The measurable angular distribution of $$ {\Lambda}_b^0\to {\Lambda}_c^{+}\left(\to {\Lambda}^0{\pi}^{+}\right){\tau}^{-}\left(\to {\pi}^{-}{v}_{\tau}\right){\overline{v}}_{\tau } $$ decay

Abstract

A bstract In $$ {\Lambda}_b^0\to {\Lambda}_c^{+}\left(\to {\Lambda}^0{\pi}^{+}\right){\tau}^{-}{\overline{v}}_{\tau } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mrow> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>Λ</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:mfenced> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:math> decay, the solid angle of the final-state particle τ − cannot be determined precisely since the decay products of the τ − include an undetected ν τ . Therefore, the angular distribution of this decay cannot be measured. In this work, we construct a measurable angular distribution by considering the subsequent decay τ − → π − ν τ . The full cascade decay is $$ {\Lambda}_b^0\to {\Lambda}_c^{+}\left(\to {\Lambda}^0{\pi}^{+}\right){\tau}^{-}\left(\to {\pi}^{-}{v}_{\tau}\right){\overline{v}}_{\tau } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mrow> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>Λ</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:mfenced> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mfenced> <mml:mrow> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:msub> <mml:mi>v</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:math> . The three-momenta of the final-state particles Λ 0 , π + , and π − can be measured. Considering all Lorentz structures of the new physics (NP) effective operators and an unpolarized initial Λ b state, the five-fold differential angular distribution can be expressed in terms of ten angular observables $$ {\mathcal{K}}_i\left({q}^2,{E}_{\pi}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mfenced> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>π</mml:mi> </mml:msub> </mml:mfenced> </mml:math> . By integrating over some of the five kinematic parameters, we define a number of observables, such as the Λ c spin polarization $$ {P}_{\Lambda_c}\left({q}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:msub> <mml:mfenced> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> and the forward-backward asymmetry of π − meson A FB ( q 2 ), both of which can be represented by the angular observables $$ {\hat{\mathcal{K}}}_i\left({q}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mi>i</mml:mi> </mml:msub> <mml:mfenced> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> . We provide numerical results for the entire set of the angular observables $$ {\hat{\mathcal{K}}}_i\left({q}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mi>i</mml:mi> </mml:msub> <mml:mfenced> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> and $$ {\hat{\mathcal{K}}}_i $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mi>i</mml:mi> </mml:msub> </mml:math> both within the Standard Model and in some NP scenarios, which are a variety of best-fit solutions in seven different NP hypotheses. We find that the NP which can resolve the anomalies in $$ \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{v}}_{\tau } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover>

Topics & Concepts