Extracting Angular Observables without a Likelihood and Applications to Rare Decays

Abstract

Our goal is to obtain a complete set of angular observables arising in a generic multi-body process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events. Instead, we apply the method of moments that relies both on the orthogonality of angular functions and the estimation of integrals by Monte Carlo techniques. The big advantage of this method is that the joint distribution of all observables can be easily extracted, even for very few events. The method of moments is shown to be robust against mismodeling of the angular distribution. Our main result is an explicit algorithm that accounts for systematic uncertainties from detector-resolution and acceptance effects. Finally, we present the necessary process-dependent formulae needed for direct application of the method to several rare decays of interest.

13 pages, 4 figures

References in corpus (16)

• Measurement of form-factor independent observables in the decay $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$
• Understanding the B->K*mu+mu- Anomaly
• Angular Distributions of B -> K ll Decays
• Implications from clean observables for the binned analysis of B -> K*ll at large recoil
• Comprehensive Bayesian Analysis of Rare (Semi)leptonic and Radiative B Decays
• Complete Anatomy of B -> K*ll and its angular distribution
• The Benefits of B ---> K* l+ l- Decays at Low Recoil
• New observables in the decay mode anti-B --> anti-K*0 l+ l-
• General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil
• On transverse asymmetries in B --> K* l+l-
• New physics reach of the decay mode $\bar{B}\to {\bar{K}}^{\ast 0}{\ell }^{+}{\ell }^{-}$
• Angular Analysis of the Decay ${\Lambda }_b\to \Lambda (\to N\pi ){\ell }^{+}{\ell }^{-}$
• Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$
• Angular analysis of charged and neutral $B\to K{\mu }^{+}{\mu }^{-}$ decays
• The effect of S-wave interference on the $B^0\to K^{\ast 0}{\ell }^{+}{\ell }^{-}$ angular observables
• Extracting CKM Phases and $B_s-{\bar{B}}_s$ Mixing Parameters from Angular Distributions of Non-Leptonic B Decays

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