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Effective theory approach to new physics in $b \to u$ and $b \to c$ leptonic and semileptonic decays

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Rupak Dutta, Anupama Bhol, Anjan K Giri

High Energy Physics - Phenomenology · Submitted 25 Jul 2013 · 41 references

Pith's verdict: A competent combined EFT fit to the b→u and b→c anomalies with useful conditional predictions, but the scalar-sector results rest on an unresolved sign convention that the paper flags and does not settle.

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arXiv ID1307.6653 (version 2)
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CitationAnjan K Giri, Anupama Bhol, Rupak Dutta. "Effective theory approach to new physics in $b \to u$ and $b \to c$ leptonic and semileptonic decays." arXiv:1307.6653 (2013). https://pith.science/paper/NXITBG3L
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The paper

The paper claims

A general effective Lagrangian for $b$ decays is fitted to three measured ratios at once, and the fits are turned into predictions for $B_c$ and $B$ decays that have not yet been seen.

The reading

Three measurements of $B$ decays disagree with the standard model: the ratio $R_{l}^{π}$ of $B^-→τ^-ν$ to $B^0→π^+l^-ν$, and the ratios $R_D$ and $R_{D^*}$ of $B→Dτν$ and $B→D^*τν$ to their light-lepton counterparts. The authors ask whether a single, general effective Lagrangian for $b→u lν$ and $b→c lν$ can absorb all three discrepancies at once, without committing to any particular model of new physics. They write down every Lorentz structure that can appear — vector, axial-vector, scalar, pseudoscalar, each with left- and right-handed neutrinos — reduce it to a handful of real couplings, and scan those couplings against the three measured ratios, keeping only points that survive at $3σ$. The payoff is a set of predictions for decays nobody has measured well yet: $B_c→τν$, $B→πτν$, and the ratio $R_π$ of $B→πτν$ to $B→π lν$. If the discrepancies are real, these predictions are where the next round of experiments should look.

What carries the argument

The load-bearing object is the effective Lagrangian in Eq. (3), written as a sum over all Dirac structures that can mediate $b→q' lν$ with $q'=u,c$: left- and right-handed vector currents, scalar and pseudoscalar currents, and tensor currents, each with an ordinary and a tilde (right-handed-neutrino) partner. Setting the tensor couplings to zero and grouping terms into $G_V$, $G_A$, $G_S$, $G_P$ and their tilde counterparts reduces the parameter space to a manageable set of real numbers, with the standard model recovered at $G_V=G_A=1$ and everything else zero. The decay rates for $B→lν$, $B→P lν$, and $B→V lν$ are then written in the helicity-amplitude formalism, where the hadronic physics enters through $B$ decay constants and $B→(π,D,D^*)$ form factors and the new physics enters as simple multiplicative factors such as $G_V^2$ or $G_A^2$. A random scan varies all form-factor, decay-constant, and CKM inputs within $3σ$ of their central values and retains only parameter points compatible with the measured ratios at $3σ$. The paper flags one deliberate departure from an earlier treatment: its $G_S$ term enters the $B→P lν$ rate with a positive sign, whereas the earlier work had it negative, a difference the authors say can matter numerically once scalar couplings are switched on.

Extended reading notes

Core claim

The paper's central claim is that a combined fit to $R_{l}^{π}$, $R_D$, and $R_{D^*}$ can be satisfied within $3σ$ by each of four simplified new-physics scenarios, and that each scenario then makes a definite, testable prediction for the unmeasured tau modes. The four scenarios switch on one pair of couplings at a time: $(V_L,V_R)$ in Scenario A, $(S_L,S_R)$ in Scenario B, $(Ṽ_L,Ṽ_R)$ in Scenario C, and $(S̃_L,S̃_R)$ in Scenario D. The resulting $3σ$ ranges are: for A, $B(B_c→τν)=(1.02,3.95)‰$, $B(B→πτν)=(1.86,59.42)×10^{-5}$, $R_π=(0.36,2.05)$; for B, $(0.21,13.66)‰$, $(1.69,119.66)×10^{-5}$, $R_π=(0.49,7.06)$; for C, $(1.09,4.13)‰$, $(1.71,69.39)×10^{-5}$, $R_π=(0.57,2.19)$; for D, $(1.11,16.71)‰$, $(1.70,93.90)×10^{-5}$, $R_π=(0.56,4.32)$. Against standard-model values of $6.70×10^{-5}$ for $B→τν$, $1.63‰$ for $B_c→τν$, $8.91×10^{-5}$ for $B→πτν$, and $R_π=0.698$, the scalar scenarios move things by up to an order of magnitude, while the vector scenarios move them by factors of a few. The authors also argue that a pure $G_V$ or pure $G_A$ coupling is excluded, because neither can shift all three ratios simultaneously.

Load-bearing premise

The analysis assumes that new physics touches only the third-generation lepton and that only one pair of couplings is nonzero at a time, so the allowed ranges and the predictions for $B_c→τν$, $B→πτν$, and $R_π$ are conditional on both simplifications.

Editorial extensions

If this is right

  • If Scenario B or D (scalar couplings) is the correct description, $B(B_c→τν)$ can reach roughly $1.4$ to $1.7$ percent, an order of magnitude above the standard-model value of about $0.16$ percent, making $B_c→τν$ a decisive discriminator between scalar and vector explanations.
  • The ratio $R_π$ can be as large as about $7$ in the scalar scenarios and about $2$ in the vector scenarios, against a standard-model value near $0.7$, so a measurement of $B→πτν$ alone would separate the operator classes.
  • In Scenarios A and C the forward-backward asymmetry in $B→πτν$ and $B→Dτν$ is predicted to be completely insensitive to the new-physics couplings, because the coupling dependence cancels in the ratio — a null result there is itself informative.
  • In $B→D^*τν$ the standard-model forward-backward asymmetry has a zero crossing near $q^2≈6$ GeV$^2$; depending on the couplings this crossing can move or disappear entirely, giving a shape-level handle on the new physics.
  • Because a pure $G_V$ or pure $G_A$ coupling cannot shift $R_{l}^{π}$, $R_D$, and $R_{D^*}$ together, any future confirmation of all three discrepancies would point to a mixed or scalar structure rather than a simple right-handed current.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The four scenarios are not equally natural in concrete models: a charged Higgs or a scalar leptoquark lands closest to Scenarios B and D, so the large $B_c→τν$ and $R_π$ values those scenarios predict are the ones most worth targeting first in a model-motivated search.
  • Allowing two operator pairs to be nonzero simultaneously would very likely widen the allowed ranges and could soften the paper's exclusion of pure $G_V$ and pure $G_A$; the exclusion should be read as holding within the one-pair-at-a-time scan, not in general.
  • The prediction that the forward-backward asymmetry in $B→πτν$ is coupling-independent under vector couplings is a clean experimental test that does not require knowing the form factors precisely, since the dependence cancels in the ratio.
  • The paper's own remark that its scalar term differs in sign from an earlier analysis means the two treatments will give different numerical ranges for the same data; comparing them on a common fit would be a cheap way to gauge how much of the quoted spread is physics and how much is convention.
Original abstract

Recent measurements of exclusive $B^{-} \to \tau^{-}\,\nu$ and $B^0 \to \pi^{+}\,l^{-}\,\bar{\nu}_l$ decays via the $b \to u\,l\,\nu$ transition process differ from the standard model expectation and, if they persist in future $B$ experiments, will be a definite hint of the physics beyond the standard model. Similar hints of new physics have been observed in $b \to c$ semileptonic transition processes as well. BABAR measures the ratio of branching fractions of $B \to (D,\,D^{\ast})\,\tau\,\nu$ to the corresponding $B \to (D,\,D^{\ast})\,l\nu$, where $l$ represents either an electron or a muon, and finds $3.4\sigma$ discrepancy with the standard model expectation. In this context, we consider a most general effective Lagrangian for the $b \to u\,l\,\nu$ and $b \to c\,l\,\nu$ transition processes in the presence of new physics and perform a combined analysis of all the $b \to u$ and $b \to c$ semi-(leptonic) data to explore various new physics operators and their couplings. We consider various new physics scenarios and give predictions for the $B_c \to \tau\nu$ and $B \to \pi\tau\nu$ decay branching fractions. We also study the effect of these new physics parameters on the ratio of the branching ratios of $B \to \pi\tau\nu$ to the corresponding $B \to \pi\,l\,\nu$ decays.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,464 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.46 · randomized assignment 0.01 · states quantitative result 0.62 · compares with prior results 0.71 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Recent measurements of exclusive $B^{-} \to \tau^{-}\,\nu$ and $B^0 \to \pi^{+}\,l^{-}\,\bar{\nu}_l$ decays via the $b \to u\,l\,\nu$ transition process differ from the standard model expectation and, if they persist in future $B$ experiments, will be a definite hint of the physics beyond the standard model. Similar hints of new physics have been observed in $b \to c$ semileptonic transition processes as well. BABAR measures the ratio of branching fractions of $B \to (D,\,D^{\ast})\,\tau\,\nu$ to the corresponding $B \to (D,\,D^{\ast})\,l\nu$, where $l$ represents either an electron or a muon, and finds $3.4\sigma$ discrepancy with the standard model expectation. In this context, we consider a most general effective Lagrangian for the $b \to u\,l\,\nu$ and $b \to c\,l\,\nu$ transition processes in the presence of new physics and perform a combined analysis of all the $b \to u$ and $b \to c$ semi-(leptonic) data to explore various new physics operators and their couplings. We consider various new physics scenarios and give predictions for the $B_c \to \tau\nu$ and $B \to \pi\tau\nu$ decay branching fractions. We also study the effect of these new physics parameters on the ratio of the branching ratios of $B \to \pi\tau\nu$ to the corresponding $B \to \pi\,l\,\nu$ decays.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Recent measurements of exclusive $B^{-} \to \tau^{-}\,\nu$ and $B^0 \to \pi^{+}\,l^{-}\,\bar{\nu}_l$ decays via the $b \to u\,l\,\nu$ transition process differ from the standard model expectation and, if they persist in future $B$ experiments, will be a definite hint of the physics beyond the standard model. background 0.99 0.04 0.07 hedged possibility 0.67
s1 Similar hints of new physics have been observed in $b \to c$ semileptonic transition processes as well. background 1.00 0.04 0.03 asserted 0.89
s2 BABAR measures the ratio of branching fractions of $B \to (D,\,D^{\ast})\,\tau\,\nu$ to the corresponding $B \to (D,\,D^{\ast})\,l\nu$, where $l$ represents either an electron or a muon, and finds $3.4\sigma$ discrepancy with the standard model expectation. background 0.99 0.05 0.04 asserted 1.00
s3 In this context, we consider a most general effective Lagrangian for the $b \to u\,l\,\nu$ and $b \to c\,l\,\nu$ transition processes in the presence of new physics and perform a combined analysis of all the $b \to u$ and $b \to c$ semi-(leptonic) data to explore various new physics operators and their couplings. contribution 0.53 0.94 0.08 asserted 0.95
s4 We consider various new physics scenarios and give predictions for the $B_c \to \tau\nu$ and $B \to \pi\tau\nu$ decay branching fractions. contribution 0.87 0.94 0.12 asserted 0.90
s5 We also study the effect of these new physics parameters on the ratio of the branching ratios of $B \to \pi\tau\nu$ to the corresponding $B \to \pi\,l\,\nu$ decays. contribution 0.99 0.93 0.07 asserted 0.77

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from analysis of existing data 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: Allowed regions of
Figure 2. Again, we want to emphasize the fact that a pure GV coupling will contribute to the B → P τν as well as B → V τν decay processes, whereas a pure GA coupling will contribute to the B → τν as well as the B → V τ ν decay modes. We do not consider pure GV and GA couplings for our analysis as a pure GV or a pure GA type NP coupling will not be able to accommodate all the existing data since current experiments on b → u and b → c semi-(leptonic) decays suggest that there could be new physics in all the three decay modes. Hence, if NP is present in Rl π , RD, and RD∗ , one can rule out the…
Figure 3. FIG. 3: Allowed ranges of (
Figure 4. We see that deviation from the SM is much larger in the case of
Figure 5. FIG. 5: Range in
Figure 6. FIG. 6: Range in DBR(
Figure 7. FIG. 7: Left panel shows the allowed range in
Figure 8. FIG. 8: Range in various observables such as DBR(

Figures reproduced from arXiv:1307.6653 by the authors.

References
How the literature uses it

36 arXiv papers cite this in 58 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 23 sentences without a confident label

Uses its method or tool 8 papers
  • We follow Ref. [ref] and write the expression for differential decay distribution for $B →(P, V) l ν$ decays in terms of the helicity amplitudes $H$'s and $𝒜$'s as follows: [equation] [equation] where $θ$ is the angle between the $P⃗_P, V$ and lepton three momentum vector in the $l-ν$ rest frame and [equation] By performing the $cosθ$ integration in Eq. [ref], we get [equation] [equation] The SM equations can be obtained by setting $G_V=G_A=1$ and $G_V = G_A = 0$.

    Impact of vector new physics couplings on $B_s \to (K,\,K^{\ast})\tau\nu$ and $B \to \pi\tau\nu$ decays · Methodology · 0.99

  • We follow Ref. [ref] and write the expression for differential decay distribution for $B_1 →B_2 l ν$ decays in terms of the helicity amplitudes $H^V/A_λ_2λ_W$ are expressed in $𝒜_1$, $𝒜_2$, $𝒜_3$, $𝒜_4$ as follows: [equation] where $θ$ is the angle between the $P⃗_B_2$ and lepton three momentum vector in the $l-ν$ rest frame and [equation]

    Implication of $R_{D^{(*)}}$ anomalies on semileptonic decays of $\Sigma_b$ and $\Omega_b$ baryons · Methodology · 1.00

  • In the presence of such NP, the three body differential branching ratios for $B_q →(P, V) lν$ decays, where $P(V)$ represents pseudoscalar (vector) meson, can be written as [ref] [equation] where [equation] Similarly [equation] where [equation] and [equation] Here we denote $G_V = 1+V_L+V_R$, $G_A =1+ V_L - V_R$, $G_S = S_L+S_R$, $G_P=S_L-S_R$, $G_V=V_L + V_R$, $G_A=V_L - V_R$, $G_S=S_L + S_R$, and $G_P=S_L - S_R$.

    Exploring $R_D$, $R_{D^{\ast}}$ and $R_{J/\Psi}$ anomalies · Theory framework · 0.82

Compares with it 1 paper
Cites it as background 22 papers
  • In this direction, several authors have incorporated a right-handed neutrino in the most general effective Hamiltonian for the $b →c τν̅_τ$ transition with different mediators (a colorless charged scalar boson, a heavy charged vector boson or a leptoquark) with the purpose of exploring scenarios of NP that could explain some observables related with this transition [ref] .

    Analysing the charged scalar boson contribution to the charged-current $B$ meson anomalies · Introduction · 0.90

  • The above anomalies have been investigated extensively both within model-independent frameworks [ref] , as well as in some specific NP models where the $b→cτν̅_τ$ transition is mediated by leptoquarks [ref] , charged Higgses [ref] , charged vector bosons [ref] , and sparticles [ref] .

    Revisiting the one leptoquark solution to the $R(D^{(\ast)})$ anomalies and its phenomenological implications · Introduction · 0.97

  • All of the existing $W'$ models assume that the missing energy in the semi-leptonic $B$ decay is a SM neutrino.[RH neutrinos have been combined with leptoquarks in [ref] and extended Higgs sector in [ref] ; a model-independent study has been done in [ref] . ] Our key modification is to make the $ν$ enhancing the $B→D^(*)τν$ rate a light right-handed neutrino, rather than a left-handed neutrino of the SM.

    It's all right(-handed neutrinos): a new $W'$ model for the $R_{D^{(*)}}$ anomaly · Introduction · 0.88

What it cites · 22 sentences without a confident label

Uses the method or tool of 2 papers
Uses data or values from 13 papers
Compares with 2 papers
Cites as background 5 papers

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