Revisiting inclusive decay widths of charmed mesons

Abstract

A bstract Determining for the first time the Darwin operator contribution for the non-leptonic charm-quark decays and using new non-perturbative results for the matrix elements of ∆ C = 0 four-quark operators, including eye-contractions, we present a comprehensive study of the lifetimes of charmed mesons and inclusive semileptonic decay rates as well as the ratios, within the framework of the Heavy Quark Expansion (HQE). We find good agreement with experiment for the ratio τ ( D + )/ τ ( D 0 ), for the total $$ {D}_s^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> -meson decay rate, for the semileptonic rates of all three mesons D 0 , D + and $$ {D}_s^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> , and for the semileptonic ratio $$ {\Gamma}_{sl}^{D^{+}}/{\Gamma}_{sl}^{D^0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mi>sl</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mi>sl</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:msubsup> </mml:math> . The total decay rates of the D 0 and D + mesons are underestimated in our HQE approach and we suspect that this is due to missing higher-order QCD corrections to the free charm quark decay and the Pauli interference contribution. For the SU(3) F breaking ratios $$ \tau \left({D}_s^{+}\right)/\tau \left({D}^0\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mi>τ</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mfenced> </mml:math> and $$ {\Gamma}_{sl}^{D_s^{+}}/{\Gamma}_{sl}^{D^0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mi>sl</mml:mi> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mi>sl</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:msubsup> </mml:math> our predictions lie closer to one than experiment. This might originate from the poor knowledge of the non-perturbative parameters $$ {\mu}_G^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>μ</mml:mi> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> , $$ {\mu}_{\uppi}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>μ</mml:mi> <mml:mi>π</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> and $$ {\rho}_D^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ρ</mml:mi> <mml:mi>D</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> in the D 0 and $$ {D}_s^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> systems. These parameters could be determined by experimental studies of the moments of inclusive semileptonic D meson decays.

Topics & Concepts