A new approach to semi-leptonic tags in $B$-meson semi-invisible decays

• Main Authors: de Marino, Gaetano, Guadagnoli, Diego, Park, Chan Beom, Trabelsi, Karim
• Format: Journal Article
• Language: English
• Published: 07-09-2022
• Subjects: Physics - High Energy Physics - Experiment; Physics - High Energy Physics - Phenomenology
• DOI: 10.48550/arxiv.2209.03387

Kinematic variables designed for pairwise decays to partly undetected final
states -- a prominent example being $M_{T2}$ and its Lorentz-invariant version
$M_2$ -- have been extensively deployed in high-$p_T$ collider searches. A new
range of potential applications at flavour facilities -- where $B$ mesons or
$\tau$ leptons are also pairwise produced -- was recently proposed.
One general challenge in these decays arises if both the signal parent and
the 'other' parent, often used as a tag, decay semi-invisibly. In such cases,
which notably include semi-leptonic tags, signal identification is generally
hindered by the ensuing lack of knowledge of the signal-parent boost. $M_2$
helps precisely to overcome this challenge, and allows to leverage the
otherwise superior efficiency of semi-leptonic decays.
Our strategy rests on two novel constraints that can be imposed on $M_2$. The
first is that of the known mass of the decaying-parent mass squared which, in
connection with other constraints, gives rise to $M_{2sB}$. The second is on
the flight direction of the signal parent, often well reconstructed at
facilities with high vertexing capabilities such as Belle II and LHCb. This
constraint gives rise to the $M_{2V}$ variable, that can be used even at
facilities where the collision energy is not known.
We test these ideas in a decay of great current interest in the context of
the persistent discrepancies in $B$ decays, namely $B \to K \tau \mu$. We find
that a bare-bones application of $M_{2sB}$ leads, alone, to an improvement that
is already halfway between the current approach and the "truth-level"
semi-leptonic case. Ceteris paribus -- in particular statistics -- our approach
thus makes semi-leptonic tags competitive with fully reconstructed hadronic
tags.