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

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

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

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.

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:

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

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:

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

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)

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* →. ( )

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

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:

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

AT(1) AT(2) aK*

B → K*(→K)l+l- in supersymmetry

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.

→ 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) ~

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’

→ 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 ~ 10-2-10-3 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) ~

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)

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

Experimental Sensitivity to AT2

Fitting AT2(s), FL(s),… from the individual angle distributions: Toy Monte Carlo: N0=4032 s. 1168 b. in 2 fb-1

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:

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

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!!!