1. B decays induced by b s transitions
in a scenario with a single Universal Extra Dimension
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/ )

2. 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

3. Kaluza-Klein excitations
Kaluza-Klein theories
Our (3+1) 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

4. 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.

5. 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.

6. Orbifold compactification in ACD
Z2 reflection symmetry S1
S1/Z2
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:

7. 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. u
Q(n)
U(n)
W(n) ,G(n),a(n)
n(n)
L(n) b l s
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.

8. 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. W
OPE
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

9. 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.

10. 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

11. main contributions come from these operators
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.

12. the short distance expansion the light-cone expansion
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
the light-cone expansion
set B

13. Branching Fraction Belle BaBar A B set B allows to exclude
W(n) ,G(n),a(n)
Q(n)
U(n)
Z(n),g(n) l u
Q(n)
U(n)
W(n) ,G(n),a(n)
n(n)
L(n) b l s
Branching Fraction
Belle
BaBar A B
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.

14. set B and Belle results seem to indicate 1/R> 200 GeV
Branching Fraction
Belle
BaBar A B
set B and Belle results seem to indicate 1/R> 200 GeV
The present discrepancy between BaBar and Belle measurements does not allow stronger conclusions; more precise data are expected.

15. Forward-Backward Asymmetryql B l+
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

16. 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/

17. Branching Fractions B A A B n b s
W(n) ,G(n),a(n)
Q(n)
U(n)
Z(n) u
Q(n)
U(n)
W(n) ,G(n),a(n) e
L(n)
E(n) b s n
Only a single penguin operator (theoretically clean channel).
Long distance effects are absent.
Branching Fractions B A A B

18. Branching Fraction A B set A allows to put set B allows to put
W(n) ,G(n),a(n) b s
Q(n)
U(n)
Branching Fraction A B
set A allows to put
set B allows to put
The sensitivity to the compactification radius is evident.

19. 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.