Form Factor Dark Matter

1. Form Factor Dark Matter In Preparation Brian Feldstein Boston University -B.F., L. Fitzpatrick and E. Katz In Preparation -B.F., L. Fitzpatrick, E. Katz and B. Tweedie

2. 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:

3. 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

4. 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.

5. -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!

6. 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 -spin of nuclei -crystal structure

7. Direct Detection Event Rates n  v -Collisions/time for one target particle: number density relative velocity cross section -Collisions/time/recoil energy/detector mass: target nuclei/detector mass dark matter velocity distribution:

8. after putting in the cross section … nuclear form factor atomic number Momentum transfer: • Everything depends only on q, except for the • factor of Z2, and the reduced mass in vmin.

9. -Light Dark Matter -Various proposed explanations for DAMA: -Gelmini, Gondolo, 2004 scatter off of Sodium at DAMA -Light Dark Matter + Channeling… -Bernabei et. al, 2007 -Drobyshevski, 2007 -Leptophilic Dark Matter -Fox, Poppitz, 2008  only electromagnetic events -Spin Dependent couplings -Savage, Gondolo, Freese, 2004

10. Light dark matter and Leptophilic dark matter have problems with the DAMA modulating spectrum.. Spin dependent couplings ruled out by COUPP.. Inelastic Dark Matter -Tucker-Smith, Weiner  vmin = q/2 + /q Presently, Inelastic Dark Matter seems to be the only viable solution

11. 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.

12. q Overlap Irreducible prediction for events in the DAMA range of q.

13. 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!

14.  Doesn’t look great with the Standard Halo model  On the other hand, halo uncertainties are significant… Via Lactea Simulations: -Diemand, Kuhlen, Madau, 2006 -Fairbairn, Schwetz, 2008  Note: the effect of baryons is not included in Via Lactea…

15. -March-Russell, McCabe, McCullough, 2008

16. 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.

17. Dark gauge forces mix with hypercharge, but with various • signs: • 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: (Λ, mi ~ hundreds of MeV, q0 ~ 50MeV)

18. Results.. 2 gauge boson model (99% constraints shown) 3 gauge boson model (95% constraints shown)  The models don’t work with the standard halo

19. 2 gauge boson model 3 gauge boson model not too far from optimal, but some room for improvement ..

20. 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.

21. 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.

22. There is a “critical channeling angle”: -Lindhard, 1965 Channeling is a real physical phenomenon: (just not necessarily at DAMA…)

23. Unfortunately, it still seems to not be enough…  Bad spectrum, or too many eventsat null experiments. (or so it seems…) But… A simple higher derivative interaction works extremely well!

25. 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…