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 Electromagnetic10 -2 Weak interaction Gravity 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 Detection Colliders: LHC Fuzzy CDM eV Axions (CDM) eV WDM keV MeV CDM MeV WIMPs (SUSY, neutralino) GeV

Dark matter detection IndirectDirect nuclear recoils Nearest MH ~0.1pc 5x 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 ~ cm 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/r 2, (a>a 0 ) a 0 ~10 -8 cm s -2 a = (GMa 0 ) 1/2 /r, (a<a 0 ) 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? AU a p ~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/ 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 ~ 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 /M D ) 1+2/n n=2, R=10 -2 cm (TeV /M D ) 2 n=3, R=10 -7 cm (TeV /M D ) 5/3 n=4, R= cm (TeV /M D ) 3/2 n=5, R= cm (TeV /M D ) 7/5 n=6, R= cm (TeV /M D ) 4/3 New Fundamental scale: M D -1 ~ cm, (M D =TeV)

1/r 2+n —law “New” Gravity in (ADD) large extra dimensions R: size of large extra dimension Newtonian New gravity R

Gravitational scattering cross section — Classical A=[(n+1)/(n-1)] (n-1)/(n+1) ~1 Newtonian: 1/r 2+n —law “New” Gravity :

Gravitational scattering cross section — Quantum 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) ?