Flat large extra dimensions: implications for

Dark matter direct detection

Bo Qin (秦波 )

National Astronomical Observatories, CAS

（中国科学院国家天文台）

with Glenn Starkman (CWRU) & Joe Silk (Oxford)

Gravity

Newtonian

New gravity

R

Four interactions in Nature

Strong interaction 1 Electromagnetic 10-2

Weak interaction 10-15

Gravity 10-39

Could gravity play a dominant role between elementary particles?(1) extra dimensions (2) dark matter particles? (strong, EM forces absent)

Extra dimensions

The question

Theory

Large extra dimensions (ADD)

Enhance

DM—baryon interaction

Experiments

WIMP DM direct detections

Put limit on

DM—baryon cross section

compare

test

Searches for Dark Matter

Direct Detection Indirect DetectionColliders: LHC

Fuzzy CDM 10-22 eV • Axions (CDM) 10-6 eV WDM keV MeV CDM MeV• WIMPs (SUSY, neutralino) 10-1000 GeV

Dark matter detection

2a DM

V

S dVIndirect Direct

nuclear recoils

nrS Nearest MH ~0.1pc5x brighter than Draco

Gravity —experimental

Gravity has only been accurately measured at

~1cm Solar system (Pluto)

But was extrapolated 33 orders of mag. down to ~10-33cm

12 orders o.m., up to 1000 Mpc

Gravity in large scales (cosmological) & weak regimes:

Modified Newtonian Dynamics (MOND) Milgrom 1983 ApJ, Sanders 2002, ARA&A, Bekenstein 2004 PRD

a = GM/r2 , (a>a0) a0 ~10-8 cm s-2

a = (GMa0)1/2 /r , (a<a0)

Pioneer Anomaly:

Anderson et al 1998 PRL, Turyshev 2005 Am.J.Phys.

Negative energy? Henry-Couannier et al

Bullet cluster—End of MOND?

Pioneer Anomaly —A Mystery?

20-70 AU

ap ~8*10-8 cm s-2

constant, toward the Sun

Experimental tests of Newton’s law of gravity at sub-mm scales

& Searches for extra dimensions

Long et al., Nature (2003)

Hoyle et al., PRL (2001); PRD (2004)

Chiaverini et al. PRL (2003)

(& e.g. hep-ph/0402168 for a review)

• No deviation from Newtonian has been found

from ~1cm down to ~20μm

Gravity—Experimental (small distance scales):

Extra Dimensions: Klein, Kaluza, 1920’

• String theory

Gravitational behavior at small distance scales, r<R• Size of extra dimensions: Planck scale ~10-33 cm

• Large Extra Dimensions: 3 + n + m = 9

Arkani-Hamed, Dimopoulos & Dvali (ADD) 1998, Phys. Lett. B

Gravity: F ~ r-(2+n) at r<R,

R~10(30/n)-17 cm (for n=2, R~1mm)

Randall & Sundrum (1999)

Opens New Window: Experimental test of string theory + Searches for extra dimensions, by precise measurement of gravity at sub-mm scales

ADD Scenario

Size of large extra dimensions:

R~10(30/n)-17 cm (TeV /MD)1+2/n

n=2, R=10-2 cm (TeV /MD)2

n=3, R=10-7 cm (TeV /MD)5/3

n=4, R=10-9.5 cm (TeV /MD)3/2

n=5, R=10-11 cm (TeV /MD)7/5

n=6, R=10-12 cm (TeV /MD)4/3

New Fundamental scale: MD-1

~ 10-17 cm, (MD=TeV)

1/r2+n—law “New” Gravity

in (ADD) large extra dimensions

R: size of large extra dimension

Newtonian

New gravity

R

Gravitational scattering cross section —Classical

1

2

2

nx

n

v

mGRA

A=[(n+1)/(n-1)] (n-1)/(n+1) ~1

4

22

v

mG Newtonian:

1/r2+n—law “New” Gravity :

Gravitational scattering cross section —Quantum

1

2

2

nx

n

v

mGRA

A=[(n+1)/(n-1)] (n-1)/(n+1) ~1

de Broglie wavelength > R or b Q.M. treatment

Q.M. cross section = 2 Classical cross section (for bosons) = 1/2 Classical cross section (for fermions)

Conclusions

• Large extra dimensions (LED) greatly enhance gravity in small distance scales

• LED could greatly increase the cross section between DM and baryons

• Current DM detection experiments give stringent constraints on flat LED (ADD)

• ADD in apparent contradiction with DM direct detection limits

• Either ADD scenario incorrect • or DM mass not in 10GeV-10TeV range• MeV CDM, or WDM (~keV) ?