Standard Model predictions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><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>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:msubsup><mml:mo>ℓ</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo></mml:msubsup><mml:msubsup><mml:mo>ℓ</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mi>ν</mml:mi><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> using form factors from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> lattice QCD

Abstract

We use HPQCD's recent lattice QCD determination of $B\ensuremath{\rightarrow}K$ scalar, vector and tensor form factors to determine Standard Model differential branching fractions for $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}_{1}^{+}{\ensuremath{\ell}}_{2}^{\ensuremath{-}}$ and $B\ensuremath{\rightarrow}K\ensuremath{\nu}\overline{\ensuremath{\nu}}$. These form factors are calculated across the full ${q}^{2}$ range of the decay and have smaller uncertainties than previous work, particularly at low ${q}^{2}$. For $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ we find the Standard Model branching fraction in the ${q}^{2}$ region below the squared $J/\ensuremath{\psi}$ mass to exceed the LHCb results, with tensions as high as $4.7\ensuremath{\sigma}$ for ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. For the high ${q}^{2}$ region we see $3\ensuremath{\sigma}$ tensions. The tensions are much reduced by applying shifts to Wilson coefficients ${C}_{9}$ and ${C}_{10}$ in the effective weak Hamiltonian, moving them away from their Standard Model values consistent with those indicated by other $B$ phenomenology. We also update results for lepton-flavor ratios ${R}_{e}^{\ensuremath{\mu}}$ and ${R}_{\ensuremath{\mu}}^{\ensuremath{\tau}}$ and the ``flat term,'' ${F}_{H}^{\ensuremath{\ell}}$ in the differential branching fraction for $\ensuremath{\ell}\ensuremath{\in}{e,\ensuremath{\mu},\ensuremath{\tau}}$. Our results for the form-factor dependent contributions needed for searches for lepton-flavor violating decays $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}_{1}^{\ensuremath{-}}{\ensuremath{\ell}}_{2}^{+}$ achieve uncertainties of 7%. We also compute the branching fraction $\mathcal{B}(B\ensuremath{\rightarrow}K\ensuremath{\nu}\overline{\ensuremath{\nu}})$ with an uncertainty below 10%, for comparison with future experimental results.

Topics & Concepts