- Slides: 31
Rahul Sinha The Institute of Mathematical Sciences, Chennai, India CKM 2016 TIFR, Mumbai
J. Matias et. al. Das, Mandal, R. S. …
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. 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 (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 matrix elements
factorizable & non factorizable contributions
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 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
4 independent observables to solve for 4 parameters
T. Blake, T. Gershon and G. Hiller, [ar. Xiv: 1501. 03309 [hep-ex]].
Hiller, Ziwcky ’ 14
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 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, 104 (2016),
Coefficients and their convergence
Convergence of coefficients
A. Bharucha, D. M. Straub and R. Zwicky, JHEP 1608, 098 (2016)
Large deviation between slopes SM What is wrong? ? ?
In the presence of right-handed currents: All angular observables are altered.
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…
Taylor expansion of form factors: