1. Disentangling Dark Matter Dynamics
Jay Wacker
SLAC
Boston University Theory Seminar
September 29, 2009
with Philip Schuster, Daniele Alves, Siavosh Behbahbani
arXiv: 0903.3945
with Mariangela Lisanti
arXiv: 0910.xxxx, 0910.xxxx
2. Status of Dark Matter
Not your grandfather’s DM Candidate
DAMA
PAMELA
ATIC
FERMI
WMAP Haze
INTEGRAL
Hints at non-trivial interactions
3. Plan of Talk
DAMA & Inelastic Dark Matter
Composite dark matter models
Experimental Prospects
Uncertainties in halo profile
Direct Detection
Directional Detection Experiments
Collider Signatures
4. DAMA
WIMP wind
Annual modulation in WIMP signal
winter
⊙
v Φwimp = σv
E
v
E
v
summer Modulation amplitude ~2.5% for
elastic scattering
v ≤ vesc + |vE − v⊙ |
v ≤ vesc + |vE + v⊙ |
5. Direct Detection
Dark matter scatters off nuclei in detectors
Measure recoil energy of nuclei
spin-independent
(χχ)(¯q)
¯ q
χ q
χ q
DM Coherently acts with entire nucleus
σSI ∝ A2 µ2 ∼ A4
Limits always stated in terms of
cross section per nucleon
6. Elastic nuclear scattering
A Bestiary of Experiments
WIMP
CDMS
Ge 10% energy
Ge, Si
Ionization
ZEPLIN2
ZEPLIN3 Liquid Xe Target Heat Al2O3, LiF
XENON10 100% energy
slowest
cryogenics
Light
1% energy CaWO4, BGO
NaI, Xe fastest
no surface effects
WIMP
CRESST
DAMA
From: Véronique Sanglard (La Thuille 2005)
7. Direct Detection
Experiments optimized to look for elastic scattering recoil spectrum
Signal Window Exposure
Experiment Element # Events
(keV) (kg day)
CDMS Ge 10-100 2 170
dRel
∝ e−ER XENON Xe 4.5-45 24 300
dER
Rate
ZEPLIN 2 Xe 14-56 29 200
ZEPLIN 3 Xe 11-31 7 150
CRESST W 10-100 7 30
Recoil Energy (keV)
DAMA 0.82 Ton Years!
8. Current Limits
-5
10 http://dmtools.brown.edu/
Cross-section [pb] (normalised to nucleon)
DAMA Gaitskell,Mandic,Filippini
N 2
P LI
ZE
T
SS
RE
-6
10 C
ZE
PL
IN3
-5
XE
10
-7 S
http://dmtools.brown.edu/
DM
[pb] (normalised to nucleon)
10
NO
C
Gaitskell,Mandic,Filippini
N
-6
10
-8 090913122401 spin-independent
10 1 2 3
10 10 10
WIMP Mass [GeV/c2]
-7
10
9. DAMA
Spectrum for DAMA modulation amplitude
Scattering off Na or I - w or w/o quenching
Chang, Pierce, Weiner (2008)
Suppressed at low recoil energy
0.07
0.06 2 GeV
0.04
0.04
Sm countskgday
0.05
0.04 7 GeV
Rate (cpd/kg/keVee)
0.03
0.03
0.03
Rate cpdkgkeVee
0.02 77 GeV
0.01 12 GeV
0.02
0.02
2 3 4 5 6
keVee
0.01
0.01 FIG. 2: We show the modulation spectra for the best fit
39.0
point where scattering off iodine dominates, mχ = 77 GeV
(dot-dashed orange), and three points where scattering off of
sodium dominates. The best fit point off sodium is mχ = 12
39.5
0.00
0.00 GeV (solid red). We also show mχ = 2 GeV (dashed green)
and mχ = 7 GeV (dotted blue). The points with error bars
0
0
2
2
4 keVee
4
Recoil Energy
6
6
8
8
40.0
are the published DAMA/LIBRA data.
Recoil Energy (keVee)
logΣn cm2
logΣn cm2
40.5
higher mass, say 20 GeV, this approach does not succeed.
As 41.0 mass moves above 12 GeV, a AMATotal
the D contribution coming
arXiv:0804.2741, Bernabei et. al. from iodine scattering begins to move into the low end of
the41.5
observed energy region, spoiling the fit. Also plotted
in Fig. 2 are spectra for WIMP SSi
CDM masses of 2 and 7 GeV
for comparison.
42.0 XENON
The 68%, 90%, and 99% CL (∆χ 2.3, 4.61, 9.21)
2
contours consistent with our nine bin DAMA/LIBRA χ 2
function are shown in Fig. 1. Both regions shrink dra-
matically compared to the Χ GeV χ2 . In the left panel,
0 20 40 60 80 100 120
m two bin
the ∆χ2 is with respect to the global best fit point at 77
10. Inelastic Dark Matter
Dark matter has two nearly
Threshold velocity necessary
degenerate states
to scatter with energy ER
δm ∼ (100 keV)
χ2 q 1 mN ER
vmin = √ + δm
2mN ER µ
χ1 q Lighter nuclei, higher threshold
Tucker-Smith and Weiner, hep-ph/0101138.
11. Inelastic Dark Matter
Threshold behavior
µv 2 ∼ 100 keV
Rate
Recoil Energy (keV)
3 Consequences
(1) Scatters off of heavier nuclei -- CDMS ineffective
(2) Large recoil energy -- ZEPLIN3 XENON didn’t look
(3) Large modulation fraction -- absolute signal is smaller
12. Standard Halo Model
Scattering rate depends on halo profile
vesc
3.5 dR dσ
∝ d vf (v)v
3
3
3.0 dER vmin dER
v 2 f (v)/10−4
2.5
2
2.0 v0
inelastic scattering sensitive to
1.5
tail of distribution
1
1.0
0.5
vesc
00
0.0
100 200 300 400 500 600
0 100 200 300 400 500 600
velocity
13. Larger Modulation Fraction
Smaller rate
One reason for apparent tension
1
2.5% modulation
0.75
Rate
0.5
0.25
50% modulation
0 0.25 0.5 0.75 1
Dec. 2nd
June 2nd
Time
14. Inelastic Dark Matter
A new number to explain:
δm
∼ 10−6
m
Sign of dark sector dynamics?
First of many splittings
New interactions to discover
Changes which questions are interesting
15. Form-Factor Suppression
Can suppress low energy scattering
Fdm (q 2 ) = c0 + c1 q 2 + c2 q 4 + · · ·
q 2 mN E R
χ Fdm (q 2 )
dRel
N ∝ (ER )n e−ER
dER
Rate
N
χ
Recoil Energy (keV)
16. Form-Factor Suppression
Can suppress low energy scattering
Fdm (q 2 ) = c0 + c1 q 2 + c2 q 4 + · · ·
q 2 mN E R
χ Fdm (q 2 )
dRel
N ∝ (ER )n e−ER
dER
Rate
N
χ
Best case scenarios 5 Recoil Energy (keV)
32
35.5
c0 = c1 = 0
33
36.0
logΣ p cm2
logΣ p cm2
34
36.5
35
Pospelov Ritz (2003)
37.0
Chang, Pierce, and Weiner (2009).
36
Feldstein, Fitzpatrick, and Katz (2009).
37.5 37
m Χ GeV m Χ GeV
0 20 40 60 80 0 20 40 60 80
a) b)
IG. 3: Plots of the SD-proton cross section σp vs DM mass mχ without (a) and with q 4 suppression (b). The colored
egions show the 68, 90, and 99% CL regions for the best DAMA fit. The 90% exclusions limits are PICASSO (gray
17. Plan of Talk
DAMA Inelastic Dark Matter
Composite dark matter models
Experimental Prospects
Uncertainties in halo profile
Direct Detection
Directional Detection Experiments
Collider Signatures
18. Composite Inelastic Dark Matter
Alves, Behbahani, Schuster, Wacker, 0903.3945.
1
Ldark = − Tr G2 + q iD q + m¯q
¯ q
2 µν
New SU(Nc) gauge sector confines at scale Λd
2π
Λdark ∼ exp −
b0 αdark
Two dark quarks qH qL
mH Λdark , mL
No flavor changing effects
19. Composite Inelastic Dark Matter
Alves, Behbahani, Schuster, Wacker, 0903.3945.
1
Ldark = − Tr G2 + q iD q + m¯q
¯ q
2 µν
New SU(Nc) gauge sector confines at scale Λd
2π
Λdark ∼ exp −
b0 αdark
Two dark quarks qH qL
mH Λdark , mL
No flavor changing effects
Meson Baryon Low Energy Stable States
¯ ¯
qL · · · qL Mesons
qH · · · qH NH asymmetric
NH asymmetric qL · · · qL
Baryons
Nc − NH asymmetric
20. Cosmology of CiDM
Alves, Behbahani, Schuster, Wacker: 0903.3945 + to appear
A primordial cosmological dark quark asymmetry
(nH − nH ) = −(nL − nL ) = 0
¯ ¯
¯
When T Λd , dark matter is in qH qL bound state
Processing into multi-core hadrons can be slow
Dominantly in NH = 1 mesons
nB
O(10−6 )
nM
21. Splitting of Ground State
Mass difference in meson states arises from hyperfine splitting
Coulombic limit
mH
¯
qL
qH α4 m2
δm ∼ d L
Energy
Λd mH
mL For U(1): Atomic Dark Matter
D. E. Kaplan, G. Z. Krnjaic, K. R. Rehermann, C.M. Wells (2009)
spin 0 spin 1 Confined
qH
¯
qL
Λ2
d
dark pion dark rho δm ∼
πd ρd mH
22. Spin Temperature
Need to explain why iDM is in ground state
Self interaction keeps DM in equilibrium
ρ d ρ d → πd πd
Solves de-excitation problem
Spin temperature low
nρd
= exp(−δm/Tspin )
n πd
Kinetically decouple late, smaller spin temperature
Tspin 10 keV
∼
23. Dark Matter Couplings
Couples to a secluded U(1)
Two choices for anomaly-free charges
Vector Coupling
µ
Jd = qH γ µ qH − qL γ µ qL
¯ ¯
Does not forbid quark masses
Axial-Vector Coupling
µ
Jd = qH γ µ γ 5 qH − qL γ µ γ 5 qL
¯ ¯
Forbids quark masses until U(1)d Higgsed
24. Coupling to Standard Model
Kinetically mix U(1)d with U(1)Y
U (1)d U (1)Y
DM SM
ψgut
1 µν 1 µν µν 1 µν 1 µν
LU(1) = − Fd Fdµν − B Bµν − Fd Bµν → −kineticFdµν − B Bµν
F mixing
4 4 2 4 d 4
25. Coupling to Standard Model
Kinetically mix U(1)d with U(1)Y
U (1)d U (1)Y
DM SM
ψgut
1 µν 1 µν µν 1 µν 1 µν
LU(1) = − Fd Fdµν − B Bµν − Fd Bµν → −kineticFdµν − B Bµν
F mixing
4 4 2 4 d 4
Higgs U(1)d near the electroweak scale
LHiggs = |Dµ φd |2 − V (φd ) → m2 A2
d d
md = 2gd vφ
26. Coupling to Standard Model
Kinetically mix U(1)d with U(1)Y
U (1)d U (1)Y
DM SM
ψgut
1 µν 1 µν µν 1 µν 1 µν
LU(1) = − Fd Fdµν − B Bµν − Fd Bµν → −kineticFdµν − B Bµν
F mixing
4 4 2 4 d 4
Higgs U(1)d near the electroweak scale
LHiggs = |Dµ φd |2 − V (φd ) → m2 A2
d d
md = 2gd vφ
Gives mass to fermions
LYuk = +c
yL q L q L φ c †
yH q H qH φ
mf = yf vφ
27. Coupling to Standard Model
Kinetically mix U(1)d with U(1)Y
U (1)d U (1)Y
DM SM
ψgut
L = −Fd − FEM − Fd FEM + m2 A2 + JEM AEM + Jd Ad
2 2
A d
28. Coupling to Standard Model
Kinetically mix U(1)d with U(1)Y
U (1)d U (1)Y
DM SM
ψgut
L = −Fd − FEM − Fd FEM + m2 A2 + JEM AEM + Jd Ad
2 2
A d
redefine SM photon AEM → AEM − Ad
L = −Fd − FEM + m2 A2 + JEM (AEM − Ad ) + Jd Ad
2 2
A d
µ
Lint ∝ Jem Adµ
SM is milli-charged under dark U(1), DM is neutral under EM
29. Effective Field Theory
Use EFT to describe interactions of mesons
Dark Matter Scattering
¯
qH qL ρµ
d
mass
πd
elastic inelastic
πd→πd πd→ρd
† 2 †
Lfree = ∂µ πd ∂ µ πd − Mπ πd πd
1 †
− ρd µν ρµν + Mρ ρ† µ ρµ
2
2 d d d
spin 0 meson spin 1 meson
πd → −πd ρdµ → (−1)µ ρdµ
Parity of new gauge boson determines the allowed
interactions in the effective Lagrangian
32. Size of Couplings
DAMA cross section set by
ρ q
2
gd 1
σDAMA ∝ ≡ 4 gd e
m2 d
A feff
π q
mAd vφ
2
feff = 2
vEW
Mass of DM given by
mDM = mH = yh vφ vEW
Sets mass of Dark Photon
mAd vEW
33. Current Limits on ε
10-2 aµ
ϒ(3S)
10-3 ae
DA MA
10-4
fixed target
10-5
10-6
10-7
supernova
10-8
10-9
10-2 10-1 1 Pospelov, 0811.1030.
Reece and Wang, 0904.1743.
mAd (GeV) Bjorken, Essig, Schuster, Toro, 0906.0580
34. Vector Coupling
Elastic Inelastic
πd→πd πd→ρd
1 † µν 1 † µ ν˜
πd ∂µ πd ∂ν Fd πd ∂ ρd Fdµν
Λ2
d Λd
charge-radius scattering velocity suppressed
Rel
Elastic scattering dominates: 108
Rin
Nearly pure Elastic: Not good for DAMA
35. CP-Violation
Θ term in dark QCD sector ˜
Lcpv = Θd TrGd Gd
Not necessarily small
Leads to mixing between
states of different parity
e.g. πd ↔ a0d
In limit mL → 0
mH chiral rotation removes Θ term
mL
Energy
For heavy quarks, mixing given by
Θd Λd
Λd sin θp =
πd |Hp |a0d
ma0d − mπd
2
λd mL
CP effects vanish as mL →0, ∞
...maximized when mL ≅ Λd
36. Effects of Parity Violation
Admixture of vector and axial interactions
θ µν θ ˜ µν
Can effectively substitute Fd → cos p Fd + sin p Fd
µν
2 2
Elastic Inelastic
θp 1 † ˜ µν θp 1 π † ∂ µ ρ ν F
cos πd ∂µ πd ∂ν Fd + cos d dµν
2 Λd
d
2 Λ2d
θp 1 † µν θp 1 † µ ν˜
+ sin sin πd ∂ ρd Fdµν
2 Λ2
πd ∂µ πd ∂ν Fd + 2 Λd
d
cel † cin †
µν
2 πd ∂µ πd ∂ν Fd
+ µν
πd ∂µ ρd ν Fd
Λd Λd
Neither axial or vector, but elastic and inelastic interactions
How to discover suppressed elastic scatterings?
37. Plan of Talk
DAMA Inelastic Dark Matter
Composite dark matter models
Experimental Prospects
Uncertainties in halo profile
Directional Detection Experiments
Collider Signatures
38. Simple Halo Model
N-body simulations indicate that density falls off more
steeply at larger radii
3.5
3 Assume velocity distribution is:
3.0
isothermal, isotropic, Gaussian
v 2 f (v)/10−4
2.5
2
2.0 v0 2 2
f (v) ∝ e−(v/v0 ) − e−(vesc /v0 ) Θ(vesc − v)
1.5
1
1.0
0.5
vesc
0
0.0
0 100 200 300 400 500 600
0 100 200 300 400 500 600
velocity
39. Modified SHM
−(v/v0 )2α −(vesc /v0 )2α
f (v) ∝ e −e Θ(vesc − v)
3.5
α parameterizes variation in the
3
3.0 α=1.1 tail of the distribution
)
v 2 f (v)/10−4
2.5
α=0.8 captures qualitative behavior of
2
2.0 v0 ) N-body simulations
1.5
1
1.0
0.5 600
vesc
0
0.0
0 100 200 300 400 500 600
0 100 200 300 400 500 600
velocity
40. Setting Limits on a Cross Section
Usually set limits on cross section per nucleon
Factor of A4 to translate
iDM has non-trivial kinematics
Light nuclei have no cross section
Should use particle physics parameters
Z 2 αEM m2 d
A
σ∝ f2
f4 cin gd
41. Marginalizing over Uncertainties
How do current experiments constrain parameters?
“Unknowns”
particle physics astrophysics
mπd , δm, cin v0 , vesc , α
cin is coupling for inelastic 0.8 ≤ α ≤ 1.25
operator
200 ≤ v0 ≤ 300
cel/cin = relative strength of 500 ≤ vesc ≤ 600
elastic sub-component
42. Marginalizing over parameters
Minimize χ2 over 6 parameters using results from direct
detection experiments
Nexp
Xipred − Xiobs
χ2 (mπd , δ, fi , v0 , vesc , α) =
ı=1
σi
Fit to DAMA recoil spectrum
Require that theory predicts ≤ number of
events seen by each null experiment
49. Correlations
The same model, but with different halo profiles...
cel/cin = 0.15 v0 = 300
0.03
vesc = 500
α = 0.95
cpdkgkeVee
0.02
v0 = 220
0.01 vesc = 550
α = 0.8
0.00
Parameters consistent
with DAMA and null
Recoil Energy keVee
0 2 4 6 8 experiments
32
24
Challenge to distinguish astrophysical parameters 16
8
0 50 100 150 200 250 300 350 400 450 500
50. LUX/Xenon100
100 kg Liquid Xe detectors (upgrade for Xenon10)
Will see a large number of events
Winter Summer
0.20
0.25
0.20 0.15
Frequency
Frequency
0.15
0.10
0.10
0.05
0.05
0.00 0.00
0 20 40 60 80 100 0 20 40 60 80 100
Total Number of Events Observed Total Number of Events Observed
(1000 kg-day exposure ~ 1 month!)
Tail down to small 5 events
51. LUX/Xenon100
Recoil Spectrum
5.00
1000 kg· day
: summer
1.00
: winter
0.50
countskeV
0.10
0.05
Recoil Energy keV
0 20 40 60 80
Elastic subcomponent apparent beneath energy threshold,
but inelastic kinematics get washed out
52. Plan of Talk
DAMA Inelastic Dark Matter
Composite dark matter models
Experimental Prospects
Uncertainties in halo profile
Directional Detection Experiments
Collider Signatures
53. Directional Detection
Experiments
Detector
πd πd Good angular resolution requires
sufficiently long tracks (~1 mm)
Head-tail discrimination requires large
1 mm
threshold energy (~50 keV)
54. Directional Detection
Experiments
Detector
πd πd Good angular resolution requires
sufficiently long tracks (~1 mm)
Head-tail discrimination requires large
1 mm
threshold energy (~50 keV)
CF4 : DMTPC, NEWAGE, MIMAC
CS2 : DRIFT } Need heavier nuclei to see inelastic signal
Iodine (A=127) or Xenon (A=131)
Finkbeiner, Lin, and Weiner, 0906.0002.
55. Directional Detection
Motivation
Detector 6 am Daily Modulation
Wind direction changes every 12 hrs
Large Amplitude
45°(
Detector
Daily modulation amplitude ~ 100%
Annual modulation amplitude ~ 5%
6 pm
Smaller Backgrounds
Spergel, Phys. Rev D 37, 1353 (1988).
56. Directional Detection
)γ
πd ¯
vE ¯
vE
πd
Different dynamics in dark matter sector result in different cosγ spectra
iDM
vesc − vmin
dR cos γ ≤
vE
d cos γ
1 mN ER
vmin = √ + δm
eDM 2mN ER µ
cos γ
59. Plan of Talk
DAMA Inelastic Dark Matter
Composite dark matter models
Experimental Prospects
Uncertainties in halo profile
Directional Detection Experiments
Collider Signatures
61. New Tools
New Strong Signal Simulation
(J. Wacker w/ S. Schumann, P. Richardson)
Dark Showering
Sherpa Herwig
Hadron Spectrum
DarkSpecGen Dark Hadronization
Sherpa Herwig
Cascading to SM
DarkSpecGen
62. Boosted Physics
When high pT particles
cascade to SM final states
producing collimated final states
“Lepton Jets”
A Challenging Environment
Reconstruction is difficult
Isolation cuts out signal
Cascades produce heterogeneous final states
63. 1 Light Flavor Spectrum
No light pions - Only eta prime
No hadronic decays
~1 dozen quasi stable particles
2Λdark
2++ 1−+ 2−−
2 +−
1+− 0−−
0−+ 1− −
Λdark 0
++
0+−
J ++ J +− J −+ J −−
Only “weak” decays: quasi-stable particles
64. 1 Light Flavor Spectrum
No light pions - Only eta prime
No hadronic decays
~1 dozen quasi stable particles
2Λdark
2++ 1−+ 2−−
2 +−
1+− 0−−
0−+ 1− −
Λdark 0
++
0+−
J ++ J +− J −+ J −−
Only “weak” decays: quasi-stable particles
!#$%'' +$,#'%-+.)(
ωD #()*#! ηD $/0$,$1'-
A∗ A∗
65. 1 Light Flavor Spectrum
No light pions - Only eta prime
No hadronic decays
~1 dozen quasi stable particles
2Λdark
2++ 1−+ 2−−
2 +−
1+− 0−−
0−+ 1− −
Λdark 0
++
0+−
J ++ J +− J −+ J −−
Only “weak” decays: quasi-stable particles
!#$%'' +$,#'%-+.)(
ωD #()*#! ηD $/0$,$1'-
A∗ A∗
66. 1 Light Flavor Spectrum
No light pions - Only eta prime
No hadronic decays
~1 dozen quasi stable particles
2Λdark
2++ 1−+ 2−−
2 +−
1+− 0−−
0−+ 1− −
Λdark 0
++
0+−
J ++ J +− J −+ J −−
Only “weak” decays: quasi-stable particles
!#$%'' +$,#'%-+.)(
ωD #()*#! ηD $/0$,$1'-
A∗ A∗
Some short-lived Some long lived
Lots of visible particles
71. No light flavors
“Quirks” (Luty et al 2008)
Spectra similar to 1 light flavor
(Lattice calculations available)
We don’t know how to hadronize
(how to cut color lines)
More theory work necessary
72. Two-Lepton Lepton Jets
2 oppositely signed leptons in a small cone
+ − + −
∆RSignal 0.1
∼ Hadron
Ad
0.1 ∆RIso 0.4
∼ ∼
Hadron
µ+ µ−
e+ e−
74. Conclusions
Inelastic DM is an elegant explanation
for DAMA vs the Rest of the World
Discovery or Refutation Imminent
New scale to explain: New Dynamics
New measurements are important
Direct Detection Colliders
