Unitarity bounds with subthreshold and anomalous cuts for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi></mml:math>-hadron decays

Abstract

We derive a generalization of the Boyd-Grinstein-Lebed (BGL) parametrization. Most form factors (FFs) in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi></a:math>-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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>B</c:mi><c:mo stretchy="false">→</c:mo><c:msup><c:mi>D</c:mi><c:mrow><c:mo stretchy="false">(</c:mo><c:mo>*</c:mo><c:mo stretchy="false">)</c:mo></c:mrow></c:msup></c:math>, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>B</h:mi><h:mo stretchy="false">→</h:mo><h:msup><h:mi>K</h:mi><h:mrow><h:mo stretchy="false">(</h:mo><h:mo>*</h:mo><h:mo stretchy="false">)</h:mo></h:mrow></h:msup></h:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi mathvariant="normal">Λ</m:mi><m:mi>b</m:mi></m:msub><m:mo stretchy="false">→</m:mo><m:mi mathvariant="normal">Λ</m:mi></m:math> 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 minimizing systematic uncertainties.