Addressing the $R_{τ/{μ,e}}\left(D^{(*)}\right)$ puzzle through New Physics four-fermion operators and their impact on $Λ_{b}\rightarrowΛ_{c}τ\barν_τ$ decay

TL;DR

The paper addresses the $R_{\tau/\mu,e}(D^{(*)})$ anomaly by performing a global fit to a complete set of dimension-6 NP four-fermion operators in the weak Hamiltonian for $b\to c\tau\bar{\nu}$. It finds the scalar-scalar pair $(C_{S_L},C_{S_R})$ as the most probable NP solution with the strongest deviation from the SM, while several vector and scalar degeneracies also provide viable fits, constrained by $B_c\to\tau\nu$ BR data and collider bounds. Using lattice QCD form factors for $\Lambda_b\rightarrow\Lambda_c$, the study examines how these NP operators modify $d\Gamma/dq^2$, $A_{FB}$, $P_L^{\Lambda_c}$, $P_L^{\tau}$, and $R_{\tau/\ell}(\Lambda_c)$, identifying key observables and correlations that can clarify the NP structure. Furthermore, model-independent sum rules relate $R_{\tau/\ell}(\Lambda_c)$ and $R_{\tau/\mu}(J/\psi)$ to mesonic LFU ratios, enabling cross-checks across decay channels. The results motivate targeted measurements at LHCb and future facilities to decisively test the proposed NP patterns.

Abstract

The Lepton Flavor Universality ratio $R_{τ/{μ,e}}\left(D^{(*)}\right)$ poses a challenge to the Standard Model (SM), as B-factory experiments, BaBar, Belle, and the LHCb show $3.31σ$ deviations from their theoretical predictions. Utilizing the latest HFLAV averages and incorporating the branching ratio constraints $60\%$, $30\%$ and $10\%$ from the lifetime of the $B_c$ meson, we determine the values of the Wilson coefficients (WCs) for different New Physics (NP) four-fermion operator with specific Lorentz structures. Our analysis finds that the WC scenario $\left(C_{S_{L}},C_{S_{R}}\right)$ is the most probable, the maximum pull from the SM, and strongly influenced by branching ratio constraints. Furthermore, we identify three degenerate solutions involving $C_{V_{L}}$, $C_{V_{L}}^{\prime}$, $C_{V_{L}}^{\prime\prime}$, and $C_{S_{R}}^{\prime\prime}$ as the second most probable NP scenarios. We then studied the influence of these NP operators on various physical observables in $Λ_{b}\rightarrowΛ_{c}τ\barν_τ$ decay by using the Lattice QCD form factors. Our results highlighted $C_{S_{L}}^{\prime\prime}$, $C_{S_{R}}$, $C_{T}$, $\left(C_{S_{L}},C_{S_{R}}\right)$, $\left(C_{S_{R}},C_{T}\right)$, and the three degenerate scenarios involving $\left(C_{S_{L}},C_{T}\right)$, $\left(C_{S_{L}}^{\prime},C_{T}^{\prime}\right)$ and $\left(C_{S_{L}}^{\prime\prime},C_{T}^{\prime\prime}\right)$ as strong indicators of NP. The correlation of different physical observables shows a direct correlation between $dΓ/dq^{2}$ and $P_{L}^τ$ for WC $\left(C_{S_{L}},C_{S_{R}}\right)$; and between $A_{FB}$ and $P_{L}^{Λ_{c}}$ for three degenerate WCs involving $\left(C_{S_{L}},C_{T}\right)$. We hope that the measurements of these observables in ongoing and future experiments will help us scrutinize these constraints on the various NP couplings.

Figures (9)

• Figure 1: The plot for $\chi^2\left(C_{V_{L}}\right)-\chi^2_{min}$ vs $C_{V_{L}}$. The horizontal grid-lines at $\chi^2= 3.51\left(68\%\right)$ and $\chi^2= 8.01\left(95\%\right)$ correspond to $1\sigma$ and $2\sigma$ thresholds for $3$ dof. The vertical grid-lines show the resulting parameter ranges. As observed, the intervals are not in a $1:2$ ratio but approximately $2:3$.
• Figure 2: Results of the fits for NP scenarios at scale $2\;\text{TeV}$. The light and dark gray colors show the $10\%$ and $60\%$ branching ratio constraints. The light (dark) color contours represent the $1(2\sigma)$ deviations from the BFP (Black color) for set $\mathcal{S}_{1}$and dashed contour represents maximum of $2\sigma$ deviations for set $\mathcal{S}_{2}$. Panels (a), (b), (c), (f), (g), (j) for unprimed WCs; (d), (h) for primed WCs; (e) and (i) for double primed WCs show the ranges of two-dimensional scenarios. Except in Fig. 1a, the orange color is not affected by either of these constraints, whereas in Figs. 1a, the red and green colors are the $60\%$ and $10\%$ constraints, respectively. Outside the dashed ellipse, the purple-shaded region represents the exclusion region due to collider bounds for the current luminosity of $139\;\text{fb}^{-1}$.
• Figure 3: Results of the fits for NP scenarios when we include WC $C_{V_{R}}$ at scale $2\text{TeV}$. The light and dark gray colors show the $10\%$ and $60\%$ branching ratio constraints. The light (dark) color contours represent the $1(2\sigma)$ deviations from the BFP (Black color). Panels are restricted by the $\mathcal{S}_1$ and the dashed ellipse shows the measurement at $2\sigma$ level by the $\mathcal{S}_2$. Except Fig. 2(a), (b), (d), the orange color is not affected by either of these constraints, whereas in Figs. 2(a), (b), (d), the red and green colors are the $60\%$ and $10\%$ constraints, respectively. The purple-shaded region outside the dashed ellipse is excluded by the collider bounds for the current luminosity of $139\text{fb}^{-1}$.
• Figure 4: The $d\Gamma/dq^{2}$, $A_{FB}$, $P_{L}^{\Lambda_{c}}$, $P_{L}^{\tau}$, and $R_{\Lambda_c}\equiv R_{\tau/\ell}\left(\Lambda_{c}\right)$ observables exhibited for various NP coupling as a function of $q^{2}$. The width of each curve comes from the theoretical uncertainties in hadronic form factors and quark masses. The SM value is shown in the black band, whereas the NP couplings depicted in color bands.
• Figure 5: The $d\Gamma/dq^{2}$, $A_{FB}$, $P_{L}^{\Lambda_{c}}$, $P_{L}^{\tau}$, and $R_{\Lambda_c}\equiv R_{\tau/\ell}\left(\Lambda_{c}\right)$ observables exhibited for various NP coupling as a function of $q^{2}$. The width of each curve comes from the theoretical uncertainties in hadronic form factors and quark masses. The NP WCs $\left(C_{S_{L}},C_{S_{R}}\right)$, $\left(C_{V_{L}},C_{S_{R}}\right)$, $\left(C_{S_{R}},C_{T}\right)$, $\left(C_{S_{L}},C_{T}\right)$, for the set of observables $\mathcal{S}_1$ are drawn with orange, green, cyan and yellow colors, respectively.