The leptonic decay B  s  → μ + μ  −  is both rare and theoretically clean, making it an excellent probe for New Physics searches. Due to its helicity suppression in the Standard Model, this decay is particularly sensitive to new (pseudo)-scalar contributions. We present a new strategy for detecting CP-violating New Physics contributions of this kind, exploiting two observables:   <math> <msubsup> <mi>A</mi> <mrow> <mi>Δ</mi> <msub> <mi>Γ</mi> <mi>s</mi> </msub> </mrow> <mi>μμ</mi> </msubsup> </math>  $$ {\mathcal{A}}_{\Delta {\varGamma}_s}^{\mu \mu} $$ , which is accessible due to the sizeable decay width difference of the B  s  system, and the mixing-induced CP asymmetry   <math> <msub> <mi>S</mi> <mi>μμ</mi> </msub> </math>  $$ {\mathcal{S}}_{\mu \mu} $$ . The strategy also uses information from B → K (*) μ + μ  −  and B  s  → ϕμ + μ  −  decays. We find remarkably constrained regions in the   <math> <msubsup> <mi>A</mi> <mrow> <mi>Δ</mi> <msub> <mi>Γ</mi> <mi>s</mi> </msub> </mrow> <mi>μμ</mi> </msubsup> </math>  $$ {\mathcal{A}}_{\Delta {\Gamma}_s}^{\mu \mu} $$ -  <math> <msub> <mi>S</mi> <mi>μμ</mi> </msub> </math>  $$ {\mathcal{S}}_{\mu \mu} $$  plane that serve as promising targets for future measurements.

Netherlands

Robert Fleischer

Germany

Eleftheria Malami

Anders Rehult

K. Vos

Targeting (pseudo)-scalar CP violation with B  s  → μ + μ  −

Intriguing results for tests of the universality of electrons and muons through measurements of rates of B → Kℓ + ℓ  −  and similar decays have been in the spotlight for years. The LHCb collaboration has recently reported new results which are in agreement with Lepton Flavour Universality, while the individual decay rates are found below their Standard Model predictions. In view of this new situation, we explore how much space is left for a violation of electron-muon universality. Considering new sources of CP violation and taking the new LHCb measurements into account, we show that significant differences between the short-distance coefficients for electronic and muonic final states are actually allowed by the current data. These patterns can be revealed through CP asymmetries in neutral and charged B → Kℓ + ℓ  −  decays. We obtain correlations between these observables and map them to the short-distance coefficients. This results in regions in New Physics parameter space with large differences between CP asymmetries of the decays with final-state electrons and muons, thereby leaving a lot of room for possible surprises in the future high-precision era.

New perspectives for testing electron-muon universality

The  $$B^0_s\rightarrow D_s^{\mp } K^{\pm }$$  <math> <mrow> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∓</mo> </msubsup> <msup> <mi>K</mi> <mo>±</mo> </msup> </mrow> </math>   system offers a determination of the Unitarity Triangle angle  $$\gamma $$  <math> <mi>γ</mi> </math>  . Intrigued by an LHCb analysis showing a surprisingly large result in tension with information on the Unitarity Triangle and other  $$\gamma $$  <math> <mi>γ</mi> </math>   measurements, we make a transparent study of the measured observables, confirming the LHCb picture. The corresponding  $$\gamma $$  <math> <mi>γ</mi> </math>   puzzle at the  $$3\sigma $$  <math> <mrow> <mn>3</mn> <mi>σ</mi> </mrow> </math>   level would require CP-violating contributions of New Physics, which should also manifest themselves in the corresponding decay branching ratios. Indeed, we find that the rates of the individual  $$B^0_s\rightarrow D_s^{\mp } K^{\pm }$$  <math> <mrow> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∓</mo> </msubsup> <msup> <mi>K</mi> <mo>±</mo> </msup> </mrow> </math>   channels show puzzling patterns, in accordance with similar decays, with tensions up to  $$4.8\sigma $$  <math> <mrow> <mn>4.8</mn> <mi>σ</mi> </mrow> </math>  , thereby making the situation much more exciting. We present a formalism to include New-Physics effects in a model-independent way and apply it to the data to constrain the corresponding parameters. Interestingly, new contributions of moderate size could accommodate the data. Utilising this formalism in the future high-precision B physics era may allow us to finally establish new sources of CP violation.

Revealing new physics in  $${\varvec{B}}^{0}_{s}\rightarrow D_s^{\mp } K^{\pm }$$  <math> <mrow> <msubsup> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> <mi>s</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∓</mo> </msubsup> <msup> <mi>K</mi> <mo>±</mo> </msup> </mrow> </math>   decays

The B → Kℓ + ℓ  −  system is particularly interesting to explore physics beyond the Standard Model. Such effects could provide new sources of CP violation, thereby giving rise to Wilson coefficients which could not only be real, as assumed in most analyses, but also be complex. We propose a new strategy to extract the complex C 9μ , C 10μ  from the data, utilising the complementarity of direct CP violation in B + → K + μ + μ  −  and mixing-induced CP violation arising — in addition to direct CP violation — in   <math> <msubsup> <mi>B</mi> <mi>d</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msub> <mi>K</mi> <mi>S</mi> </msub> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>−</mo> </msup> </math>  $$ {B}_d^0\to {K}_S{\mu}^{+}{\mu}^{-} $$ , as well as the differential rate in appropriate q 2 bins. The long-distance effects, which play a key role to generate the direct CP asymmetries, cannot be reliably calculated due to their non-perturbative nature. In order to describe them, we apply a model by the LHCb Collaboration employing experimental data. Assuming specific scenarios, we demonstrate the fingerprinting of CP-violating New Physics and the distinction between ambiguities in the model of the long-distance contributions. Finally, New Physics could couple differently to muons and electrons, as probed through the lepton flavour universality ratio R  K . We discuss these effects in the presence of CP violation and present a new way to measure the direct CP asymmetries of the B → Ke + e  −  channels.

Fingerprinting CP-violating New Physics with B → Kμ + μ −

The LHCb collaboration has recently reported the first observation of CP violation in the penguin-dominated   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → K  −  K + decay and further new measurements, indicating differences between the direct CP asymmetries of both the   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → K  −  K +,   <math> <msubsup> <mi>B</mi> <mi>d</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_d^0 $$  → π  −  K + and the   <math> <msubsup> <mi>B</mi> <mi>d</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_d^0 $$  → π  −  π +,   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → K  −  π + modes. We show that these puzzling differences can be accommodated through sizeable penguin annihilation and exchange topologies in the Standard Model, and constrain them. Utilising the U-spin symmetry, we extract the angle γ of the unitarity triangle from the CP asymmetries in the   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → K  −  K +,   <math> <msubsup> <mi>B</mi> <mi>d</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_d^0 $$  → π  −  π + system alone, finding   <math> <mi>γ</mi> <mo>=</mo> <mfenced> <msubsup> <mn>65</mn> <mrow> <mo>−</mo> <mn>7</mn> </mrow> <mrow> <mo>+</mo> <mn>11</mn> </mrow> </msubsup> </mfenced> <mo>°</mo> </math>  $$ \gamma =\left({65}_{-7}^{+11}\right){}^{\circ} $$ , in perfect agreement with the determination from tree-level B → DK decays. The   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>−</mo> <msubsup> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0-{\overline{B}}_s^0 $$  mixing phase ϕ  s  can be extracted from CP violation measurements in   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → K  −  K + in a clean way. We present a new strategy and extract ϕ  s  = −(3.6 ± 5.4)°. This result is in agreement with the determination from   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> </math>  $$ {B}_s^0 $$  → J/ψϕ decays. New CP-violating contributions would influence these determinations differently. Hence it is interesting to keep monitoring both as the experimental picture sharpens.

Ruben Jaarsma

Zooming into CP violation in B (s) → hh decays

The system of <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>∓</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> decays offers a theoretically clean determination of the angle <math><mi>γ</mi></math> of the unitarity triangle. A corresponding LHCb analysis resulted in a surprisingly large result, which is in tension with other determinations and global analyses of the unitarity triangle. Paying special attention to discrete ambiguities, we confirm this picture and resolve a final ambiguity. Moreover, we extract the branching ratios of the underlying <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> modes. Combining them with information from semileptonic <math><msub><mi>B</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub></math> decays, we arrive at another puzzling situation, which we obtain also for other decays with similar dynamics. These patterns could be footprints of New Physics in the <math><mrow><mi>b</mi><mo>→</mo><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>s</mi></mrow></math> and <math><mrow><mi>b</mi><mo>→</mo><mi>u</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>s</mi></mrow></math> processes which govern the dynamics of the <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>∓</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> channels. Employing a model-independent parametrization, we present a strategy to reveal such effects. Applying it to the present data, we obtain strongly correlated New-Physics contributions with potentially large <math><mi>C</mi><mi>P</mi></math>-violating phases. We find that new contributions sizeably smaller than the Standard Model amplitudes could actually accommodate the current data. This strategy offers an exciting probe for new sources of <math><mi>C</mi><mi>P</mi></math> violation at the future high-precision frontier of <math><mi>B</mi></math> physics.

Using <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>∓</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> decays as a portal to new physics

Decays of B mesons with leptons in the final state offer an interesting laboratory to search for possible effects of physics from beyond the Standard Model. In view of puzzling patterns in experimental data, the violation of lepton flavour universality is an interesting option. We present a strategy, utilising ratios of leptonic and semileptonic B decays, where the elements  $$|V_{ub}|$$  <math> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>ub</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </math>   and  $$|V_{cb}|$$  <math> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>cb</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </math>   of the Cabibbo–Kobayashi–Maskawa (CKM) matrix cancel, to constrain the short-distance coefficients of (pseudo)-scalar, vector and tensor operator contributions. The individual branching ratios allow us then to extract also the CKM matrix elements, even in the presence of new-physics contributions. Bounds on unmeasured leptonic and semileptonic decays offer important additional constraints. In our comprehensive analysis, we give also predictions for decays which have not yet been measured in a variety of scenarios.

Gilberto Tetlalmatzi-Xolocotzi

Mapping out the space for new physics with leptonic and semileptonic  $$B_{(c)}$$  <math> <msub> <mi>B</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> </math>   decays

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 $$D_{(s)}$$ <math><msub><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub></math>  mesons which originate from $$c \rightarrow d \bar{{\ell }} \nu _l$$ <math><mrow><mi>c</mi><mo>→</mo><mi>d</mi><mover><mrow><mi>ℓ</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mi>ν</mi><mi>l</mi></msub></mrow></math>  and $$c \rightarrow s \bar{{\ell }} \nu _{\ell }$$ <math><mrow><mi>c</mi><mo>→</mo><mi>s</mi><mover><mrow><mi>ℓ</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mi>ν</mi><mi>ℓ</mi></msub></mrow></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 $$|V_{cd}|$$ <math><mrow><mrow><mo>|</mo></mrow><msub><mi>V</mi><mrow><mi>cd</mi></mrow></msub><mrow><mo>|</mo></mrow></mrow></math>  and $$|V_{cs}|$$ <math><mrow><mrow><mo>|</mo></mrow><msub><mi>V</mi><mrow><mi>cs</mi></mrow></msub><mrow><mo>|</mo></mrow></mrow></math>  of the Cabibbo–Kobayashi–Maskawa matrix and extract them from the $$D_{(s)}$$ <math><msub><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub></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 $$D_{(s)}^+ \rightarrow e^+ \nu _e$$ <math><mrow><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>+</mo></msubsup><mo>→</mo><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></mrow></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.

Gabriël Koole

Testing lepton flavour universality with (semi)-leptonic $$\varvec{D_{(s)}}$$ <math><mrow><msub><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub></mrow></math>  decays

The $$B\rightarrow \pi \pi ,\pi K$$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>π</mi><mo>,</mo><mi>π</mi><mi>K</mi></mrow></math>  system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic $$B\rightarrow \pi \pi $$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>π</mi></mrow></math>  parameters from data where new measurements of direct CP violation in $$B^0_d\rightarrow \pi ^0\pi ^0$$ <math><mrow><msubsup><mi>B</mi><mi>d</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></mrow></math>  resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the $$B\rightarrow \pi \pi $$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>π</mi></mrow></math>  parameters can be converted into their $$B\rightarrow \pi K$$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>K</mi></mrow></math>  counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is $$B^0_d\rightarrow \pi ^0 K_\mathrm{S}$$ <math><mrow><msubsup><mi>B</mi><mi>d</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>K</mi><mi>S</mi></msub></mrow></math>  as it exhibits mixing-induced CP violation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of $$B^0_d\rightarrow \pi ^0 K_\mathrm{S}$$ <math><mrow><msubsup><mi>B</mi><mi>d</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>K</mi><mi>S</mi></msub></mrow></math> , which are the theoretically cleanest $$B\rightarrow \pi K$$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>K</mi></mrow></math>  probes. Interestingly, they show tensions with respect to the Standard Model. Should this $$B\rightarrow \pi K$$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>K</mi></mrow></math>  puzzle originate from New Physics, electroweak penguins offer an attractive scenario for new particles to enter. We present a strategy to determine the parameters characterising these topologies and obtain the state-of-the-art picture from current data. In the future, this method will allow us to reveal the $$B\rightarrow \pi K$$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>K</mi></mrow></math>  dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.

Exploring $$B\rightarrow \pi \pi , \pi K$$ <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mi>π</mi><mo>,</mo><mi>π</mi><mi>K</mi></mrow></math>  decays at the high-precision frontier

We consider leptonic $$B^-\rightarrow \ell ^- {\bar{\nu }}_\ell $$ <math><mrow><msup><mi>B</mi><mo>-</mo></msup><mo>→</mo><msup><mi>ℓ</mi><mo>-</mo></msup><msub><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>ℓ</mi></msub></mrow></math>  and semileptonic $${\bar{B}} \rightarrow \pi \ell ^- {\bar{\nu }}_\ell $$ <math><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>π</mi><msup><mi>ℓ</mi><mo>-</mo></msup><msub><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>ℓ</mi></msub></mrow></math> , $${\bar{B}} \rightarrow \rho \ell ^- {\bar{\nu }}_\ell $$ <math><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>ρ</mi><msup><mi>ℓ</mi><mo>-</mo></msup><msub><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>ℓ</mi></msub></mrow></math>  decays and present a strategy to determine short-distance coefficients of New-Physics operators and the CKM element $$|V_{ub}|$$ <math><mrow><mrow><mo>|</mo></mrow><msub><mi>V</mi><mrow><mi>ub</mi></mrow></msub><mrow><mo>|</mo></mrow></mrow></math> . As the leptonic channels play a central role, we illustrate this method for (pseudo)-scalar operators which may lift the helicity suppression of the corresponding transition amplitudes arising in the Standard Model. Utilising a new result by the Belle collaboration for the branching ratio of $$B^-\rightarrow \mu ^- {\bar{\nu }}_\mu $$ <math><mrow><msup><mi>B</mi><mo>-</mo></msup><mo>→</mo><msup><mi>μ</mi><mo>-</mo></msup><msub><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>μ</mi></msub></mrow></math> , we explore theoretically clean constraints and correlations between New Physics coefficients for leptonic final states with $$\mu $$ <math><mi>μ</mi></math>  and $$\tau $$ <math><mi>τ</mi></math>  leptons. In order to obtain stronger bounds and to extract $$|V_{ub}|$$ <math><mrow><mrow><mo>|</mo></mrow><msub><mi>V</mi><mrow><mi>ub</mi></mrow></msub><mrow><mo>|</mo></mrow></mrow></math> , we employ semileptonic $${\bar{B}} \rightarrow \pi \ell ^- {\bar{\nu }}_\ell $$ <math><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>π</mi><msup><mi>ℓ</mi><mo>-</mo></msup><msub><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>ℓ</mi></msub></mrow></math>  and $${\bar{B}} \rightarrow \rho \ell ^- {\bar{\nu }}_\ell $$ <math><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>ρ</mi><msup><mi>ℓ</mi><mo>-</mo></msup><msub><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>ℓ</mi></msub></mrow></math>  decays as an additional ingredient, involving hadronic form factors which are determined through QCD sum rule and lattice calculations. In addition to a detailed analysis of the constraints on the New Physics contributions following from current data, we make predictions for yet unmeasured decay observables, compare them with experimental constraints and discuss the impact of CP-violating phases of the New-Physics coefficients.