Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays

Abstract

We derive a generalisation of the Boyd-Grinstein-Lebed (BGL) parametrization. Most form factors (FFs) in $b$-hadron decays exhibit additional branch cuts -- namely subthreshold and anomalous branch cuts -- beyond the ``standard'' unitarity cut. These additional cuts cannot be adequately accounted for by the BGL parametrization. For instance, these cuts arise in the FFs for $B\to D^{(\ast )}$, $B\to K^{(\ast )}$, and ${\Lambda }_b\to \Lambda$ processes, which are particularly relevant from a phenomenological standpoint. We demonstrate how to parametrize such FFs and derive unitarity bounds in the presence of subthreshold and/or anomalous branch cuts. Our work paves the way for a wide range of new FF analyses based solely on first principles, thereby minimising systematic uncertainties.

7 pages, 2 figures, minor changes

References in corpus (12)

• FLAG Review 2021
• Improved Theory Predictions and Global Analysis of Exclusive $\mathbf{b}\to \mathbf{s}{\mathbf{\mu }}^{+}{\mathbf{\mu }}^{-}$ Processes
• Constraints on Lepton Universality Violation from Rare $B$ Decays
• Non-local matrix elements in $B_{(s)}\to \{K^{(\ast )},\varphi \}{\ell }^{+}{\ell }^{-}$
• To (b)e or not to (b)e: No electrons at LHCb
• Standard Model predictions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{-}{\ell }_2^{+}$ and $B\to K\nu \bar{\nu }$ using form factors from $N_f=2+1+1$ lattice QCD
• Dispersive Analysis of $B\to K^{(\ast )}$ and $B_s\to \varphi$ Form Factors
• Test of lepton flavor universality in B${}^{\pm }$ $\to$ K${}^{\pm }{\mu }^{+}{\mu }^{-}$ and B${}^{\pm }$ $\to$ K${}^{\pm }$e${}^{+}$e${}^{-}$ decays in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Dispersion representations and anomalous singularities of the triangle diagram
• Dispersive bounds for local form factors in ${\Lambda }_b\to \Lambda$ transitions
• Anomalous thresholds in $B\to (P,V){\gamma }^{\ast }$ form factors
• $B\to D_1(2420)$ and $B\to D_1^{\prime }(2430)$ form factors from QCD light-cone sum rules

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• Impact on $L$-observables of a new combined analysis of $B_{d,s}\to K^{(\ast )}$ form factors
• Advanced parametrisations for hadronic form factors
• Investigating non-local contributions in $B_s\to \varphi \bar{\ell }\ell$ including higher-twist effects