Stefano Scopel

Supersymmetric Dark Matter

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

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

Ωdark matter~ 0.22

(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

Over-constrained scenario: the concordance model

thermal cosmological density of a WIMP X

ΩXh2 ~ 1/<σannv>int

<σannv>int=∫<σannv>dxxf

x0

xf=M/Tf

x0=M/T0

Tf=freeze-out temperature

T0=present (CMB) 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 massY0 : 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 problem of the Standar Model:

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

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

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

1. solves the hierarchy problem 2. explains the Dark Matter

The bottom line

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

•susy

conserved symmetry

DM candidate

R-parity

K-parity

T-parity

χ (neutralino)

•extra dimensions

•little Higgs

B(1)(KK photon)

BH (heavy photon)

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

*

the most popular

• 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)

Why susy is so appealing:

GUT unification of gauge couplings

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

dangerous, don’t want it!

the sneutrino

[Arina, Fornengo, JHEP0711(2007)029

[Arina, Fornengo, JHEP0711(2007)029

the sneutrino

allowed due to rescaling

[Arina, Fornengo, JHEP0711(2007)029

mixing with a right-handed component makes thing easier

2

mixing with a right-handed component makes thing easier

•low see-saw scale M=1 TeV needed•inelastic scattering in direct detection!

[Arina, Fornengo, JHEP0711(2007)029

relic abundance direct detection

Z

The neutralinoThe neutralino is defined as the lowest-

mass linear superposition of bino B, wino W(3) and the two higgsino states H1

0, H20 :

021

011

)3(21

~~~~ HaHaWaBa

neutral, colourless, only weak-type interactions

stable if R-parity is conserved, thermal relicnon relativistic at decoupling Cold Dark

Matter (required by CMB data + structure formation models)

relic density can be compatible with cosmological observations: 0.095 ≤ Ωχh2 ≤ 0.131

IDEAL CANDIDATE FOR COLD DARK MATTER

~ ~~ ~

3 4

SUGRA(a.k.a. CMSSM)

focus point

[Feng, Machev, Moroi, Wilczek]

stau coannihilation Higgs funnel

[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?

Many contributions to neutralino annihilation…

…but two main classes:

• fermion diagrams: mf/MW helicity 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 WIMP paradigm is fine but the devil is in the details!

The Next-to-Minimal MSSM (NMSSM)

solves the μ problem, i.e. why μ~MEW

superpotential:

Higgs soft terms in the NMSSM:

NMSSM particle content: MSSM+ 2 Higgs (CP-even, CP-odd)1 neutralino dof

The lightest neutralino:

CP-even Higgs:

Relic density and direct detection rate in NMSSM[Cerdeño, Hugonie, López-Fogliani, Muñoz, Teixeira]

relic abundance direct detection

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)

tachyons

Landau pole

unphysical minima

W

H1

H2/2

χ,H lighter

χ singlino

Z

Effective MSSM: 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

• μ Higgs mixing mass parameter

• tan β ratio 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±)

• mq soft mass common to all squarks

• ml soft mass common to all sleptons

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

• R ≡ M1/M2

~

~

~

~

~

~

~

SUGRAR=0.5

Cosmological lower bound on mχ

upper bound on ΩCDMh2

scatter plot: full calculation

curve: analytical approximation forminimal ΩCDMh2

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

The elastic cross section is bounded from below:

“funnel” at low mass

Neutralino – nucleon cross sectionColor code:● Ωχh2 < 0.095 Ωχh2 > 0.095

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)

• 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 σ C.L. effect

Bernabei at al., arXiv:1002.1028

The DAMA/Libra annual modulation result

6 years of DAMA/Libra (0.87 ton year)

Bernabei at al., arXiv:1002.1028

DAMA WIMP interpretation and other direct searches

From Savage et al., arXiv:0901.2713

small viable window with MWIMP 10≲

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

Z. Ahmed at al., arXiv:0912.3592

When signal region is unblinded2 events survived

Resulting exposure~194.1 kg-day

The CDMS2 result

Background estimation due to surface “leakage” :•before unblinding: 0.6±0.1 (stat.)•after unblinding: 0.8±0.1 (stat.) ±0.2 (stat.)

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:

90% C.L. interval for 2 observed events:0.53→5.3

DAMA no channeling

DAMA channeling

effMSSM including uncertainty on hadronic matrix elements

x 0.098<Ωχh2<0.122 • Ωχh2<0.098

Scatter plot: reference value for hadronic matrix elements

The 2 CDMS events and light relic neutralinos

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

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

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

DAMA no channeling

DAMA channeling

effMSSM including uncertainty on hadronic matrix elements

x 0.098<Ωχh2<0.122 • Ωχh2<0.098

Scatter plot: reference value for hadronic matrix elements

The 2 CDMS events and light relic neutralinos

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

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

DAMA no channeling

DAMA channeling

effMSSM including uncertainty on hadronic matrix elements

x 0.098<Ωχh2<0.122 • Ωχh2<0.098

Scatter plot: reference value for hadronic matrix elements

The 2 CDMS events and light relic neutralinos

The CoGeNT experimentGermanium ionization detector with new geometry (P-type point contact, PPC)

standard coaxial geometry P-type Point Contact (PPC)

Reduction of electronic noiseSurface event rejection using rise-time cuts

→ very low threshold<400 eV

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

The XENON10 limit• 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 (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.

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

MAY 2010: the first XENON100 result (1005.0380):

A small threshold is crucial to be sensitive to WIMP induced nuclear recoils

Two major limitations:

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.

Aprile et al., arXiv:1001.2834

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

Energy calibration only available at 122 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).

DAMA calibration:

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

Comparison with other experiments

CDMS and Edelweiss calibration:

Neutrons from 252Cf source activate 71Ge that decays to 71Ga (T1/2~16 days) producing a peak at 10.4 keVAdditional calibration points: 133Ba (γ lines at 303, 356 and 384 keV)

50

Relative intensity.....

Am calibration-> ~5 p.e /keV

Am241 calibration in KIMS

E(keV)

13.9keV Np L X-ray17.8keV Np L X-ray20.8keV Np L X-ray26.35keV gammaCs, I X –ray escape59.54 gamma

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

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

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

This was supposed to be the “easy” part (gammas calibration). What about nuclear recoils?

The efficiency factor (quenching) of xenon

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

• 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

directly measured using a fixed-energy neutron flux

The XENON10 efficiency factor saga• 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.

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

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?

Aprile et al., PRC79,045807(2009)

Manzur et al., arXiv: 0909.1063

0.19

0.19

MC

For the moment it would be safe to take XENON10n with a grain of salt, although improvements are likely in the future

Conclusions

• 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)

Neutralino