Transcript 118

Form Factor Dark Matter
Brian 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
-spin of nuclei
-crystal structure
Direct Detection Event Rates
-Collisions/time for one target particle:
n  v
number density
cross section
relative velocity
-Collisions/time/recoil energy/detector mass:
target nuclei/detector mass
dark matter velocity distribution:
after putting in the cross section …
atomic number
nuclear form factor
Momentum transfer:
 Everything depends only on q, except for the
factor of Z2, and the reduced mass in vmin.
-Various proposed explanations for DAMA:
-Light Dark Matter
-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
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
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:
-Diemand, Kuhlen, Madau, 2006
-Fairbairn, Schwetz, 2008
 Note: the effect of baryons is not included in Via Lactea…
-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.
- 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)
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.
-There is a “critical channeling angle”:
Channeling is a real physical phenomenon:
(just not necessarily at DAMA…)
-Lindhard, 1965
Unfortunately, it still seems to not be enough…
 Bad spectrum, or too many events at null experiments.
(or so it seems…)
But…
A simple higher derivative interaction works extremely well!
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…