Physics of Extra Dimensions -A potential discovery for LHC/ILC -

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Physics of Extra Dimensions-A potential
discovery for LHC/ILC -
Abdel Pérez-Lorenzana CINVESTAV
PASI-2006, Puerto Vallarta. México.
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Program

• Introduction Why considering Extra Dimensions?
• Dimensional reduction, KK decomposition
• Gravitons Phenomenology
• Phenomenology of XD matter fields
• KK modes of Matter Fields Universal Extra
  Dimensions
• New Theoretical ideas for the use of XD

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D-brane models and XD
Bottom-up To study of these models we can use an
effective field theory description with M as the
UV-cutoff.
Type I String Theory framework
Brane world.- Our Universe could be described as
a hyper-surface extended in p spatial dimensions
a p-brane
160?m gt R gtgt r gtgt lP
Matter would be trapped to the brane, whereas
gravity propagates on all 4n dimensions
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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)

• Graviton exchange

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Cosmological bounds

• BBN is very sensible to the expansion rate
• At a temperature T there are N (TR)n gKK
  kinematically accessible
• T MeV n2 R0.1 mm ? N1018
• Production rate

?
?
M ? 10 TeV n2 ? Tr lt 100 MeV
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Astrophysical bounds
Hannestad Raffelt PRD 64 (2001) PRL 88 (2002)

• SN 1987a
  ? 30 TeV ( n2 )
• EGRET
• GRO M gt 500 TeV
• Neutron star heating M gt 1700 TeV

• These bounds
• Assume no short extra dimensions, and apply only
  for R lt MeV-1
• Assume no graviton decay into ligther KK modes
• gkk ? gKK gKK

Mohapatra, Nussinov Pérez-Lorenzana, PRD 68
(2003)
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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 (4n)D Schwarzschild radious
If impact parameter in a collision is smaller
than rS, a BH will form MBH vs
Cross section
About 107 BHs per year LHC !!! (?).
Rapid evaporation
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Large and short XD
Well now turn into studying physics of KK SM
exitations..
R gtgt r M-1
To have TeV String scale n 2, thus p 6-n 4

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General aspects of matter in XD
As for the graviton, any field living on the
parallel brane shall develop KK modes
The specific profile of ?n(y) is compactification
dependent.
There are few subtleties that are worth to review

• E lt 1/r Physics looks 4D
• 1/r lt E lt M Evidence of extra dimensions.
• Experimental signatures
• direct KK production
• virtual KK exchange
• E M Effective Field Theory breaks down.
• Quantum Gravity regime.

Obviously r shuld be shorter than 10-16 m (1/r gt
few hundred GeV)
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Dimensional reduction for fermions in XD
Naively, we will take massless fermions as the
solution to the Dirac equation
where GM satisfies the Clifford algebra
In 4D and chiral representations, that we use
and there is
used to define chiral states
weak interactions only couple to ?L
such that
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Dimensional reduction for fermions in XD
Naively, we will take massless fermions as the
solution to the Dirac equation
where GM satisfies the Clifford algebra
In 5D we take
Thus, with ?5 included, there is no chirality.
All fermions in 5D are four components
Extra degrees of freedom can be projected out by
orbifolding.
The overall sign will later become useful for
Model buiding
Thus, orbifolding would be a need for XD matter
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Dimensional reduction for fermions in XD
Naively, we will take massless fermions as the
solution to the Dirac equation
where GM satisfies the Clifford algebra
On can go further. In 6D
In this representation one gets
but still
In general there would be chirality in any even
dimension
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Dimensional reduction for fermions in XD
Dimensional reduction U(1)
On the other hand, since G5i?5
Last term gives
After integrating, the derivative connects odd to
even modes in mass terms
For a Dirac mass term, however
Thus
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Gauge bosons in 5D
where
Then, consider
or simply
We then get
However,
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Gauge bosons in 5D
Thus
Similarly, 5D gauge invariance
can be written as
We use this freedom and fix the gauge to
introduce the massive boson
That is, by fixing the gauge KK A5 modes are eaten
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Gauge bosons in 5D
After compactifying on the circle, we get
Since Thus, gauge coupling has mass dimensions.
So we write
Effective 4D gauge coupling is suppressed
A5 has no zero mode
By orbifolding
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Model Building

• General aspects for Model Building
• SM fields zero mode level
• Charge conservation ?? ? Gauge on bulk
  (simplest model)
• Some particles may still be attached to the
  3-brane
• ? KK number non conserved on brabe-bulk
  couplings
• ? virtual KK contribution in SM processes

? ?01/r gt 1.6 TeV

• ? In general 1/r bounded by precision tests. The
  prediction of the 5DSM for a given observable
  (using KK exchange at tree level)
• Optional SUSY

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KK virtual exchange bounds
A. Mücka, A. Pilaftsis, R. Rückl,hep-ph/0312186
Thomas G. Rizzo,hep-ph/9909232 ...
Phenomenology is very model dependent.
If all SM fields are on the bulk (Universal Extra
Dimensions), the lower limit on 1/r is rather
weak. KK loop contributions to ? parameter and
Z ? b b, indicate 1/r gt 700 GeV.
Flacke, Hooper, March-Russell (2005)
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KK mode production in colliders
KK matter couplings are the same as those of
their SM partners.
The amplitude squared for the production process
will be of order as2 but the cross-section will
be suppressed by the kinematics.
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KK mode production in colliders
KK matter couplings are the same as those of
their SM partners.
The amplitude squared for the production process
will be of order as2 but the cross-section will
be suppressed by the kinematics.
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UED and KK parity

• In 5D UED models we start with a theory that is
  5D Lorentz invariant
• KK number is conserved at tree level.
• Compactification (Orbifolding) breaks 5D Lorentz
  invariance

KK parity (-1)KK remains as a conserved
number. Interactions require an even
number of odd KK modes 1st KK modes must
be pair produced at colliders
Lightest KK particle (LKP) is stable!
DM candidate
Appelquist, Cheng, Dobrescu (2001), Rizzo (2001)
Macesanu, McMullen, Nandi (2002), Appelquist,
Yee (2002)
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Signals of UED models in colliders

• Due to KK parity a large center-of-mass energy
  is needed to produce two massive particles in the
  final state
• Radiative corrections to any electroweak
  precision observable are suppressed by the
  requirement of having two massive particles in
  the loop
• SM and 1st KK do not mix
• ?Experimental constraints on UED are Weak
  1/r gt 700 GeV
• The mass range accessible for UED models at
  present and future colliders is similar to that
  of SUSY models, in fact many aspects of UED are
  parallel to SUSY
• a sector of heavy particles with same couplings
  and SM quantum numbers
• SUSY partners ? KK Modes
• R Parity ? KK parity
• An obvious difference superpartners masses are
  generally non-degenerate, vs. high degeneracy of
  KK states in UED models at tree level
• Also No boson - fermion symmetry

Flacke, Hooper, March-Russell (2005)
Cheng, Matchev, Schmaltz, (2002)
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One loop mass spectrum for UED SM

tree level spectrum
DM candidate ?1
Cheng, Matchev Schmaltz (2002)
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Outlook for UED

• In UED, DM candidates could be
• KK photon (most likely in sole SM scenario)
• KK neutrinos
• KK Gravitons, ( NLKP B1? ? g1 with t 1012 s.
  Diffuse gamma flux signal )
• Light Radions
• LKP is stable due to remnant space-time
  symmetries. It fulfills the characteristics of a
  WIMP
• 1st KK level quarks and gluons produced at a
  hadron collider will decay to the LKP, radiating
  semi-soft leptons and jets.
• Overall Experimental signals for this scenario
  will be similar to that of a SUSY model with
  almost degenerate mass spectrum for the
  superpartners, and the LSP being a neutralino (a
  detailed analysis is still needed)
• Graviton production signals should also be
  present (there should large XD)

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KK pair production at LHC
Macesanu, hep-ph/0510418
Total
q G
q q
GG
LHC production rates for KK quark and gluon pairs
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XD Relic abundance
Relic abundance consistent with WMAP observation
at 1s (2 s)
Kakizaki, Matsumoto Senami, PRD 74 023504
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Detection of XD DM

• Direct detection
• WIMP nuclei scattering

Ge detectors
NaI detectors
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• Addressing Theoretical issues
• What happened to gauge Unification?
• How do we get small neutrino mass?
• What about proton decay?
• Other theoretical uses of XD
• ? New ideas for Symmetry Breaking
• Do we really need large XD to get TeV physics?
• ? RS Models

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Running of gauge couplings

• 4D RGE (MS)

for
The one-loop beta functions
Using SU(5) normalization
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Running of gauge couplings
Dienes, Dudas, Gherghetta PLB436, 55 (1998)

• Running in XD

KK modes provide the contribution
Thus, one gets a Power Law Running
The formula can be verified using standard step
by step running
with ?0 1/r
Using Stirlings formula
Pérez-Lorenzana, Mohapatra (1999)
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Running of gauge couplings
The one-loop running
provides the Unification formula
which amounts to the condition

• FP 0 ? ?0 M MGUT
• With the right KK fields ?0 could be free
• One loop unification is bad though ( gt2? )
• Successful unification needs threshold effects
  (UV dependence).

Typically Mr 10 - 100
Dienes, Dudas, Gherghetta (1998) Ghilenchea,
Ross (1998)Delgado, Quiros (1999)
Pérez-Lorenzana, Mohapatra (1999), Hebecker,
Westphal (2003),...
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Ideas for neutrino mass
Arkani-Hammed et al. Dienes et al., 1998

• MS on brane with L global ? NO (LH)2
  ?L2
• with a bulk neutrino

Thus

• No ßß0? !

• Notice the mass is R independent !!
• KK neutrinos disturb the oscillation pattern !!

Current neutrino data excludes light ?KK
1/R 10 eV ? R 10-2 ?m
Dvali Smirnov (1999) Mohapatra, Nandi
Pérez-Lorenzana (1999), (2000)
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Ideas for neutrino mass
Mohapatra, Pires Pérez-Lorenzana (2000)
Bulk Models for Majorana mases

• Consider a bulk scalar singlet ?(L 2)
• ( LH )2 NOT allowed by L-symmetry,

Take for instance d 2 with ? (10 GeV)2
and M 100 TeV
mM h10 eV
Small vevs need a light mass

• Possible emission of Majorons in ßß0?

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Split Fermions. Hierarchies without Symmetries
Arkani-Hamed, Schmaltz, PRD61, 033005 (2000)
Localization of fermions within a tick brane in
5D L M-1
Consider a massless fermion on a tick wall
background
The equations of motion go as
for
Zero mode level (?0 0)
For a kink
a localized mode
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Split Fermions. Hierarchies without Symmetries
Generalizing to more fermions
Chiral (zero mode) fermions would be localized at
the zeros of
Consider the Yukawa Coupling ? H L Ec
Exponentially suppressed couplings
Consider the operator
where
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Baryon number violation in 6D Models

• A larger Lorentz symmetry implies more
  constraints on effective physics

Appelquist, et al., (2001)
6D SM
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SM in 6D and the number of generations

• Theory is free of local gravitational anomalies
  if

• Cancellation of global gauge anomalies requires

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Orbifold Symmetry Breaking

• Orbifold conditions can be used to break down
  continuos symmetries

Consider a local SU(2)
The invariance of kinetic term requires
Inner automorphism
For we get the parities
A further orbifolding may remove the extra
massless scalar
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Scherk-Schwarz Breaking
From Ordinary to Scherk-Schwarz compactification

• C is constructed by the identification y
  tg(y) for tg in rep(G) For instance, using
  tg(y) y 2 nR
• A necessary and sufficient condition to keep
  the invariance
• f(tg(y)) Tg f(y) (twist) for Tg a
  rep. of G acting on field space. Ordinary
  compactification Tg 1 for any g in G
• Scherk-Schwarz compactification Tg ? 1 for
  some g in G
• Twisted Fields are NOT single-value functions
  on C

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Hosotani Breaking
Hosotani, PLB126, 309 (1983)
Tr FMNFMN contains the term
Suppose that from some dynamics
we then get the mass term
Thus
Cheng, Matchev, Schmaltz, PRD66, 036005 (2003)
Indeed, in compact space an A5 mass is not
protected
One loop radiative corrections give in general
SSB if
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RS Models
Randall, Sundrum, PRL83 3370 (1999) M.
Gogberashvili, hep-ph/9812296
Bulk geometry is non factorizable, but
preserve 4D Poincaré Invariance
Model setup
Now, effective Planck scale
One can easily make v mEW if v0 MP and ?
r 12 A large scales hierarchy with small
dimensions
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Final Remarks

• Extra Dimensional models are an attempt to
  explore, using an effective field theory
  approach, the possible low energy String theory
  effects that might appear in experiments,
  provided the Fundamental scale comes out to be
  much smaller than the Planck scale
• However, although Models with extra dimensions
  are usually built using ideas that are well
  motivated by String Theory constructions, most of
  the time no real String Theory calculations are
  actually done, which, on the other hand, may be
  justified when we explore physics well below
  Fundamental scale, where only the first KK modes
  are really relevant.
• If it happens that indeed extra dimensions are
  large, and fundamental scale is close to mEW ,
  LCH and any future collider would be in the
  position to detect and explore the very first
  manifestations of String Theory, through KK mode
  physics.
• A draw back of Models with Extra Dimensions is
  that, apart from some very generic features in
  graviton and KK mode physics, most Extra
  Dimensional predictions are very model dependent
  (so far).
• Nevertheless, some special scenarios seem to be
  very appealing from the theoretical grounds, and
  I believe they deserve to be considered
  seriously.
• Furthermore , from the theoretical point of
  view, Extra dimensions continue providing new
  ways to look at old problems (hierarchy problems,
  symmetry breaking, unification, etc.)