<p>Recent publications by three lattice QCD collaborations have provided an unprecedented wealth of theoretical predictions for the <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mi>B</mi> <mo stretchy="true">¯</mo> </mover> <mi>q</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>q</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {\overline{B}}_q\to {D}_q^{\left(\ast \right)} \)</EquationSource> </InlineEquation> form factors, for spectator flavours <i>q</i> = <i>u</i>/<i>d</i> and <i>q</i> = <i>s</i>. We analyse these predictions within the framework of the heavy-quark expansion (HQE) to order <i>α</i><sub><i>s</i></sub>, 1/<i>m</i><sub><i>b</i></sub>, and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mn>1</mn> <mo>/</mo> <msubsup> <mi>m</mi> <mi>c</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( 1/{m}_c^2 \)</EquationSource> </InlineEquation>. For the first time, our analysis imposes unitarity bounds for all of the <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mover accent="true"> <mi>B</mi> <mo stretchy="true">¯</mo> </mover> <mi>q</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>q</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {\overline{B}}_q^{\left(\ast \right)}\to {D}_q^{\left(\ast \right)} \)</EquationSource> </InlineEquation> form factors; this includes newly identified tensor form factors arising in <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mover accent="true"> <mi>B</mi> <mo stretchy="true">¯</mo> </mover> <mi>q</mi> <mo>∗</mo> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>q</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {\overline{B}}_q^{\ast}\to {D}_q^{\left(\ast \right)} \)</EquationSource> </InlineEquation>. This enables us to treat all form factors in the same fashion. At the level of our present analysis, the inclusion of the tensor bounds is not yet constraining the HQE parameter space. We find the lattice QCD results to be well compatible with each other in a joint HQE fit as well as with QCD sum rule estimates that were used in previous HQE analyses. This is in contrast to the strong variability of the posterior predictions, in particular of the form factors ratios <i>R</i><sub>0</sub> and <i>R</i><sub>2</sub>. Using the posterior distributions of our HQE analysis, we provide predictions for angular observables and LFU ratios in the <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mi>B</mi> <mo stretchy="true">¯</mo> </mover> <mi>q</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>q</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msubsup> <msup> <mi>ℓ</mi> <mo>−</mo> </msup> <mover accent="true"> <mi>ν</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( {\overline{B}}_q\to {D}_q^{\left(\ast \right)}{\ell}^{-}\overline{\nu} \)</EquationSource> </InlineEquation> decays.</p>

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Challenging \( {\overline{B}}_{(s)}\to {D}_{(s)}^{\left(\ast \right)} \) form factors with the heavy quark expansion

  • Marzia Bordone,
  • Nico Gubernari,
  • Martin Jung,
  • Danny van Dyk

摘要

Recent publications by three lattice QCD collaborations have provided an unprecedented wealth of theoretical predictions for the B ¯ q D q \( {\overline{B}}_q\to {D}_q^{\left(\ast \right)} \) form factors, for spectator flavours q = u/d and q = s. We analyse these predictions within the framework of the heavy-quark expansion (HQE) to order αs, 1/mb, and 1 / m c 2 \( 1/{m}_c^2 \) . For the first time, our analysis imposes unitarity bounds for all of the B ¯ q D q \( {\overline{B}}_q^{\left(\ast \right)}\to {D}_q^{\left(\ast \right)} \) form factors; this includes newly identified tensor form factors arising in B ¯ q D q \( {\overline{B}}_q^{\ast}\to {D}_q^{\left(\ast \right)} \) . This enables us to treat all form factors in the same fashion. At the level of our present analysis, the inclusion of the tensor bounds is not yet constraining the HQE parameter space. We find the lattice QCD results to be well compatible with each other in a joint HQE fit as well as with QCD sum rule estimates that were used in previous HQE analyses. This is in contrast to the strong variability of the posterior predictions, in particular of the form factors ratios R0 and R2. Using the posterior distributions of our HQE analysis, we provide predictions for angular observables and LFU ratios in the B ¯ q D q ν ¯ \( {\overline{B}}_q\to {D}_q^{\left(\ast \right)}{\ell}^{-}\overline{\nu} \) decays.