B → D1(2420) and B → $$ {\mathrm{D}}_1^{\prime } $$(2430) form factors from QCD light-cone sum rules

Abstract

A bstract We perform the first calculation of form factors in the semileptonic decays B → D 1 (2420) ℓν ℓ and B → $$ {D}_1^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>1</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> (2430) ℓν ℓ using QCD light-cone sum rules (LCSRs) with B -meson distribution amplitudes. In this calculation the c -quark mass is finite. Analytical expressions for two-particle contributions up to twist four are obtained. To disentangle the D 1 and $$ {D}_1^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>1</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> contributions in the LCSRs, we suggest a novel approach that introduces a combination of two interpolating currents for these charmed mesons. To fix all the parameters in the LCSRs, we use the two-point QCD sum rules for the decay constants of D 1 and $$ {D}_1^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>1</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> mesons augmented by a single experimental input, that is the B → D 1 (2420) ℓν ℓ decay width. We provide numerical results for all B → D 1 and B → $$ {D}_1^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>1</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> form factors. As a byproduct, we also obtain the D 1 - and $$ {D}_1^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>1</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> -meson decay constants and predict the lepton-flavour universality ratios R ( D 1 ) and R ( $$ {D}_1^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>1</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> ).