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Supersymmetric Dark Matter. Stefano Scopel. PPC2010, Torino, 12 July 2010. Outline. Dark Matter & susy in a nutshell examples of susy scenarios The low mass WIMP conspiracy: DAMA, CDMS2 and CoGeNT the XENON100 exclusion plot light neutralinos in the MSSM. Ω dark matter ~ 0.22.

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Supersymmetric Dark Matter

Stefano Scopel

PPC2010, Torino, 12 July 2010


  • Dark Matter & susy in a nutshell

  • examples of susy scenarios

  • The low mass WIMP conspiracy: DAMA, CDMS2 and CoGeNT

  • the XENON100 exclusion plot

  • light neutralinos in the MSSM

Ωdark matter~ 0.22

Evidence for Dark Matter

  • Spiral galaxies

    • rotation curves

  • Clusters & Superclusters

    • Weak gravitational lensing

    • Strong gravitational lensing

    • Galaxy velocities

    • X rays

  • Large scale structure

    • Structure formation

  • CMB anisotropy: WMAP

    • Ωtot=1

    • Ωdark energy~0.7

    • Ωmatter~ 0.27

    • Ωbaryons~0.05

    • Ωvisible~0.005

Incomplete list of dm candidates
(Incomplete) List of DM candidates

  • Neutrinos

  • Axions

  • Lightest Supersymmetric particle (LSP) – neutralino, sneutrino, axino

  • Lighest Kaluza-Klein Particle (LKP)

  • Heavy photon in Little Higgs Models

  • Solitons (Q-balls, B-balls)

  • Black Hole remnants

  • Hidden-sector tecnipions

  • BEC/scalar field

BEC/scalar field




thermal cosmological density of a WIMP X

ΩXh2 ~ 1/<σannv>int


T0=present (CMB) temperature


Tf=freeze-out temperature

Xf>>1, X non relativistic at decoupling, low temp expansion for <σannv>: <σannv>~a+b/x

if σann is given by weak-type interactions → ΩX~0.1-1

…+ cohannihilations with other particle(s)

close in mass + resonant annihilations

today’s entropy

critical density

freeze-out temperature

# of degrees of freedom

m = WIMP mass

Y0 : from Boltzmann equation

N.B. Very different scales conjure up to lead to the weak scale!

CMB temp.

Hubble par.

Planck scale

the WIMP “miracle”

Hierarchy scale!problem of the Standar Model:

Higgs mass expected to be below a few TeV (on general grounds, perturbativity of the theory)

radiative corrections to the Higgs boson:

δmH2~λ2, where λ is the scale beyond which the low-energy theory no longer applies (λ=cut-off of the SM)

a huge cancellation needed unless λ~TeV itself

The bottom line scale!

  • new physics at the electro-weak scale is cool because it kills two birds with one stone:

  • solves the hierarchy problem

  • explains the Dark Matter

most popular thermal WIMP candidates from particle physics scale!(solve hierarchy problem: MW/MPl~ 10-16)

DM candidate

conserved symmetry


  • susy


χ (neutralino)

  • extra dimensions


B(1)(KK photon)

  • little Higgs


BH (heavy photon)

all thermal candidates, massive, with weak-type interactions (WIMPs)

the most popular

Why scale!susy is so appealing:

  • suggested by string theory

  • renormalizable

  • solves the hierarchy problem (why mW<<mplanck)

  • compatible to GUT unification of gauge couplings

  • provides a DM candidate (if R-parity is introduced to prevent nucleon decay so that the LSP is stable)

dangerous, don’t want it! scale!

WIMP signal at accelerators: missing energy+new particles produced in pairs

the sneutrino scale!

[Arina, Fornengo, JHEP0711(2007)029

the sneutrino scale!

allowed due to rescaling

[Arina, Fornengo, JHEP0711(2007)029

mixing with a right-handed component makes thing easier scale!


[Arina, Fornengo, JHEP0711(2007)029

mixing with a right-handed component makes thing easier scale!

relic abundance

direct detection

  • low see-saw scale M=1 TeV needed

  • inelastic scattering in direct detection!


[Arina, Fornengo, JHEP0711(2007)029

The neutralino
The neutralino scale!





  • The neutralino is defined as the lowest-mass linear superposition of bino B, wino W(3)and the two higgsino states H10, H20 :



  • neutral, colourless, only weak-type interactions

  • stable if R-parity is conserved, thermal relic

  • non relativistic at decoupling  Cold Dark Matter (required by CMB data + structure formation models)

  • relic density can be compatible with cosmologicalobservations:0.095 ≤Ωχh2 ≤ 0.131


stau coannihilation scale!

Higgs funnel

focus point

[Feng, Machev, Moroi, Wilczek]


(a.k.a. CMSSM)

[Ellis, Olive, Santoso, Spanos, 1001.3651]

  • only few regions cosmologically allowed

  • variants (e.g. non-universality of soft masses at the GUT scale or lower unification scale) that increase Higgsino content of the neutralino→ lower relic abundance and higher signals

neutralino density tends to be too large

is the WIMP “miracle” failing?

…but two main classes: scale!

  • fermion diagrams: mf/MWhelicity suppression due to Majorana nature of neutralino

  • Gauge boson diagrams: suppressed if neutralino~Bino (this is usually the case when Radiative ElectroWeak Symmetry Breaking is implemented, |μ|>>M1,M2)

the scale!WIMP paradigm is fine but the devil is in the details!

The Next-to-Minimal MSSM (NMSSM) scale!

2 Higgs (CP-even, CP-odd)


1 neutralino dof

solves the μproblem, i.e. why μ~MEW


Higgs soft terms in the NMSSM:

NMSSM particle content:

The lightest neutralino:

CP-even Higgs:

Relic density and direct detection rate in NMSSM scale!

[Cerdeño, Hugonie, López-Fogliani, Muñoz, Teixeira]

relic abundance

direct detection

Landau pole


χ,H lighter χ singlino





unphysical minima

M1=160 GeV, M2=320, Aλ=400 GeV, Ak=-200 GeV, μ=130 GeV, tan β=5

(sizeable direct detection)

  • very light neutral Higgs (mainly singlet)

  • light scalars imply more decay channels and resonant decays

  • neutralino relatively light (< decay thresholds) and mostly singlino

  • high direct detection cross sections (even better for lower M1)

Effective MSSM: scale! effective model at the EW scale with a few MSSM parameters which set the most relevant scales


  • M1 U(1)gaugino soft breaking term

  • M2 SU(2) gaugino soft breaking term

  • μHiggs mixing mass parameter

  • tan βratio of two Higgs v.e.v.’s

  • mA mass of CP odd neutral Higgs boson (the extended Higgs sector of MSSM includes also the neutral scalars h, H, and the charged scalars H±)

  • mqsoft mass common to all squarks

  • mlsoft mass common to all sleptons

  • A common dimensionless trilinear parameter for the third family (Ab = At ≡ Amq; Aτ≡ Aml)

  • R ≡M1/M2








Cosmological lower bound on scale!mχ

A. Bottino, F. Donato, N. Fornengo, S. Scopel, Phys. Rev. D 68, 043506 (2003)

scatter plot:

full calculation

upper bound on ΩCDMh2

curve: analytical

approximation for

minimal ΩCDMh2

Color code: scale!

● Ωχh2 < 0.095

Ωχh2 > 0.095

Neutralino – nucleon cross section

The elastic cross section is bounded from below:

 “funnel” at low mass

A. Bottino, N. Fornengo, S. Scopel ; Phys.Rev.D67:063519,2003 ; A. Bottino, F. Donato, N. Fornengo, S. Scopel, PRD69:037302,2004

The field of Dark Matter searches has been quite active recently…

  • CDMS2 (December 2009)

  • DAMA/Libra (February 2010)

  • CoGeNT (February 2010)

  • XENON100 ( May 2010)

The DAMA/Libra annual modulation result recently…

  • two further annual cycles collected, the first with the same setup of previous data, the second after detector upgrade in 2008

  • corresponds to a further exposure of 0.34 ton year

  • combining DAMA/NaI and DAMA/Libra a total of 13 annual cycles collected (7 DAMA/NaI+6 DAMA/Libra) corresponding to 1.17 ton year

  • 8.9 σC.L. effect

Bernabei at al., arXiv:1002.1028

6 years of DAMA/Libra (0.87 ton year) recently…

Bernabei at al., arXiv:1002.1028

DAMA recently…WIMP interpretation and other direct searches

small viable window with MWIMP≲ 10

From Savage et al., arXiv:0901.2713

The CDMS2 result recently…

14 Ge detectors (out of a total of 30 detectors, 19 Ge and 11 Si)

After the timing cut (to remove “surface events”)

Efficiency of the cut~25% close to threshold

Resulting exposure~194.1 kg-day

When signal region is unblinded2 events survived

Z. Ahmed at al., arXiv:0912.3592

~23% probability that the 2 events are just background

Final comment from J. Cooly’s talk @ SLAC, 17 December 2009:

Z. Ahmed at al., arXiv:0912.3592

The 2 CDMS events recently…and light relic neutralinos

effMSSM including uncertainty on hadronic matrix elements

DAMA no channeling

DAMA channeling

Scatter plot: reference value for hadronic matrix elements

90% C.L. interval for 2 observed events:


x 0.098<Ωχh2<0.122


Bottino, Donato, Fornengo, Scopel, PRD81 107302(2010), arXiv:0912.4025

The 2 CDMS events recently…and light relic neutralinos

effMSSM including uncertainty on hadronic matrix elements

DAMA no channeling

DAMA channeling

Scatter plot: reference value for hadronic matrix elements

95% C.L. interval using spectral info (maximum likelihood method, no background)

x 0.098<Ωχh2<0.122


Bottino, Donato, Fornengo, Scopel, PRD81 107302(2010), arXiv:0912.4025

The 2 CDMS events recently…and light relic neutralinos

effMSSM including uncertainty on hadronic matrix elements

DAMA no channeling

DAMA channeling

Scatter plot: reference value for hadronic matrix elements

85% C.L. interval using spectral info (maximum likelihood method, background included)

x 0.098<Ωχh2<0.122


Bottino, Donato, Fornengo, Scopel, PRD81 107302(2010), arXiv:0912.4025

The recently…CoGeNT experiment

Germanium ionization detector with new geometry (P-type point contact, PPC)

standard coaxial geometry

P-type Point Contact (PPC)

Reduction of electronic noise

Surface event rejection using rise-time cuts

→ very low threshold<400 eV

The new recently…CoGeNT result (C.E. Aalseth et al., 1002.4703)

fit of the observed count rate using 28 bins and 3 components:

  • L/K shell electron-capture peaks from 71Ge (1 parameter)

  • Exponentially decaying background (2 parameters, amplitude and exponent)

  • Free constant background (1 parameter)

  • DM component (2 parameters)

  • For 7 GeV < mWIMP<11 GeV the chi square probability drops < 10% if the DM component is zero

  • → need additional exponential, WIMP signal indication?

The new recently…CoGeNT result (C.E. Aalseth et al., 1002.4703)

The XENON10 limit recently…

  • nowadays widely considered the most competitive Dark Matter Search experiment

  • dual-phase Xenon allows to measure ionization and scintillation at the same time

Anticorrelation between the prompt scintillation in the liquid and the proportional scintillation in the gas (the latter produced by the charges produced in ionization and taken out by electric field). The sum of ionization and scintillation is proportional to the total deposited energy

Discrimination between background ( recently…β and γ) and recoils+neutrons

←for a gamma source S2/S1 is larger

←for a neutron source S2/S1 is smaller

J. Angle et al., Phys. Rev. Lett. 100 (2008) 021303, arXiv: 0706.0039.

MAY 2010: the first XENON100 result (1005.0380): recently…

N.B.: the XENON100 limit is slightly less constraining than the XENON10 one

Two major limitations: nuclear recoils

The response in the detector is not homogeneous (ionization strongly depends on the position due to different reflection at the liquid-gas surface, impurities, charge recombination, local electric field). However position information is available event by event (89 photomultipliers + vertical drift timing info), so the response can be mapped using internal neutron-activated 131Xe (emitting 164 keV gammas) and 129Xe (emitting 236 keV gammas)

This map, along with a Monte Carlo, is used to renormalize the events.

However no direct map is available at energies below 164 keV. What happens @ 4 keV?

Aprile et al., arXiv:1001.2834

Energy calibration only available at 122 nuclear recoils keV and 662 kev (the characteristic X-ray peak @ 30 keV from 57Co is barely visible at the edge of the sensitive volume)

The energy scale at lower energy is extrapolated from 122 kev to 4 kev assuming a linear response. However between 122 keV and 662 keV the response is already non linear (the light yield is 2.2 p.e./kev @662 keV and 3.1 p.e./keV @122 keV).

Comparison with other experiments nuclear recoils

CDMS and Edelweiss calibration:

Neutrons from 252Cf source activate 71Ge that decays to 71Ga (T1/2~16 days) producing a peak at 10.4 keV

Additional calibration points: 133Ba (γ lines at 303, 356 and 384 keV)

DAMA calibration:

the 3.2 keV peak from 40K provides the lowest-energy calibration point

Am241 nuclear recoils calibration in KIMS

Am calibration

-> ~5 p.e /keV

13.9keV Np L X-ray

17.8keV Np L X-ray

20.8keV Np L X-ray

26.35keV gamma

Cs, I X –ray escape

59.54 gamma

Relative intensity.....


S. C. Kim’s talk, KIMS Coll. , Yongpyong, February 2010

People in XENON are aware of the problem and plan to use a lower calibration point

from E. Aprile’s talk, SJTU workshop, june 2009

In short: for the time being, the 4 keV threshold and the linear response of XENON10(0) rely on an extrapolation at the energies where the WIMP signal is expected

This was supposed to be the “easy” part (gammas calibration).

What about nuclear recoils?

The efficiency factor (quenching) of xenon calibration).

  • Defined as the scintillation yield of nuclear recoils relative to that of 122-keV γ rays

  • Crucial in determining the energy scale of WIMP recoils starting from the gamma calibration

From: Aprile et al., PRC79,045807(2009)

directly measured using a fixed-energy neutron flux

The XENON10 efficiency factor saga calibration).

  • in the 2007 paper (arXiv:0706.0039) the XENON10 limit widely used in the literature was derived assuming a constant Leff=0.19

  • in 2008 a part of the Collaboration measured again the efficiency, finding a lower value, depending on the energy. The exclusion plot weakened accordingly.

Aprile et al., PRC79,045807(2009)


  • in 2009 another (smaller) part of the Collaboration repeated the measurement, finding an even lower value of Leff:

Manzur et al., arXiv: 0909.1063



N.B. larger effect (~1 order of magnitude) at low WIMP masses. Large error bars, the limit corrected using the central value of Leff. What is the conservative exclusion plot?

For the moment it would be safe to take XENON10 calibration). n with a grain of salt, although improvements are likely in the future

Conclusions calibration).

  • susy still the most popular solution to the dark matter problem (soon checked @ LHC? see next talk by A. Polesello)

  • several scenarios on the market: SUGRA, NMSSM, Light Neutralinos,…

  • The low-mass WIMP connection: DAMA/Libra, CDMS 2, Cogent

  • XENON100 claims to exclude these effects but for the moment take it with a grain of salt


light WIMPs (~10 GeV) are fashionable these days. First dicussed in connection to experimental results as early as 2003 (Bottino et al., Phys.Rev.D67:063519,2003 ; PRD69:037302,2004)