On measurement of photon polarization in radiative penguin $B$ decays to baryons

A measurement of the photon polarization in radiative penguin $B$ decays provides a test of the Standard Model and a probe for New Physics, that can lead to a deviation from the Standard Model prediction of left-handed photons in $b\to s\gamma$. We propose a new method to measure the photon polarization using the baryonic decay $B^{-}\to \mathrm{\Lambda }\bar{p}\gamma$. The $P$-violating $\mathrm{\Lambda }$-hyperon decay allows a measurement of the $\mathrm{\Lambda }$ helicity to be performed, which can be uniquely related to the photon polarization in a model-independent way. The $B^{-}\to \mathrm{\Lambda }\bar{p}\gamma$ decay was recently measured to have a large branching fraction providing a possibility to get meaningful results with the data already available at LHC and B-factory experiments. An increase of the $B$-meson sample at high luminosity LHC experiments and Belle II should provide a really stringent test by using this method already in the near future.