Semileptonic transition of $$\varLambda _{b}$$ baryon
Kaushal Thakkar
Abstract
Abstract The semileptonic transition of $$\varLambda _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> baryon is studied using the Hypercentral constituent quark model. The six-dimensional hyperradial $$Schr\ddot{o}dinger$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>c</mml:mi> <mml:mi>h</mml:mi> <mml:mi>r</mml:mi> <mml:mover> <mml:mi>o</mml:mi> <mml:mo>¨</mml:mo> </mml:mover> <mml:mi>d</mml:mi> <mml:mi>i</mml:mi> <mml:mi>n</mml:mi> <mml:mi>g</mml:mi> <mml:mi>e</mml:mi> <mml:mi>r</mml:mi> </mml:mrow> </mml:math> equation is solved in the variational approach to get masses and wavefunctions of heavy baryons. The matrix elements of weak decay are written in terms of the overlap integrals of the baryon wave function. The Isgur-Wise function is determined to calculate exclusive semileptonic decay $$\varLambda _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> $$\rightarrow $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>→</mml:mo> </mml:math> $$\varLambda _c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> $${\bar{\nu }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> . The calculated decay rate and the branching ratio of $$\varLambda _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> baryon are consistent with other theoretical predictions and with the available experimental observations.