Experimental Constraints on Extra Dimensions

Experimental Constraints on Extra D imensions Salvatore M ele CERN/EP & INFN/NA

• Introduction • Sh ort-ra ng e g ra v ity • Arkani-H am e d Dim o p o u l o s Dv al i s ce na rio: Dire ct & indire ct s e a rch e s • Rand al l Su nd ru m s ce na rio • O th e r s ce na rios : T e V s tring s & b ra nons • C oncl us ions (Shameless) Introduction Three amazing facts:

1 9 2 1. MPl~ 10 G e V > > Me w ~ 10 G e V (Hierarchy problem) 2 . T h e S t a n d a r d Mo d e l i s t e s t e d a t i t s c h a r a c t e r i s t i c d i s t a n c e 1/ Me w ( a n d Fi t w o r k s , w i t h i n s o m e ) 3 . G r a v i t y c a n n o t b e t e s t e d a t i t s c h a r a c t e r i s t i c d i s t a n c e -( t o o -m u c h ) 1/ MPl~ 10

Salvatore Mele 2 Breakthrough (and popular) i d ea Inspired by some concepts from strings… Antoniadis PLB246(1990)377, R u b ak ov & S h ap osh nik ov PLB125 (198 3)139 V isse r PLB15 9(198 5 )22, Ly k k e n PR D 5 4(1996)3693

…introdu ce mech a nisms w h ich bring th e sca l e of gra v ity to a new sca l e ~ M ew Ar k ani-H am e d e t al . PLB429(1998 )263 hence no hierarchy any m ore ! Antoniadis e t al . PLB436(1998 )25 7 R andal l & S u ndr u m PR L8 3(1999)3370

T h ese mech a nisms impl y th e ex istence of L a r–ge E x tra D imensions a nd modify: – gravity on short ranges p artic l e interac tions at c ol l id ers Many models at the same time: inflation 7 7 …of notation for the new scale MS,MD,MH,MF, T, π Salvatore Mele 3 Some general concepts Extra-dimensional Bulk Rc Gravity (at MD, not MPl)

Matter

Standard Model fields

Matter

Three-dimensional Brane (or Wall)

Salvatore Mele 4 Short range tests of gravity Long & Price h ep -p h / 0 3 0 3 0 5 7

Add a Y u k aw a t e r m to Newton potential

s tr eng th r ang e

Sensitivity to: • Sm a l l d evia tions a t l a r g e d ista nc e ( p end u l u m s) • L a r g e d evia tions a t sh or t d ista nc e ( h ig h -f r eq u enc y tec h niq u es) (Electrostatic, magnetic and C asimir f orces b ecome strong) Salvatore Mele 5 Salvatore Mele 6 The E ö t -W a s h ex p er i m en t Hoyle et al. PRL86(2001)1418

1 mm

Salvatore Mele 7 The Colorado experiment Long et al. NPB539(1999)23

100 µm

Salvatore Mele 8 The Stanford experiment Chiaverini et al . hep -p h/ 0 2 0 9 3 2 5

15 µm Au S i

Salvatore Mele 9 What can we learn?

New scale

E x tr a dim ensio ns

Typical distance (co m pactif icatio n r adiu s)

How do extra dimensions modify the N ewton p otential ?

Salvatore Mele 1 0 What can we learn?

New scale

E x tr a dim ensio ns

Typical distance (co m pactif icatio n r adiu s)

• α δ λ δ µ For MD~ 1 T e V , =2 , R C= l i mi t =2 a t R C< 1 9 0 m • δ C a n n ot s e t l i mi t s f or > 2 • W e re a l l y d o n ot k n ow g ra v i t y a n d E x t ra D i me n s i on s mi g h t b e j u s t t h e re Salvatore Mele 1 1 Collider(*) Con s t ra in t s on E x t ra D im en s ion s Salvatore M ele CERN/EP & INFN/NA

Arkani-H am e d Dim o p o u l o s Dv al i s c e n a r i o : Di r e c t & i n d i r e c t s e a r c h e s Rand al l Su nd ru m s c e n a r i o O t h e r s c e n a r i o s : T e V s t r i n g s & b r a n o n s C o n c l u s i o n s

(*) L E P , T E V AT RO N (Ru n I & Ru n I I ) , H E RA Numerology and disclaimers • All limits are at 95% Confidence Level. • N ot all resu lts from all ex p eriments are q u oted. • At h adron mach ines, not all k -factors are in. • M any resu lts are p reliminary , u nless indicated oth erw ise. • T h e name of th e g ame is to g ive a look to th e T eV scale to sp ot effects from E x tra D imensions • I n any case, p lease refer to: http://cern.ch/aleph http://w w w -cd f .f nal.g o v / http://cern.ch/d elphi http://w w w -d 0 .f nal.g o v / http://cern.ch/l3 http://w w w -h1 .d es y .d e/ http://cern.ch/o pal http://w w w -z eu s .d es y .d e • All th eory concep ts are over-simp lified

Salvatore Mele 1 3 The ADD scenario Arkani-H am e d e t al . P L B 4 2 9 ( 1 9 9 8 ) 2 6 3 Arkani-H am e d e t al . P R D 5 9 ( 1 9 9 9 ) 0 8 6 0 0 4 Ant o niad is e t al . P L B 4 3 6 ( 1 9 9 8 ) 2 5 7 • δ There is a large volume for -ex t ra d imen sion al sp ac e ( min d t hat in t his b usin ess “ large” is ab ove ~ 1 0 fm! ) • G ravit y alon e c an t ravel in t he b ulk • G auss law relat es P lan c k ( MPl) an d L ow S c ale G ravit y ( M) sc ales

• δ I f = 2 an d R ~ 1 mm w e get M~ 1 TeV an d t he field w hic h t ravels in t he b ulk ( G ravit y ! ) med d les w it h t he P hy sic s at t he TeV sc ale ( S t an d ard Mod el ! ) • Thin k of a n ew p art ic le, t he sp in -2 gravit on , w hic h is p rod uc ed or ex c han ged at c ollid ers ( w hic h in d eed w ork at t he TeV sc ale ! ) Salvatore Mele 1 4 Collider s ea rc h es f or t h e A D D s c en a rio • Direct searches – + - → γ e e G a t L E P – - → γ p p G X a t t h e T E V A T R O N – - → p p G j et s a t t h e T E V A T R O N • I n d irect searches – D ev i a t i o n s i n f er m i o n a n d b o s o n p a i r - p r o d u c t i o n a t L E P – D ev i a t i o n s i n n eu t r a l -c u r r en t s c a t t er i n g a t H E R A – D ev i a t i o n s i n d i -l ep t o n a n d d i -p h o t o n p r o d u c t i o n a t t h e T E V A T R O N

Salvatore Mele 1 5 Direct searches at LEP

Giudice et a l . N P B 5 4 4 ( 1 9 9 9 ) 3

Look for events with photons a nd m issing energ y Mind that it is experimentally very tricky to lo o k f o r thing s that are missing …

Salvatore Mele 1 6 LEP: The machine…

Salvatore Mele 1 7 LEP: The detectors…

Aleph D elphi

L 3 O pa l

Salvatore Mele 1 8 LEPitaph

+ - Circular e e coo llidd er,, 22 77 kk mm rinn gg EE nn ergg yy upp gg radd eabb le 88 88 -22 00 99 GG eVV LL argg e lumm inn oo ss itt yy :: 11 ff bb // exx pp .. 22 00 MM illioo nn ZZ evv enn tt ss WW hh ere nn oo bb oo dd yy hh ass gg oo nn e bb eff oo re……

Salvatore Mele 1 9 Single photon events L3

2 f b -1

D a t a : 7 5 6 1 M C : 7 6 7 6

Salvatore Mele 2 0 Limits

Compare graviton cross section F it ex pected graviton w ith th e measu red one energy spectru m

ee(

* =2 MD> 1 . 5 T e V * =3 MD> 1 . 1 T e V * =4 MD> 0 . 9 T e V

Salvatore Mele 2 1 The TEVATRON CDF

Run I ~110pb-1 RunII ~120pb-1

Salvatore Mele 2 2 Photons and missing ET at the T EV A T R O N

Giudice et a l . N P B 5 4 4 ( 1 9 9 9 ) 3

(Is ET a n d n o t E a s a t L EP b e c a u se o f p r o t o n r e m n a n t s a l o n g t h e b e a m a x i s)

Salvatore Mele 2 3 Photons and missing ET at the T EV A T R O N

R u n I Data: 11 events B ac k g r o u nd : 11C 2 events

n=4 MD> 0 . 5 5 T e V n=6 MD> 0 . 5 8 T e V n=8 MD> 0 . 6 0 T e V

Salvatore Mele 2 4 Photons and missing ET at the T EV A T R O N

R u n I Data: 11 events B ac k g r o u nd : 11C 2 events

n=4 MD> 0 . 5 5 T e V n=6 MD> 0 . 5 8 T e V n=8 MD> 0 . 6 0 T e V

CDF Preliminary, 84 pb -1 γ After trigger, photon ID and E cuts (9025) 3 T 10 After ET > 42 GeV cut (4040) After cosmic ray/beam background cuts (350) VV

ee After jet/track vetoes (17)

GG 2

22 10 // ss tt nn ee vv

EE R u n I I 10 Data: 17 events B ac k g r o u nd : 18 C 2 events 1 0 50 100 150 200 250 300 ET (GeV) Salvatore Mele 2 5 Jets and missing ET at th e T EV A T R O N

Giudice et a l . N P B 5 4 4 ( 1 9 9 9 ) 3 Salvatore Mele 2 6 Jets and missing ET

D0 C DF

Data: 3 8 events Data: 284 events B ac k g r o u nd : 3 8C 1 0 events B ac k g r o u nd : 27 4C 1 6 events n = 2, 4, 6 n = 2, 4, 6 MD> 0 . 9 , 0 . 7 , 0 . 6 T e V MS> 1 . 0 , 0 . 8 , 0 . 7 T e V

Salvatore Mele 2 7 Summary of direct limits

Improvements expected from TEVATRON Run II with l a rg e l uminosity a nd l a rg er energ y Salvatore Mele 2 8 Limits on the size of the E x tr a D imensions

2 E x t r a D i m e n s i o n s 3 4 5 6 7 8

-4 -5 -6 -7 -8 -9 -1 0 -1 1 -1 2 -1 3 -1 4 -1 5 10 10 10 10 10 10 10 10 10 10 10 10 ( m ) N u c l e u s A tom Proton

G ra in of s a nd

D N A tu rn

Print dot Salvatore Mele 2 9 Virtual graviton exchange

• λ The value of d ep en d s on t he full t heor y • λ ± C hoos e = 1 for t he t w o s i g n s of t he i n t er fer en c e • G i ve r es ult s w i t h t he ‘H ew et t ’ MS c on ven t i on ( N o d e p e n d e n c e o n n u m b e r o f e x t r a d i m e n s i o n s ) Hewett P R L 8 2 ( 1 9 9 9 ) 4 7 6 5 Salvatore Mele 3 0 H1 HERA

H 1 Z eu s

Z e u s

- √ -1 e p s = 3 1 9 G eV 2 0 p b + √ -1 e p s = 3 0 0 -3 1 9 G eV 1 6 0 p b

Salvatore Mele 3 1 Virtual graviton exchange at HERA

Salvatore Mele 3 2 Virtual graviton exchange at HERA

H 1

λ=+ 1 M S > 0 . 7 3 T e V λ=-1 M S > 0 . 7 0 T e V ZEUS

λ=+ 1 M S > 0 . 7 2 T e V λ=-1 M S > 0 . 7 3 T e V

π 1/4 Scale original limits by (2/ ) to recov er H ew ett’s MS conv ention Salvatore Mele 3 3 Virtual graviton exchange at LEP Look for deviations in di-p h oton and l ep ton-p air events

Salvatore Mele 3 4 Virtual graviton exchange at LEP

Deviation (%) for boson pairs Agashe & D eshp an d e P L B 4 5 6 ( 1 9 9 9 ) 6 0

Salvatore Mele 3 5 + -→ Virtual graviton exchange, e e ((

γ→ e+e-

LEP combined

λ=+ 1 M S > 0 . 9 3 T eV λ=-1 M S > 1 . 0 1 T eV

Salvatore Mele 3 6 + -→ + - Virtual graviton exchange, e e e e Interference

Giudice et a l . N P B 5 4 4 ( 1 9 9 9 ) 3 R iz z o P R D 5 9 ( 1 9 9 9 ) 1 1 5 0 1 0

L o w S ca l e G ra v i ty

• Clean experimental channel • L arg e t-channel cro s s s ectio n • L arg e interf erence w ith L S G • H ig h s ens itiv ity

Salvatore Mele 3 7 + -→ + - Virtual graviton exchange, e e e e

LEP combined

λ=+ 1 M S > 1 . 2 0 T eV λ=-1 M S > 1 . 0 9 T eV

Salvatore Mele 3 8 Virtual graviton exchange at the TEVATRON

Di-m u o n & d i-e l e c t r o n p r o d u c t io n

Di-p h o t o n p r o d u c t io n

Salvatore Mele 3 9 → + - Virtual graviton exchange p p ((X , e e X D 0

Instrumental b ac k g ro und

Salvatore Mele 4 0 →(( + - VirtuMCal Simulationgrav ioft theon ED esignaturesxchange p p X , e e X D 0

ENTRIES 4790817 ENTRIES 4790817 4 1 SM σ4 -3 -1 10 /bin, pb

σ 10

-2 /bin, pb TeV 10 4 σ

-3 -4 10 1 10 1 0 0.75 0 0.75 250 500 0.5 250 500 0.5 M(EM-EM) 750 0.25 * M(EM-EM) 750 0.25 * 10000 θ ) 10000 θ ) cos( cos( 4 SM term Interference term, f/M S

ENTRIES 4790817 ENTRIES 14372451 ¡ 8 1 M = 1 T e V σ8 S -3 n = 4 -1

10 /bin, pb 8 10 ¡

/bin, pb TeV -2 8 10 σ SM+ED -4 -3 10 1 10 1 0 0.75 0 0.75 SM 250 500 0.5 250 500 0.5 M(EM-EM) 750 0.25 * M(EM-EM) 750 0.25 * 10000 θ ) 10000 θ ) cos( cos( B a c k . 2 8 ED term, f /M S Total cross section, M S = 1 TeV, n = 4

Salvatore Mele 4 1 → + - Virtual graviton exchange p p ((X , e e X C D F

CDF

λ=+ 1 M S > 0 . 9 3 T e V λ=-1 M S > 0 . 8 5 T e V

λ=+ 1 M S > 1 . 1 T e V λ=-1 M S > 1 . 0 T e V

Salvatore Mele 4 2 →µ+µ- First results from Run II p p X ( D 0 )

Salvatore Mele 4 3 → + - First results from Run II pp ((X , e e X ( D 0 )

Salvatore Mele 4 4 → + - First results from Run II pp ((X , e e X ( D 0 )

Most massive candidate

R u n I MS > 1 . 1 T e V R u n I I MS > 1 . 1 T e V R u n I + I I MS > 1 . 2 T e V

Salvatore Mele 4 5 Summary of limits from virtual effects

L E P e e γγ D 0 ( I + I I ) e e , g g γγ D 0 ( I I ) e e , g g γγ L E P g g C D F ( I ) e e , γg γg L E P W W H E R A L E P Z Z µµ D 0 ( I I ) m m µµ L E P m m ττ L E P t t

0 0. 5 1 1. 5 9 5 % C L L i m i t o n M S S ( T e V )

Salvatore Mele 4 6 The RS scenario Randall & S u ndr u m P RL 8 3 ( 1 9 9 9 ) 3 3 7 0 Randall & S u ndr u m P RL 8 3 ( 1 9 9 9 ) 4 6 9 0 • We’re on a b rane, g rav i t y on anot h er • O ne ex t ra d i m ens i on i n t h e m i d d l e • η µ ν “ Warp ed ” m et ri c d s 2= e–2ky µνd x d x -d y 2 • Λπ π –1 / 2 –ky N ew s c al e = ( 8 ) e MP l , d es c ri b es S t and ard Mod el on π ou r b rane w i t h y = R • N o h i erarc h y , k / MP l ~ 1 j u s t ou r p os i t i on i n y !

Salvatore Mele 4 7 Searches at the TEVATRON

Graviton resonant p rod u c tion and d ec ay in d i-j et or d i-l ep tons

D av ou d iasl et al P R D 6 3 ( 2 0 0 1 ) 0 7 5 0 0 4

Higher resonances

First resonance

Di-l e p t o n s p e c t r u m Salvatore Mele 4 8 Resonances in the d i-j et channel ?

So far, no resonances observed

Salvatore Mele 4 9 Resonances in the d i-l ep ton channel ?

Good agreement between data and expectations

Salvatore Mele 5 0 First limits on the Randall-S u ndru m sc enario

Di-j e t s

Di-l e p t o n s

CDF

Salvatore Mele 5 1 TeV s c a l e s t r i n g s Antoniadis et al. PLB436(1998)257 Ac c om ando et al. N PB579(20 0 0 )3 C u llen et al. PR D 52(20 0 0 )0 550 12 • Quantum gravity is the underlying theory f or E x tra D imensions • Quantum gravity is desc rib ed b y strings • S tandard M odel p artic les may b e desc rib ed b y strings • U nleashing strings at the T eV sc ale imp lies ef f ec ts on S tandard M odel amp litudes

Salvatore Mele 5 2 Massive string mode oscillations Modify the differential c ros s s ec tion for B hab ha s c attering

MS= 0 . 4 2 T e V

+ -→ + - e e e e MS> 0 . 5 5 T e V

A D D MS = ( 1 . 6 -3 . 0 ) x MS

Salvatore Mele 5 3 Branons Dobado & M ar ot o N P B 5 9 2 ( 2 0 0 1 ) 2 0 3 C e m br an os e t al . P R D6 5 ( 2 0 0 2 ) 0 2 6 0 0 5 A l c ar az e t al . P R D6 7 ( 2 0 0 3 ) 0 7 5 0 1 0 • The simultaneous presence of our b rane A N D ex tra d imensions may imply ad d itional d eg rees of freed om • The b rane can fluctuate along the ex tra d imensions • This manifests w ith new particles, the b ranons • I f the b rane tension f < < M S, b ranons are accessib le at collid ers w hile K K g rav itons are N O T!

Salvatore Mele 5 4 Branons

+ - Pair-p ro d u c t io n in e e c o l l is io n s ( f o r L o ren t z in v arian c e) A g ain , s ig n at u re o f m is s in g en erg y an d p h o t o n s

Brane t ens i o n ( G eV ) Salvatore Mele 5 5 Conclusions & Outlook

• The experimental community reacted vigorously and f ast to a new idea: E xtra D imensions sought f or at all high energy machines • N o sign of ef f ects of E xtra D imensions at the TeV scale w as f ound • I mprovements to the TE V A TR O N machine might lead to surprises • The L H C is not that f ar aw ay, af ter all!

Salvatore Mele 5 6 The LHC is st a r t in g in a b o u t f o u r y ea r s! 106 1 . 0

Standard Model l P -1 -1 M R S G r a v i t o n s C M S , 1 0 0 f b

s 1 0 0 f b / t k

n 103 e

v 0. 1 E A D D Theory µ e

1 γ 0 5 00 1000

T M i s s i n g E (G e V ) 0. 01 1 000 2 000 3 000 4 000 5000 0. 1 γγ p p -> X mG (G e V )

γ ¢ A D D M i s s i n g E T sensitive up to 9 T eV

¡ 1 D i-ph otons sensitive up to 6 T eV

σ R S g r a vitons sensitive to a l l spa c e Standard Model Kabachenko et al A T L A S -P H Y S -2 0 0 1 -0 1 2 C ol l ar d et al C M S -2 0 0 2 -0 5 0 0. 1 H i nchl i f f e et al J P G 2 7 ( 2 0 0 1 ) 1 8 3 9 1000 2 000 3 000 4 000 Salvatore Mele 5 7 mγγ (G e V )