Form Factor Dark MatterBrian Feldstein

Boston University

In Preparation

-B.F., L. Fitzpatrick and E. Katz

In Preparation

-B.F., L. Fitzpatrick, E. Katz and B. Tweedie

Dark Matter- The Standard Story

-Roughly 23% of the universe seems to consist of an exotic form of non-luminous, non-baryonic dark matter.

-A compelling possibility: Weakly Interacting Massive Particles (WIMPs)

-Weak Scale cross sections give approximately the right relic abundance:

Dark Matter Direct Detection

-Look for nuclear recoils due to dark matter scattering.

-Limits placed on cross section vs mass.

-Many such experiments: CDMS, CRESST, XENON, etc..

-arxiv:0809.1829

The DAMA Mystery- DAMA sees an 8.2σ annual modulation in its nuclear

recoil events.

-arxiv:0804.2741

- Phase is consistent with Dark Matter induced recoils.

-There is no proposed standard model explanation for the DAMA signal.

-DAMA looked at: Neutron flux, temperature variation, muons, neutrinos, etc..

-All calculated modulation amplitudes are much too small to explain the signal.

-But: standard WIMPs capable of explaining DAMA also seem completely ruled out!

On the other hand…-No experiment can rule out a dark matter origin for the

DAMA signal in a model independent way.

What distinguishes DAMA from other experiments?

-masses of nuclei used in experiment (NaI)

-range of recoil energies probed (10’s of keV)

-searching for annual modulation

-not vetoing purely electromagnetic events

-crystal structure

-spin of nuclei

Direct Detection Event Rates

-Collisions/time for one target particle: n v

-Collisions/time/recoil energy/detector mass:

number density

cross sectionrelative velocity

target nuclei/detector mass dark matter velocity distribution:

atomic numbernuclear form factor

Momentum transfer:

Everything depends only on q, except for the factor of Z2, and the reduced mass in vmin.

after putting in the cross section …

-Various proposed explanations for DAMA:

-Light Dark Matter

-Leptophilic Dark Matter

scatter off of Sodium at DAMA

only electromagnetic events

-Light Dark Matter + Channeling…

-Spin Dependent couplings

-Fox, Poppitz, 2008

-Savage, Gondolo, Freese, 2004

-Bernabei et. al, 2007

-Drobyshevski, 2007

-Gelmini, Gondolo, 2004

Light dark matter and Leptophilic dark matter have problems with the DAMA modulating spectrum.. Spin dependent couplings ruled out by COUPP..

Presently, Inelastic Dark Matter seems to be the only viable solution

Inelastic Dark Matter

vmin = q/2 + /q

-Tucker-Smith, Weiner

Form Factor Dark Matter

-Multiply the cross section by a new function F(q) coming from the dark sector.

-Comes from dark matter with internal structure (c.f. the nuclear form factor).

-Two goals: Fix the DAMA spectrum and reduce events at other experiments. Need F(q) to fall towards low q.

-Very general.. but a priori might not even work.

q Overlap

Irreducible prediction for events in the DAMA range of q.

Best Case Scenario

-Choose a form factor by hand...

-Two requirements:

In the DAMA region of q, match the DAMA spectrum exactly (to within error bars)

Outside the DAMA region of q, set F(q) = 0.

-Are the number of events predicted at other experiments acceptable?

If no, we can give up on this idea!

Doesn’t look great with the Standard Halo model

On the other hand, halo uncertainties are significant…

Via Lactea Simulations:

Note: the effect of baryons is not included in Via Lactea…

-Diemand, Kuhlen, Madau, 2006

-Fairbairn, Schwetz, 2008

-March-Russell, McCabe, McCullough, 2008

Model Building…

-Need a form factor which dies rapidly at low energies

A simple higher dimension interaction is not sufficient.

-Look for a relatively simple proof of principle.

-Introduce a new mechanism: Interfering gauge bosons.

- We assume the dark matter particle is neutral under the new gauge forces, but that it contains charged constituents.

- Leading interaction is a higher dimension operator:

- Dark gauge forces mix with hypercharge, but with various signs:

(Λ, mi ~ hundreds of MeV, q0 ~ 50MeV)

Results..

2 gauge boson model (99% constraints shown)

3 gauge boson model (95% constraints shown)

The models don’t work with the standard halo

2 gauge boson model

3 gauge boson model

not too far from optimal, but some room for improvement ..

Channeling

- Most experiments do not measure the full recoil energy, but only a fraction.

- The actual recoil energy is inferred through a “quenching factor”.

- Sometimes large uncertainties Can be very important.

- Not measured directly at all relevant energies.

- Proposal: The extrapolation of the DAMA quenching factor down to the energies of its signal are incorrect.

- Usually the Iodine quenching factor is taken to be ~.09

- At low energies, perhaps it can become much higher, at least for some fraction of events.

- Recoils which travel along a crystal axis at low energy are expected to have a quenching factor of ~1.

“Channeling”

If Channeling at DAMA is real..

DAMA is sensitive to much lower recoil energies than was originally thought!

DAMA becomes a much more sensitive detector, especially for light WIMPS.

Channeling is a real physical phenomenon:

(just not necessarily at DAMA…)

-There is a “critical channeling angle”: -Lindhard, 1965

Unfortunately, it still seems to not be enough…

Bad spectrum, or too many events at null experiments.

A simple higher derivative interaction works extremely well!

(or so it seems…)

But…

Conclusions

- DAMA presents an exciting experimental puzzle.- If it is correct, we may be able to learn a lot

about the structure of the dark sector.- Models with dynamical form factors are a viable

solution, but a certain amount of complexity is required.

- With channeling included, simple form factor models work nicely as well.

- New experimental results should be coming soon…