$$ B\to {D}_0^{\ast } $$ and $$ {B}_s\to {D}_{s0}^{\ast } $$ form factors from QCD light-cone sum rules

Abstract

A bstract We present the first application of QCD light-cone sum rules (LCSRs) with B ( s ) -meson distribution amplitudes to the $$ {B}_{(s)}\to {D}_{(s)0}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mfenced> <mml:mi>s</mml:mi> </mml:mfenced> </mml:msub> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mfenced> <mml:mi>s</mml:mi> </mml:mfenced> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> form factors, where $$ {D}_{(s)0}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mfenced> <mml:mi>s</mml:mi> </mml:mfenced> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> is a charmed scalar meson. We consider two scenarios for the $$ {D}_0^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> spectrum. In the first one, we follow the Particle Data Group and consider a single broad resonance $$ {D}_0^{\ast }(2300) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mn>2300</mml:mn> </mml:mfenced> </mml:math> . In the second one, we assume the existence of two scalar resonances, $$ {D}_0^{\ast }(2105) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mn>2105</mml:mn> </mml:mfenced> </mml:math> and $$ {D}_0^{\ast }(2451) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mn>2451</mml:mn> </mml:mfenced> </mml:math> , as follows from a recent theoretically motivated analysis of B → Dππ decays. The $$ B\to {D}_0^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> form factors are calculated in both scenarios, also taking into account the large total width of $$ {D}_0^{\ast }(2300) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mn>2300</mml:mn> </mml:mfenced> </mml:math> . Furthermore, we calculate the $$ {B}_s\to {D}_{s0}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> form factors, considering in this case only the one-resonance scenario with D s 0 (2317). In this LCSRs calculation, the c -quark mass is kept finite and the s -quark mass is taken into account. We also include contributions of the two- and three-particle distribution amplitudes up to twist-four. Our predictions for semileptonic $$ B\to {D}_0^{\ast}\ell {\nu}_{\ell } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mi>ℓ</mml:mi> <mml:msub> <mml:mi>ν</mml:mi> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:math> and $$ {B}_s\to {D}_{s0}^{\ast}\ell {\nu}_{\ell } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mi>ℓ</mml:mi> <mml:msub> <mml:mi>ν</mml:mi> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:math> branching ratios are compared with the available data and HQET-based predictions. As a byproduct, we also obtain the $$ {D}_0^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> - and $$ {D}_{s0}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> -meson decay constants and predict the lepton flavour universality ratios $$ R\left({D}_0^{\ast}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:mfenced> </mml:math> and $$ R\left({D}_{s0}^{\ast}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>∗</mml:mo>