EXTRA DIMENSIONS INPARTICLE PHYSICS

EPS conference – Aachen, July 2003

Ferruccio Feruglio

SET-UPbrane 1)TeV1( L

0L in the 1st part of this talk

bulkSpace) Extra(4 ESM

length R21SES

TES volume

21 / ZSES length R

)2( RV

only gravity is admitted to the bulk(few exceptions)

warped geometry branes can carry some energy density and, by the laws of GR, they may warp the space-time geometry.

KK modesgraviton momentum along ED is quantizedin units of 1/R. To the 4D observer, gravitonscome in infinite copies with 4D masses n/R(=a tower)

particles

MNGfull space-time metric in D = 4+ contains

4D graviton )(xg )()( xg n

radionone combination of specifies the volume of the extra spacee.g. = 1

MNG

)()0(55 xrG MRxr )(

much as scale Fermi2

vH

KK modesand itsR

nmKK

other particles, specifying the shape of the ES or the fluctuationsof the brane, can be present (not covered by this review…)

General motivationunification of gravity with other fundamental interactionsKaluza-Klein (1919-1926), still valid today. String theories, candidates for a unified descriptionof all interactions, are formulated in D = 10 (or D = 11)

specific motivations

1. Hierarchy problem

2. ``little’’ hierarchy problem

3. flavour problem

4. problems of conventional GUTs

5. cosmological constant

PMscale e.w.

scale e.w.Hm

tdue mmmm ,...,,uscbub VVV

yrKp 33102)(

43eV)10(

HIERARCHY PROBLEMthere is only one fundamental scale in D=4+ dimensions TeV1DM

Rr 12

11

rMV

Dgrav all KK gravitons contribute

Rr only the 4D graviton zero mode contributes

rVMV

PM

Dgrav

11

2

2

VM

M

MD

D

P

2

4D gravity is weak because the graviton wave functions is diluted in a big volume.

Now we should explain why1 DMR

(L=0 here)

...)(

),(

V

xgyxG

.

VM P

11

Arkani-Hamed, Dimopoulos, DvaliAntoniadis

R

1

2

3

… … …

7

1-R

mm1.0Km108

mm10 6

mm10 12

eV10 18

eV10 3

eV100

MeV100

TeV1DM

excluded: R ~ Sun-Earth distance

of special interest: sizeable deviations from Newton law

clearly allowed

KK graviton states can be produced- at colliders- in processes of astrophysical and/or cosmological relevance

Sub-mm tests of gravity

re

r

mGrV

rN 1)(

we expect 2

degeneracy of the1st KK level

R 2wavelength of the 1st KK mode

2 CLm %95150

Further improvements are an experimental challenge!

EOT-WASHex/0202008

important: deviations in this range are expected also in other scenarios(more on this later on…)

FLAVOUR I: and LEDLED provide a nice argument for the smallness of masses:standard Yukawa couplings to a singlet fermion who lives in the bulk s

)()(2

v )0( xxM

Mysa

P

DYuk

L ...

)(),(

)0(

V

xyx s

s

originates from

can we test this idea?

then, few might take part in oscillations

but

large mixing angles between and are excluded (SN1987A)

oscillations into disfavoured by both atmospheric and solar data

effects subdominant, if present

)(ns

)(nsa

s)(n

s

if some states are sufficiently light

eV01.0mass)( 2, solatmm

)(ns

(not unconceivable:R ~ 0.02 mm)

Dienes, Dudas, Gherghetta, Arkani-Hamed,Dimopoulos, Dvali, March-Russell, Barbieri, Creminelli, Strumia

Collider bounds on LED:

1KK graviton production in association with a or a jet

)(missing or TEj

2

DM

Esingle KK production

PM

1 rescued by the very

large phase space

combined 95% CL limits on from LEP and Tevatron'DM

2 3 4 5 6

(TeV) 1.45 1.09 0.87 0.72 0.65

2 virtual graviton exchange

sensitive to UV physics: divergent amplitudes already at the tree-level for parametrized in terms of effective operators(or computed in string theory)

2)(ng

RMM

MD

D

P )'(8'

2

reviews: Cheung; Hewett, Spiropulu; Sanders this conf.

Giudice, Strumia

22

TTTT

cc

2

5

fYY ffcc

d=8 (tree-level)

d=6 (one-loop)

energy-momentum tensorT

Y is C-even and singlet under all gauge and global symmetries (flavour universal);

No more d8 operators from fermion-gauge boson sectors alone

2

2

DM

c

42

22

DY

Mc

cut-off scale

present 95% CL limits

TeV3.18

4/1

c

TeV21164

2/1

Yc

dilepton (LEP)diphoton (Tevatron)

contact interaction (LEP)dijet, Drell-Yan (Tevatron)

pepe

pepe

(Hera)

(Hera)

If, naively, then Y gives the strongest bound onDM DMotherwise DD MM TeV1 remember GIM where

Fc Gm /1

Chang, Lebedev, Loinaz, Takeuchi

Giudice, Strumia

Limits on from astrophysics (in TeV)

RMM

MD

D

P )''(''

2)(

=2 =3

31 2.75

454 27

1680 60

)('' DM

SN cooling form KK-g productionSN1987A

Diffuse -rays from decay ofKK-g trapped in NS halo

NS heat excess from KK-gdecay

they are the strongest limits on fundamental scale

bounds rapidly soften for higher

They rely on the (essentially) gapless spectrum of KK gravitons

Hannestad, Raffelt

cosmology reminder

The universe has a standard evolution up to temperatures of order

6)(GeV102)(MeV10 T

above the cooling proceeds mainly by bulk graviton production(instead of standard adiabatic expansion) =2 barely consistent with BBN

T

such a low makes inflation and baryogenesis problematic T

both astrophysical and cosmological problems are eliminated if the spectrum of KK gravitons has a sufficient gap

for instanceevades all the astrophysical bounds of present hottest astrophysical object

MeV100KKm TMeV100

How can we make ? MeV100KKm

1. KK spectrum also depends on the shape of ES, not just from R

2. New relation between and due to warped geometry

in RS set-up the branes carry some energy density and this warps the surrounding ST

2)(22 dydxdxeds Ryk

V

kR

DD

P

k

eM

M

M

)1( 22

in a loose sense, since Vcannot be precisely defined

PM DM

if a large can be obtained with a natural

TeV1kMD PM 110 kR

KK modes are now at and astrophysical and cosmologicalbounds do not apply

TeV/1 R

Randall, Sundrum

Dienes

collider phenomenology

TeV KKm

)1(1 )( nTgM

n

D

(unevenly spaced)

resonance enhancements at hadron colliders in Drell-Yan processesa portion of the parameter space already probed by Tevatron

radion

TeV )11.0( rm

TrMD

1

KK gravitons

large anomalous couplingto gluons. At hadron colliders- production mainly through gluon fusion- decay into dijet or into ZZ if kin. allowed(similar to Higgs. Indeedradion-Higgs mixing possible)no significant bound frompresent data

Up to now

SM fields confined on a brane having vanishing width

strong and e.w. interactionssuccessfully tested only up to

a part of (or all=UED) the SM fields might live in a sized ED

0L

TeV)(OE

1-TeV)(1-TeV)(L

motivations for 1-TeV)(L

early: SUSY breaking via compactificationL

mSUSY2

more recently: solutions to the `little’ hierarchy problem scale e.w.Hm

EW precision tests search for new physics

indirect evidence for a gapbetween the Higgs mass and theEW symmetry breaking scale

Antoniadis

`LITTLE’ HIERARCHY PROBLEM22

22

2

3newtFH mmGm

from the solution to the `big’ hierarchy problem: finite corrections controlledby the mass of some new particle

from EWPT CL95%GeV204Hm

GeV100newm or even lighterexpected (think, for instance to the chargino in constraint MSSM)

modest gap (factor ~ 10) can be filled

1. by a moderate fine-tuning of the parameters in the underlying theory

2. by looking to specific theories where this gap is natural

1-TeV)(L

new light weakly interacting particles: not seen in either direct searches or in EWPT

in ED with new states are expected at the TeV scale

can be protected by either- SUSY or

- gauge symmetry

2Hm

1. SUSYbroken by boundary conditions on an interval of size L

EWSB triggered by the top Yukawa couplings

is finite and calculable in terms of2 parameters (L,M)

including two-loop corrections

t

),( st

Hm

GeV)125110( HmTeV)42(1 L

42 ML

characteristic spectrum mild experimental bounds: momentum conservation along EDpreserved by gauge interactionsas in UED

- no single KK mode production- no 4f operators from tree-level KK exchange

Pomarol, Quiros; Barbieri, Hall, Nomura; Ghilencea, Groot Nibbelink, Nilles;Scrucca, Serone, Silvestrini, Zwirner,…

Appelquist, Cheng, Dobrescu

Barbieri, Marandella,Papucci

2. gauge symmetry: Higgs-gauge unificationYang-Mills theory in D>4gauge group G

MA

D gauge vector bosons

3,2,1,0De ,...,5 4D vector bosons

4D scalars

Example: G = SU(3) (8 independent generators)

A eAaA

aAaeAˆ a

eA

aeA

aeAˆ

aA ˆ

aA ˆ

8,3,2,1a7,6,5,4ˆ a

7,6,5,4ˆ a8,3,2,1aunseen unseen

WZ ,, Higgs

we can eliminate the `unseen’ by compactification on an orbifold

all fields required to have a well-defined parity

the `unseen’ states have no zero modes because they are odd

2Z

2Z

21 / ZS

Manton 1979

4D viewpoint: SU(2)xU(1) gauge symmetry + 1 Higgs doublet

general problems solutions

Higgs embedding Y(H)=1/2usually leads to wrong

- large corrections from branes at y=0,L- choose the right group e.g.

W2sin

25.0sin22 WG

Higgs self-coupling for EWSB D=5: from D-terms if SUSYD6 includes Higgsself-interactions

MNMNFF

absence of quadratic divergences from gauge sector (crucial)

key feature: residual gauge symmetry

aaa AA ˆ5

ˆ5

ˆ5

realistic Yukawa couplingsinteractions of H are universalif minimally coupled

Wilson lines

D=5 forbiddenD=6 absent in specific models

Csaki, Grojean, MurayamaBurdman, Nomura

Von Gersdorff, Irges, Quiros

)(][)0( 0

ˆ5 )(

LfePfy Lj

yAdyi

RifijYuk

La

L

invariant under both local and residual gaugetransformations

YL USU )1()2( aaa AA ˆ

5ˆ

5ˆ

5 [however may reintroduce quadratic divergences for at 1 or 2 loops]

fijy Hm

features:

- naturally light Higgs boson- KK gauge vector bosons of an extended group G- not necessarily KK replica for fermions

remarkable progress towards a realistic model in the last year!

we put fermions here and here

Csaki, Grojean, MurayamaScrucca, Serone, Silvestrini

FLAVOUR II

In ED we have a new tool to understand fermion mass hierarchy:geometry

tdue mmmm ,...,,uscbub VVV

examples

generations are `copies’ inED. FS broken by a non-trivialHiggs VEV

c ty y

several generations may arise as independent zero modes ofa single higher-dimensional fermion.

related to the properties of compactification mechanism unexplained in D=4!

gN

D.B. Kaplan, Arkani-Hamed, Schmaltz, Mirabelli

Dvali, Shifman

Troitsky, Libanov, Nougaev, FrereBiggio, Feruglio, Masina, Perez-Victoria

can we test these ideas?

most stringent bounds from FCNC

KK modes of gauge bosonshave non-constant wavefunctions

sAsgdAdg ssdd)1()1()1()1(

)1()1(ddss gg

after rotation from flavour basis to mass eigenstate basis

...2sin

2

2)1(

stdstdM

g aa

c

dd

2sin)100(/1 TeVOL

Km

Del Aguila, Santiago; Delgado, Pomarol, Quiros; Lillie, Hewett,…

Sub-mm gravity (again)

all previous statements assume that some dynamics stabilizes the radionat the right scale:

1-TeV)1()(

2

DM

xrL

in explicit models of weak scale compactification(not a theorem)

TeV1/1 LM c

eV10 32

P

cr M

Mm

radion couplingto matter mgravity-like

PM

m

observable deviations from Newton’s law at 100 m even for

1-TeV)1(Lradion becomes cosmologically `active’ if

inflation of scalecM

Chacko, Perazzi

Kolb, Servant, Tait

generic problems of ED models with cut-off scale TeV1

potentially large corrections to EW observables, conflict with EWPT

how can we understand approximate B and L conservation?

yrep

yrKp330

33

104.4)(

109.1)(

WMAPeV1

eV105.2 232

ii

atm

m

m

B & L violating operators d>4are allowed by knownlow-energy symmetries

...2

v))((2

2

LHLHL uu

QQQL

B 0 suggest GUTM

gauge coupling unification 002.0118.0)(exp3 Zm 118.0)(3 Zm

SUSY 1-loop LO

01.03 2-loop, thresholds

- the running is log- high sensitive to light particle content- unification conditions at

323

5 YGUTM

approximate B & L conservationgauge coupling unification

natural within `UV desert’

possible, but not a generic feature of IR desert

scale e.w.D1/MR

problematic if TeV1L

especially if complemented by a Grand Unified picture where

- particle classification clarified

- unification condition automatic323

5 Y GUTMat

GRAND UNIFICATION AND EDUrgent problems of conventional 4D GUTs

The Problem: DT splitting

D

du

Tdu

duH

HH

,

,,

GUTM

scale e.w.- fine-tuned in minimal models- baroque Higgs structure in non-minimal ones- usually spoiled by radiative corrections after SUSY breaking or by non-renormalizable operators

p-decay

yrGeVm

Kp T2

17

2

232

10

)(

tan1

tan210)(

Hisano, Murayama, Yanagida;Goto, Nihei

CLyrKp %90109.1)( 33

minimal SUSY SU(5) predictions

Altarelli, Feruglio, Masina

both solved if G=SU(5) is broken by compactification

AaA

aA ˆ

aA ˆ

aA

bosons gauge SMa

SM/)5(ˆ SUa

the zero modes of can be removed by appropriate parity assignment

)1()2()3()5( USUSUSU

aA ˆ

if then, for a 4D observer:

scale e.w.'/1 GUTMR

SU(5) does not exist in 4D!

in SUSY version additionalstates and one more parity

DduH ,

TduH , and parities fixed

from gauge sector

AUTOMATIC DT SPLITTINGKawamura

p-decayAltarelli, FeruglioHebecker, March-Russel

d=5 operators arise from a mass term

such a term is forbidden by a U(1) symmetry characteristicof the bulk action and extendibleto the whole theoryno d=5 (and d=4) p-decay

duHH

3)(

3)(

3)2(

33 )()( hlZ

LOZ mm

130.0...log)(

7

3 23

c

LO

M

GeV

GeVM c

17

15

10

10

Hall, Nomura Contino, Pilo, Rattazzi, Trincherini

Hall, Nomura

gauge coupling unification preserved

test:p-decay dominated by d=6 operators

FFTTM

gcO

c2

2

yrp

3410

KKKeep ,,,,, 0000

uncertainties: mixing angles and cno uncertainties from SUSY breakingRc /1

TcT brane coupling

Hebecker, March-Russel Hall, Nomura

cosmological constant and EDTwo problems

1. why is nearly zero?

2. cosmic coincidence why now? (nothing to say about this here)

1. 4D + generalcovariace

massless gravitonuniversally coupled to all sources

43 eV)10( 4scale) e.w.(

4)( PM

matter

2

1

PN

MG

then vacuum energy curves our space-time

22

PN

MGH

this is what we measure

in D>4 this is not necessarily true: can curve the ED space leaving our space flat

this might occur if depends on the wavelength of the sourceNG

wavelength coupling )(NG

cmH 2810 10 2

1

PM

10H

standard cosmology

2

1

PM

vacuum energy is the sourcewith the largest wavelengtha large does not curveour 4D space time

21

02 )(

PN

MHGH

...)( 2442* RMgxdRgydxdMS Pind

2/1 PN MG )/(1)( 2*

MGN

Dvali, Gabadadze, PorratiDvali, Gabadadze, Shifman

)2(2

2

*2

2

PPP MM

M

MH

here ED are infinite , otherwise a massless 4D graviton exists10HR

gravity modified belowdeparture from Newton potential at the sub- mm scale expected

mM 1001*

eV10 3*

Mabove gravity becomes strong and should be soften e.g. by string theory (production of Regge states)

one testable prediction

- effective field theory necessitates careful treatment - closely related picture derivable from string theory

- related approaches

PMM *

SundrumArkani-Hamed, Dimopoulos, Dvali, Gabadadze

Antoniadis, Minasian, Vanhove

Rubakov, Luty, Porrati, Rattazzi

The fine-tuning is not eliminated but the hierarchy becomes stable

Laurels beckoned us, so we started outWith Nightingale towards a mountain height.While I grappled with the sheer cliffs below,She seized her prize in easy, graceful flight.

What I may perhaps never ever reach, Took but a brief moment for the bird; O Heaven don't be so unjust, I plead, Grant me wings too. Let my prayer be heard. Roland von Eotvos