<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi mathvariant="normal">Λ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mn>1520</mml:mn><mml:mo mathvariant="bold" stretchy="false">)</mml:mo><mml:msup><mml:mo>ℓ</mml:mo><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mo>ℓ</mml:mo><mml:mo>−</mml:mo></mml:msup></mml:math> form factors from lattice QCD
Stefan Meinel, Gumaro Rendon
Abstract
We present the first lattice QCD determination of the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$ vector, axial vector, and tensor form factors that are relevant for the rare decays ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{*}(1520){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$. The lattice calculation is performed in the ${\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$ rest frame with nonzero ${\mathrm{\ensuremath{\Lambda}}}_{b}$ momenta, and is limited to the high-${q}^{2}$ region. An interpolating field with covariant derivatives is used to obtain good overlap with the ${\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$. The analysis treats the ${\mathrm{\ensuremath{\Lambda}}}^{*}(1520)$ as a stable particle, which is expected to be a reasonable approximation for this narrow resonance. A domain-wall action is used for the light and strange quarks, while the $b$ quark is implemented with an anisotropic clover action with coefficients tuned to produce the correct ${B}_{s}$ kinetic mass, rest mass, and hyperfine splitting. We use three different ensembles of lattice gauge-field configurations generated by the RBC and UKQCD collaborations, and perform extrapolations of the form factors to the continuum limit and physical pion mass. We give Standard-Model predictions for the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{*}(1520){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ differential branching fraction and angular observables in the high-${q}^{2}$ region.