Diapositiva 1

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Rossella Ferrandes Bari University and INFN
LNF Spring School, Frascati 15/19 May 2006
Outline

• Introduction to Extra Dimensions
• The ACD model with a single Universal Extra
  Dimension
• Rare B decays to constrain the ACD scenario

based on work in collaboration with P.Colangelo,
F. De Fazio and T.N. Pham (hep-ph/0604029)
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Motivations to introduce Extra Dimensions

• unification of gravity and SM gauge interactions
• quantization of gravitational interactions
  (string theory)
• hierarchy problem
• dark matter
• cosmological constant problem

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Kaluza-Klein theories
Our (31) space-time is assumed to be embedded in
a D-dimensional space-time, known as the bulk.
The extra-dimensions form a compact space with
certain compactification scale R.
Physical implications of the compact extra
dimensions
Consider a single extra-dimension compactified on
a circle of radius R.
Fourier expanding
Kaluza-Klein excitations
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The size and geometry of the bulk, as well as the
types of particles which are allowed to propagate
in the bulk, vary among different models.

• Braneworld models

It is common practice to assume that the SM
fields are confined to our 4 dimensional world
(brane). Only gravity propagates in the bulk.

• Arkani-Hamed, Dimopoulos, Dvali (ADD) model
• Randall Sundrum (RS) models

• Universal Extra Dimensions models

All the SM fields are allowed to propagate in the
extra dimensions. All the SM particles aquire a
KK tower of excitations.
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Appelquist-Cheng-Dobrescu (ACD) model with a
single UED

• Universal Extra Dimensions
• Single new parameter the compactification radius
  R
• Experimental bounds on 1/R are different than
  other extra-dimensional models
• Provides good dark matter candidate (the lightest
  KK particle, LKP, which is stable, due to the KK
  parity conservation)

Bounds from electroweak precision observables
ACD model may have interesting predictions for
collider phenomenology.
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Orbifold compactification in ACD
Consider a single extra-dimension compactified on
S1/Z2
SM field
KK excitations
SM fields are identified with zero-modes.
We require that fields have definite properties
under the reflection
even
fields which have a correspondent in the SM
fields having no SM partner (for example fermions
with unwanted chirality or the fifth component of
gauge fields)
odd
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Rare FCNC B transitions can be used to constrain
the ACD scenario
FCNC transitions are induced at loop level and
hence they are strongly suppressed in the SM.
Their investigation allows to probe indirectly
high energy scales of the theory, since the
loop-contributions from high energy modes could
be non negligible.
For example, KK modes could be obtained
indirectly through the analysis of processes
induced by transitions.
It is possible to establish a lower bound on 1/R
from the following decays, by comparing
theoretical predictions with experimental data
inclusive decays
exclusive decays
non affected by form factors uncertainty
experimentally cleaner

• Buras et al., Nucl. Phys. B 660 (2003)
• Buras et al., Nucl. Phys. B 678 (2004)

These decays are described in the framework of
the Operator Product Expansion.
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Operator Product Expansion (OPE)
OPE allows to disentangle SD and LD effects by
integrating out the W boson and other fields
with mass larger than a certain factorization
scale.
Wilson coefficients, determined by matching
full theory
Due to asymptotic freedom of QCD, the strong
interaction effects at short distances are
calculable in perturbation theory.
MW
short distance
However, as a result of matching procedure at the
scale MW and RG equations
effective theory
m (a few GeV)
long distance
LARGE! spoils the validity of the usual
perturbation theory
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Renormalization Group improved perturbation theory
It is necessary to perform a RG analysis which
allows an efficient summation of logarithmic
terms to all orders in perturbation theory.
LO summation of terms
NLO summation of
terms
Wilson coefficients
RG contributions from the scale MW down to m

• INAMI-LIM functions
• short distance loop functions (penguins, boxes)

In transitions the main
contributions come from the top quark.
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Basic structure of decay amplitudes
Inami-Lim fuctions (perturbation theory)
(nonperturbative)
QCD RG factors (RG improved perturbation theory)
The Inami-Lim functions are modified in the ACD
model
The KK modes can contribute as intermediate
states in penguin and box diagrams.
computed by Buras et al. GIM mechanism improves
the convergence of the sum over the KK modes of
top.
SM
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Minimal Flavour Violation (no new operators CKM
matrix)
current-current operators
long distance effects (neglected)
QCD penguin operators
small Wilson coefficients
magnetic penguin operators
main contributions come from these operators
semileptonic EW penguin operators
We only need the coefficients C7, C9, C10. The
impact of the KK modes consists in an enhancement
of C10 and a suppression of C7.
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Form factors
Hadronic form factors are the main source of
theoretical uncertainty. Their uncertainty must
be taken into account, since it can overshadow
the sensitivity to 1/R. We shall show this is not
always the case. To take into account this
uncertainty, we use two sets of results
form factors obtained by three-point QCD sum
rules based on

• the short distance expansion

set A
set B

• the light-cone expansion

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Branching Fraction
Belle
BaBar
B
A
set B allows to exclude
In the SM limit set A prefers BaBar result,
while set B is in better agreement with Belle
data.
Improved measurements should resolve the present
discrepancy between the two experiments.
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Branching Fraction
Belle
BaBar
A
B
set B and Belle results seem to indicate 1/Rgt 200
GeV
The present discrepancy between BaBar and Belle
measurements does not allow stronger conclusions
more precise data are expected.
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Forward-Backward Asymmetry
In the SM, due to the opposite sign between C7
and C9, Afb has a zero. Its position is almost
independent of the model for the form factors
(theoretically clean observable).
. The zero of Afb could distinguish among SM
predictions and models beyond SM.
In the ACD model it is sensitive to the
compactification radius, so that its experimental
determination could constrain R.
A
B
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Large forward-backward asymmetry is observed
The analysis performed by Belle Collaboration
indicates that the relative sign of the Wilson
coefficients C7 and C9 is negative, confirming
that Afb should have a zero. Its accurate
measurement is within the reach of current
experiments.
Belle hep-ex/0603018
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Only a single penguin operator (theoretically
clean channel). Long distance effects are absent.
Branching Fractions
B
A
A
B
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Branching Fraction
B
A
set B allows to put
set A allows to put
The sensitivity to the compactification radius is
evident.
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Conclusions and perspectives
We have analysed the rare
, and
decays in the ACD model with a single
universal extra dimension.
We have studied how their BR, various
distributions and the lepton Afb in
are modified by the introduction of the fifth
dimension.
The possibility to constrain 1/R is slightly
model dependent. However, various distribution
are very promising in order to constrain 1/R.
With the improved experimental data and the
theoretical uncertainties reduced, it should be
possible in the future to distinguish the
predictions of the ACD model from the SM ones,
and to establish more stringent constraints on
1/R.