We investigate the Λ c  → Λℓ + ν  ℓ  decay with a focus on potential new physics (NP) effects in the ℓ = μ channel. We employ an effective Hamiltonian within the framework of the Standard Model Effective Field Theory (SMEFT) to consider generalized dimension-6 semileptonic c → s operators of scalar, pseudoscalar, vector, axial-vector and tensor types. We rely on Lattice QCD (LQCD) for the hadronic transition form factors, using heavy quark spin symmetry (HQSS) to determine those that have not yet been obtained on the lattice. Uncertainties due to the truncation of the NP Hamiltonian and different implementations of HQSS are taken into account. As a result, we unravel the NP discovery potential of the Λ c  → Λ semileptonic decay in different observables. Our findings indicate high sensitivity to NP in lepton flavour universality ratios, probing multi-TeV scales in some cases. On the theoretical side, we identify LQCD uncertainties in axial and vector form factors as critical for improving NP sensitivity, alongside better SMEFT uncertainty estimations.

Spain

Fernando Alvarado

Luis Alvarez-Ruso

Eliecer Hernández

Juan Nieves

Neus Penalva

The Λ c  → Λ ℓ + ν  ℓ  weak decay including new physics

We benefit from the lattice QCD determination by the HPQCD of the Standard Model (SM) form factors for the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msub> <mi>D</mi> <mi>s</mi> </msub> </math>  $$ {\overline{B}}_s\to {D}_s $$  [Phys. Rev. D 101 (2020) 074513] and the SM and tensor ones for the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> </math>  $$ {\overline{B}}_s\to {D}_s^{\ast } $$  ( arXiv:2304.03137   [hep-lat]) semileptonic decays, and the heavy quark effective theory (HQET) relations for the analogous B → D (*) decays obtained by F.U. Bernlochner et al. in Phys. Rev. D 95 (2017) 115008, to extract the leading and sub-leading Isgur-Wise functions for the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> </math>  $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)} $$  decays. Further use of the HQET relations allows us to evaluate the corresponding scalar, pseudoscalar and tensor form factors needed for a phenomenological study of new physics (NP) effects on the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> </math>  $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)} $$  semileptonic decay. At present, the experimental values for the ratios   <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> <mo>=</mo> <mi>Γ</mi> <mfenced> <mrow> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> <mfenced> <mrow> <mo>/</mo> <mi>Γ</mi> </mrow> </mfenced> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mi>e</mi> <mo>−</mo> </msup> <mfenced> <msup> <mi>μ</mi> <mo>−</mo> </msup> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mrow> <mi>e</mi> <mfenced> <mi>μ</mi> </mfenced> </mrow> </msub> </mrow> </mfenced> </math>  $$ {\mathcal{R}}_{D^{\left(\ast \right)}}=\Gamma \left[\overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau}\left]/\Gamma \right[\overline{B}\to {D}^{\left(\ast \right)}{e}^{-}\left({\mu}^{-}\right){\overline{\nu}}_{e\left(\mu \right)}\right] $$  are the best signal in favor of lepton flavor universality violation (LFUV) seen in charged current (CC) b → c decays. In this work we conduct a study of NP effects on the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$  semileptonic decays by comparing tau spin, angular and spin-angular asymmetry distributions obtained within the SM and three different NP scenarios. As expected from SU(3) light-flavor symmetry, we get results close to the ones found in a similar analysis of the   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </math>  $$ \overline{B}\to {D}^{\left(\ast \right)} $$  case. The measurement of the   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> <mi>ℓ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> </math>  $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}\ell {\overline{\nu}}_{\ell } $$  semileptonic decays, which is within reach of present experiments, could then be of relevance in helping to establish or rule out LFUV in CC b → c transitions.

United Kingdom

Jonathan Flynn

Study of new physics effects in   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mfenced> <mo>∗</mo> </mfenced> </msubsup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$  semileptonic decays using lattice QCD form factors and heavy quark effective theory

Erratum to: Visible energy and angular distributions of the charged particle from the τ-decay in   <math> <mi>b</mi> <mo>→</mo> <mi>cτ</mi> <mfenced> <mrow> <mi>μ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <mrow> <mi>π</mi> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <mrow> <mi>ρ</mi> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ b\to c\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },\pi {\nu}_{\tau },\rho {\nu}_{\tau}\right){\overline{\nu}}_{\tau } $$  reactions

We use a <math><mi>O</mi><mo>(</mo><msub><mi>α</mi><mi>s</mi></msub><mo>,</mo><msub><mi>Λ</mi><mi>QCD</mi></msub><mo>/</mo><msub><mi>m</mi><mi>c</mi></msub><mo>)</mo></math> heavy quark effective theory scheme, where only <math><mi>O</mi><mo>(</mo><msub><mi>Λ</mi><mi>QCD</mi></msub><mo>/</mo><msub><mi>m</mi><mi>b</mi></msub><mo>)</mo></math> corrections are neglected, to study the matrix elements of the scalar, pseudoscalar, vector, axial-vector and tensor currents between the <math><msub><mi>Λ</mi><mi>b</mi></msub></math> ground state and the odd parity charm <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><msup><mo>)</mo><mo>+</mo></msup></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonances. We show that in the near-zero recoil regime, the scheme describes reasonably well, taking into account uncertainties, the results for the 24 form factors obtained in lattice QCD (LQCD) just in terms of only four Isgur-Wise (IW) functions. We also find some support for the possibility that the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><msup><mo>)</mo><mo>+</mo></msup></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonances might form a heavy quark spin symmetry (HQSS) doublet. However, we argue that the available LQCD description of these two resonances is not accurate enough to disentangle the possible effects of the <math><msub><mi>Σ</mi><mi>c</mi></msub><mi>π</mi></math> and <math><msubsup><mi>Σ</mi><mi>c</mi><mo>*</mo></msubsup><mi>π</mi></math> thresholds, located only a few MeV above their position, and that it cannot be ruled out that these states are not HQSS partners. Finally, we study the ratio <math><mfrac><mrow><mi>d</mi><mi>Γ</mi><mo>[</mo><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup><mo>ℓ</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mo>ℓ</mo></msub><mo>]</mo><mo>/</mo><mi>d</mi><msup><mi>q</mi><mn>2</mn></msup></mrow><mrow><mi>d</mi><mi>Γ</mi><mo>[</mo><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup><mo>ℓ</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mo>ℓ</mo></msub><mo>]</mo><mo>/</mo><mi>d</mi><msup><mi>q</mi><mn>2</mn></msup></mrow></mfrac></math> of the Standard Model differential semileptonic decay widths, with <math><mi>q</mi></math> the four-momentum transferred between the initial and final hadrons. We provide a natural explanation for the existence of large deviations, near the zero recoil, of this ratio from <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> (value predicted in the infinite heavy quark mass limit, assuming that the <math><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup></math> and <math><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup></math> are the two members of a HQSS doublet) based on S-wave contributions to the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mrow><mi>c</mi><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow><mo>*</mo></msubsup></math> decay amplitude driven by a subleading IW function.

China

Meng-Lin Du

Is the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><msup><mo>)</mo><mo>+</mo></msup></math> the heavy quark spin symmetry partner of the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><msup><mo>)</mo><mo>+</mo></msup></math>?

We benefit from a recent lattice determination of the full set of vector, axial and tensor form factors for the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup><mo>(</mo><mn>2595</mn><mo>)</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> and <math><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup><mo>(</mo><mn>2625</mn><mo>)</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> semileptonic decays to study the possible role of these two reactions in lepton flavor universality violation studies. Using an effective theory approach, we analyze different observables that can be accessed through the visible kinematics of the charged particles produced in the tau decay, for which we consider the <math><msup><mi>π</mi><mo>−</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub><mo>,</mo><msup><mi>ρ</mi><mo>−</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math> and <math><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub><msub><mi>ν</mi><mi>τ</mi></msub></math> channels. We compare the results obtained in the Standard Model and other schemes containing new physics (NP) interactions, with either left-handed or right-handed neutrino operators. We find a discriminating power between models similar to the one of the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub></math> decay, although somewhat hindered in this case by the larger errors of the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup></math> lattice form factors. Notwithstanding this, the analysis of these reactions is already able to discriminate between some of the NP scenarios and its potentiality will certainly improve when more precise form factors are available.

New physics effects on <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>*</mo></msubsup><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> decays

We study the d 2Γ d /(dωd cos θ  d ), dΓ d /d cos θ  d  and dΓ d /dE  d  distributions, which are defined in terms of the visible energy and polar angle of the charged particle from the τ −decay in   <math> <mi>b</mi> <mo>→</mo> <mi>cτ</mi> <mfenced> <mrow> <mi>μ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <msub> <mi>πν</mi> <mi>τ</mi> </msub> <msub> <mi>ρν</mi> <mi>τ</mi> </msub> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ b\to c\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },{\pi \nu}_{\tau },{\rho \nu}_{\tau}\right){\overline{\nu}}_{\tau } $$  reactions. These differential decay widths could be measured in the near future with certain precision. The first two contain information on the transverse tau-spin, tau-angular and tau-angular-spin asymmetries of the   <math> <msub> <mi>H</mi> <mi>b</mi> </msub> <mo>→</mo> <msub> <mi>H</mi> <mi>c</mi> </msub> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ {H}_b\to {H}_c\tau {\overline{\nu}}_{\tau } $$  parent decay and, from a dynamical point of view, they are richer than the commonly used one, d 2Γ d /(dωdE  d ), since the latter only depends on the tau longitudinal polarization. We pay attention to the deviations with respect to the predictions of the standard model (SM) for these new observables, considering new physics (NP) operators constructed using both right- and left-handed neutrino fields, within an effective field-theory approach. We present results for   <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mo>→</mo> <msub> <mi>Λ</mi> <mi>c</mi> </msub> <mi>τ</mi> <mfenced> <mrow> <mi>μ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <msub> <mi>πν</mi> <mi>τ</mi> </msub> <msub> <mi>ρν</mi> <mi>τ</mi> </msub> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ {\Lambda}_b\to {\Lambda}_c\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },{\pi \nu}_{\tau },{\rho \nu}_{\tau}\right){\overline{\nu}}_{\tau } $$  and   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <mi>τ</mi> <mfenced> <mrow> <mi>μ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <msub> <mi>πν</mi> <mi>τ</mi> </msub> <msub> <mi>ρν</mi> <mi>τ</mi> </msub> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ \overline{B}\to {D}^{\left(\ast \right)}\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },{\pi \nu}_{\tau },{\rho \nu}_{\tau}\right){\overline{\nu}}_{\tau } $$  sequential decays and discuss their use to disentangle between different NP models. In this respect, we show that dΓ d /d cos θ  d , which should be measured with sufficiently good statistics, becomes quite useful, especially in the τ → πν  τ  mode. The study carried out in this work could be of special relevance due to the recent LHCb measurement of the lepton flavor universality ratio   <math> <msub> <mi>ℛ</mi> <msub> <mi>Λ</mi> <mi>c</mi> </msub> </msub> </math>  $$ {\mathrm{\mathcal{R}}}_{\Lambda_c} $$  in agreement with the SM. The experiment identified the τ using its hadron decay into π  −  π + π  −  ν  τ , and this result for   <math> <msub> <mi>ℛ</mi> <msub> <mi>Λ</mi> <mi>c</mi> </msub> </msub> </math>  $$ {\mathrm{\mathcal{R}}}_{\Lambda_c} $$ , which is in conflict with the phenomenology from the b-meson sector, needs confirmation from other tau reconstruction channels.

Visible energy and angular distributions of the charged particle from the τ −decay in   <math> <mi>b</mi> <mo>→</mo> <mi>cτ</mi> <mfenced> <mrow> <mi>μ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <msub> <mi>ν</mi> <mi>τ</mi> </msub> </mrow> <msub> <mi>πν</mi> <mi>τ</mi> </msub> <msub> <mi>ρν</mi> <mi>τ</mi> </msub> </mfenced> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ b\to c\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },{\pi \nu}_{\tau },{\rho \nu}_{\tau}\right){\overline{\nu}}_{\tau } $$  reactions

In the context of lepton flavor universality violation (LFUV) studies, we fully derive a general tensor formalism to investigate the role that left- and right-handed neutrino new-physics (NP) terms may have in b → cτ   <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   τ  transitions. We present, for several extensions of the Standard Model (SM), numerical results for the Λ b  → Λ c  τ   <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   τ  semileptonic decay, which is expected to be measured with precision at the LHCb. This reaction can be a new source of experimental information that can help to confirm, or maybe rule out, LFUV presently seen in   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> </math>  $$ \overline{B} $$  meson decays. The present study analyzes observables that can help in distinguishing between different NP scenarios that otherwise provide very similar results for the branching ratios, which are our currently best hints for LFUV. Since the τ lepton is very short-lived, we consider three subsequent τ-decay modes, two hadronic πν  τ  and ρν  τ  and one leptonic μ   <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ  ν  τ , which have been previously studied for   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> </math>  $$ \overline{B} $$  → D (*) decays. Within the tensor formalism that we have developed in previous works, we re-obtain the expressions for the differential decay width written in terms of visible (experimentally accessible) variables of the massive particle created in the τ decay. There are seven different τ angular and spin asymmetries that are defined in this way and that can be extracted from experiment. Those asymmetries provide observables that can help in constraining possible SM extensions.

The role of right-handed neutrinos in b → c  τ  (πν  τ  , ρν  τ  , μ   <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ  ν  τ )  <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   τ  from visible final-state kinematics

For a general H  b  →   <math> <msub> <mi>H</mi> <mi>c</mi> </msub> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ {H}_c\tau {\overline{\nu}}_{\tau } $$  decay we analyze the role of the τ polarization vector   <math> <msup> <mi>P</mi> <mi>μ</mi> </msup> </math>  $$ {\mathcal{P}}^{\mu } $$  in the context of lepton flavor universality violation studies. We use a general phenomenological approach that includes, in addition to the Standard Model (SM) contribution, vector, axial, scalar, pseudoscalar and tensor new physics (NP) terms which strength is governed by, complex in general, Wilson coefficients. We show that both in the laboratory frame, where the initial hadron is at rest, and in the center of mass of the two final leptons, a   <math> <mover> <mi>P</mi> <mo>→</mo> </mover> </math>  $$ \overrightarrow{\mathcal{P}} $$  component perpendicular to the plane defined by the three-momenta of the final hadron and the τ lepton is only possible for complex Wilson coefficients, being a clear signal for physics beyond the SM as well as time reversal (or CP-symmetry) violation. We make specific evaluations of the different polarization vector components for the Λ b  → Λ c ,   <math> <msub> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mi>c</mi> </msub> </math>  $$ {\overline{B}}_c $$  → η  c  , J/ψ and   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> </math>  $$ \overline{B} $$  → D (*) semileptonic decays, and describe NP effects in the complete two-dimensional space associated with the independent kinematic variables on which the polarization vector depends. We find that the detailed study of   <math> <msup> <mi>P</mi> <mi>μ</mi> </msup> </math>  $$ {\mathcal{P}}^{\mu } $$  has great potential to discriminate between different NP scenarios for 0 −  → 0 −  decays, but also for Λ b  → Λ c  transitions. For this latter reaction, we pay special attention to corrections to the SM predictions derived from complex Wilson coefficients contributions.

New physics and the tau polarization vector in b →   <math> <mi>c</mi> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ \mathrm{c}\tau {\overline{\nu}}_{\tau } $$  decays

We apply the general formalism derived by Penalva et al. [Phys. Rev. D 101, 113004 (2020)] to the semileptonic decay of pseudoscalar mesons containing a <math><mi>b</mi></math> quark. While present <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></math> data give the strongest evidence in favor of lepton flavor universality violation, the observables that are normally considered are not able to distinguish between different new physics (NP) scenarios. In the above reference we discussed the relevant role that the various contributions to the double differential decay widths <math><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Γ</mi><mo>/</mo><mo>(</mo><mi>d</mi><mi>ω</mi><mi>d</mi><mi>cos</mi><msub><mrow><mi>θ</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo>)</mo></mrow></math> and <math><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Γ</mi><mo>/</mo><mo>(</mo><mi>d</mi><mi>ω</mi><mi>d</mi><msub><mrow><mi>E</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo>)</mo></mrow></math> could play to this end. Here <math><mi>ω</mi></math> is the product of the two hadron four-velocities, <math><msub><mi>θ</mi><mo>ℓ</mo></msub></math> is the angle made by the final lepton and final hadron three-momenta in the center of mass of the final two-lepton system, and <math><msub><mi>E</mi><mo>ℓ</mo></msub></math> is the final charged lepton energy in the laboratory system. The formalism was applied by Penalva et al. to the analysis of the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub></math> semileptonic decay, showing the new observables were able to tell apart different NP scenarios. Here we analyze the <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mi>τ</mi><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math>, <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>τ</mi><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math>, <math><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>D</mi><mi>τ</mi><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> and <math><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mi>τ</mi><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> semileptonic decays. We find that, as a general rule, the <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> observables, even including <math><mi>τ</mi></math> polarization, are less optimal for distinguishing between NP scenarios than those obtained from <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> decays, or those presented by Penalva et al. for the related <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub></math> semileptonic decay. Finally, we show that <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><mi>D</mi></math> and <math><msub><mover><mi>B</mi><mo>¯</mo></mover><mi>c</mi></msub><mo>→</mo><msub><mi>η</mi><mi>c</mi></msub></math>, and <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><msup><mi>D</mi><mo>*</mo></msup></math> and <math><msub><mover><mi>B</mi><mo>¯</mo></mover><mi>c</mi></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decay observables exhibit similar behaviors.

<math><msub><mover><mi>B</mi><mo>¯</mo></mover><mi>c</mi></msub><mo>→</mo><msub><mi>η</mi><mi>c</mi></msub></math>, <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> and <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></math> semileptonic decays including new physics

We extend our general framework for semileptonic decay, originally introduced in N. Penalva et al. [Phys. Rev. D 100, 113007 (2019)], with the addition of new physics (NP) tensor terms. In this way, all the NP effective Hamiltonians that are considered in lepton flavor universality violation (LFUV) studies have now been included. Those are left and right vector and scalar NP Hamiltonians and the NP tensor one. Besides, we now also give general expressions that allow for complex Wilson coefficients. The scheme developed is totally general and it can be applied to any charged current semileptonic decay, involving any quark flavors or initial and final hadron states. We show that all the hadronic input, including NP effects, can be parametrized in terms of 16 Lorentz scalar structure functions, constructed out of the NP complex Wilson coefficients and the genuine hadronic responses, with the latter determined by the matrix elements of the involved hadron operators. In the second part of this work, we use this formalism to obtain the complete NP effects in the <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> semileptonic decay, where LFUV, if finally confirmed, is also expected to be seen. We stress the relevance of the center of mass (CM) <math><msup><mi>d</mi><mn>2</mn></msup><mi>Γ</mi><mo>/</mo><mo>(</mo><mi>d</mi><mi>ω</mi><mi>d</mi><mi>cos</mi><msub><mi>θ</mi><mo>ℓ</mo></msub><mo>)</mo></math> and laboratory (LAB) <math><msup><mi>d</mi><mn>2</mn></msup><mi>Γ</mi><mo>/</mo><mo>(</mo><mi>d</mi><mi>ω</mi><mi>d</mi><msub><mi>E</mi><mo>ℓ</mo></msub><mo>)</mo></math> differential decay widths, with <math><mi>ω</mi></math> the product of the hadron four-velocities, <math><msub><mi>θ</mi><mo>ℓ</mo></msub></math> the angle made by the three-momenta of the charged lepton and the final hadron in the <math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> CM frame and <math><msub><mi>E</mi><mo>ℓ</mo></msub></math> the charged lepton energy in the decaying hadron rest frame. While models with very different strengths in the NP terms give the same differential <math><mi>d</mi><mi>Γ</mi><mo>/</mo><mi>d</mi><mi>ω</mi></math> and total decay widths for this decay, they predict very different numerical results for some of the <math><mi>cos</mi><msub><mi>θ</mi><mo>ℓ</mo></msub></math> and <math><msub><mi>E</mi><mo>ℓ</mo></msub></math> coefficient-functions that determine the above two distributions. Thus, the combined analysis of the CM <math><msup><mi>d</mi><mn>2</mn></msup><mi>Γ</mi><mo>/</mo><mo>(</mo><mi>d</mi><mi>ω</mi><mi>d</mi><mi>cos</mi><msub><mi>θ</mi><mo>ℓ</mo></msub><mo>)</mo></math> and LAB <math><msup><mi>d</mi><mn>2</mn></msup><mi>Γ</mi><mo>/</mo><mo>(</mo><mi>d</mi><mi>ω</mi><mi>d</mi><msub><mi>E</mi><mo>ℓ</mo></msub><mo>)</mo></math> differential decay widths will help clarifying what kind of NP is a better candidate in order to explain LFUV.