There have been several experiments in recent times, all related to bottom (or beauty) meson sector, which show deviations from the predictions of standard model (SM) of particle physics. Out of these, the most interesting is related to lepton flavor universality (LFU) violation. In the SM, the coupling of weak gauge bosons are family independent. This is known as lepton flavor universality. LFU violation is the most enduring hints for new physics in recent times. The fact that makes it more interesting is that it has been observed in two completely different types of quark level decays, one occurring at the tree level in SM (b -> c tau nu) and another occurring at the loop level (b -> s mu+ mu-). It is surprising and also promising to see a hint of new physics in any tree level decays. These anomalies are confirmed by series of experiments performed by Belle (KEK, Japan), BaBar (SLAC, Stanford, USA) and LHCb (CERN, Geneva, Switzerland) experiments. So now the task of the theoretician is to identify the Lorentz structure of this new physics (known as a model independent analysis, just like it was done for beta decay) and then identify new physics model(s) which can accommodate these measurements.
By doing a complete model independent analysis of new physics in b->c tau nu, the group of Zoltan Ligeti ( Lawrence Berkeley National Laboratory, Berkeley, USA) in 2015, identified the possible Lorentz stricture of new physics which can explain all the experimental measurements related to b->c tau nu sector. They found that there are many such solutions. In August 2017, LHCb reported another anomaly in this sector. After this result, we revisited the model independent analysis and showed that there are four independent solutions that can explain all anomalies in b->c tau nu sector and with the present experimental technique, one can only distinguish one type of solution from other three (arXiv:1710.04127). Finally in April 2018, we resolved this puzzle ! We were able to show how one can distinguish between all four solutions (arXiv:1804.08078). We did this work with Uma Sankar & Suman (IIT Bombay) and Dinesh (NCBJ, Warsaw, Poland).
Now coming to b->s mu+ mu- sector. On April 18, 2017, LHCb announced its famous result related to LFU violation in B ->K* mu+ mu-. Within few days after this results, seven groups identified Lorentz structure of new physics independently. Our group, David London & Jacky (UdeM, Montreal, Canada), Alakabha (Mississippi U., USA), Bhubanjyoti (Wayne State U., USA) and Dinesh was one of them. Almost all of us found that there are three independent solutions. But we went beyond and showed that one of these solutions are not allowed, so we are left with only two (arXiv:1704.07397).
The final task is to come up with new physics models to explain anomalies in these two sectors. However this is a tricky task as one process occurs at tree and another occurs at loop level in SM. A minimal framework was developed to explain these anomalies. This framework is widely used in literature to explain these anomalies. However we showed that this framework doesn't work !