoms if the dark matter particle has a fairly small mass of order 5 GeV (although there is some controversy about this interpretation). This post is about another scenario called inelastic dark matter, iDM in short. It was originally proposed quite some time ago, but recently it is becoming more and more fashionable.

A typical WIMP particle scatters elastically on the target nucleons, that is to say, it retains its identity in the process. In the iDM scenario, on the other hand, the cross section for elastic scattering is assumed to be suppressed. Instead, the dark matter particle scatters inelastically into a slightly heavier partner. If the mass splitting between the two dark matter particles is of order 100 keV - the typical kinetic energy in the dark matter sea - the DAMA signal can be, with a bit of luck, reconciled with the bounds from other experiments.

The way it works is the following. All direct detection experiments attempt to measure the recoil energy of a nucleon that has been hit by a passing dark matter particle. In the iDM scenario, the minimal velocity of the incoming dark matter particle needed to produce the recoil $E_R$ is given by the formula
$v_{min} = \frac{\delta+ m_N E_R/\mu_N }{\sqrt{2 m_N E_R}}$,
where $\mu_N$ is the reduced mass of the dark matter + nucleon system and $\delta$ is the mass splitting between the two dark matter states. As long as the splitting term dominates, heavier targets require lower velocity to give them a kick. DAMA's target contains pretty heavy iodine (A=127) (as compared to CDMS germanium with A=73). The sea of dark matter is expected to have the Maxwellian distribution of velocities that rapidly fall above the peak velocity which is of order $v \sim 0.001$, so that even a small change of the minimal velocity may significantly affect the number of events. Also for that reason, the oscillation signal studied by DAMA is enhanced, because the small summer/winter variation of the dark matter velocity distribution (in the Earth reference frame) may lead to a large variation of the signal. All in all, there remains some allowed parameter space, as can be seen in the example plot borrowed from this paper. For a fixed dark matter mass, the DAMA region in the mass splitting - cross section plane is marked in magenta, while black lines are the current bounds, the most stringent coming from CDMS (solid) and CRESST (dashed).

There is also a purely sociological reason why the bounds from other experiments get relaxed: iDM has not really been searched for...The nature of iDM leads to a very peculiar nucleon recoil spectrum. Whereas for the standard WIMP the number of events grows exponentially at low recoil energies, the recoil spectrum in the iDM scenario is suppressed at low energies and displays a "resonant" shape. Most experiments derive their bounds assuming the standard recoil spectrum and they do not optimize their search strategies to probe non-standard scenarios. For this reason, the idea of iDM is relevant for dark matter searches irrespectively of DAMA. It is a phenomenologically distinct possibility that should be taken into account, and one may easily miss the Nobel prize by restricting to the standard WIMP paradigm.

From the theoretical point of view, models of iDM are not difficult to write down. One simple possibility is the dark matter particle being a Dirac fermion with a large mass of order 100 GeV spiced up by a small 100 keV Majorana mass. The later leads to the required splitting between the two Majorana mass eigenstates. Furthermore, if the Dirac fermion has vector interactions the vector couples non-diagonally in the eigenstate basis, and the elastic scattering is suppressed with respect to the inelastic one. Another simple realization of iDM is a complex scalar whose two real components are split by a small "holomorphic" mass term. There is no obstacles to embed iDM into mainstream theories beyond the Standard Model. For example, in the MSSM, the Standard Model neutrino is partnered by a sneutrino who is a complex scalar, and the mass splitting could originate from a small lepton-violating term $(L H)^2$ in the superpotential.

So, just keep our fingers crossed while waiting for the new results from CRESST, XENON-100, LUX, KIMS and many others.

m said...

does the too long lifetime of the excited DM state exclude the Inelastic DM interpretation of DAMA?

Jester said...

I'm not sure what you mean by too long lifetime. I guess as long as there is enough DM particles in the ground state everything works fine.

m said...

If the lifetime is longer than the age of the universe (as typical for a 100keV mass splitting) cosmology predicts that the two states are equally populated, and DAMA can no longer be explained

Jester said...

Why? Maybe I'm missing something, but it seems that one half of dark matter would still be available for scatter.

m said...

The problem is the other half, that would give a comparably large signal, not suppressed by inelasticity in CDMS and other searches

NW said...

Some models are stable, some are not, but even those that are stable can be de-populated in the early universe through scattering. So, no, not ruled out.