<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>1520</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> form factors from lattice QCD and improved analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>1520</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>2595</mml:mn><mml:mo>,</mml:mo><mml:mn>2625</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> form factors
Stefan Meinel, Gumaro Rendon
Abstract
We present the first lattice-QCD calculation of the form factors governing the charm-baryon semileptonic decays ${\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{*}(1520){\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$. As in our previous calculation of the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$ form factors, we work in the ${\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$ rest frame, but here we use four different heavy-baryon momenta instead of just two. Because of the lower mass of the ${\mathrm{\ensuremath{\Lambda}}}_{c}$, the moderately sized momenta used here are sufficient to determine the form factors in the full kinematic range of the semileptonic decay. We also update the analysis of our lattice results for the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595,2625)$ form factors by imposing exact relations among the different form factors at zero recoil that follow from rotational symmetry. Imposing these relations ensures the correct behavior of the angular observables near the endpoint.