1. The Transverse asymmetry AT2 of B→K*(→K)l+l- in SM and supersymmetry
Joaquim Matias
Universitat Autònoma de Barcelona
Orsay, Nov. 2007
U. Egede, T. Hurth, J.M. in progress
E.Lunghi, J.M., JHEP 0704:058,2007.
F.Kruger, J.M. Phys.Rev.D71:094009,2005

2. Outline
Motivation
Angular distribution and Transversity Amplitudes of B→K*(→K)l+l-
Phenomenological discussion of AT2(s) :
SM prediction for the K* polarization at NLO and AT2(s)
Main theoretical uncertainties
AT2(s) of B→K*(→K)l+l- in supersymmetry
Experimental sensitivity to AT2(s) .
Conclusions

3. Motivation K* spin amplitudes: A,A ,A0 ,At
B0→K*l+l- provides valuable information in different ways:
Branching ratio, FB and isospin asymmetry
Angular distribution B→K*(→K)l+l- provide an excellent test of the chiral structure of the fundamental theory that lies beyond the SM
Step I
Step II
Step III
K* spin amplitudes: A,A ,A0 ,At
Quantities with controlled QCD uncertainties sensitive to right-handed currents.
Experimental resolution

4. Angular Distribution in B→K*(→K)l+l- Theoretical Framework
Effective Hamiltonian for decays based on b→sl+l-:
We focus on magnetic penguins and semi-leptonic operators:
and the primed operator
Also chiral partners are considered.

5. Given Heff the matrix element for the decay B→K*(→K)l+l- reads:
q is the four-momentum of the lepton pair
mb=mb() is the running mass in the MS scheme.
Hadronic matrix elements parametrized in terms of B→K* form factors:

6. How to deal with form factors? Leading order:
Key observation: in the limit of M heavy and Efinal meson large:
Ai(s), Ti(s), V(s) form factors reduce to TWO universal form factors (, )
Valid for the soft contribution to the form factor at large recoil.
Predictions restricted to the kinematic region:
where EK* is large and dilepton mass is small.
Violated by symmetry breaking corrections of order s and 1/mb
Next to Leading Order:
Factorizable & non-factorizable strong interaction corrections in QCDF

7. Transversity amplitudes
The differential decay rate of the decay B0→K*(→K)l+l- is described by four
independent kinematic variables:
Evaluation using Transversity (or Helicity) amplitudes:
lepton and hadron tensors in helicity space:

8. These define
the angles
of the distribution:
in the physical
region: *

9. Ii depend on products of the four K* spin amplitudes A,A ,A0 ,At.
Next question is the evaluation of the spin amplitudes (helicity amplitudes)

10. Transversity amplitudes in the heavy quark and E limit:
In the SM (C’7eff=0) recover naive quark-model prediction A=-A in the limit mB → and EK* →. ( )

11. Transversity amplitudes at NLO
We include factorizable & non-factorizable corrections at NLL order replacing:
with the Wilson coefficients C9 taken at NNLL order.
(f) factorizable and (nf) non-factorizable contributions
and

12. The angular distribution of the decay B0→K
The angular distribution of the decay B0→K*(→K)l+l- allows to extract information on K* spin amplitudes.
Transverse asymmetries:
K* polarization parameter:
Fraction of K* polarization:
Integrated quantities:

13. Main sources of uncertainty:
The dependence on soft form factors (0) play a fundamental role:
AT1(s) and AT2(s) cancel (0) exactly at LO in the limit.
Sensitivity of NLL result to scale dependence
Variation of mc/mb used 0.27 mc/mb0.31 affects matrix elements of chromomagnetic operator, mainly F1,2(7,9)
Error associated to the rest of input parameters (masses, decay
constants, etc.) are taken in quadrature.
What about the /mb power corrections?
we allow

14. AT(1)
AT(2)
aK*

15. B → K*(→K)l+l-
in supersymmetry

16. Gluino mediated FCNC:
New Physics model allowing for a large C7eff ’ : AT2(s)  C7eff x C7eff ’
Model: MSSM with non-minimal flavour changing in down-squark sector.
The down-squark mass matrix is:
where
Off-diagonal entries parametrized:
We perform exact diagonalization of squark mass matrices.

17. → Main contributions: Penguin diagrams with gluino- down squark.
Minimal Flavour Violation: suppressed by ms/mb
Non-zero mass insertion in down sector.
From the approximate expressions:
Main Parameters of the model:
Mgl , (32d)LR , md , tan=5 (low) ~

18. can only increase/decrease
→ Experimental Constraints:
Most recent NNLO results reproduced:
NLONNLO
BR(B→Xs)
and
Integrated
Transverse asymmetries
1 GeV2<s<6 GeV2 SM
Exp 95%
BR(B→Xs) and AT1
can only increase/decrease
with C7eff’

19. → Experimental Constraints:
Mass insertion (32d)LR impacts MBs via:
We impose also the constraints from:
 parameter: =(-0.5±1.1) x 10-3
Higgs mass: mh > 89.8 GeV
supersymmetric particle searches:
m± > 100 GeV, m0 > 40 GeV, mq > 100 GeV
Automatic fulfillment of Bs→ for low tan 
Vacuum stability constraints (absence of CCB and UFB) are ALSO FULFILLED:
and
both are ~ depending on the average of squark masses and in
agreement with our ranges (Don’t be confused with the constrain to a
different mass insertion which is irrelevant to us) ~

20. We have explored the space of parameters in two regions:
Results:
We have explored the space of parameters in two regions:
→ SCENARIO A: Specifically:
Common: a) b)

21. → SCENARIO B: Specifically:
Common: c) d)

22. Experimental Sensitivity to
AT2

23. Fitting AT2(s), FL(s),… from the individual angle distributions:
Toy Monte Carlo: N0=4032 s b. in 2 fb-1

24. Fit values of AT(2) from 500 toy Monte Carlo: (VERY PRELIMINAR!!!)
1 < q2 < 6 GeV2/c4 using SM assumptions with 2 fb-1
RESOLUTION:

25. AT(1,2): NP in C’7eff and in C9,10
We take also into account the constrain on C9,10 from rare decays
A determination of the magnitude of RH currents is possible even in presence of NP in C9,10 of 20%.
AT(1,2) are a useful probe of the electromagnetic penguin operator O’7

26. Conclusions
The analysis of the angular distribution in the decay B0→K*(→Kp)l+l-
provides a new way to test the chiral structure of the fundamental theory.
AT(2) asymmetry is the most promising and robust observable:
- Low sensitivity to hadronic uncertainties (0),
- A measurement in the low dilepton mass region different from their SM
values could be a hint of new physics with right-handed quark currents.
- They are a useful probe of the operator O7’.
Supersymmetry with a with non-minimal flavour changing in down-squark sector has a huge impact on AT(2) even for low tan .
Expected resolution for AT(2) is 0.42 but improves tremendously to 0.14 in the
very low q2 region where the sensitivity to O7’ is maximal!!!