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Physics of Extra Dimensions - A potential discovery for LHC/ILC -. Abdel Pérez-Lorenzana CINVESTAV. PASI-2006, Puerto Vallarta. México. Introduction: Why considering Extra Dimensions? Dimensional reduction: The Effective Field Theory KK decomposition on torii and orbifolds

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physics of extra dimensions a potential discovery for lhc ilc
Physics of Extra Dimensions-A potential discovery for LHC/ILC -

Abdel Pérez-Lorenzana

CINVESTAV

PASI-2006, Puerto Vallarta. México.

program
Introduction: Why considering Extra Dimensions?

Dimensional reduction: The Effective Field Theory

KK decomposition on torii and orbifolds

General phenomenological aspects

Gravitons Phenomenology

Phenomenology of XD matter fields

KK modes of Matter Fields: Universal Extra Dimensions

New Theoretical ideas for the use of XD

Program
wonders from the xx century

´

´

SU

(

3

)

SU

(

2

)

U

(

1

)

c

L

Y

=

+

Q

T

Y

1

3

2

-

-

-

Q

(

3

,

2

,

);

L

(

1

,

2

,

1

);

e

(

1

,

1

,

2

);

u

(

3

,

1

,

);

d

(

3

,

1

,

)

4

1

2

R

R

R

3

3

3

H

(

1

,

2

,

1

)

(

)

d

»

-

l

-

L

2

2

2

:

m

f

+

H

p

8

G

-

=

R

g

R

T

1

N

mn

mn

mn

2

4

c

Wonders from the XX century
  • Fundamental interactions are described using two different frameworks:
    • Electroweak and Strong forces in the Standard Model:
      • Gauge Quantum Field Theories

with matter in irrep

      • Symmetry Breaking by Higgs Mechanism
          • Hierarchy problem
          • Gauge and Flavor Problems…
    • Gravity as Geometry of the Space Time: General Relativity
        • Not a Quantum Theory (non renormalizable),…. DM, DE, …
the unification scheme

Gravity

Theory of Everything??

Weak

E-M

QG ??

Strong

The Unification Scheme

While MGUT is calculable, the only plausible scale for Quantum Gravity seems to be the Planck Scale

the dream for a unified theory

Non Rel QM

Class FT

Relativistic Mech

GN 0

c  0

QFT

GN  0

GN 0

ħ  0

ToE[α(GN ,ħ,c)]

c  0

ħ  0

Gen Rel

c  0

ħ  0

Newtonian Mech

The Dream for a Unified Theory

The best known candidate for the ToE is String Theory…

string theory and extra dimensions

Moduli Space of M Theory

HE

Sugra D=10

String Theory needs extra compact space-like dimensions to be consistent ( D=10 or D=11 for M Theory ).

S

T

S

HO

M-Theory

Type II A

S

T

XD are compact and usually assumed to be

small

Type I

Type II B

L

Planck

String Theory and Extra Dimensions
the scale of st

In the Perturbative Heterotic String Theory Gravity and Gauge interactions have the same origin, as massless modes of the closed Heterotic String, and they are Unified at the String Scale

=

a

M

M

S

s

P

a

»

0

.

04

S

Along the 80’s some authors (Antoniadis, Benakli, Quirós) suggested the possibility of having intermediate scales

11

M

~

v

M

~

10

GeV

*

P

Recent developments on String Theory have given support to the idea that (some) extra dimensions could rather be larger than Planck length (Horava-Witten,´96)

ST

Can MString« MPlanck ?

The scale of ST
d brane models and xd

Parallel XD

Dp-brane

3-brane

Open String

Closed String

( Gravity )

r

(Gauge)

R

Perperdicular XD

In 1998 Arkani-Hammed, Dimopoulus and D’vali made the key observation that extra dimensions could even be of millimeter size and M* as low as few TeV !!

D-brane models and XD

Type I Sring Theory framework

Brane world.-Our Universe could be described as a hyper-surface extended in p spatial dimensions:a p-brane

R >> r >> ℓP

Matter would be trapped to the brane, whereas gravity propagates on all 4+n dimensions

Bottom-up: To study of these models we can use an effective field theory description with M* as the UV-cutoff.

d brane models and xd9

Parallel XD

Dp-brane

3-brane

Open String

Closed String

( Gravity )

r

(Gauge)

R

Perperdicular XD

D-brane models and XD

Type I Sring Theory framework

  • Experimental signals of TeV scale strings in LCH/ILC may come from:
  • new compactified parallel dimensions (D-brane SM)
  • new extra large transverse dimensions and low scale quantum gravity
  • genuine string and quantum gravity effects
  • There exist interesting implications in non accelerator experiments due to bulk states

Bottom-up: To study of these models we can use an effective field theory description with M* as the UV-cutoff.

m p vs m

vs.

MP vs. M*

If Einstein gravity theory holds, fundamental gravity coupling does not necessarily coincide with the Newton constant!!

The simplest scenario would be considering a flat topology for the extra space, where the bulk is a factorized manifold of the form M4×T n

ADD, 1998

M* ≈ few TeV ?!!

Notice:Vn encodes the actual geometry of the internal manifold.

large and short xd

R

3-brane

r

4 brane

Large and short XD

A simple toy model one can consider is an effective field theory on a the torus topology.

R >> r ≥ M*−1

effective field theory prescriptions
Effective Field Theory Prescriptions
  • To begin with,
  • We identify M*as the String scale or Quantum Gravity scale, so bellow such a scale we can use an effective field theory approach
  • We’ll take the brane just as an effective (p+1)D flat surface, inspired on the low energy limit of a p-brane.
  • As for the compact manifold, we will also assume it flat, with some given coordinates y, such that the brane is localized at some (fixed) point y0
  • Thus, we need to describe a theory containing fields living on the brane (as SM fields) and in the bulk (as gravity and perhaps SM singlets), as well as the interactions among them.
effective field theory prescriptions13
Effective Field Theory Prescriptions
  • Bulk fields are described by the higher dimensional action

as S is dimensionless:

  • 3-Brane fields, as usual, are described by a four dimensional action, which is easily promoted into a 4 + n dimensional expression
  • Brane-Bulk field interactions are localized on space
dimensional reduction 5d toy model

x

- πR

0

πR

zero mode

KK modes

Dimensional reduction: 5D toy model

Consider a bulk scalar field φ(x; y).φ(x; y) = φ(x; y + 2R)

Thus, φ(x; y) can be Fourier expanded

After inserting in the bulk action:

for A=,5

we get the effective action:

where the KK mass:

Expected from PAPA = p p + p52= m2

dimensional reduction 5d toy model15

b

1

2

R

n=3

n=2

n=1

n=0

Dimensional reduction: 5D toy model

On the Torus Tn the spectrum would be similar, but degeneracy on KK levels increases.

  • E < 1/R: Physics looks 4D
  • 1/R < E < M*: up to N~(ER)n KK modes involved. Evidence of extra dimensions.
    • Experimental signatures
      • direct KK production
      • virtual KK exchange
  • E ≥ M*: Effective Field Theory breaks down.
  • Quantum Gravity regime.
dimensional reduction the s 1 z 2 orbifold

x

- πR

0

Z2

πR

x

0

πR

U(1)/Z2

cos(ny/R)

sin(ny/R)

n=3

n=2

n=1

odd modes

even modes

n=0

Dimensional reduction: the S1/Z2 orbifold

Take the circle and identify opposite points on it.

Z2 : y →- y

  • Thus:
  • - The physical space becomes the interval [0; πR]
  • There are two fixed points: y = 0; πR
  • A scalar field living on this space should now satisfy the conditions
  • periodicity:φ(x; y) = φ(x; y + 2πR)
  • - parity: Z2 φ(x; y) = ± φ(x; y)
brane to bulk couplings

φn

Brane to Bulk Couplings

To get a feeling for the phenomenology, consider:

Using the KK expansion, we get:

One gets asuppressed effective coupling:

  • Only half of the modes.
  • KK modes get an extra √2
  • - p┴ is not conserved !!

Production of a bulk mode out of brane collisions:

Decay rates:

kk exchange by brane fields
KK exchange by brane fields
  • Consider the effectuve interaction
  • By summing up (5D):
  • At low energies, q2 << m2 << 1/R2, we get:
  • At high energies, q2 >> 1/R2,on the other hand:

since N = MR = MP2 / M*2

bulk to bulk coupling suppression

p

k

k ± p

Bulk to Bulk Coupling Suppression

Take for instance the coupling in 5D on [ -πR, πR ]

Integrating over the extra dimension we shall get

Orthogonality implies

Fifth momentum is “conserved” in a way that does not constrain the actual direction of the transverse component( the sign of p5 is “irrelevant”)

Actually, former p5 conservation is now manifested only as a parity: (-1 )KK

We’ll come back to the orbifold latter…

the graviton

®

h

+

g

h

1

MN

MN

MN

+

1

n

/

2

2

M

*

The Graviton

Giudice, Ratazzi & Wells, NPB 544,3 (1999)

Han, Lykken & Zhang, PRD 59, 105006 (1999)

Take the action for a particle on the brane

and consider the perturbed metric

hMNis a symmetric tensor, + general coordinates invariance of GR, implies: D(D - 3)/2 independent deg. of freedom

we get, at first order in h the Matter to graviton effective coupling

Possible physical processes are:

i) Graviton exchange

ii) Graviton emission

where

gravity at short distances
Gravity at short distances

At the classical limit Graviton exchange should provide the law for Gravitational interactions

Existence of extra dimensions could be probed by short distance gravity experiments

At large distances, gravity would appear as effectively four dimensional:

At short distances, however, it would

reveal its higher dimensional nature

Both regimes do match :

At intermediate scales, just above threshold:

But,… How large could R be?...

simplest bounds on m and r

r1

r2

C.D. Hoyle et al., hep-ph/0405262

a

r ≥ a

Sensible to 10–16 N·m

Simplest Bounds on M* and R

Testing Newton’s law at short distances is not that easy …

F~ GNr1 r2 a4

For: r ~ 20 gr/cm3:

F ~ 10–5 N × ( a/10 cm )4

This was indeed the strength measured by Cavendish in 1798 !!

Going to smaller distances must face:

– Surface electrostatic potentials:~ r −2

– Magnetic forces~ r −4

– Casimir forces, important for r ~  m

simplest bounds on m and r23
Simplest Bounds on M* and R

Experiments probing short distance gravity have tested Newton’s law down to 160 m.No deviations had been found.

Eöt-Was experiment (Washington)

C.D. Hoyle et al.,hep-ph/0405262

Testing for:

where, for extra dimensions (r ≥ R )

α= 8n/3

simplest bounds on m and r24

1

-

³

3

10

eV

R

Simplest Bounds on M* and R

Consider

  • Thus, R < 160 m or equivalently
  • On the other hand, from collider physics we know that M*≥ 1 TeV

For n=1:

  • If we take R < 160 m, then
  • Notice that if we would rather prefer to take M ~ 1 TeV, say to have a “natural” solution to the hierarchy problem, thus:
simplest bounds on m and r25

1

-

³

3

10

eV

R

Simplest Bounds on M* and R

Consider

  • Thus, R < 160 m or equivalently
  • On the other hand, from collider physics we know that M*≥ 1 TeV

For n=2:

  • Lets take again R ≈ 160 m. Now

A solution to the Hierarchy Problem?

Might such a low fundamental scale be possible?

  • In general, for arbitrary n, with M* ~ 1 TeV, one gets
graviton phenomenology and bounds

gKK

Feynman diagrams for

During a collision of center mass energy√s there are about accesible KK graviton modes!!

Graviton phenomenology and bounds

Some Processes:Main signal would be energy loss by gravitational radiation into the bulk by any physical process on the world brane

  • Single Graviton emission: Copious production of gravitons in colliders

Giudice, Ratazzi & Wells, NPB 544,3 (1999)

Han, Lykken & Zhang, PRD 59, 105006 (1999)

Each mode has Planck suppressed couplings

Thus:

graviton phenomenology and bounds27

ILC:

Feynman diagrams for

Graviton phenomenology and bounds

Giudice, Rattazzi, Wells (1999); Mirabelli, Perelstein, Peskin (1999); Han, Likken, Zhang (1999); Cheung, Keung (1999); Balázs et al., (1999); Hewet (1999)…

LHC:

  • Single JET: p+p− → JETgKK
  • Drell-Yang: p+p− → ℓ+ℓ− gKK X
  • Background: νν
  • Background: + νν
graviton phenomenology and bounds28

up to 7 TeV

Missing energy due to graviton emission atLHC, as a function of M*, in a mono-jet production

Graviton phenomenology and bounds

Giudice, Rattazzi, Wells (1999)

graviton phenomenology and bounds29
Graviton phenomenology and bounds

unpolarized beams background limit

Total cross section forγ + gKKproduction ate+ e- linear colliderat 1 TeV center mass energy.

Giudice, Rattazzi, Wells (1999)

graviton phenomenology and bounds30
Graviton phenomenology and bounds

Abazov, et al., DØ Collab. 2003

95% C.L. exclusion contours on M* and number of extra dimensions (n) for monojet production at DØ (solid lines).

Dashed curves correspond to limits from LEP, and the dotted curve is the limit from CDF, both for γ + gKK production

graviton phenomenology and bounds31

ILC:

Explicit computations of graviton emission leads to some bounds:

Giudice & Strumia, 2003

  • Based onVn=Rn
  • Relaxed if one takes different radii

95% CL limits on M* (in TeV) for n extra dimensions from graviton emission processes in differente experiments

Graviton phenomenology and bounds

LHC:

  • Single JET: p+p− → JETgKK
  • Drell-Yang: p+p− → ℓ+ℓ− gKK X
graviton phenomenology and bounds32

gKK

  • e+ e− → f + f− Tevatron/HERA: 0.94 TeV
  • e+ e− → γγ ; W + W − ; ZZ LEP: 0.7 − 1 TeV
  • Bhabha LEP: 1.4 TeV
  • GG, q q →γγ ;CDF: 0.9 TeV

Giudice & Strumia, 2003

Graviton phenomenology and bounds
  • Graviton exchange

Giudice, Ratazzi & Wells, NPB 544,3 (1999)

Han, Lykken & Zhang, PRD 59, 105006 (1999)

graviton phenomenology and bounds33

SM Back.

Bin integrated lepton pair invariant mass distribution for Drell-Yang production for M*=2.5 and 4.0 TeV at LHC

95 % C.L. search reach for M* as a function of the integrated luminosity at LHC

Graviton phenomenology and bounds

J.L. Hewett, 1999

graviton phenomenology and bounds34

SM Background

Bin integrated angular distribution (z=cos θ) for e+ e- → + - and M*=1.5 TeV

Graviton phenomenology and bounds

95 % C.L. search reach for M* as a function of the integrated luminosity at e+ e- colliders

J.L. Hewett, 1999

cosmological bounds

+

n

2

M

+

n

1

<

*

T

r

M

P

Cosmological bounds
  • BBN is very sensible to the expansion rate
  • At a temperatureTthere are N= (TR)ngKK kinematically accessible:
  • T ~ MeV; n=2; R~0.1 mm N~1018
  • Production rate:

M* 10 TeV; n=2  Tr < 100 MeV

astrophysical bounds
Astrophysical bounds

Hannestad & Raffelt PRD 64 (2001); PRL 88 (2002)

  • SN 1987a : →30 TeV ( n=2 )
  • EGRET :
    • GRO: M* > 500 TeV
    • Neutron star heating: M* > 1700 TeV

These bounds:

  • Assume no short extra dimensions, and apply only for R < MeV−1
  • Assume no graviton decay into ligther KK modes

gkk→ gKK + gKK

Mohapatra, Nussinov & Pérez-Lorenzana, PRD 68 (2003)

microscopic black holes
Microscopic Black Holes

Microscopic Black Hole production

S.B. Giddings, S. Thomas, PRL 65 (2002) 056010

S. Dimopoulos, G. Landsberg, PRL 87 (2001) 161602

If M* ~ TeV, we may be exploring effects of Quantum Gravity in LHC/ILC

In (4+n)D Schwarzschild radious:

If impact parameter in a collision is smaller than rS, a BH will form MBH = √s

Cross section:

About 107 BH’s per year LHC !!! (?).

Rapid evaporation:

kk virtual exchange bounds
KK virtual exchange bounds

A. Mücka, A. Pilaftsis, & R. Rückl,hep-ph/0312186