Theory determination of $$\varvec{\bar{B}\rightarrow D^{(*)}\ell ^-\bar{\nu }}$$ form factors at $$\varvec{\mathcal {O}(1/m_c^2)}$$

<jats:p>We carry out an analysis of the full set of ten <jats:inline-formula><jats:alternatives><jats:tex-math>$$\bar{B}\rightarrow D^{(*)}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:mo>→</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow /><mml:mo>∗</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> form factors within the framework of the Heavy-Quark Expansion (HQE) to order <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathcal {O}\left( \alpha _s,\,1/m_b,\,1/m_c^2\right) $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mfenced><mml:msub><mml:mi>α</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace /><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace /><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD light-cone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\bar{B}\rightarrow D^{(*)}\lbrace e^-,\mu ^-\rbrace \bar{\nu }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:mo>→</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow /><mml:mo>∗</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>{</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>}</mml:mo></mml:mrow><mml:mover><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> measurements. The coefficients entering at the <jats:inline-formula><jats:alternatives><jats:tex-math>$$1/m_c^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> level are found to be of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathcal {O}(1)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, indicating convergence of the HQE. The phenomenological implications of our study include an updated exclusive determination of <jats:inline-formula><jats:alternatives><jats:tex-math>$$|V_{cb}|$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>cb</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> in the HQE, which is compatible with both the exclusive determination using the BGL parametrization and with the inclusive determination. We also revisit predictions for the lepton-flavour universality ratios <jats:inline-formula><jats:alternatives><jats:tex-math>$$R_{D^{(*)}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow /><mml:mo>∗</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:msub></mml:math></jats:alternatives></jats:inline-formula>, the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\tau $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> polarization observables <jats:inline-formula><jats:alternatives><jats:tex-math>$$P_\tau ^{D^{(*)}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>P</mml:mi><mml:mi>τ</mml:mi><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow /><mml:mo>∗</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:msubsup></mml:math></jats:alternatives></jats:inline-formula>, and the longitudinal polarization fraction <jats:inline-formula><jats:alternatives><jats:tex-math>$$F_L$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula>. Posterior samples for the HQE parameters are provided as ancillary files, allowing for their use in subsequent studies.</jats:p>

• Publication year

  2019

• Venue

  The European Physical Journal C

• Publication date

  2019-08-25

• Fields of study

  Art, Physics

• Identifiers
  DOI 10.1140/epjc/s10052-020-7616-4arXiv 1908.09398
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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