Rahul Sinha The Institute of Mathematical Sciences Chennai

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 Rahul Sinha The Institute of Mathematical Sciences, Chennai, India CKM 2016 TIFR, Mumbai

Rahul Sinha The Institute of Mathematical Sciences, Chennai, India CKM 2016 TIFR, Mumbai

 J. Matias et. al. Das, Mandal, R. S. …

J. Matias et. al. Das, Mandal, R. S. …

Our approach differs from the previous approaches • Previous approach is to try and

Our approach differs from the previous approaches • Previous approach is to try and evaluate the angular observables as accurately as possible. See talks by ⁃ J. M. Camlich, J. Mathias, J. Virto ⁃ S. Wehle, J. Mathias Lepton flavor violation • Given the large number of observables our approach is to try and eliminate theoretical parameters in terms of observables. Easier said than done… ⁃ Talk by R. Mandal

One cannot eliminate all theoretical parameters. At least one parameter will always be left.

One cannot eliminate all theoretical parameters. At least one parameter will always be left. Reparameterization Invariance … • Can one measure the weak phase of a penguin diagram? David London, Nita Sinha and R. S. , Phys. Rev. D 60, 074020 (1999). • Patterns of new physics in B decays, M. Imbeault, D. London, C. Sharma, N. Sinha and R. S. , Phys. Lett. B 653, 254 (2007) [ar. Xiv: hep-ph/0608169]. Understanding both long distance and short distance effects (i. e. , evaluating SM Wilson coefficients) accurately is essential to discover New Physics. However, we attempt to eliminate all but one parameter.

 nonlocal hadronic matrix elements M. Beneke and T. Feldmann, Nucl. Phys. B 592

nonlocal hadronic matrix elements M. Beneke and T. Feldmann, Nucl. Phys. B 592 (2001) 3 A. Khodjamirian, T. Mannel, A. A. Pivovarov and Y. -M. Wang, JHEP 1009, 089 (2010). A. Khodjamirian ar. Xiv: 1312. 6480

Lorentz invariance to write the most general form of the Matrix element Nonlocal hadronic

Lorentz invariance to write the most general form of the Matrix element Nonlocal hadronic matrix elements

 factorizable & non factorizable contributions

factorizable & non factorizable contributions

 Accents from some characters have been dropped for simplicity of notation when compared

Accents from some characters have been dropped for simplicity of notation when compared with our papers - Rusa Mandal, Rahul Sinha, Diganta Das, Phys. Rev. D 90, 096006 (2014).

We have the helicity amplitudes: An important step is to separate the real and

We have the helicity amplitudes: An important step is to separate the real and imaginary parts of the amplitude. Three observables are non-zero only if the amplitude has an imaginary part Note: Ours is not merely a change of notation. Nonfactorizable loop corrections, power-corrections are all notionally included. We will use data to directly instead of theory ….

The observables recast to look simple for analytic solutions where

The observables recast to look simple for analytic solutions where

 4 independent observables to solve for 4 parameters

4 independent observables to solve for 4 parameters

 T. Blake, T. Gershon and G. Hiller, [ar. Xiv: 1501. 03309 [hep-ex]].

T. Blake, T. Gershon and G. Hiller, [ar. Xiv: 1501. 03309 [hep-ex]].

 Hiller, Ziwcky ’ 14

Hiller, Ziwcky ’ 14

 Grinstein, Prijol ’ 04 C. Bobeth, G. Hiller and D. van Dyk, Phys.

Grinstein, Prijol ’ 04 C. Bobeth, G. Hiller and D. van Dyk, Phys. Rev. D 87 (2013) 3, 034016

 Resonances cannot be accommodated in a Taylor expansion. Experimental binned measurements include resonance

Resonances cannot be accommodated in a Taylor expansion. Experimental binned measurements include resonance contributions. We will see that the effect of resonances is such that it will strengthen the conclusions. Thanks to Marcin, Nicola, Danny, Gino… for discussions on this

Fit to 14 bin LHCb data R. Aaij et al. [LHCb Collaboration], JHEP 1602,

Fit to 14 bin LHCb data R. Aaij et al. [LHCb Collaboration], JHEP 1602, 104 (2016),

Coefficients and their convergence

Coefficients and their convergence

Convergence of coefficients

Convergence of coefficients

A. Bharucha, D. M. Straub and R. Zwicky, JHEP 1608, 098 (2016)

A. Bharucha, D. M. Straub and R. Zwicky, JHEP 1608, 098 (2016)

 Large deviation between slopes SM What is wrong? ? ?

Large deviation between slopes SM What is wrong? ? ?

 In the presence of right-handed currents: All angular observables are altered.

In the presence of right-handed currents: All angular observables are altered.

 SM input Abinash Nayak, Anirban Karan, Rusa Mandal, R. S. , Tom Browder

SM input Abinash Nayak, Anirban Karan, Rusa Mandal, R. S. , Tom Browder ar. Xiv: 1603: 04355

where For those suspicious among audience to verify later…

where For those suspicious among audience to verify later…

Taylor expansion of form factors:

Taylor expansion of form factors: