On sum rules for semi-leptonic $b\to c$ and $b\to u$ decays

Abstract

The semi-leptonic $b\to cl\nu$ processes are receiving a lot of attention, as the lepton flavor universality violation has been hinted by the measured ratios $R_{D^{(\ast )}}=\Gamma (B\to D^{(\ast )}\tau \nu )/\Gamma (B\to D^{(\ast )}\ell \nu )$ for $\ell =e,\mu$. Recently, it has also been pointed out that the baryonic counterpart, $R_{{\Lambda }_c}=\Gamma ({\Lambda }_b\to {\Lambda }_c\tau \nu )/\Gamma ({\Lambda }_b\to {\Lambda }_c\ell \nu )$, has a strong correlation with $R_{D^{(\ast )}}$, referred to as the R ratio sum rule in this paper. The correlation is almost independent of the new physics (NP) contributions and hence can predict $R_{{\Lambda }_c}$ from the measured $R_{D^{(\ast )}}$. On the other hand, we have fewer measurements and/or theoretical studies of the semi-leptonic $b\to ul\nu$ processes, although the same arguments can be applied to the ratios $R_{\pi }$, $R_{\rho }$, and $R_p$ as above. Since these processes are measurable at the ongoing LHCb run-3 and/or Belle~II experiments, precise studies on them are important as well. In this paper, we obtain the semi-analytic formulae for all the aforementioned $R_X$ ratios in the presence of model-independent NP contributions by using the available lattice QCD and/or light-cone sum rule fits to the form factors. Two novel points are highlighted: (i) We evaluate uncertainties of $R_X$ including both the Standard Model (SM) and NP terms, inherited from the form factor fits, and discuss how the uncertainties affect the $R$ ratio sum rules. (ii) We obtain the R ratio sum rule among the semi-leptonic $b\to ul\nu$ processes for the first time, which provides a complementary motivation for observing these processes. In addition, based on our model-independent results, we investigate how the different NP scenarios work in the $b\to c$ and $b\to u$ sectors and perform a combined study in the framework of SM effective field theory with specific flavor symmetries.

arXiv comment36 pages (main text), 4 figures, 6 tables, (v2) published version

References in corpus (80)

• Dimension-Six Terms in the Standard Model Lagrangian
• Minimal Flavour Violation: an effective field theory approach
• PHOTOS Monte Carlo: a precision tool for QED corrections in Z and W decays
• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• The Standard Model as an Effective Field Theory
• $B\to V{\ell }^{+}{\ell }^{-}$ in the Standard Model from Light-Cone Sum Rules
• Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors
• Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching
• Minimal Flavor Violation in the Lepton Sector
• U(2) and Minimal Flavour Violation in Supersymmetry
• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• Updated Global SMEFT Fit to Higgs, Diboson and Electroweak Data
• Precision Corrections to Dispersive Bounds on Form Factors
• Revisiting $B\to D\ell \nu$
• $R(D^{\ast })$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors
• Flavour physics from an approximate U(2)^3 symmetry
• Sensitivity to charged scalars in $B\to D^{(\ast )}\tau {\nu }_{\tau }$ and $B\to \tau {\nu }_{\tau }$ decays
• Review of Lepton Universality tests in B decays
• $B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist
• Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays
• Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions
• Scalar contributions to $b\to c(u)\tau \nu$ transitions
• Determination of the quark coupling strength $|V_{ub}|$ using baryonic decays
• A fresh look at the determination of |V_cb| from B-> D^* l nu
• Simultaneous Explanation of the $R_K$ and $R_{D^{(\ast )}}$ Puzzles: a Model Analysis
• Low-energy effective field theory below the electroweak scale: matching at one loop
• Power-enhanced leading-logarithmic QED corrections to $B_q\to {\mu }^{+}{\mu }^{-}$
• Light-cone sum rules for $B\to \pi$ form factors revisited
• ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ form factors, differential branching fraction, and angular observables from lattice QCD with relativistic $b$ quarks
• Charged Higgs Effects on Exclusive Semi-tauonic $\bbox{B}$ Decays
• Model-Independent Extraction of |V_{cb}| Using Dispersion Relations
• The Mono-Tau Menace: From $B$ Decays to High-$p_T$ Tails
• Enhanced electromagnetic correction to the rare $B$-meson decay $B_{s,d}\to {\mu }^{+}{\mu }^{-}$
• The Standard Model effective field theory at work
• QCD corrections to $B\to \pi$ form factors from light-cone sum rules
• Status of the semileptonic $B$ decays and muon g-2 in general 2HDMs with right-handed neutrinos
• Addendum to "Impact of polarization observables and $B_c\to \tau \nu$ on new physics explanations of the $b\to c\tau \nu$ anomaly"
• Phenomenology of ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ using lattice QCD calculations
• With or without U(2)? Probing non-standard flavor and helicity structures in semileptonic B decays
• Phenomenology of semileptonic B-meson decays with form factors from lattice QCD
• QED Corrections in $\bar{B}\to \bar{K}{\ell }^{+}{\ell }^{-}$ at the Double-Differential Level
• $B_s\to K\ell {\nu }_{\ell }$ and $B_{(s)}\to \pi (K){\ell }^{+}{\ell }^{-}$ decays at large recoil and CKM matrix elements
• Precision calculations of $B\to V$ form factors in QCD
• $B\to D^{(\ast )}$ Form Factors from QCD Light-Cone Sum Rules
• $B$ Flavour Anomalies: 2021 Theoretical Status Report
• Semileptonic form factors for $B\to D^{\ast }\ell \nu$ at nonzero recoil from 2 + 1-flavor lattice QCD
• Flavour symmetries in the SMEFT
• Electroweak and QCD Corrections to $Z$ and $W$ pole observables in the SMEFT
• The Inclusive $\bar{B}\to \tau \bar{\nu }X$ Decay in Two Higgs Doublet Models
• Semitauonic $b$-hadron decays: A lepton flavor universality laboratory
• Precise predictions for ${\Lambda }_b\to {\Lambda }_c$ semileptonic decays
• QCD calculations of $B\to \pi ,K$ form factors with higher-twist corrections
• ${\Lambda }_b\to p,\Lambda$ transition form factors from QCD light-cone sum rules
• Neutrino masses and LFV from minimal breaking of U(3)^5 and U(2)^5 flavor symmetries
• $b\to c\tau {\nu }_{\tau }$ Decays: A Catalogue to Compare, Constrain, and Correlate New Physics Effects
• Charged Higgs on $B^{-}\to \tau {\bar{\nu }}_{\tau }$ and $\bar{B}\to P(V)\ell {\bar{\nu }}_{\ell }$
• The role of right-handed neutrinos in $b\to c\tau \bar{\nu }$ anomalies
• Testing Leptoquark/EFT in $\bar{B}\to D^{(\ast )}l\bar{\nu }$ at the LHC
• Right-handed Neutrinos and $R(D^{(\ast )})$
• ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ decay in scalar and vector leptoquark scenarios
• A Theory of $R(D^{\ast },D)$ Anomaly With Right-Handed Currents
• Tension in the inclusive versus exclusive determinations of $|V_{cb}|$: a possible role of new physics
• Precision calculations of $B_{d,s}\to \pi ,K$ decay form factors in soft-collinear effective theory
• The $\bar{B}\to \pi$ form factors from QCD and their impact on $|V_{ub}|$
• Inclusive Semitauonic $B$ Decays to Order $\mathcal{O}({\Lambda }_{QCD}^3/m_b^3)$
• Global fit to $b\to c\tau \nu$ anomalies as of Spring 2024
• ${\rm Y}$ and $\psi$ leptonic decays as probes of solutions to the $R_D^{(\ast )}$ puzzle
• Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme
• $B\to \rho l\bar{\nu }$ and $\omega l\bar{\nu }$ in and beyond the Standard Model: Improved predictions and $|V_{ub}|$
• The measurable angular distribution of ${\Lambda }_b^0\to {\Lambda }_c^{+}(\to {\Lambda }^0{\pi }^{+}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decay
• The role of right-handed neutrinos in $b\to c\tau (\pi {\nu }_{\tau },\rho {\nu }_{\tau },\mu {\bar{\nu }}_{\mu }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ from visible final-state kinematics
• New physics in inclusive semileptonic $B$ decays including nonperturbative corrections
• Structure-Dependent QED Effects in Exclusive B Decays at Subleading Power
• Toward a complete description of $b\to u{\ell }^{-}\bar{\nu }$ decays within the Weak Effective Theory
• ${\Lambda }_b\to p,N^{\ast }(1535)$ Form Factors from QCD Light-Cone Sum Rules
• A closer look at observables from exclusive semileptonic $B\to (\pi ,\rho )\ell {\nu }_{\ell }$ decays
• Notes on QED Corrections in Weak Decays
• New physics contributions to moments of inclusive $b\to c$ semileptonic decays
• Structure-dependent QED effects in exclusive $B$-meson decays
• Probing New Physics in light of recent developments in $b\to c\ell \nu$ transitions

Cited by in corpus (1)

• Predictions for ${\Lambda }_b\to {\Lambda }_c\tau \bar{\nu }$ in BLSSM with Inverse seesaw