Testing lepton flavour universality with (semi)-leptonic $$\varvec{D_{(s)}}$$ decays

Abstract

Abstract Data in B -meson decays indicate violations of lepton flavour universality, thereby raising the question about such phenomena in the charm sector. We perform a model-independent analysis of NP contributions in (semi)-leptonic decays of $$D_{(s)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:math> mesons which originate from $$c \rightarrow d \bar{{\ell }} \nu _l$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>c</mml:mi><mml:mo>→</mml:mo><mml:mi>d</mml:mi><mml:mover><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:msub><mml:mi>ν</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:math> and $$c \rightarrow s \bar{{\ell }} \nu _{\ell }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>c</mml:mi><mml:mo>→</mml:mo><mml:mi>s</mml:mi><mml:mover><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:msub><mml:mi>ν</mml:mi><mml:mi>ℓ</mml:mi></mml:msub></mml:mrow></mml:math> charged-current interactions. Starting from the most general low-energy effective Hamiltonian containing four-fermion operators and the corresponding short-distance coefficients, we explore the impact of new (pseudo)-scalar, vector and tensor operators and constrain their effects through the interplay with current data. We pay special attention to the elements $$|V_{cd}|$$ <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>cd</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:math> and $$|V_{cs}|$$ <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>cs</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:math> of the Cabibbo–Kobayashi–Maskawa matrix and extract them from the $$D_{(s)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:math> decays in the presence of possible NP decay contributions, comparing them with determinations utilizing unitarity. We find a picture in agreement with the Standard Model within the current uncertainties. Using the results from our analysis, we make also predictions for leptonic $$D_{(s)}^+ \rightarrow e^+ \nu _e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo></mml:msubsup><mml:mo>→</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msub><mml:mi>ν</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math> modes which could be hugely enhanced with respect to their tiny Standard Model branching ratios. It will be interesting to apply our strategy at the future high-precision frontier.

Topics & Concepts