Catalog · Beauty · B025

B025 $R_D$

LFU ratio in B $ \to $ D $\tau \nu$ over B $ \to $ D light-lepton $\nu$

Status REVIEWED VERIFIED High Code: NO Priority Low

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
R(D) = B(B $ \to $ D $\tau \nu_\tau$) / B(B $ \to $ D l $\nu_l$), $l=e,\mu$	0.358 dimensionless ratio	2025	HFLAV semileptonic B averages, CKM 2025	source ↑

Why this constrains the RS scan

$R_D$ probes $b\to c\tau\nu$ charged currents rather than neutral $\Delta F=2$ mixing. It is therefore not a direct constraint on the current quark-scan lane, but it is important for any warped/anarchic extension with non-universal charged currents, third-generation enhanced lepton couplings, charged scalar exchange, $W'$-like vectors, or leptoquark-motivated matching. The ratio cancels many normalization inputs, so a persistent excess is a clean diagnostic of LFU violation once the model supplies the relevant semileptonic Wilson coefficients and neutrino-flavor assumptions.

What's changed since the original paper

The Csaki--Falkowski--Weiler 2008 baseline predates the $R_D^{(*)}$ anomaly program. The key post-2008 shift was BaBar's 2012 and 2013 evidence for an excess in $B\to D^{(*)}\tau\nu$, followed by Belle hadronic-tag and semileptonic-tag measurements, LHCb measurements with muonic tau decays, and Belle II semileptonic-tag and CKM-2025 hadronic-tag inputs. HFLAV now uses a joint correlated average rather than a single-experiment comparison. On the SM side, lattice and form-factor work matured substantially: HFLAV references FNAL/MILC, HPQCD, JLQCD, FLAG 2024, and later phenomenological combinations, so the tension is now limited by correlated experimental averaging and form factor conventions rather than by the absence of a basic SM prediction.

Validity and model dependence

The experimental ratio is robust, but interpreting it as an RS bound is model-dependent. A live constraint needs the operator basis for $(\bar c\,\Gamma b)(\bar\tau\,\Gamma\nu)$, the assumed neutrino species, and the integrated $B\to D$ form-factor response to vector, scalar, and tensor operators. Because HFLAV fits $R_D$ together with $R_{D^*}$, a serious implementation should use the two-dimensional likelihood or covariance rather than a standalone Gaussian for $R_D$.

Code coverage in this repo

NO. The author reran the required coverage greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/. The broad plan greps recover the existing neutral-meson $\Delta F=2$ and $\mu\to e\gamma$ surfaces, but no $R_D$, $B\to D\tau\nu$, $b\to c$ charged-current, charged-Higgs, or leptoquark observable implementation.

Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):

Implementation difficulty

HIGH. Promotion to a live constraint requires a new semileptonic charged-current observable, form-factor/mode integration for at least the $B\to D$ final state, and a correlated treatment with $R_{D^*}$. This belongs in the modern constraint surface if it is later implemented.

Reason: A live R(D) constraint needs new charged-current semileptonic operators, $B \to D$ form-factor or integrated-rate machinery, and a correlated R(D)-R(D*) likelihood; none of this is present in the current $\Delta F = 2$ or $\mu \to e \gamma$ surfaces.

Key references

Process-local snapshots before bibliography consolidation: hflav\_ckm2025\_rdrds.txt, hflav\_ckm2025\_logfile.txt, babar2012\_arxiv1205\_5442.txt, babar2013\_arxiv1303\_0571.txt, belle2015\_arxiv1507\_03233.txt, belle2019\_arxiv1910\_05864.txt, lhcb2023\_arxiv2302\_02886.txt, lhcb2025\_arxiv2406\_03387.txt, belleii2025\_arxiv2504\_11220.txt, flag2024\_arxiv2411\_04268.txt, and cfw2008\_arxiv0804\_1954.txt.

fallback_value_uncertainty R(D) = B(B -> D tau nu_tau) / B(B -> D l nu_l), l=e,mu = 0.358 +- 0.024 dimensionless ratio

RESOLVED

Match snapshot line 175

L172:          <a href="../../r_dtaunu/logfile_ckm25_new.txt">logfile.txt</a>&nbsp;
L173:         </td>
L174:       <td bgcolor="#ccccc0"><b><!--val-->0.281 &plusmn;  0.011 </b> </td>
L175:       <td bgcolor="#ccccc0"><b><!--xval-->0.358 &plusmn;  0.024 </b> </td>
L176:       <td bgcolor="#ccccc0"><b><!--corr-->-0.374 </b> </td>
L177:       <td bgcolor="#ccccc0"><b><!--chi2-->chi2/dof = 16.683/14 (CL = 0.27) </b> </td>
L178:       <td bgcolor="#ccccc0">

fallback_value_uncertainty = 0.281 +- 0.011

RESOLVED

Match snapshot line 174

L171:       <td bgcolor="#ccccc0"><b><!--ana-->Average</b>
L172:          <a href="../../r_dtaunu/logfile_ckm25_new.txt">logfile.txt</a>&nbsp;
L173:         </td>
L174:       <td bgcolor="#ccccc0"><b><!--val-->0.281 &plusmn;  0.011 </b> </td>
L175:       <td bgcolor="#ccccc0"><b><!--xval-->0.358 &plusmn;  0.024 </b> </td>
L176:       <td bgcolor="#ccccc0"><b><!--corr-->-0.374 </b> </td>
L177:       <td bgcolor="#ccccc0"><b><!--chi2-->chi2/dof = 16.683/14 (CL = 0.27) </b> </td>

fallback_value_uncertainty = 0.296 +- 0.004

AMBIGUOUS

Match 1 of 2 snapshot line 324

L321: 
L322:     <tr valign=top>
L323:       <td> G. Martinelli, S. Simula, L. Vittorio, Phys.RevD 105 (2022) 3, 034503 [<a href="https://arxiv.org/abs/2105.08674">arXiv:2105.08674 [hep-ph]</a>] </td>
L324:       <td>0.296 &plusmn;  0.008 </td>
L325:       <td></td>
L326:     </tr>
L327:

Match 2 of 2 snapshot line 474

L471: 
L472:     <tr>
L473:       <td bgcolor="#ccccc0"><b>Arithmetic average</b> </td>
L474:       <td bgcolor="#ccccc0"><b>0.296 &plusmn;  0.004 </b> </td>
L475:       <td bgcolor="#ccccc0"><b>0.254 &plusmn;  0.005 </b> </td>
L476:       <td bgcolor="#ccccc0"><b>3.79 </b> </td>
L477:     </tr>

fallback_value_uncertainty babar2012_arxiv1205_5442 = 0.44 +- 0.058

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Match snapshot line 16

L13:     <updated>2012-09-20T19:54:26Z</updated>
L14:     <link href="https://arxiv.org/abs/1205.5442v2" rel="alternate" type="text/html"/>
L15:     <link href="https://arxiv.org/pdf/1205.5442v2" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>Based on the full BaBar data sample, we report improved measurements of the ratios R(D(*)) = B(B -&gt; D(*) Tau Nu)/B(B -&gt; D(*) l Nu), where l is either e or mu. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure R(D) = 0.440 +- 0.058 +- 0.042 and R(D*) = 0.332 +- 0.024 +- 0.018, which exceed the Standard Model expectations by 2.0 sigma and 2.7 sigma, respectively. Taken together, our results disagree with these expectations at the 3.4 sigma level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. We also report the observation of the decay B -&gt; D Tau Nu, with a significance of 6.8 sigma.</summary>
L17:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>
L18:     <published>2012-05-24T13:43:06Z</published>
L19:     <arxiv:comment>Expanded section on systematics, text corrections, improved the format of Figure 2 and included the effect of the change of the Tau polarization due to the charged Higgs</arxiv:comment>

fallback_value_uncertainty babar2013_arxiv1303_0571 = 0.44 +- 0.058

RESOLVED

Match snapshot line 16

L13:     <updated>2013-03-03T21:25:32Z</updated>
L14:     <link href="https://arxiv.org/abs/1303.0571v1" rel="alternate" type="text/html"/>
L15:     <link href="https://arxiv.org/pdf/1303.0571v1" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>Based on the full BaBar data sample, we report improved measurements of the ratios R(D(*)) = B(B -&gt; D(*) Tau Nu)/B(B -&gt; D(*) l Nu), where l is either e or mu. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure R(D) = 0.440 +- 0.058 +- 0.042 and R(D*) = 0.332 +- 0.024 +- 0.018, which exceed the Standard Model expectations by 2.0 sigma and 2.7 sigma, respectively. Taken together, our results disagree with these expectations at the 3.4 sigma level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. Kinematic distributions presented here exclude large portions of the more general type III two-Higgs-doublet model, but there are solutions within this model compatible with the results.</summary>
L17:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>
L18:     <published>2013-03-03T21:25:32Z</published>
L19:     <arxiv:comment>32 pages, 30 postscript figures, submitted to Phys. Rev. D</arxiv:comment>

fallback_value_uncertainty belle2015_arxiv1507_03233 = 0.375 +- 0.064

RESOLVED

Match snapshot line 16

L13:     <updated>2015-10-10T21:01:28Z</updated>
L14:     <link href="https://arxiv.org/abs/1507.03233v3" rel="alternate" type="text/html"/>
L15:     <link href="https://arxiv.org/pdf/1507.03233v3" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>We report a measurement of the branching fraction ratios R(D(*)) of Bbar -&gt; D(*) tau- nubar_tau relative to Bbar -&gt; D()* l- nubar_l (where l = e or mu) using the full Belle data sample of 772 x 10^6 BBbar pairs collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. The measured values are R(D)= 0.375 +- 0.064(stat.) +- 0.026(syst.) and R(D*) = 0.293 +- 0.038(stat.) +- 0.015(syst.). The analysis uses hadronic reconstruction of the tag-side B meson and purely leptonic tau decays. The results are consistent with earlier measurements and do not show a significant deviation from the standard model prediction.</summary>
L17:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>
L18:     <published>2015-07-12T13:34:21Z</published>
L19:     <arxiv:comment>Accepted for publication in Phys.Rev.D</arxiv:comment>

fallback_value_uncertainty belle2019_arxiv1910_05864 = 0.307 +- 0.037

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Match snapshot line 16

L13:     <updated>2019-10-16T23:13:56Z</updated>
L14:     <link href="https://arxiv.org/abs/1910.05864v2" rel="alternate" type="text/html"/>
L15:     <link href="https://arxiv.org/pdf/1910.05864v2" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>The experimental results on the ratios of branching fractions $\mathcal{R}(D) = {\cal B}(\bar{B} \to D τ^- \barν_τ)/{\cal B}(\bar{B} \to D \ell^- \barν_{\ell})$ and $\mathcal{R}(D^*) = {\cal B}(\bar{B} \to D^* τ^- \barν_τ)/{\cal B}(\bar{B} \to D^* \ell^- \barν_{\ell})$, where $\ell$ denotes an electron or a muon, show a long-standing discrepancy with the Standard Model predictions, and might hint to a violation of lepton flavor universality. We report a new simultaneous measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$, based on a data sample containing $772 \times 10^6$ $B\bar{B}$ events recorded at the $Υ(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. In this analysis the tag-side $B$ meson is reconstructed in a semileptonic decay mode and the signal-side $τ$ is reconstructed in a purely leptonic decay. The measured values are $\mathcal{R}(D)= 0.307 \pm 0.037 \pm 0.016$ and $\mathcal{R}(D^*) = 0.283 \pm 0.018 \pm 0.014$, where the first uncertainties are statistical and the second are systematic. These results are in agreement with the Standard Model predictions within $0.2$, $1.1$ and $0.8$ standard deviations for $\mathcal{R}(D)$, $\mathcal{R}(D^*)$ and their combination, respectively. This work constitutes the most precise measurements of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ performed to date as well as the first result for $\mathcal{R}(D)$ based on a semileptonic tagging method.</summary>
L17:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>
L18:     <published>2019-10-13T23:32:28Z</published>
L19:     <arxiv:comment>8 pages, 1 figure, submitted to Physical Review Letters</arxiv:comment>

fallback_value_uncertainty lhcb2023_arxiv2302_02886 = 0.441 +- 0.06

RESOLVED

Match snapshot line 16

L13:     <updated>2024-04-22T17:17:50Z</updated>
L14:     <link href="https://arxiv.org/abs/2302.02886v3" rel="alternate" type="text/html"/>
L15:     <link href="https://arxiv.org/pdf/2302.02886v3" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>The ratios of branching fractions $\mathcal{R}(D^{*})\equiv\mathcal{B}(\bar{B}\to D^{*}τ^{-}\barν_τ)/\mathcal{B}(\bar{B}\to D^{*}μ^{-}\barν_μ)$ and $\mathcal{R}(D^{0})\equiv\mathcal{B}(B^{-}\to D^{0}τ^{-}\barν_τ)/\mathcal{B}(B^{-}\to D^{0}μ^{-}\barν_μ)$ are measured, assuming isospin symmetry, using a sample of proton-proton collision data corresponding to 3.0 fb${ }^{-1}$ of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode $τ^{-}\toμ^{-}ν_τ\barν_μ$. The measured values are $\mathcal{R}(D^{*})=0.281\pm0.018\pm0.024$ and $\mathcal{R}(D^{0})=0.441\pm0.060\pm0.066$, where the first uncertainty is statistical and the second is systematic. The correlation between these measurements is $ρ=-0.43$. Results are consistent with the current average of these quantities and are at a combined 1.9 standard deviations from the predictions based on lepton flavor universality in the Standard Model.</summary>
L17:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>
L18:     <published>2023-02-06T15:53:08Z</published>
L19:     <arxiv:comment>All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-039.html (LHCb public pages)</arxiv:comment>

fallback_value_uncertainty lhcb2025_arxiv2406_03387 = 0.249 +- 0.043

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Match snapshot line 18

L15:     <link href="https://arxiv.org/pdf/2406.03387v2" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>The branching fraction ratios of $\overline{B}^0\to D^+τ^-\overlineν_τ$ and $\overline{B}^0\to D^{*+}τ^-\overlineν_τ$ decays are measured with respect to their muonic counterparts, using a data sample corresponding to an integrated luminosity of 2.0 fb$^{-1}$ collected by the LHCb experiment in proton-proton collisions at $\sqrt{s} = 13$ TeV. The reconstructed final states are formed by combining $D^+$ mesons with $τ^-\toμ^-\overlineν_μν_τ$ candidates, where the $D^+$ is reconstructed via the $D^+\to K^-π^+π^+$ decay. The results are
L17:   \begin{align*}
L18:   R(D^{+}) &amp;= 0.249 \pm 0.043 \pm 0.047,
L19:   R(D^{*+}) &amp;= 0.402 \pm 0.081\pm 0.085,
L20:   \end{align*} where the first uncertainties are statistical and the second systematic. The two measurements have a correlation coefficient of $-0.39$ and are compatible with the Standard Model.</summary>
L21:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>

fallback_value_uncertainty belleii2025_arxiv2504_11220 = 0.418 +- 0.074

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Match snapshot line 16

L13:     <updated>2026-03-19T13:30:49Z</updated>
L14:     <link href="https://arxiv.org/abs/2504.11220v3" rel="alternate" type="text/html"/>
L15:     <link href="https://arxiv.org/pdf/2504.11220v3" rel="related" type="application/pdf" title="pdf"/>
L16:     <summary>We report measurements of the ratios of branching fractions ${\cal R}(D^{(*)+}) = \frac{{\cal B}(\overline{B}{}^0 \to D^{(*)+} \,τ^- \, \overlineν_τ)}{{\cal B}(\overline{B}{}^0 \to D^{(*)+} \, \ell^- \, \overlineν_\ell)}$, where $\ell$ denotes either an electron or a muon. These ratios test the universality of the charged-current weak interaction. The results are based on a $365\, \mathrm{fb}^{-1}$ data sample collected with the Belle II detector at the SuperKEKB $e^+e^-$ collider, which operates at a center-of-mass energy corresponding to the $Υ(4S)$ resonance, just above the threshold for $B\overline{B}{}$ production. Signal candidates are reconstructed by selecting events in which the companion $B$ meson from the $Υ(4S) \to B\overline{B}{}$ decay is identified in semileptonic modes. The $τ$ lepton is reconstructed via its leptonic decays. We obtain ${\cal R}(D^+) = 0.418 \pm 0.074 ~({\mathrm{stat}}) \pm 0.051 ~({\mathrm{syst}})$ and ${\cal R}(D^{*+}) = 0.306 \pm 0.034 ~({\mathrm{stat}}) \pm 0.018 ~({\mathrm{syst}})$, which are consistent with world average values. Accounting for the correlation between them, these values differ from the Standard Model expectation by a collective significance of $1.7$ standard deviations.</summary>
L17:     <category term="hep-ex" scheme="http://arxiv.org/schemas/atom"/>
L18:     <published>2025-04-15T14:22:58Z</published>
L19:     <arxiv:primary_category term="hep-ex"/>