Photon polarization in $B_s^0 \to \phi \gamma$ decays at the LHCb experiment

The Standard Model predicts a predominance of left handed photons emitted in the $b \to s\gamma$ interaction, due to the coupling of the $W$ boson to only left handed quarks. Moreso, several Beyond Standard Model theories predict an enhancement of right handed photon emission. A measurement of the photon polairization is therefore a direct probe of New Physics. The photon polarization sensible parameter $\mathcal{A}^\Delta$ is measured through a fit to the ratio of untagged time dependent decay rates of $B_s^0 \to \phi \gamma$ over that of $B^0 \to K^\ast \gamma$, the former being sensitive to the parameter because of its non-negligible decay width difference (Phys.Lett.B664:174-179,2008) and the latter being the control channel due to its kinematical similarities and sixfold larger yield. Using 3 fb$^{-1}$ of data collected at LHCb during 2011 and 2012 at centre of mass energies of 7 and 8 TeV, respectively, 4200 $B_s^0 \to \phi \gamma$ and 25700 $B^0 \to K^\ast \gamma$ events are reconstructed. The selection of events is optimized for significance and to reduce differences between the proper time acceptance functions of the signal and control channel, and a mass fit is performed over the selected distributions to identify the remaining background after the selection. The sPlot technique (Nucl.Instrum.Meth.A555:356-369,2005) is used to subtract these backgrounds, and the technique is cross-checked with a traditional sideband and monte carlo subtraction method. The signal distributions are binned and divided and a blinded $\chi^2$ fit is performed. The statistical and systematic uncertainties are studied and the value is unblinded afterwards, resulting in a measured value of $\mathcal{A}^\Delta= -0.85\substack{+0.43\\-0.46}\mathrm{(stat)}\substack{+0.21\\-0.22}\mathrm{(syst)}$, compatible within two standard deviations with the Standard Model prediction of $\mathcal{A}^\Delta_{\mathrm{SM}}= 0.047\substack{+0.029\\-0.025}$.