INTRODUCTION TO EXTRA DIMENSIONS

Transcription

1 INTRODUCTION TO EXTRA DIMENSIONS MARIANO QUIROS, ICREA/IFAE MORIOND 2006 INTRODUCTION TO EXTRA DIMENSIONS p.1/36

2 OUTLINE Introduction Where do extra dimensions come from? Strings and Branes Experimental detection New theoretical ideas from extra dimensions Conclusions INTRODUCTION TO EXTRA DIMENSIONS p.2/36

3 Introduction Extra dimensions have been introduced to solve classical problems of Particle Physics. In particular to solve the hierarchy problem If there is a warped extra dimension, large scales at the Planck brane are redshifted at the TeV brane [L. Randall and R. Sundrum, hep-ph/ ] PLANCK BRANE 2 k R y a = e TEV BRANE INTRODUCTION TO EXTRA DIMENSIONS p.3/36

4 Introduction Extra dimensions have been introduced to solve classical problems of Particle Physics. In particular to solve the hierarchy problem If there is a warped extra dimension, large scales at the Planck brane are redshifted at the TeV brane [L. Randall and R. Sundrum, hep-ph/ ] INTRODUCTION TO EXTRA DIMENSIONS p.3/36

5 Introduction If there are very large extra dimensions where only gravity propagates the Planck scale is reduced by the large compactification volume [N. Arkani-Hamed, D. Dimopoulos and G. Dvali, hep-ph/ ] FLAT EXTRA DIMENSION INTRODUCTION TO EXTRA DIMENSIONS p.4/36

6 Introduction If there are very large extra dimensions where only gravity propagates the Planck scale is reduced by the large compactification volume [N. Arkani-Hamed, D. Dimopoulos and G. Dvali, hep-ph/ ] INTRODUCTION TO EXTRA DIMENSIONS p.4/36

7 Where do they come from? For a consistent quantum theory of gravity we must abandon the concept of particle and introduce the concept of string (SUPER) STRINGS EXTRA DIMENSIONS A string is a generalization of a point particle String is a one-dimensional spatially extended object propagating in D space-time dimensions and spanning a world sheet INTRODUCTION TO EXTRA DIMENSIONS p.5/36

8 Where do they come from? Z WORLD LINE µ X ( τ ) Y X PARTICLE INTRODUCTION TO EXTRA DIMENSIONS p.6/36

9 Where do they come from? WORLD SHEET Z σ µ X ( σ, τ ) τ Y X CLOSED STRING INTRODUCTION TO EXTRA DIMENSIONS p.7/36

10 Where do they come from? WORLD SHEET Z i σ µ X ( σ, τ ) j τ Y X OPEN STRING INTRODUCTION TO EXTRA DIMENSIONS p.8/36

11 Strings & Branes Cancellation of conformal anomaly D=10 EXTRA DIMENSIONS Extra dimensions must be compactified D-branes are subsurfaces where open strings can end Extra dimensions can be LONGITUDINAL to the brane TRANSVERSE to the brane INTRODUCTION TO EXTRA DIMENSIONS p.9/36

12 Strings & Branes CLOSED STRING n X (DIRICHLETT) T OPEN STRING COMPACT DIMENSIONS p 3 X (NEUMANN) INTRODUCTION TO EXTRA DIMENSIONS p.10/36

13 Strings & Branes D BRANE µ X (NEUMANN) ω=0 ω =2 µ X (DIRICHLET) T ω =1 INTRODUCTION TO EXTRA DIMENSIONS p.11/36

14 ) ( ' '. # - ",+ %* ' ( # - ",+ %* #+ 6 # Strings & Branes To make contact with experiments we will describe the different string theories from the point of view of effective field theories. Parameters are "&% $ # "! 1 /0 # "! COMPACTIFICATION ) - 6* 8 $ * -76 INTRODUCTION TO EXTRA DIMENSIONS p.12/36

15 C E ( ) D C <? =) < > > ' ' ' Strings & Branes Closed strings describe gravity Open strings with ends bounded to propagate on Dp-branes describe gauge interaction 6 internal compact dimensions= [p-3] (longitudinal)+[n=(9-p)](transverse) 2. 9;@A B ( 2. ' 9;: EXTRA DIMENSIONS COMPACTIFIED INTRODUCTION TO EXTRA DIMENSIONS p.13/36

16 V FN F O O E ' ). ' ' D ^ ' ^ Strings & Branes IKJJ SUT N IML IKJJ ) R Q O PO ) HG F C ( XY WW WW YWW # D ]\ JJ Z&[R ^ as Defining the (4+n) Planck scale ` Y WW _ # D ADD RELATION D a\ INTRODUCTION TO EXTRA DIMENSIONS p.14/36

17 2 ^ ' _ 2 2 \ \ _ 2 2 b Experimental detection If reach at LHC TeV string excitations can be at The ADD relation can explain the weakness of gravitational interactions by the size of extralarge transverse dimensions TeV Kaluza-Klein excitations of transverse dimensions can affect gravitational (and collider) experiments Kaluza-Klein excitations of longitudinal dimensions with size TeV can be detected at LHC INTRODUCTION TO EXTRA DIMENSIONS p.15/36

18 \ D ^ \ 1. Transverse dimensions Only gravity propagates in transverse extra dimensions. These dimensions can be extra-large Let be the (common) radius of transverse dimensions where gravity propagates ADD relation relates the scales of quantum gravity in the higher dimensional theory and the transverse radius C ]\ Present gravitational experiments put lower bounds on in the sub-millimeter region INTRODUCTION TO EXTRA DIMENSIONS p.16/36

19 2 ^? 32 \ 32 c ^ d 32 \ 1. Transverse dimensions From ADD relation for TeV n Km 0.7 mm 0.3 fm ev 30 MeV EXCLUDED INCONSISTENT CONSISTENT For TeV n Km 0.2 mm 0.1 fm EXCLUDED BARELY CONSISTENT CONSISTENT INTRODUCTION TO EXTRA DIMENSIONS p.17/36

20 a. Gravitational experiments Extra dimensions produce deviations from Newton s law INTRODUCTION TO EXTRA DIMENSIONS p.18/36

21 j i 2 \ l l l e f \ e a. Gravitational experiments Extra dimensions produce deviations from Newton s law m L o nz g INTRODUCTION TO EXTRA DIMENSIONS p.18/36

22 a. Gravitational experiments Extra dimensions produce deviations from Newton s law INTRODUCTION TO EXTRA DIMENSIONS p.18/36

23 s r D q e b. Collider signatures Based on missing energy in reactions corresponding to the production of KK-gravitons in the bulk. For instance INTRODUCTION TO EXTRA DIMENSIONS p.19/36

24 s r D q e _ 2 D _ k $ ^ b. Collider signatures Based on missing energy in reactions corresponding to the production of KK-gravitons in the bulk. For instance Every single graviton couples large amount of gravitons cancels (using ADD relation) the dependence but the INTRODUCTION TO EXTRA DIMENSIONS p.19/36

25 \ ^ \ ^ { yz yz ˆ ˆ ƒ Šˆ Š Šˆ Š b. Collider signatures The 95% confidence limits on, [cm] and [GeV]. and related by ADD relation COLLIDER / thu ( vxw ) / thu ( vxw ) LEP 2 TEVATRON LC LHC }~ ƒ~ { ƒ ~ } ~ ƒ U ƒ ƒ U ƒ U / 1200 / 750 / 7700 / 4500 ~ ~ ~ ƒ ~ ƒ ƒ ƒ ƒ / 520 / 610 / 3100 / 3300 E. Mirabelli, M. Perelstein and M. Peskin, hep-ph/ N. Arkani-Hamed, S. Dimopoulos and G. Dvali, hep-ph/ INTRODUCTION TO EXTRA DIMENSIONS p.20/36

26 2. Longitudinal dimensions The SM propagate in a brane, with p-3 longitudinal dimensions wrapped on compact space (orbifold) with 4D boundaries at the fixed points I X I=1,...,p 3 (n) g Z (n) (n) γ LOCALIZED STATES Dp brane INTRODUCTION TO EXTRA DIMENSIONS p.21/36

27 Œ s r s r q a. Indirect detection Through the modification of EW observables by the exchange of KK-modes, + e FF ŒŽ A F e e e = 1 M (n) 2 e e e e A. Delgado, A. Pomarol and M. Quirós, JHEP 01 (2000) 030 INTRODUCTION TO EXTRA DIMENSIONS p.22/36

28 Y ) 2 X a. Indirect detection The numerical results are [, thick (MSSM), thin (SM)] _ WW _ Y, INTRODUCTION TO EXTRA DIMENSIONS p.23/36

29 Y ) 2 X a. Indirect detection The numerical results are [, thick (MSSM), thin (SM)] _ WW _ Y, M c (TeV) sin 2 β INTRODUCTION TO EXTRA DIMENSIONS p.23/36

30 Y ) 2 X a. Indirect detection The numerical results are [, thick (MSSM), thin (SM)] _ WW _ Y, 6 5 M c (TeV) sin 2 β INTRODUCTION TO EXTRA DIMENSIONS p.23/36

31 b. Direct detection In hadron colliders through Drell-Yan processes q q (n) (n) g Z γ (n) LOCALIZED STATES q BULK STATES q I. Antoniadis, K. Benakli and M. Quirós, hep-ph/ INTRODUCTION TO EXTRA DIMENSIONS p.24/36

32 _ 2 _ b e b. Direct detection For LHC, D=1,2 extra dimensions, as a function of 5 LHC 4 D=1 D= /R (GeV) INTRODUCTION TO EXTRA DIMENSIONS p.25/36

33 b. Direct detection Production at LHC of gluon Kaluza-Klein excitations 30 R 1 = 4 TeV R 1 = 5 TeV 20 SM backg. Events/GeV M(jj ) (GeV) INTRODUCTION TO EXTRA DIMENSIONS p.26/36

34 š b. Direct detection Production at LHC of Kaluza-Klein excitations R 1 = 4 TeV R 1 = 5 TeV R 1 = 6 TeV Events/GeV M T (GeV) INTRODUCTION TO EXTRA DIMENSIONS p.26/36

35 b. Direct detection Production at LHC of q Kaluza-Klein excitations γ + Z γ Z Events / GeV Dilepton mass INTRODUCTION TO EXTRA DIMENSIONS p.26/36

36 New ideas from extra dimensions c 2 Extra dimensions also exhibit the feature of providing NEW solutions to OLD problems in Particle Physics Supersymmetry can be broken on the fixed points by orbifold boundary conditions: the number of supersymmetries on the branes is halved. For instance in the case of one or two extra dimensions compactified on orbifolds the number of supersymmetries of zero modes is INTRODUCTION TO EXTRA DIMENSIONS p.27/36

37 3 2 _ 2 k ) 1. Supersymmetry breaking Supersymmetry can be further broken by twisted boundary conditions: the so-called Scherk-Schwarz breaking. Then in the effective four-dimensional theory In particular if gauginos (and squarks) propagate in the bulk of extra dimensions they acquire masses proportional to the compactification scale INTRODUCTION TO EXTRA DIMENSIONS p.28/36

38 ž j 2 c 2. Higgs-gauge unification It is possible to unify the Higgs and gauge sectors by using for the former the extra dimensional components of the higher-dimensional gauge bosons: this is called Higgs-gauge unification " <Ÿ % œ It requires to enlarge the SM gauge group e.g. This is an alternative solution to the hierarchy problem because the extra dimensional gauge theory protects the Higgs mass from quadratic divergences INTRODUCTION TO EXTRA DIMENSIONS p.29/36

39 s r ) r s r ) r s k r E e 2. Higgs-gauge unification Electroweak breaking proceeds via the Hosotani mechanism (Wilson line) s = SM gauge bosons s = SM Higgs bosons The Higgs mass parameter becomes tachyonic radiatively _ 2 ª «K It is difficult to obtain realistic models: quadratically divergent localized tadpoles can appear, Higgs mass requires more than five dimensions, fermion masses,... INTRODUCTION TO EXTRA DIMENSIONS p.30/36

40 4 _ e 3. Higgs EWSB By using the SS mechanism to break supersymmetry (gaugino mediated supersymmetry breaking) and the matter localized on the 4D boundary one obtains a realistic model of EWSB [D. Diego, G. Gersdorff, M.Q., JHEP in preparation] where GeV for TeV Lightest neutralino (Higgsino like) is the LSP and a good candidate to DM Light Higgsinos ( GeV) and heavy gauginos Squarks in the TeV region and sleptons in the few hundred GeV region INTRODUCTION TO EXTRA DIMENSIONS p.31/36

41 3. Higgs EWSB as a function of 1/R [in TeV] INTRODUCTION TO EXTRA DIMENSIONS p.32/36

42 3. Higgs EWSB as a function of 1/R [all masses are in TeV] INTRODUCTION TO EXTRA DIMENSIONS p.33/36

43 3. Higgs EWSB and ± as a function of 1/R [all masses are in TeV] INTRODUCTION TO EXTRA DIMENSIONS p.34/36

44 ² b 3. Higgs EWSB as a function of 1/R [in TeV] INTRODUCTION TO EXTRA DIMENSIONS p.35/36

45 CONCLUSION Large Extra Dimensions well motivated theoretically Large Extra Dimensions + Low Scale quantum Gravity effects at reach at present (Tevatron) and future (LHC) colliders Large Extra Dimensions have unambiguous experimental signatures Large Extra Dimensions can also help to solve theoretical Particle Physics problems (hierarchy, flavor,...) INTRODUCTION TO EXTRA DIMENSIONS p.36/36

46 CONCLUSION If found it would possibly be the most important revolution in the History of Particle Physics! INTRODUCTION TO EXTRA DIMENSIONS p.36/36