Introduction to WIMPs - Institute for Theoretical Physics

WIMPs: An Introduction
Manuel Drees
Bonn University & Bethe Center for Theoretical Physics
Introduction to WIMPs – p. 1/59
Contents
1 The “WIMP Miracle”
Introduction to WIMPs – p. 2/59
Contents
1 The “WIMP Miracle”
2 Have WIMPS been Detected (Directly)?
Introduction to WIMPs – p. 2/59
Contents
1 The “WIMP Miracle”
2 Have WIMPS been Detected (Directly)?
3 Asymmetric Dark Matter?
Introduction to WIMPs – p. 2/59
Contents
1 The “WIMP Miracle”
2 Have WIMPS been Detected (Directly)?
3 Asymmetric Dark Matter?
4 WIMPs and Colliders
Introduction to WIMPs – p. 2/59
Contents
1 The “WIMP Miracle”
2 Have WIMPS been Detected (Directly)?
3 Asymmetric Dark Matter?
4 WIMPs and Colliders
5 Summary
Introduction to WIMPs – p. 2/59
Conditions for Dark Matter Candidates
Requirements for a good DM candidate χ:
Must have lifetime τχ ≫ τU
Introduction to WIMPs – p. 3/59
Conditions for Dark Matter Candidates
Requirements for a good DM candidate χ:
Must have lifetime τχ ≫ τU
Must be electrically neutral (otherwise not dark)
Introduction to WIMPs – p. 3/59
Conditions for Dark Matter Candidates
Requirements for a good DM candidate χ:
Must have lifetime τχ ≫ τU
Must be electrically neutral (otherwise not dark)
Must have correct relic density: Ωχ ≃ 0.22
Introduction to WIMPs – p. 3/59
Conditions for Dark Matter Candidates
Requirements for a good DM candidate χ:
Must have lifetime τχ ≫ τU
Must be electrically neutral (otherwise not dark)
Must have correct relic density: Ωχ ≃ 0.22
If DM consists of thermally produced “elementary” particles:
Leads to events with missing ET at colliders!
Introduction to WIMPs – p. 3/59
Conditions for Dark Matter Candidates
Requirements for a good DM candidate χ:
Must have lifetime τχ ≫ τU
Must be electrically neutral (otherwise not dark)
Must have correct relic density: Ωχ ≃ 0.22
If DM consists of thermally produced “elementary” particles:
Leads to events with missing ET at colliders!
Counter–examples: axions; dark atoms; primordial black holes; keV
neutrinos: not covered in this talk. Note: Proves that LHC does not “recreate
conditions of the early universe”!
Introduction to WIMPs – p. 3/59
The “WIMP Miracle”
Assume χ was in full thermal equilibrium with SM
particles at sufficiently high temperature T :
χ production rate nχ hσ(χχ → SM)vχ i > expansion rate H
Introduction to WIMPs – p. 4/59
The “WIMP Miracle”
Assume χ was in full thermal equilibrium with SM
particles at sufficiently high temperature T :
χ production rate nχ hσ(χχ → SM)vχ i > expansion rate H
nχ ∝ e−mχ /T , hσ(χχ → SM)vi ∝ T 0 or2 , H ∝ T 2 /MPlanck
Introduction to WIMPs – p. 4/59
The “WIMP Miracle”
Assume χ was in full thermal equilibrium with SM
particles at sufficiently high temperature T :
χ production rate nχ hσ(χχ → SM)vχ i > expansion rate H
nχ ∝ e−mχ /T , hσ(χχ → SM)vi ∝ T 0 or2 , H ∝ T 2 /MPlanck
=⇒ equality (“freeze-out”) reached at TF ≃ mχ /20
Introduction to WIMPs – p. 4/59
The “WIMP Miracle”
Assume χ was in full thermal equilibrium with SM
particles at sufficiently high temperature T :
χ production rate nχ hσ(χχ → SM)vχ i > expansion rate H
nχ ∝ e−mχ /T , hσ(χχ → SM)vi ∝ T 0 or2 , H ∝ T 2 /MPlanck
=⇒ equality (“freeze-out”) reached at TF ≃ mχ /20
0.1 pb · c
=⇒ Ωχ h ≃
hσ(χχ → SM)vi
2
Introduction to WIMPs – p. 4/59
The “WIMP Miracle”
Assume χ was in full thermal equilibrium with SM
particles at sufficiently high temperature T :
χ production rate nχ hσ(χχ → SM)vχ i > expansion rate H
nχ ∝ e−mχ /T , hσ(χχ → SM)vi ∝ T 0 or2 , H ∝ T 2 /MPlanck
=⇒ equality (“freeze-out”) reached at TF ≃ mχ /20
0.1 pb · c
=⇒ Ωχ h ≃
hσ(χχ → SM)vi
2
Indicates weak–scale χχ annihilation cross section:
hσ(χχ → any)vi ≃ 3 · 10−26 cm3 s−1
Introduction to WIMPs – p. 4/59
WIMPs and Early Universe
Ωχ h2 can be changed a lot in non–standard cosmologies
(involving T ≫ TBBN ):
Increased: Higher expansion rate H(T ∼ TF );
additional non–thermal χ production at T < TF ; . . .
Introduction to WIMPs – p. 5/59
WIMPs and Early Universe
Ωχ h2 can be changed a lot in non–standard cosmologies
(involving T ≫ TBBN ):
Increased: Higher expansion rate H(T ∼ TF );
additional non–thermal χ production at T < TF ; . . .
Decreased: Reduced expansion rate H(T ∼ TF );
entropy production at T < TF ; . . .
Introduction to WIMPs – p. 5/59
WIMPs and Early Universe
Ωχ h2 can be changed a lot in non–standard cosmologies
(involving T ≫ TBBN ):
Increased: Higher expansion rate H(T ∼ TF );
additional non–thermal χ production at T < TF ; . . .
Decreased: Reduced expansion rate H(T ∼ TF );
entropy production at T < TF ; . . .
Determining σ(χχ → SM) allows probe of very early
Universe, once χ has been established to be “the” DM
particle! e.g. MD, Iminniyaz, Kakizaki, arXiv:0704.1590
Introduction to WIMPs – p. 5/59
High−T Production of DM Particles
Sometimes χ production from thermalized SM particles is
called “thermal production” even if χ never was in thermal
equilibrium:
Introduction to WIMPs – p. 6/59
High−T Production of DM Particles
Sometimes χ production from thermalized SM particles is
called “thermal production” even if χ never was in thermal
equilibrium:
If σ(χχ → SM) ∝ 1/s: Production maximal at T ≃ mχ
(“freeze–in”, Hall et al., arXiv:0911.1120)
Introduction to WIMPs – p. 6/59
High−T Production of DM Particles
Sometimes χ production from thermalized SM particles is
called “thermal production” even if χ never was in thermal
equilibrium:
If σ(χχ → SM) ∝ 1/s: Production maximal at T ≃ mχ
(“freeze–in”, Hall et al., arXiv:0911.1120)
If σ(χχ → SM) ∝ s/Λ4 : Produced dominantly at highest
possible temperature, TR .
Introduction to WIMPs – p. 6/59
High−T Production of DM Particles
Sometimes χ production from thermalized SM particles is
called “thermal production” even if χ never was in thermal
equilibrium:
If σ(χχ → SM) ∝ 1/s: Production maximal at T ≃ mχ
(“freeze–in”, Hall et al., arXiv:0911.1120)
If σ(χχ → SM) ∝ s/Λ4 : Produced dominantly at highest
possible temperature, TR .
Either way, χ interactions with SM particles are too weak to
give missing ET signal, unless χ has “partners” that can be
produced via gauge interactions (ex.: gravitino G̃, axino ã)
Introduction to WIMPs – p. 6/59
High−T Production of DM Particles
Sometimes χ production from thermalized SM particles is
called “thermal production” even if χ never was in thermal
equilibrium:
If σ(χχ → SM) ∝ 1/s: Production maximal at T ≃ mχ
(“freeze–in”, Hall et al., arXiv:0911.1120)
If σ(χχ → SM) ∝ s/Λ4 : Produced dominantly at highest
possible temperature, TR .
Either way, χ interactions with SM particles are too weak to
give missing ET signal, unless χ has “partners” that can be
produced via gauge interactions (ex.: gravitino G̃, axino ã)
Interactions are too weak for direct detection; indirect
detection is possible only for unstable DM candidates.
Introduction to WIMPs – p. 6/59
Have WIMPs Been Detected Directly?
Direct detection ≡ search for elastic WIMP–nucleon
scattering
Introduction to WIMPs – p. 7/59
Have WIMPs Been Detected Directly?
Direct detection ≡ search for elastic WIMP–nucleon
scattering
Kinematics: vχ ∼ vSun ∼ 10−3 c
Introduction to WIMPs – p. 7/59
Have WIMPs Been Detected Directly?
Direct detection ≡ search for elastic WIMP–nucleon
scattering
Kinematics: vχ ∼ vSun ∼ 10−3 c
=⇒ energy transfer to nculeus A:
2
m
< min 10−6 χ , 10−6 mA < 100 keV
Q∼
mA
∼
Introduction to WIMPs – p. 7/59
Have WIMPs Been Detected Directly?
Direct detection ≡ search for elastic WIMP–nucleon
scattering
Kinematics: vχ ∼ vSun ∼ 10−3 c
=⇒ energy transfer to nculeus A:
2
m
< min 10−6 χ , 10−6 mA < 100 keV
Q∼
mA
∼
=⇒ Cannot excite (most) nuclei!
Introduction to WIMPs – p. 7/59
Have WIMPs Been Detected Directly?
Direct detection ≡ search for elastic WIMP–nucleon
scattering
Kinematics: vχ ∼ vSun ∼ 10−3 c
=⇒ energy transfer to nculeus A:
2
m
< min 10−6 χ , 10−6 mA < 100 keV
Q∼
mA
∼
=⇒ Cannot excite (most) nuclei!
< 100 MeV =⇒ may need to worry
Momentum transfer ∼
about elastic form factors; quite well understood (for spin–indep.
scattering)
Introduction to WIMPs – p. 7/59
Recoil Spectrum
dR
dQ
∝
2 R vmax dv
|F (Q)| vmin v f1 (v)
Introduction to WIMPs – p. 8/59
Recoil Spectrum
dR
dQ
∝
2 R vmax dv
|F (Q)| vmin v f1 (v)
f1 (v) : WIMP velocity distribution. Usually assumed
Maxwellian in rest frame of the galaxy, cut off at
vesc =⇒ vmax . Gives roughly exponentially falling spectrum.
Introduction to WIMPs – p. 8/59
Normalized Recoil Spectra
1
mχ=100 GeV, A=73
mχ=100 GeV, A=136
mχ=10 GeV, A=73
1/R dR/dQ [1/keV]
0.1
mχ=10 GeV, A=16
0.01
0.001
0.0001
0
20
40
60
80
100
Q [keV]
Introduction to WIMPs – p. 9/59
Experimental Challenges
Spectrum “backed up” against instrumental threshold
Qmin
Introduction to WIMPs – p. 10/59
Experimental Challenges
Spectrum “backed up” against instrumental threshold
Qmin
Rates of current interest ≪ background rate, e.g. from
radioactive decay (for most materials)
=⇒ try to discriminate between nuclear recoil (signal)
and e/γ induced events (background)!
Introduction to WIMPs – p. 10/59
Experimental Challenges
Spectrum “backed up” against instrumental threshold
Qmin
Rates of current interest ≪ background rate, e.g. from
radioactive decay (for most materials)
=⇒ try to discriminate between nuclear recoil (signal)
and e/γ induced events (background)!
Will go through three claimed signals: DAMA(/LIBRA),
CoGeNT, CRESST.
Introduction to WIMPs – p. 10/59
DAMA
Pure scintillation detectors (doped NaI) in Gran Sasso:
6 years with 100 kg (DAMA)
6 years with 250 kg (DAMA/LIBRA)
Introduction to WIMPs – p. 11/59
DAMA
Pure scintillation detectors (doped NaI) in Gran Sasso:
6 years with 100 kg (DAMA)
6 years with 250 kg (DAMA/LIBRA)
All events are counted.
Introduction to WIMPs – p. 11/59
DAMA
Pure scintillation detectors (doped NaI) in Gran Sasso:
6 years with 100 kg (DAMA)
6 years with 250 kg (DAMA/LIBRA)
All events are counted.
Observe few percent modulation of total rate
Introduction to WIMPs – p. 11/59
DAMA
Pure scintillation detectors (doped NaI) in Gran Sasso:
6 years with 100 kg (DAMA)
6 years with 250 kg (DAMA/LIBRA)
All events are counted.
Observe few percent modulation of total rate
Compatible with ∼ 50 GeV WIMP scattering off I, or ∼ 10
GeV WIMP scattering off Na.
Introduction to WIMPs – p. 11/59
DAMA Results
Residuals (cpd/kg/keV)
2-6 keV
DAMA/NaI (0.29 ton×yr)
(target mass = 87.3 kg)
DAMA/LIBRA (0.53 ton×yr)
(target mass = 232.8 kg)
Time (day)
Residuals (cpd/kg/keV)
2-6 keV
DAMA/LIBRA ≈ 250 kg (0.87 ton×yr)
Time (day)
Introduction to WIMPs – p. 12/59
DAMA: Problems
No e/γ discrimination is attempted, although some (statistical)
discrimination should be possible using light curve
Introduction to WIMPs – p. 13/59
DAMA: Problems
No e/γ discrimination is attempted, although some (statistical)
discrimination should be possible using light curve
Deduced shape of spectrum weird: Falls towards small
Q! (Depends on 3–dimensional WIMP velocity distribution.)
Introduction to WIMPs – p. 13/59
DAMA: Problems
No e/γ discrimination is attempted, although some (statistical)
discrimination should be possible using light curve
Deduced shape of spectrum weird: Falls towards small
Q! (Depends on 3–dimensional WIMP velocity distribution.)
Amplitude of modulation is getting smaller!
E.g. in 2–6 keVee bin (in units of 10−3 /kg · day · keVee ):
DAMA 1995–2001: 20.0 ± 3.2
LIBRA 2003–2007: 10.7 ± 1.9
LIBRA 2007–2009: 8.5 ± 2.2
Ratio LIBRAII
DAMA = 0.43 ± 0.13
More than 4σ away from 1! Results for 2–4, 2–5 keVee bins similar.
Introduction to WIMPs – p. 13/59
DAMA: Problems
No e/γ discrimination is attempted, although some (statistical)
discrimination should be possible using light curve
Deduced shape of spectrum weird: Falls towards small
Q! (Depends on 3–dimensional WIMP velocity distribution.)
Amplitude of modulation is getting smaller!
E.g. in 2–6 keVee bin (in units of 10−3 /kg · day · keVee ):
DAMA 1995–2001: 20.0 ± 3.2
LIBRA 2003–2007: 10.7 ± 1.9
LIBRA 2007–2009: 8.5 ± 2.2
Ratio LIBRAII
DAMA = 0.43 ± 0.13
More than 4σ away from 1! Results for 2–4, 2–5 keVee bins similar.
No convincing non–WIMP interpretation of modulation
known.
Introduction to WIMPs – p. 13/59
CoGeNT: Time–Averaged Analysis
Operate cryogenic Ge detectors with very low threshold
Qmin .
Introduction to WIMPs – p. 14/59
CoGeNT: Time–Averaged Analysis
Operate cryogenic Ge detectors with very low threshold
Qmin .
Originally: Found excess relative to simple bckgd model at
very low Q =⇒ small mχ ;
Introduction to WIMPs – p. 14/59
CoGeNT: Time–Averaged Analysis
Operate cryogenic Ge detectors with very low threshold
Qmin .
Originally: Found excess relative to simple bckgd model at
very low Q =⇒ small mχ ;
χ2 fit with signal not significantly better than with pure
background: no claim of signal in published paper!
Introduction to WIMPs – p. 14/59
CoGeNT: Time–Averaged Analysis
Operate cryogenic Ge detectors with very low threshold
Qmin .
Originally: Found excess relative to simple bckgd model at
very low Q =⇒ small mχ ;
χ2 fit with signal not significantly better than with pure
background: no claim of signal in published paper!
This September: More data, re–evaluateed background =⇒
size of possible “signal” reduced by ∼ factor 5!
Introduction to WIMPs – p. 14/59
CoGeNT: Results
Introduction to WIMPs – p. 15/59
CoGeNT: Results
Introduction to WIMPs – p. 15/59
CoGeNT: Modulation
After 15 months of data taken: Find 2.8σ “evidence” for
annual modulation
Introduction to WIMPs – p. 16/59
CoGeNT: Modulation
After 15 months of data taken: Find 2.8σ “evidence” for
annual modulation
Much too large to be compatible with time–averaged
“signal”, for standard halo
Introduction to WIMPs – p. 16/59
CoGeNT: Modulation
After 15 months of data taken: Find 2.8σ “evidence” for
annual modulation
Much too large to be compatible with time–averaged
“signal”, for standard halo
No event–by–event e/γ rejection at these low energies
Introduction to WIMPs – p. 16/59
CoGeNT: Summary
No signal claimed in time–averaged analysis!
Introduction to WIMPs – p. 17/59
CoGeNT: Summary
No signal claimed in time–averaged analysis!
There is a large, poorly understood background
Introduction to WIMPs – p. 17/59
CoGeNT: Summary
No signal claimed in time–averaged analysis!
There is a large, poorly understood background
Modulation “signal” statistically very weak, and way too
large
Introduction to WIMPs – p. 17/59
CRESST
Uses cryogenic CaWO4 crystals; detect scintillation light
and heat: Allows event–by–event discrimination! See 67
events after cuts.
Introduction to WIMPs – p. 18/59
CRESST
Uses cryogenic CaWO4 crystals; detect scintillation light
and heat: Allows event–by–event discrimination! See 67
events after cuts.
Unfortunately, quite large backgrounds (rough estimates, not final fit):
e/γ events: 8
α background: 9.2
n background: 1.5 to 11.4
Pb recoil (from 210 Po decay): 17
Introduction to WIMPs – p. 18/59
CRESST
Uses cryogenic CaWO4 crystals; detect scintillation light
and heat: Allows event–by–event discrimination! See 67
events after cuts.
Unfortunately, quite large backgrounds (rough estimates, not final fit):
e/γ events: 8
α background: 9.2
n background: 1.5 to 11.4
Pb recoil (from 210 Po decay): 17
Much of fitted excess has essentially no light: only “half a
signal”
Introduction to WIMPs – p. 18/59
CRESST
Uses cryogenic CaWO4 crystals; detect scintillation light
and heat: Allows event–by–event discrimination! See 67
events after cuts.
Unfortunately, quite large backgrounds (rough estimates, not final fit):
e/γ events: 8
α background: 9.2
n background: 1.5 to 11.4
Pb recoil (from 210 Po decay): 17
Much of fitted excess has essentially no light: only “half a
signal”
No. of α events is correlated with no. of signal events after
α subtraction.
Introduction to WIMPs – p. 18/59
CRESST: Results
Introduction to WIMPs – p. 19/59
CRESST: Results
Introduction to WIMPs – p. 19/59
CRESST: Results
What is negative light yield?
Introduction to WIMPs – p. 19/59
events in signal region (α subtracted)
CRESST: Correlation
20
2
y = 0.44x + 2.1 (χ = 7.3 / 6 d.o.f.)
Data
2
y = 7.2 (χ = 11.4 / 7 d.o.f.)
15
10
5
0
5
10
15
events in α reference region
20
Introduction to WIMPs – p. 20/59
Exclusion Limits from Other Expts
Best limit for larger masses from Xenon100. Uses ionization
and scintillation. Very few events after cuts. Alas, not safe for
mχ ≤ 12 GeV: bound strongly depends on high−v tail of f1 (v),
and on experimental energy resolution.
Introduction to WIMPs – p. 21/59
Exclusion Limits from Other Expts
Best limit for larger masses from Xenon100. Uses ionization
and scintillation. Very few events after cuts. Alas, not safe for
mχ ≤ 12 GeV: bound strongly depends on high−v tail of f1 (v),
and on experimental energy resolution.
Xenon10 more robust at small Q; excludes DAMA, CRESST,
original CoGeNT “signal” for “usual WIMP”
Introduction to WIMPs – p. 21/59
Exclusion Limits from Other Expts
Best limit for larger masses from Xenon100. Uses ionization
and scintillation. Very few events after cuts. Alas, not safe for
mχ ≤ 12 GeV: bound strongly depends on high−v tail of f1 (v),
and on experimental energy resolution.
Xenon10 more robust at small Q; excludes DAMA, CRESST,
original CoGeNT “signal” for “usual WIMP”
CDMS (+ EDELWEISS) second best for not too small mχ .
Uses phonons and ionization. Very few events after cuts. Not
safe below 12 GeV.
Introduction to WIMPs – p. 21/59
Exclusion Limits from Other Expts
Best limit for larger masses from Xenon100. Uses ionization
and scintillation. Very few events after cuts. Alas, not safe for
mχ ≤ 12 GeV: bound strongly depends on high−v tail of f1 (v),
and on experimental energy resolution.
Xenon10 more robust at small Q; excludes DAMA, CRESST,
original CoGeNT “signal” for “usual WIMP”
CDMS (+ EDELWEISS) second best for not too small mχ .
Uses phonons and ionization. Very few events after cuts. Not
safe below 12 GeV.
CDMS low−Q analysis uses phonons only; sizable number of
events. Excludes DAMA, original CoGeNT for “usual WIMP”.
Introduction to WIMPs – p. 21/59
Exclusion Limits from Other Expts
Best limit for larger masses from Xenon100. Uses ionization
and scintillation. Very few events after cuts. Alas, not safe for
mχ ≤ 12 GeV: bound strongly depends on high−v tail of f1 (v),
and on experimental energy resolution.
Xenon10 more robust at small Q; excludes DAMA, CRESST,
original CoGeNT “signal” for “usual WIMP”
CDMS (+ EDELWEISS) second best for not too small mχ .
Uses phonons and ionization. Very few events after cuts. Not
safe below 12 GeV.
CDMS low−Q analysis uses phonons only; sizable number of
events. Excludes DAMA, original CoGeNT for “usual WIMP”.
SIMPLE heated droplet detector: Challenges DAMA.
Introduction to WIMPs – p. 21/59
Theory of WIMP–Nucleus Scattering
Leff = cN N̄ N χ̄χ + aN N̄ γµ N χ̄γ µ χ + bN N̄ γµ γ5 N χ̄γ µ γ5 χ
For scalar χ: γ µ → i∂ µ in 2nd term; 3rd term absent
For Majorana χ: 2nd term absent
1st , 2nd term give spin–independent (s.i.) interaction, 3rd
term gives spin–dependent (s.d.) interaction.
“Usual WIMP”: same s.i. scattering on p and n!
Introduction to WIMPs – p. 22/59
Isospin violation in s.i. interaction?
s.i. ≃ σ s.i. true for Higgs exchange (in particular, in
σχp
χn
(N)MSSM): massive quarks are same for p, n!
Introduction to WIMPs – p. 23/59
Isospin violation in s.i. interaction?
s.i. ≃ σ s.i. true for Higgs exchange (in particular, in
σχp
χn
(N)MSSM): massive quarks are same for p, n!
Not true for q̃, q (1) exchange: quark charges matter!
But: M(χq → χq) has same sign for all quarks: no
cancellations =⇒ isospin violation in praxis not
important, since all nuclei have similar n/p ratio.
Introduction to WIMPs – p. 23/59
Isospin violation in s.i. interaction?
s.i. ≃ σ s.i. true for Higgs exchange (in particular, in
σχp
χn
(N)MSSM): massive quarks are same for p, n!
Not true for q̃, q (1) exchange: quark charges matter!
But: M(χq → χq) has same sign for all quarks: no
cancellations =⇒ isospin violation in praxis not
important, since all nuclei have similar n/p ratio.
Gauge boson exchange can break isospin: coefficients
ap , an may differ in sign! M(χq → χq) is now linear in
(new) quark charges.
Introduction to WIMPs – p. 23/59
Large isospin violation in s.i. interaction?
|M(χA → χA)|2 ∝ |Zap + (A − Z)an |2
=⇒ need ap an < 0 for significant isospin violation:
arrange for cancellation in unwanted nuclei (e.g. Xe).
Introduction to WIMPs – p. 24/59
Large isospin violation in s.i. interaction?
|M(χA → χA)|2 ∝ |Zap + (A − Z)an |2
=⇒ need ap an < 0 for significant isospin violation:
arrange for cancellation in unwanted nuclei (e.g. Xe).
Does not work for CDMS vs. CoGeNT: same target!
Introduction to WIMPs – p. 24/59
Large isospin violation in s.i. interaction?
|M(χA → χA)|2 ∝ |Zap + (A − Z)an |2
=⇒ need ap an < 0 for significant isospin violation:
arrange for cancellation in unwanted nuclei (e.g. Xe).
Does not work for CDMS vs. CoGeNT: same target!
Increases required |ap | even more, to describe claimed
signals
=⇒ Need new light gauge bosons!
Introduction to WIMPs – p. 24/59
Large isospin violation in s.i. interaction?
|M(χA → χA)|2 ∝ |Zap + (A − Z)an |2
=⇒ need ap an < 0 for significant isospin violation:
arrange for cancellation in unwanted nuclei (e.g. Xe).
Does not work for CDMS vs. CoGeNT: same target!
Increases required |ap | even more, to describe claimed
signals
=⇒ Need new light gauge bosons!
Combined analyses: (e.g. Kopp, Schwetz, Zupan, arXiv:1110.2721
[hep-ph]) Still cannot explain all data consistently!
Introduction to WIMPs – p. 24/59
Weisskopf’s (?) Theorem
A theory that explains all data must be wrong, since at any
given point some data are wrong.
Introduction to WIMPs – p. 25/59
Weisskopf’s (?) Theorem
A theory that explains all data must be wrong, since at any
given point some data are wrong.
Competition between null experiments with few
(background) events after cuts, and claimed “signals” with
large, not always well understood backgrounds!
Introduction to WIMPs – p. 25/59
Asymmetric Dark Matter?
Cosmology: ΩDM ≃ 5Ωbaryon : strange coincidence?
Introduction to WIMPs – p. 26/59
Asymmetric Dark Matter?
Cosmology: ΩDM ≃ 5Ωbaryon : strange coincidence?
Ωbaryon determined by baryon–antibaryon asymmetry,
not by thermal decoupling of baryons: try same thing for
WIMPs?
Introduction to WIMPs – p. 26/59
Asymmetric Dark Matter?
Cosmology: ΩDM ≃ 5Ωbaryon : strange coincidence?
Ωbaryon determined by baryon–antibaryon asymmetry,
not by thermal decoupling of baryons: try same thing for
WIMPs?
Most attractive: χ − χ̄ asymmetry related to baryon
asymmetry [O(50) papers]
=⇒ number density nχ ≃ np after annihilating away
symmetric component
Introduction to WIMPs – p. 26/59
Asymmetric Dark Matter?
Cosmology: ΩDM ≃ 5Ωbaryon : strange coincidence?
Ωbaryon determined by baryon–antibaryon asymmetry,
not by thermal decoupling of baryons: try same thing for
WIMPs?
Most attractive: χ − χ̄ asymmetry related to baryon
asymmetry [O(50) papers]
=⇒ number density nχ ≃ np after annihilating away
symmetric component
Needs 2 to 3 times larger χχ̄ annihilation cross section
than for thermal WIMPs!
Introduction to WIMPs – p. 26/59
“Explaining” ΩDM/Ωbaryon
Follows if mχ ≃ 5mp !
Introduction to WIMPs – p. 27/59
“Explaining” ΩDM/Ωbaryon
Follows if mχ ≃ 5mp !
Alas: mχ has no known relation to mp . mχ ≃ 5mp just as
mysterious as ΩDM ≃ 5Ωbaryon
=⇒ Haven’t explained anything!
Introduction to WIMPs – p. 27/59
“Explaining” ΩDM/Ωbaryon
Follows if mχ ≃ 5mp !
Alas: mχ has no known relation to mp . mχ ≃ 5mp just as
mysterious as ΩDM ≃ 5Ωbaryon
=⇒ Haven’t explained anything!
Circular logic: ADM with mχ ≃ 5 GeV interesting
because there are “signals” for low–mass WIMPs;
low–mass WIMPs interesting because ADM “explains”
ΩDM /Ωbaryon ??
Introduction to WIMPs – p. 27/59
WIMPs and Colliders
1 Generalities: WIMP DM Production and Missing ET
Introduction to WIMPs – p. 28/59
WIMPs and Colliders
1 Generalities: WIMP DM Production and Missing ET
2 Light Gauge Bosons
Introduction to WIMPs – p. 28/59
WIMPs and Colliders
1 Generalities: WIMP DM Production and Missing ET
2 Light Gauge Bosons
3 SUSY DM and the “LHC Inverse Problem”
Introduction to WIMPs – p. 28/59
WIMPs and Colliders
1 Generalities: WIMP DM Production and Missing ET
2 Light Gauge Bosons
3 SUSY DM and the “LHC Inverse Problem”
4 Higgs Searches and Direct DM Detection
Introduction to WIMPs – p. 28/59
Cannot predict missing ET from χχ production
Thermal WIMP: Only know total χχ → SM cross
section; contribution of specific final states
(e+ e− , uū + dd¯) not known
Introduction to WIMPs – p. 29/59
Cannot predict missing ET from χχ production
Thermal WIMP: Only know total χχ → SM cross
section; contribution of specific final states
(e+ e− , uū + dd¯) not known
Ωχ h2 determined from σ(χχ → SM) near threshold
(TF ≃ mχ /20 =⇒ s ≃ 4m2χ ). At colliders need ≥ 3 body
final state to get signature (e.g. e+ e− → χχγ, q q̄ → χχg )
=⇒ typically need σ(χχ → SM) at s ∼ 6 to 10m2χ !
Introduction to WIMPs – p. 29/59
“Model-independent” approach
Goodman et al., arXiv:1005.1286 and 1008.1783; Bai, Fox, Harnik, arXiv:1005.3797; Wang,
Li, Shao, Zhang, arXiv:1107.2048; Fox, Harnek, Kopp, Tsai, arXiv:1103.0240
Parameterize χ interaction with relevant SM fermion
through dim–6 operator; e.g. for hadron colliders:
Leff = Gχ χ̄Γχ χq̄Γq q
Introduction to WIMPs – p. 30/59
“Model-independent” approach
Goodman et al., arXiv:1005.1286 and 1008.1783; Bai, Fox, Harnik, arXiv:1005.3797; Wang,
Li, Shao, Zhang, arXiv:1107.2048; Fox, Harnek, Kopp, Tsai, arXiv:1103.0240
Parameterize χ interaction with relevant SM fermion
through dim–6 operator; e.g. for hadron colliders:
Leff = Gχ χ̄Γχ χq̄Γq q
χ Majorana =⇒ Γχ ∈ {1, γ5 , γµ γ5 }
Γq ∈ {1, γ5 , γµ , γµ γ5 }
If Γχ , Γq ∈ {1, γ5 } : Gχ = mq /(2M∗3 ) (chirality violating!), else
Γχ = 1/(2M∗2 ) Rajamaran, Shepherd, Tait, Wijango, arXiv:1108.1196.
Introduction to WIMPs – p. 30/59
“Model-independent” approach
Goodman et al., arXiv:1005.1286 and 1008.1783; Bai, Fox, Harnik, arXiv:1005.3797; Wang,
Li, Shao, Zhang, arXiv:1107.2048; Fox, Harnek, Kopp, Tsai, arXiv:1103.0240
Parameterize χ interaction with relevant SM fermion
through dim–6 operator; e.g. for hadron colliders:
Leff = Gχ χ̄Γχ χq̄Γq q
χ Majorana =⇒ Γχ ∈ {1, γ5 , γµ γ5 }
Γq ∈ {1, γ5 , γµ , γµ γ5 }
If Γχ , Γq ∈ {1, γ5 } : Gχ = mq /(2M∗3 ) (chirality violating!), else
Γχ = 1/(2M∗2 ) Rajamaran, Shepherd, Tait, Wijango, arXiv:1108.1196.
Compute monojet signal from q q̄ → χχg , compare with
monojet limits (current bound) and background (ultimate
reach)!
Introduction to WIMPs – p. 30/59
Γχ = γµ γ5 (corr. to spin-dep. interact.)
Introduction to WIMPs – p. 31/59
Γχ = 1 (corr. to spin-indep. interact.)
Introduction to WIMPs – p. 32/59
Remarks
For Γχ = 1 (spin-indep. interact.): Current bound poor;
ultimate LHC reach interesting only for mχ ≤ 5 GeV.
Introduction to WIMPs – p. 33/59
Remarks
For Γχ = 1 (spin-indep. interact.): Current bound poor;
ultimate LHC reach interesting only for mχ ≤ 5 GeV.
For Γχ = γµ γ5 (spin-dep. interact.): LHC bound better
than (comparable to) direct search limit for mχ ≤ (≥) 20
GeV; future reach factor 103 better, if no other BSM
source of missing ET exists.
Introduction to WIMPs – p. 33/59
Remarks
For Γχ = 1 (spin-indep. interact.): Current bound poor;
ultimate LHC reach interesting only for mχ ≤ 5 GeV.
For Γχ = γµ γ5 (spin-dep. interact.): LHC bound better
than (comparable to) direct search limit for mχ ≤ (≥) 20
GeV; future reach factor 103 better, if no other BSM
source of missing ET exists.
Γχ = γ5 similar to first case; cannot be probed in direct
WIMP detection (rate ∝ vχ2 )
Introduction to WIMPs – p. 33/59
Remarks
For Γχ = 1 (spin-indep. interact.): Current bound poor;
ultimate LHC reach interesting only for mχ ≤ 5 GeV.
For Γχ = γµ γ5 (spin-dep. interact.): LHC bound better
than (comparable to) direct search limit for mχ ≤ (≥) 20
GeV; future reach factor 103 better, if no other BSM
source of missing ET exists.
Γχ = γ5 similar to first case; cannot be probed in direct
WIMP detection (rate ∝ vχ2 )
Bound does not hold if mass of mediator particle
≤ max(mχ , E
/ T )!
Introduction to WIMPs – p. 33/59
Remarks
For Γχ = 1 (spin-indep. interact.): Current bound poor;
ultimate LHC reach interesting only for mχ ≤ 5 GeV.
For Γχ = γµ γ5 (spin-dep. interact.): LHC bound better
than (comparable to) direct search limit for mχ ≤ (≥) 20
GeV; future reach factor 103 better, if no other BSM
source of missing ET exists.
Γχ = γ5 similar to first case; cannot be probed in direct
WIMP detection (rate ∝ vχ2 )
Bound does not hold if mass of mediator particle
≤ max(mχ , E
/ T )!
Altogether: very limited usefulness for most actual WIMP
models.
Introduction to WIMPs – p. 33/59
2 DM and Light (Gauge) Bosons
(At least) 3 kinds of WIMP models require light (m ≤ few
GeV) (gauge) bosons U :
MeV DM: Suggested as explanation of 511 keV line
(=⇒ slow e+ ) excess from central region of our galaxy
(Boehm et al., astro-ph/0309686). Should have mχ ≤ 10 MeV (γ
constraints)
=⇒ mχ ≤ mU ≤ 200 MeV to mediate χχ → e+ e− ; fixes
gU χχ gU e+ e− /m2U ! (Unless 2mχ ≃ mU .)
Introduction to WIMPs – p. 34/59
2 DM and Light (Gauge) Bosons
(At least) 3 kinds of WIMP models require light (m ≤ few
GeV) (gauge) bosons U :
MeV DM: Suggested as explanation of 511 keV line
(=⇒ slow e+ ) excess from central region of our galaxy
(Boehm et al., astro-ph/0309686). Should have mχ ≤ 10 MeV (γ
constraints)
=⇒ mχ ≤ mU ≤ 200 MeV to mediate χχ → e+ e− ; fixes
gU χχ gU e+ e− /m2U ! (Unless 2mχ ≃ mU .)
PAMELA/FermiLAT inspired TeV DM: Needs light
boson for Sommerfeld enhancement (e.g. Arkani-Hamed et al.,
arXiv:0810.0713(4)) (χχ → U U → 4l is also somewhat less
constrained by γ spectrum than χχ → 2l.)
Introduction to WIMPs – p. 34/59
DAMA/CoGeNT inspired few GeV DM: Needs light
mediator to achieve sufficiently large σχp . (2 different
mediators for isospin violation to evade bounds:
Cline, Frey,
arXiv:1108.1391)
Introduction to WIMPs – p. 35/59
Light Gauge Bosons (cont’d)
In all cases: U couplings to (most) SM particles must be
≪ 1 to evade bounds! (gµ − 2, meson decays, ν cross
sections, APV, . . . ).
Introduction to WIMPs – p. 36/59
Light Gauge Bosons (cont’d)
In all cases: U couplings to (most) SM particles must be
≪ 1 to evade bounds! (gµ − 2, meson decays, ν cross
sections, APV, . . . ).
Possible explanation: kinetic mixing with γ/B boson! Is
1-loop effect =⇒ squared U f f¯ coupling is O(α3 ).
Introduction to WIMPs – p. 36/59
Light Gauge Bosons (cont’d)
In all cases: U couplings to (most) SM particles must be
≪ 1 to evade bounds! (gµ − 2, meson decays, ν cross
sections, APV, . . . ).
Possible explanation: kinetic mixing with γ/B boson! Is
1-loop effect =⇒ squared U f f¯ coupling is O(α3 ).
U χχ coupling may well be large.
Introduction to WIMPs – p. 36/59
Signatures of light gauge bosons
If mU > 2mχ : U → χχ dominant! Is invisible =⇒ need extra
tag, e.g. e+ e− → γU → γ+ nothing.
Introduction to WIMPs – p. 37/59
Signatures of light gauge bosons
If mU > 2mχ : U → χχ dominant! Is invisible =⇒ need extra
tag, e.g. e+ e− → γU → γ+ nothing.
Physics background ∝ s =⇒ lower energy is better!
Borodatchenkova, Choudhury, MD, hep-ph/0510147
Introduction to WIMPs – p. 37/59
Signatures of light gauge bosons
If mU > 2mχ : U → χχ dominant! Is invisible =⇒ need extra
tag, e.g. e+ e− → γU → γ+ nothing.
Physics background ∝ s =⇒ lower energy is better!
Borodatchenkova, Choudhury, MD, hep-ph/0510147
Instrumental backgrounds (not from e+ e− annihilation)
seem large
Introduction to WIMPs – p. 37/59
Sensitivity at B−factories (100 fb− 1)
1
0.01
gχ g e
R
mχ > MU/2
0.0001
max. sensitivity
+ (e e channel)
upper bound
from ge-2
max. sensitivity
(invisible channel)
1e-06
mχ < MU/2
1e-08
0.001
0.01
0.1
MU [GeV]
Red, black: Regions allowed by Ωχ , σ(χχ → e+ e− ).
Introduction to WIMPs – p. 38/59
Signatures of light gauge bosons (cont.d)
If mU < 2mχ : U → ℓ+ ℓ−
Introduction to WIMPs – p. 39/59
Signatures of light gauge bosons (cont.d)
If mU < 2mχ : U → ℓ+ ℓ−
Sufficiently light U can even be produced in fixed–target
experiments: e− N → e− e+ e− N (tridents), with peak in
Me+ e−
Introduction to WIMPs – p. 39/59
Signatures of light gauge bosons (cont.d)
If mU < 2mχ : U → ℓ+ ℓ−
Sufficiently light U can even be produced in fixed–target
experiments: e− N → e− e+ e− N (tridents), with peak in
Me+ e−
First exptl. results from MAMI A1 arXiv:1101.4091 and JLAB
APEX arXiv:1108.2750 Excludes new mass ranges around 200
to 300 MeV for A′ ≡ U kinetically mixed with photon.
Introduction to WIMPs – p. 39/59
Signatures of light gauge bosons (cont.d)
If mU < 2mχ : U → ℓ+ ℓ−
Sufficiently light U can even be produced in fixed–target
experiments: e− N → e− e+ e− N (tridents), with peak in
Me+ e−
First exptl. results from MAMI A1 arXiv:1101.4091 and JLAB
APEX arXiv:1108.2750 Excludes new mass ranges around 200
to 300 MeV for A′ ≡ U kinetically mixed with photon.
Also, KLOE-2 performed search, mostly for φ → U η : no
signal. arXiv:1107.2531
Introduction to WIMPs – p. 39/59
A1 and APEX results
Introduction to WIMPs – p. 40/59
3 SUSY DM and LHC “Inverse Problem”
Saw above: WIMP searches at colliders not promising, if
WIMP is only accessible new particle. Fortunately, in many
cases the WIMP is the lightest of many new particles! True
in SUSY. (Also in Little Higgs.)
Introduction to WIMPs – p. 41/59
3 SUSY DM and LHC “Inverse Problem”
Saw above: WIMP searches at colliders not promising, if
WIMP is only accessible new particle. Fortunately, in many
cases the WIMP is the lightest of many new particles! True
in SUSY. (Also in Little Higgs.)
Recall: Primary motivation for SUSY not related to DM!
Introduction to WIMPs – p. 41/59
3 SUSY DM and LHC “Inverse Problem”
Saw above: WIMP searches at colliders not promising, if
WIMP is only accessible new particle. Fortunately, in many
cases the WIMP is the lightest of many new particles! True
in SUSY. (Also in Little Higgs.)
Recall: Primary motivation for SUSY not related to DM!
2
Stabilizes hierarchy m2Higgs ≪ MPlanck
Introduction to WIMPs – p. 41/59
3 SUSY DM and LHC “Inverse Problem”
Saw above: WIMP searches at colliders not promising, if
WIMP is only accessible new particle. Fortunately, in many
cases the WIMP is the lightest of many new particles! True
in SUSY. (Also in Little Higgs.)
Recall: Primary motivation for SUSY not related to DM!
2
Stabilizes hierarchy m2Higgs ≪ MPlanck
Allows unification of gauge couplings
Introduction to WIMPs – p. 41/59
3 SUSY DM and LHC “Inverse Problem”
Saw above: WIMP searches at colliders not promising, if
WIMP is only accessible new particle. Fortunately, in many
cases the WIMP is the lightest of many new particles! True
in SUSY. (Also in Little Higgs.)
Recall: Primary motivation for SUSY not related to DM!
2
Stabilizes hierarchy m2Higgs ≪ MPlanck
Allows unification of gauge couplings
In scenarios with unified Higgs masses: EWSB requires
sizable hierarchy! (Not in NUHM2.)
Introduction to WIMPs – p. 41/59
3 SUSY DM and LHC “Inverse Problem”
Saw above: WIMP searches at colliders not promising, if
WIMP is only accessible new particle. Fortunately, in many
cases the WIMP is the lightest of many new particles! True
in SUSY. (Also in Little Higgs.)
Recall: Primary motivation for SUSY not related to DM!
2
Stabilizes hierarchy m2Higgs ≪ MPlanck
Allows unification of gauge couplings
In scenarios with unified Higgs masses: EWSB requires
sizable hierarchy! (Not in NUHM2.)
HLS theorem, relation to superstrings: don’t single out weak
scale.
Introduction to WIMPs – p. 41/59
Features of SUSY
Need superpartner for each SM particle: Same rep. of gauge
group, spin differs by 1/2
Introduction to WIMPs – p. 42/59
Features of SUSY
Need superpartner for each SM particle: Same rep. of gauge
group, spin differs by 1/2
Need at least 2 Higgs doublets (anomalies, mt · mb 6= 0)
Introduction to WIMPs – p. 42/59
Features of SUSY
Need superpartner for each SM particle: Same rep. of gauge
group, spin differs by 1/2
Need at least 2 Higgs doublets (anomalies, mt · mb 6= 0)
SUSY implies equal masses for partners =⇒ SUSY must be
broken
Introduction to WIMPs – p. 42/59
Features of SUSY
Need superpartner for each SM particle: Same rep. of gauge
group, spin differs by 1/2
Need at least 2 Higgs doublets (anomalies, mt · mb 6= 0)
SUSY implies equal masses for partners =⇒ SUSY must be
broken
Naturalness: sparticle masses should be at weak scale (strictly
true only for 3rd generation, elw gauginos)
Introduction to WIMPs – p. 42/59
Features of SUSY
Need superpartner for each SM particle: Same rep. of gauge
group, spin differs by 1/2
Need at least 2 Higgs doublets (anomalies, mt · mb 6= 0)
SUSY implies equal masses for partners =⇒ SUSY must be
broken
Naturalness: sparticle masses should be at weak scale (strictly
true only for 3rd generation, elw gauginos)
In simplest, R−parity invariant scenario: lightest superparticle
LSP is stable: satisfies one condition for DM candidate!
Introduction to WIMPs – p. 42/59
SUSY DM candidate: sneutrino ν̃
Disfavored theoretically: not LSP in constrained models
Introduction to WIMPs – p. 43/59
SUSY DM candidate: sneutrino ν̃
Disfavored theoretically: not LSP in constrained models
Excluded experimentally by direct searches
Introduction to WIMPs – p. 43/59
SUSY DM candidate: sneutrino ν̃
Disfavored theoretically: not LSP in constrained models
Excluded experimentally by direct searches
ν̃R can be candidate in extended theories, e.g. with
gauged U (1)B−L at TeV scale
Introduction to WIMPs – p. 43/59
SUSY DM candidate: neutralino χ̃01
f3 , h̃0u , h̃0
Mixture of B̃, W
d
Introduction to WIMPs – p. 44/59
SUSY DM candidate: neutralino χ̃01
f3 , h̃0u , h̃0
Mixture of B̃, W
d
In constrained models: often is lightest sparticle in
visible sector! (Other possibility: lightest stau τ̃1 )
Introduction to WIMPs – p. 44/59
SUSY DM candidate: neutralino χ̃01
f3 , h̃0u , h̃0
Mixture of B̃, W
d
In constrained models: often is lightest sparticle in
visible sector! (Other possibility: lightest stau τ̃1 )
In “most” of parameter space: χ̃01 ≃ B̃ , and predicted
Ωχ̃01 h2 too large! O(1 to 10) rather than O(0.1) in
standard cosmology,
Introduction to WIMPs – p. 44/59
SUSY DM candidate: neutralino χ̃01
f3 , h̃0u , h̃0
Mixture of B̃, W
d
In constrained models: often is lightest sparticle in
visible sector! (Other possibility: lightest stau τ̃1 )
In “most” of parameter space: χ̃01 ≃ B̃ , and predicted
Ωχ̃01 h2 too large! O(1 to 10) rather than O(0.1) in
standard cosmology,
but DM–allowed regions of parameter space do exist
even in constrained models!
Introduction to WIMPs – p. 44/59
Regions with correct Ωχ̃01 h2
Co–annihilation region: mχ̃01 ≃ mτ̃1
Introduction to WIMPs – p. 45/59
Regions with correct Ωχ̃01 h2
Co–annihilation region: mχ̃01 ≃ mτ̃1
Higgs funnel(s): mχ̃01 ≃ mh /2, mA /2
Introduction to WIMPs – p. 45/59
Regions with correct Ωχ̃01 h2
Co–annihilation region: mχ̃01 ≃ mτ̃1
Higgs funnel(s): mχ̃01 ≃ mh /2, mA /2
Well–tempered neutralino: µ − M1 ≤ MZ =⇒ χ̃01 is
B̃ − h̃0 mixture. (Requires mq̃ ≫ mg̃ in cMSSM; can be
arranged “anywhere” in NUHM.)
Introduction to WIMPs – p. 45/59
Regions with correct Ωχ̃01 h2
Co–annihilation region: mχ̃01 ≃ mτ̃1
Higgs funnel(s): mχ̃01 ≃ mh /2, mA /2
Well–tempered neutralino: µ − M1 ≤ MZ =⇒ χ̃01 is
B̃ − h̃0 mixture. (Requires mq̃ ≫ mg̃ in cMSSM; can be
arranged “anywhere” in NUHM.)
Note: DM–allowed region of (m0 , m1/2 ) plane of cMSSM
depends on A0 , tan β !
Introduction to WIMPs – p. 45/59
Impact of LHC searches
Is model dependent: Only probe g̃, q̃ sector so far! Here:
Assume cMSSM for defineteness.
Introduction to WIMPs – p. 46/59
Impact of LHC searches
Is model dependent: Only probe g̃, q̃ sector so far! Here:
Assume cMSSM for defineteness.
Well–tempered neutralino, A−pole need large mq̃ : limits
still fairly weak: mg̃,min increased from ∼ 400 GeV to
∼ 550 GeV
Introduction to WIMPs – p. 46/59
Impact of LHC searches
Is model dependent: Only probe g̃, q̃ sector so far! Here:
Assume cMSSM for defineteness.
Well–tempered neutralino, A−pole need large mq̃ : limits
still fairly weak: mg̃,min increased from ∼ 400 GeV to
∼ 550 GeV
τ̃1 co–annihilation requires mq̃ ≤ mg̃ : good for LHC
searches; still plenty of allowed region left.
Introduction to WIMPs – p. 46/59
Impact of Indirect DM Searches
No halo signal in co–annihilation region; ν from Sun
small
Introduction to WIMPs – p. 47/59
Impact of Indirect DM Searches
No halo signal in co–annihilation region; ν from Sun
small
Signals very small in A−funnel
Introduction to WIMPs – p. 47/59
Impact of Indirect DM Searches
No halo signal in co–annihilation region; ν from Sun
small
Signals very small in A−funnel
Well-tempered neutralino most promising, especially ν
from Sun, but present limits not constraining
Introduction to WIMPs – p. 47/59
Impact of direct WIMP Searches
XENON, CDMS⊕EDELWEISS begin to probe
well–tempered neutralino
Introduction to WIMPs – p. 48/59
Impact of direct WIMP Searches
XENON, CDMS⊕EDELWEISS begin to probe
well–tempered neutralino
Signals in other regions very small
Introduction to WIMPs – p. 48/59
Impact of Future WIMP Discovery at Collider
Generically: could determine:
WIMP mass: Very useful for indirect searches (greatly
reduced “look elsewhere” problem); less so for direct
searches, once mχ ≥ mN
Introduction to WIMPs – p. 49/59
Impact of Future WIMP Discovery at Collider
Generically: could determine:
WIMP mass: Very useful for indirect searches (greatly
reduced “look elsewhere” problem); less so for direct
searches, once mχ ≥ mN
WIMP couplings: Determine cross sections and final
states in indirect searches; determine cross sections in
direct searches
Introduction to WIMPs – p. 49/59
Impact of Future WIMP Discovery at Collider
Generically: could determine:
WIMP mass: Very useful for indirect searches (greatly
reduced “look elsewhere” problem); less so for direct
searches, once mχ ≥ mN
WIMP couplings: Determine cross sections and final
states in indirect searches; determine cross sections in
direct searches
Most interesting to me: Predict Ωχ h2 , compare with
observation: Constrain very early universe!
Introduction to WIMPs – p. 49/59
Fitting SUSY parameters at LHC (“inverse problem”)
Feasibility (resulting errors) very strongly depend on where
we are in parameter space!
Introduction to WIMPs – p. 50/59
Fitting SUSY parameters at LHC (“inverse problem”)
Feasibility (resulting errors) very strongly depend on where
we are in parameter space!
Good: Low sparticle masses, many leptons e, µ in final
states.
Introduction to WIMPs – p. 50/59
Fitting SUSY parameters at LHC (“inverse problem”)
Feasibility (resulting errors) very strongly depend on where
we are in parameter space!
Good: Low sparticle masses, many leptons e, µ in final
states.
Not so good: Large masses, mostly hadronic final
states.
Introduction to WIMPs – p. 50/59
Fitting SUSY parameters at LHC (“inverse problem”)
Feasibility (resulting errors) very strongly depend on where
we are in parameter space!
Good: Low sparticle masses, many leptons e, µ in final
states.
Not so good: Large masses, mostly hadronic final
states.
Two approaches: Case studies, broad scans of parameter
space
Introduction to WIMPs – p. 50/59
Case study: τ̃1 co–annihilation region in cMSSM
Arnowitt et al., arXiv:0802.2968
Needs mτ̃1 − mχ̃01 ≤ 15 GeV
±
→
τ̃
=⇒ χ̃02 → τ̃1 τ, χ̃±
1 ντ have nearly unit branching
1
ratio
=⇒ no di–lepton edges!
Introduction to WIMPs – p. 51/59
Case study: τ̃1 co–annihilation region in cMSSM
Arnowitt et al., arXiv:0802.2968
Needs mτ̃1 − mχ̃01 ≤ 15 GeV
±
→
τ̃
=⇒ χ̃02 → τ̃1 τ, χ̃±
1 ντ have nearly unit branching
1
ratio
=⇒ no di–lepton edges!
τ̃1 → χ̃01 τ gives rather soft τ : Difficult to detect!
Introduction to WIMPs – p. 51/59
Case study: τ̃1 co–annihilation region in cMSSM
Arnowitt et al., arXiv:0802.2968
Needs mτ̃1 − mχ̃01 ≤ 15 GeV
±
→
τ̃
=⇒ χ̃02 → τ̃1 τ, χ̃±
1 ντ have nearly unit branching
1
ratio
=⇒ no di–lepton edges!
τ̃1 → χ̃01 τ gives rather soft τ : Difficult to detect!
Study three classes of final states:
(i) 2τ + 2j + E
/T
(ii)4 non − b j + E
/T
(iii) leading b + 3j + E
/T
Introduction to WIMPs – p. 51/59
Case study: τ̃1 co–annihilation region in cMSSM
Arnowitt et al., arXiv:0802.2968
Needs mτ̃1 − mχ̃01 ≤ 15 GeV
±
→
τ̃
=⇒ χ̃02 → τ̃1 τ, χ̃±
1 ντ have nearly unit branching
1
ratio
=⇒ no di–lepton edges!
τ̃1 → χ̃01 τ gives rather soft τ : Difficult to detect!
Study three classes of final states:
(i) 2τ + 2j + E
/T
(ii)4 non − b j + E
/T
(iii) leading b + 3j + E
/T
Fit many kinematical distributions simultaneously,
including slope of softer pτT spectrum in sample (i) =⇒
predict Ωχ̃01 h2 to 10%!
Introduction to WIMPs – p. 51/59
Result of fit
0.12
1
χ
Ω ~ 0h
2
0.11
0.1
0.09
0.08
8
9
10
11
∆M (GeV)
12
13
Introduction to WIMPs – p. 52/59
Result of fit
0.12
1
χ
Ω ~ 0h
2
0.11
0.1
0.09
0.08
8
9
10
11
∆M (GeV)
12
13
Unfortunately, chosen benchmark point (mg̃ = 830 GeV,
mq̃ ≃ 750 GeV) is most likely excluded!
Introduction to WIMPs – p. 52/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Introduction to WIMPs – p. 53/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Fix mA = 850 GeV, A3 = 800 GeV
Introduction to WIMPs – p. 53/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Fix mA = 850 GeV, A3 = 800 GeV
Randomly choose mq̃,g̃ ∈ [600, 1000] GeV,
other masses ∈ [100, 1000] GeV, tan β ∈ [2, 50]
Introduction to WIMPs – p. 53/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Fix mA = 850 GeV, A3 = 800 GeV
Randomly choose mq̃,g̃ ∈ [600, 1000] GeV,
other masses ∈ [100, 1000] GeV, tan β ∈ [2, 50]
Consider 1808 observables, both counting rates and binned
distributions
Introduction to WIMPs – p. 53/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Fix mA = 850 GeV, A3 = 800 GeV
Randomly choose mq̃,g̃ ∈ [600, 1000] GeV,
other masses ∈ [100, 1000] GeV, tan β ∈ [2, 50]
Consider 1808 observables, both counting rates and binned
distributions
Introduce “χ2 −like” variable
2
nsig A
B
X
si − si
1
2
(∆SAB ) =
AB
nsig
σ
i
i=1
Only “significant” signatures included
Introduction to WIMPs – p. 53/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Fix mA = 850 GeV, A3 = 800 GeV
Randomly choose mq̃,g̃ ∈ [600, 1000] GeV,
other masses ∈ [100, 1000] GeV, tan β ∈ [2, 50]
Consider 1808 observables, both counting rates and binned
distributions
Introduce “χ2 −like” variable
2
nsig A
B
X
si − si
1
2
(∆SAB ) =
AB
nsig
σ
i
i=1
Only “significant” signatures included
Allow 1% syst. error (15% on total signal rate), 10 fb−1 of
14 TeV data, no background
Introduction to WIMPs – p. 53/59
Scan of Parameter Space
Arkani-Hamed et al., hep-ph/0512190
15 parameter description of weak–scale MSSM
Fix mA = 850 GeV, A3 = 800 GeV
Randomly choose mq̃,g̃ ∈ [600, 1000] GeV,
other masses ∈ [100, 1000] GeV, tan β ∈ [2, 50]
Consider 1808 observables, both counting rates and binned
distributions
Introduce “χ2 −like” variable
2
nsig A
B
X
si − si
1
2
(∆SAB ) =
AB
nsig
σ
i
i=1
Only “significant” signatures included
Allow 1% syst. error (15% on total signal rate), 10 fb−1 of
14 TeV data, no background
MC: (∆SAB )2 > 0.285 =⇒ models differ at > 95% c.l.
Introduction to WIMPs – p. 53/59
Results and Remarks
Found 283 degenerate pairs, with (δSAB )2 < 0.285, for
43,026 “models” (i.e., sets of parameters)
Introduction to WIMPs – p. 54/59
Results and Remarks
Found 283 degenerate pairs, with (δSAB )2 < 0.285, for
43,026 “models” (i.e., sets of parameters)
Note
Their observables are correlated
=⇒ (δSAB )2 is no true χ2
=⇒ need MC to intepret it, from comparing runs with
different random no. seed: is this reliable estimator for
comparing different parameter sets?
Introduction to WIMPs – p. 54/59
Results and Remarks
Found 283 degenerate pairs, with (δSAB )2 < 0.285, for
43,026 “models” (i.e., sets of parameters)
Note
Their observables are correlated
=⇒ (δSAB )2 is no true χ2
=⇒ need MC to intepret it, from comparing runs with
different random no. seed: is this reliable estimator for
comparing different parameter sets?
Statistics looks weird! Comparing two simulations of
same “model”, get 611 (out of 2600) cases where some
2ℓ observable has > 5σ discrepancy: way too many!
Introduction to WIMPs – p. 54/59
Simpler approach
Bornhauser and MD, in progress
Define 12 disjunct event classes, depending on no.,
charge, flavor of leptons
Introduction to WIMPs – p. 55/59
Simpler approach
Bornhauser and MD, in progress
Define 12 disjunct event classes, depending on no.,
charge, flavor of leptons
Consider 7 mostly uncorrelated observables for each
class: No. of events; hnτ ± i; hnb i; hnj i; hn2j i; hHT i
Introduction to WIMPs – p. 55/59
Simpler approach
Bornhauser and MD, in progress
Define 12 disjunct event classes, depending on no.,
charge, flavor of leptons
Consider 7 mostly uncorrelated observables for each
class: No. of events; hnτ ± i; hnb i; hnj i; hn2j i; hHT i
Define proper χ2 , incl. corr. between hnj i, hn2j i, only
including significant observables: test with MC.
Introduction to WIMPs – p. 55/59
Results of simpler approach
W/o syst. error: only one of 283 “degenerate” pairs has
p > 0.05, and two parameter sets really are very similar!
(Except for heavy sleptons.)
Introduction to WIMPs – p. 56/59
Results of simpler approach
W/o syst. error: only one of 283 “degenerate” pairs has
p > 0.05, and two parameter sets really are very similar!
(Except for heavy sleptons.)
Introducing syst. errors as Arkani-Hamed et al.: 41 out
of 283 pairs have p > 0.05; still are pretty similar
physically
Introduction to WIMPs – p. 56/59
Results of simpler approach
W/o syst. error: only one of 283 “degenerate” pairs has
p > 0.05, and two parameter sets really are very similar!
(Except for heavy sleptons.)
Introducing syst. errors as Arkani-Hamed et al.: 41 out
of 283 pairs have p > 0.05; still are pretty similar
physically
Introducing SM background, but no syst. error: 12 pairs
have p > 0.05
Introduction to WIMPs – p. 56/59
Results of simpler approach
W/o syst. error: only one of 283 “degenerate” pairs has
p > 0.05, and two parameter sets really are very similar!
(Except for heavy sleptons.)
Introducing syst. errors as Arkani-Hamed et al.: 41 out
of 283 pairs have p > 0.05; still are pretty similar
physically
Introducing SM background, but no syst. error: 12 pairs
have p > 0.05
With systematic errors and background: 71 pairs have
p > 0.05.
Introduction to WIMPs – p. 56/59
4 Impact of Higgs Searches
In many WIMP models, Higgs exch. dominates χp
scattering, in which case σχp ∝ 1/m4H : crucial to know
Higgs mass!
Introduction to WIMPs – p. 57/59
4 Impact of Higgs Searches
In many WIMP models, Higgs exch. dominates χp
scattering, in which case σχp ∝ 1/m4H : crucial to know
Higgs mass!
In SUSY at large tan β : σχ̃01 p ∝ tan2 β/m4A : need info on
heavy Higgses!
Introduction to WIMPs – p. 57/59
4 Impact of Higgs Searches
In many WIMP models, Higgs exch. dominates χp
scattering, in which case σχp ∝ 1/m4H : crucial to know
Higgs mass!
In SUSY at large tan β : σχ̃01 p ∝ tan2 β/m4A : need info on
heavy Higgses!
TeVatron and CMS searches for H, A → τ + τ −
significantly increase lower bound on DM–allowed mχ̃01
in general MSSM (Aborno Vasquez, Belanger, Boehm, arXiv:1108.1338);
exclude scenarios with very large σχ̃01 p .
Introduction to WIMPs – p. 57/59
4 Impact of Higgs Searches
In many WIMP models, Higgs exch. dominates χp
scattering, in which case σχp ∝ 1/m4H : crucial to know
Higgs mass!
In SUSY at large tan β : σχ̃01 p ∝ tan2 β/m4A : need info on
heavy Higgses!
TeVatron and CMS searches for H, A → τ + τ −
significantly increase lower bound on DM–allowed mχ̃01
in general MSSM (Aborno Vasquez, Belanger, Boehm, arXiv:1108.1338);
exclude scenarios with very large σχ̃01 p .
Higgs searches can also be used to distinguish
between WIMP models and to help determine
parameters. E.g. mh in MSSM constrains stop sector.
Introduction to WIMPs – p. 57/59
Summary 1
Rumours of the direct detection of WIMPs are greatly
exaggerated
Introduction to WIMPs – p. 58/59
Summary 1
Rumours of the direct detection of WIMPs are greatly
exaggerated
“Asymmetric Dark Matter” doesn’t explain
ΩDM ≃ 5Ωbaryon
Introduction to WIMPs – p. 58/59
Summary 2
Well–motivated WIMP models can be tested at
colliders!
Introduction to WIMPs – p. 59/59
Summary 2
Well–motivated WIMP models can be tested at
colliders!
Scenarios with new light gauge bosons with
suppressed couplings to SM fermions are now being
probed at low−E colliders, fixed–target expts.
Introduction to WIMPs – p. 59/59
Summary 2
Well–motivated WIMP models can be tested at
colliders!
Scenarios with new light gauge bosons with
suppressed couplings to SM fermions are now being
probed at low−E colliders, fixed–target expts.
LHC not very good for “model–independent” WIMP
search. (Signal is O(α2 αS ), background is O(ααS ).)
Introduction to WIMPs – p. 59/59
Summary 2
Well–motivated WIMP models can be tested at
colliders!
Scenarios with new light gauge bosons with
suppressed couplings to SM fermions are now being
probed at low−E colliders, fixed–target expts.
LHC not very good for “model–independent” WIMP
search. (Signal is O(α2 αS ), background is O(ααS ).)
If WIMP signal is found at LHC, LHC experiments will
be better at extracting parameters than indicated by
theory analyses that have been published so far; many
avenues remain to be explored.
Introduction to WIMPs – p. 59/59
Summary 2
Well–motivated WIMP models can be tested at
colliders!
Scenarios with new light gauge bosons with
suppressed couplings to SM fermions are now being
probed at low−E colliders, fixed–target expts.
LHC not very good for “model–independent” WIMP
search. (Signal is O(α2 αS ), background is O(ααS ).)
If WIMP signal is found at LHC, LHC experiments will
be better at extracting parameters than indicated by
theory analyses that have been published so far; many
avenues remain to be explored.
Higgs sector also very important for WIMP physics!
Introduction to WIMPs – p. 59/59