The $$\Lambda _{b} \rightarrow \Lambda $$ transition form factors in perturbative QCD approach

Abstract We perform a systematic analysis of the $$\Lambda _b \rightarrow \Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> </mml:mrow> </mml:math> transition form factors using the perturbative QCD (PQCD) approach, taking into account contributions from higher-twist light-cone distribution amplitudes (LCDAs). Using inputs from lattice QCD, we show that the baryon higher-twist LCDAs give numerically dominant contributions to the form factors. By combining our PQCD results at low- $$q^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> region with lattice QCD predictions at high $$q^2,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> we carry out z -series expansion fits to obtain a unified description of the form factors over the full physical kinematic range. We also provide predictions for physical observables in the rare decay $$\Lambda _b \rightarrow \Lambda \mu ^+ \mu ^-,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> <mml:msup> <mml:mi>μ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>μ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> such as the differential branching fraction, the longitudinal polarization fraction of the dimuon system, and the forward–backward asymmetries.