High Power n of m_b in Beauty Widths and n=5 -> oo Limit

A. Vainshtein; I. Bigi; M. Shifman; N. Uraltsev

REVIEW

High Power n of m_b in Beauty Widths and n=5 -> oo Limit

I. Bigi, M. Shifman, N. Uraltsev, A. Vainshtein

High Energy Physics - Phenomenology · Submitted 5 Apr 1997 · 28 references

Pith's verdict: A clean, useful reorganizing idea — treat the mass power as a free parameter and the scale question answers itself — with the numerical reliability at n=5 resting on a step that is argued rather than proved.

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arXiv IDhep-ph/9704245 (version 1)

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CitationA. Vainshtein, I. Bigi, M. Shifman, N. Uraltsev. "High Power n of m_b in Beauty Widths and n=5 -> oo Limit." arXiv:hep-ph/9704245 (1997). https://pith.science/paper/LJZCE3EH

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Editor's note

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The thing to take away is the device, not the numbers. Making the exponent n a free parameter by adding fictitious scalar leptons to the weak vertex is a legitimate trick, and it buys a real qualitative result: the characteristic scale in inclusive semileptonic decays is not the energy release but roughly Δ/n, which is why the small-velocity kinematics are relevant for b→c even though m_c/m_b is small. That is the extended SV limit, and it explains a numerical coincidence that had been noticed but not understood. The second contribution is the low-scale Euclidean mass definition in Section 4, Eq. (33), built from the SV structure function with an explicit cut. It is gauge-invariant by construction and it is the kind of object the OPE actually wants. Both of these are worth having in the literature and I expect to cite them. The algebraic core is right: Eq. (4) and Eq. (43) show correctly that a mass shift by c·α_s/π generates the (nα_s/π)^k series and that summing it is just a change of scheme. That part is self-contained and I have no quarrel with it. Where I would push is Section 3.2. The claim that the moments of the structure functions are smooth and n-independent in the scaling limit is what makes the resummation complete, and it is argued by analogy with the tree-level factorization of Eq. (15) plus threshold behavior, not proved. The appendix checks the refined expansion at tree level (Table 1, ~10%) and one loop (Eq. 50–51, 2%), which is thin for a phenomenological claim about the total width. The note added cites Ref. [28] at q²=0; that supports small non-BLM corrections at one kinematic point, not the integrated width. I would not, though, read the 'the exact scale would be a meaningless notion' line in Section 5 as a symptom of this gap — that is just the normal fuzziness of an asymptotic expansion, and the authors are right to say so. The abstract's 'both requirements are met' is a shade sharper than the body, which is a minor framing issue. The paper is honest that n=5 is not large enough for the leading expansion and that subleading terms matter; that is acknowledged, not hidden. Who should read it: anyone working on the heavy quark expansion, inclusive widths, or scheme dependence of quark masses. It deserves a serious referee, mainly to press on the smoothness step and on what the appendix checks actually establish at n=5.

Referee report

Significance

If correct, the result removes a widely quoted source of perturbative uncertainty in the extraction of |V_cb| and reframes the large higher-order coefficients emphasized in Ref. [20] as an artifact of using MS-bar masses without resummation. The ESV parameter (m_b − m_c)/(n m_c) is a genuinely useful organizing idea that explains an empirical fact about b → c decays, and the low-scale mass definition of Eq. (33) is a concrete, gauge-invariant, and falsifiable construction rather than a scheme choice of convenience. Credit where due: the algebraic core in Eqs. (4) and (43) is clean and independently checkable, the expansion of (1 − c)^n (1 + nc) is correct through third order, Table 1 and Eqs. (50)–(51) provide quantitative validation of the refined expansion at tree and one-loop level, and the paper is explicit in §2.2 that the leading-n approximation is not expected to be quantitatively adequate at n = 5.

Major objections (2)

[§3.2, Eq. (29) and following paragraph] The resummation argument rests on the assertion that 'the moments of w_i are smooth and independent of n in the scaling limit.' The δ-function mechanism of Eq. (29) is a convincing partial argument for the leading source of n-enhancement, but the manuscript does not show that no other source of n-dependence survives beyond the mass redefinition. Since the claim in §5 that the higher-order uncertainty 'is actually absent' depends on this step, please either give an explicit demonstration (e.g. at two loops) that the residual n-dependence is subleading once the low-scale mass is used, or state the assumption and its consequences plainly rather than presenting the resummation as complete.
[Note added, Ref. [28]] The two-loop calculation cited is performed at the kinematic point q² = 0, and the manuscript infers from it that the non-BLM perturbative corrections to the total width are small. The total width requires the integral over q², and the q² = 0 point is not representative of the SV-dominated region that saturates the integrated rate. Either soften the inference or explain why the q² = 0 result transfers to the integrated width.

Minor objections (5)

[Eq. (17)] The second argument of J_1 and J_2 is written as Δ²(l+1) and Δ²l, which has dimensions of mass squared, whereas σ in Eq. (16) enters as e^{−ε/σ} and must have dimensions of mass; from Eq. (15) one would expect σ = Δ/(2(l+1)). Please check this displayed equation.
[Abstract, [abstract:s4] and [abstract:s7]] The phrases 'automatically resummed' and 'both requirements are met' read as unconditional, whereas §2.2 and §5 acknowledge that the treatment is leading in 1/n and that the exact normalization scale is not determined. Please qualify the abstract to reflect the leading-in-n nature of the result and the residual scale dependence.
[Table 1] The per-channel deviations are much larger than the total: at m_c/m_b = 0.2, BR(A)_1 is 0.524 versus the exact 0.396, while the total γ_sl ratio is 1.11. The caption should make clear that the total γ_sl ratio is the meaningful comparison and that the individual channels are not separately reliable.
[§5, 'the exact scale would be a meaningless notion'] The residual dependence on the normalization scale µ is formally subleading in 1/n, but the manuscript should state the size of the residual term at the order retained rather than only citing the ±1% figure of Ref. [19].
[§4, Eq. (35)] The low-scale mass is given explicitly only to one loop. Please state at what order m_Q(µ) is defined for the numerical results quoted in Eq. (44), and whether the Υ-spectroscopy input of Ref. [24] is consistent with that order.

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The paper

The paper claims

By treating the fifth power of the bottom quark mass as a free parameter and letting it grow, the authors argue that the right mass to use in beauty decay widths is a low-scale Euclidean mass near 1 GeV, not the mass at the b scale.

The reading

The semileptonic width of a beauty hadron scales as the fifth power of the heavy quark mass, and that high power is usually treated as a fixed nuisance: a small error in $m_b$ becomes a large error in $|V_{cb}|$. This paper turns the exponent into a dial. By adding fictitious scalar leptons to the weak vertex, the power $n$ becomes $5+2l$, so the width can be studied as $n$ grows and the physics can be organized as an expansion in $1/n$. The point of the exercise is to locate the momentum scale at which the hadronic part of the decay is really being probed. The authors find it is not the energy release $m_b-m_c$ but roughly $(m_b-m_c)/n$, about 1 GeV in the real world. If that is right, then expressing the width in terms of a quark mass normalized at that low scale automatically resums the perturbative corrections that come enhanced by powers of $n$, and the large higher-order coefficients that appeared when MS-bar masses were used are an artifact of the scheme rather than a real theoretical uncertainty.

What carries the argument

The load-bearing device is the promotion of the exponent $n$ to a free parameter by emitting $l$ extra scalar 'leptons' from the weak vertex, so that $n = 5+2l$ and the width becomes $gamma(n)$ with an extra factor $(q^2)^l$ in the phase-space integral. In the large-$n$ limit the phase-space weight becomes a Gaussian in the excitation energy and three-momentum, $exp[-2(l+1)epsilon/Delta]$, so the $epsilon$ and $T$ integrations decouple and are saturated at $epsilon sim Delta/n$ and $T sim Delta^2/(n M_B)$. The hadronic dynamics then sits in Borel-type moments $J_i(T;sigma) = (1/2pi) int d epsilon, e^{-epsilon/sigma} w_i(epsilon,T)$ of the structure functions, which are the ordinary heavy-flavor sum rules with a built-in cutoff. That cutoff is what lets the authors separate the infrared part of the quark mass, which cancels between the meson mass and the spectral integrals, from the short-distance part that must be computed perturbatively.

Extended reading notes

Core claim

The central claim is that the leading $n$-enhanced perturbative corrections to the inclusive semileptonic width are resummed once the width is written in terms of a Euclidean heavy quark mass normalized at a scale of order the energy release divided by $n$, around 1 GeV. The mechanism is algebraic and is displayed explicitly: if the width computed with one mass has $n$-independent coefficients, rewriting it in terms of a mass shifted by $c$ times $alpha_s/pi$ generates the series $(n c alpha_s/pi)^k$, which sums into a redefinition of the mass. With $c=4/3$ for the MS-bar mass and $n=5$, the second-order coefficient is inflated past 25, which is what made the perturbative expansion look out of control; with a low-scale mass the enhancement is absent. The same large-$n$ kinematics explains a second puzzle, namely why inclusive $b to c$ decays behave as if close to the small-velocity limit even though $m_c^2/m_b^2$ is small: the relevant parameter is $(m_b-m_c)/(n m_c)$, not $(m_b-m_c)/m_c$, and the authors call this regime the extended small-velocity, or ESV, limit. They also give a gauge-invariant, OPE-compatible definition of the low-scale mass through a ratio of moments of the structure function at small recoil, cut off at $mu$, so that the same object serves both the perturbative resummation and the nonrelativistic effective theory.

Load-bearing premise

The argument needs the moments of the hadronic structure functions to be smooth and free of residual $n$-dependence once the perturbative thresholds are absorbed into the low-scale mass; this is argued from the threshold behavior of the perturbative spectral densities rather than demonstrated to all orders.

Editorial extensions

If this is right

The apparent large higher-order perturbative uncertainty in extracting $|V_{cb}|$ from inclusive widths, raised for MS-bar masses, is a scheme artifact: with a mass normalized near 1 GeV the second-order coefficient is small, so the extraction is under better control than feared.
Inclusive $b to c$ semileptonic decays can be treated with small-velocity methods even at $m_c/m_b approx 0.3$, because the controlling parameter is $(m_b-m_c)/(n m_c)$ rather than $(m_b-m_c)/m_c$; this justifies using zero-recoil form factors and heavy quark symmetry for the leading terms.
The scale at which duality between partonic and hadronic descriptions holds is $m_Q/n$, not $m_Q$, which sharpens where duality violation could enter, particularly in nonleptonic decays where the color flow can be rerouted.
A gauge-invariant low-scale heavy quark mass and matching renormalized higher-dimension operators can be defined from small-recoil structure-function moments, giving the nonrelativistic effective theory a consistent mass parameter below $m_Q$.
The same reasoning is proposed to apply outside beauty physics, for instance to second-order QED corrections to the muon lifetime, where large coefficients are expected to be absent if the muon mass is normalized near $m_mu/3$ to $m_mu/2$.

Reading between the lines

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

If the resummation argument holds, the practical bottleneck in $|V_{cb}|$ moves from perturbative coefficients to the nonperturbative matrix element $mu_pi^2$, whose coefficient is itself enhanced by the same power $n$; the paper notes this explicitly but offers no independent handle on it.
The claim that the appropriate scale is 'about 1 GeV' is deliberately vague, and the authors say the exact scale is a meaningless notion; a reader could reasonably read this as an invitation to check whether the width is genuinely flat under scale variation between roughly 0.7 and 1.5 GeV, which is a sharper and more falsifiable statement than the paper makes.
The extended small-velocity picture suggests a cross-check against exclusive $B to D^*$ data: if the leading large-$n$ term really reduces to the zero-recoil form factor times the meson mass difference to the $n$th power, then the inclusive and exclusive determinations of $|V_{cb}|$ should agree at the level the paper's power counting allows, which is a comparison the paper only gestures at.
The same moment-based definition of a low-scale mass could in principle be extracted from lattice spectral densities rather than from perturbation theory, which would turn the scheme choice from a convention into a measurable quantity.

Original abstract

The leading term in the semileptonic width of heavy flavor hadrons depends on the fifth power of the heavy quark mass. We present an analysis where this power can be self-consistently treated as a free parameter n and the width can be studied in the limit n -> oo. The resulting expansion elucidates why the small velocity (SV) treatment is relevant for the inclusive semileptonic b->c transition. The extended SV limit (ESV limit) is introduced. The leading terms in the perturbative alpha_s expansion enhanced by powers of n are automatically resummed by using the low-scale Euclidean mass. The large-n treatment explains why the scales of order m_b/n are appropriate. On the other hand, the scale cannot be too small since the factorially divergent perturbative corrections associated with running of alpha_s show up. Both requirements are met if we use the short-distance mass normalized at a scale around m_b/n \sim 1 GeV. A convenient definition of such low-scale OPE-compatible masses is briefly discussed.

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.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.62 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.28 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The leading term in the semileptonic width of heavy flavor hadrons depends on the fifth power of the heavy quark mass. We present an analysis where this power can be self-consistently treated as a free parameter n and the width can be studied in the limit n -> oo. The resulting expansion elucidates why the small velocity (SV) treatment is relevant for the inclusive semileptonic b->c transition. The extended SV limit (ESV limit) is introduced. The leading terms in the perturbative alpha_s expansion enhanced by powers of n are automatically resummed by using the low-scale Euclidean mass. The large-n treatment explains why the scales of order m_b/n are appropriate. On the other hand, the scale cannot be too small since the factorially divergent perturbative corrections associated with running of alpha_s show up. Both requirements are met if we use the short-distance mass normalized at a scale around m_b/n \sim 1 GeV. A convenient definition of such low-scale OPE-compatible masses is briefly discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The leading term in the semileptonic width of heavy flavor hadrons depends on the fifth power of the heavy quark mass.	background 1.00	0.09	0.07	asserted 1.00
s1	We present an analysis where this power can be self-consistently treated as a free parameter n and the width can be studied in the limit n -> oo.	contribution 0.84	0.93	0.16	asserted 0.90
s2	The resulting expansion elucidates why the small velocity (SV) treatment is relevant for the inclusive semileptonic b->c transition.	interpretation 0.95	0.74	0.21	asserted 0.99
s3	The extended SV limit (ESV limit) is introduced.	contribution 0.96	0.82	0.08	asserted 0.98
s4	The leading terms in the perturbative alpha_s expansion enhanced by powers of n are automatically resummed by using the low-scale Euclidean mass.	result 0.84	0.74	0.14	asserted 1.00
s5	The large-n treatment explains why the scales of order m_b/n are appropriate.	interpretation 0.91	0.74	0.15	asserted 1.00
s6	On the other hand, the scale cannot be too small since the factorially divergent perturbative corrections associated with running of alpha_s show up.	limitation 0.51	0.43	0.05	asserted 0.99
s7	Both requirements are met if we use the short-distance mass normalized at a scale around m_b/n \sim 1 GeV.	result 0.74	0.74	0.32	asserted 0.97
s8	A convenient definition of such low-scale OPE-compatible masses is briefly discussed.	contribution 0.53	0.52	0.05	asserted 0.63

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from proof or derivation 0.92.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
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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.** The decay distribution over invariant mass of the lepton pa

Figures reproduced from arXiv:hep-ph/9704245 by the authors.

References

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The $q^2$ moments in inclusive semileptonic $B$ decays
hep-ph 2023-10 accept novelty 5.0 of 10

Adding new O(α_s²β_0) corrections and the Belle/Belle II q² moments to the global OPE fit yields |Vcb| = (41.97 ± 0.48) × 10⁻³, with the uncertainty on ρ³D roughly halved.
Revisiting lifetimes of doubly charmed baryons
hep-ph 2023-05 unverdicted novelty 5.0 of 10

Updated predictions within the heavy quark expansion confirm the lifetime hierarchy τ(Ξ_cc^+) < τ(Ω_cc^+) < τ(Ξ_cc^++) with τ(Ξ_cc^++) = 0.32 ± 0.05 +0.08/-0.07 ps matching LHCb data and provide ratios for the other states.
On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks
hep-ph 2020-11 accept novelty 5.0 of 10

The three-loop relation between the MS-bar and kinetic heavy-quark masses is computed, reducing the bottom-quark conversion uncertainty to about 15 MeV.
Bs mixing observables and Vtd/Vts from sum rules
hep-ph 2019-04 accept novelty 5.0 of 10

Including finite strange-quark mass in HQET sum rules gives Bs bag parameters and the ratio xi = 1.2014(+0.0065/-0.0072), yielding |Vtd/Vts| = 0.2045(+0.0012/-0.0013) and a Standard Model Delta M_s of 18.5 ps^-1, belo...
$b\to c\tau\nu$ Transitions in the Standard Model Effective Field Theory
hep-ph 2018-10 conditional novelty 5.0 of 10

A global SMEFT fit to b to c tau nu data leaves eleven viable one- and two-operator scenarios, most of which the authors argue can be separated by 31 predicted observables.
Inclusive semileptonic fits, heavy quark masses, and V_cb
hep-ph 2013-07 accept novelty 5.0 of 10

A global fit to semileptonic B decay moments with NNLO corrections and an external charm mass yields |Vcb| = 42.42(86) x 10^-3 and m_b^kin = 4.541(23) GeV.
B semileptonic moments at NNLO
hep-ph 2011-07 conditional novelty 5.0 of 10

The first three lepton-energy and hadronic-mass moments in inclusive B semileptonic decays are computed at complete O(alpha_s^2), and the non-BLM corrections are found to be small, confirming the earlier O(alpha_s^2 b...
Three loop calculations and inclusive $V_{cb}$
hep-ph 2021-07 conditional novelty 4.0 of 10

Feeding new three-loop QCD corrections and improved lattice quark masses into the global semileptonic fit gives |Vcb| = 42.16(51) x 10^-3, cutting the inclusive uncertainty by about one third.
Implications of LHCb measurements and future prospects
hep-ex 2012-08 accept novelty 4.0 of 10

LHCb's first 1.0 fb^-1 of 7 TeV data already constrain several new-physics scenarios, and a proposed upgrade to 50 fb^-1 would sharpen those constraints by roughly an order of magnitude.
Lifetimes and HQE
hep-ph 2014-05 accept novelty 3.0 of 10

The Heavy Quark Expansion survives all current lifetime tests, and updated predictions give tau(B+)/tau(Bd) = 1.04, tau(Bs)/tau(Bd) = 1.001, tau(Lambda_b)/tau(Bd) = 0.935 and tau-bar(Xi_b^0)/tau-bar(Xi_b^+) = 0.95.
Hadronic mass and q^2 moments in B->Xu l nu
hep-ph 2006-03 unverdicted novelty 3.0 of 10

This paper is a short proceedings summary presenting OPE predictions for B->Xu l nu hadronic mass and q^2 moments, but the derivations and numerical results are entirely in the authors' earlier paper.
The Semileptonic B Frontier: LHC, B-factories, Lattice QCD & the Hunt for Precision
hep-ph 2026-10 accept novelty 2.0 of 10

A comprehensive review of semileptonic B decays, including charged-current and neutral-current processes, with emphasis on CKM determinations, LFU tests, and the interplay between experiment and theory.

How later papers used it

50 later papers cite it

Evidence: substantial. 46 of the citing papers share no author with it, and 18 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 84 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

7 later papers by other authors are listed below: 7 used its method or tool.

Uses its method or tool 7 of 13 papers with this label

Used the kinetic scheme with a cutoff at 1 GeV for the bottom mass and OPE parameters.

Precision determination of the CKM element Vcb (2014) · 1.00 · paraphrased: the licence does not allow quoting
In , we use the so-called kinetic scheme [ref] for the bottom quark and the HQE operators.

Kolya: an open-source package for inclusive semileptonic $B$ decays (2024) · Kinetic and $MS$ scheme · 0.92
Worked in the kinetic scheme, where a hard cutoff separates perturbative and non-perturbative effects.

Normalizing inclusive rare B decays (2008) · 0.99 · paraphrased: the licence does not allow quoting
Used a simple cut-off scheme cutting the absolute value of gluon three-momenta, as originally proposed in this paper.

Extending the Kinetic Mass to Higher Orders in $1/m_Q$ (2026) · 1.00 · paraphrased: the licence does not allow quoting
Focused on the kinetic scheme.

Lepton energy moments in semileptonic charm decays (2010) · 0.88 · paraphrased: the licence does not allow quoting
Translated its predictions to the kinetic scheme.

The $q^2$ moments in inclusive semileptonic $B$ decays (2023) · 0.89 · paraphrased: the licence does not allow quoting
To avoid renormalon issues with the short-distance pole mass, we employ the kinetic mass for the $b$ quark [ref] and the $MS$ mass for the quark.

Inclusive semileptonic $B_{s}^{0}$ meson decays at the LHC via a sum-of-exclusive modes technique: possibilities and prospects (2023) · Heavy Quark Expansion · 0.86

How the literature uses it

51 arXiv papers cite this in 82 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 · 46 sentences without a confident label

Uses its method or tool 14 papers

We work in the kinetic scheme [ref] and follow the implementation described in [ref] .

Inclusive semileptonic fits, heavy quark masses, and V_cb · Observables included in the fits · 1.00
We use the kinetic scheme [ref] with cutoff at 1 GeV for $m_b$ and the OPE parameters and three different options for the charm mass.

Precision determination of the CKM element Vcb · The calculation · 1.00
In particular, we describe our approach based on expansion by regions [ref] to compute the SV sum rules [ref] that define the kinetic mass to higher orders in $α_s$.

On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks · Heavy quark mass definitions · 1.00

Uses its data or values 4 papers

To calculate the ratio $R(X_c)$, we take [ref] : $μ_π^2=0.464(67) GeV^2$, $μ_G^2=0.333(61) GeV^2$, $ρ_D^3=0.175(40) GeV^3$, and $ρ_LS^3=-0.146(96) GeV^3$, with $m_b^kin(1GeV)=4.561(21) GeV$ and $m_c^kin(1GeV)=1.092(20) GeV$ in the kinetic scheme [ref] ; the correlations between these parameters [ref] are also considered.

$b\to c\tau\nu$ Transitions in the Standard Model Effective Field Theory · $B→X_cτν$ · 1.00
To be consistent with the results of both fits by Refs. [ref] and [ref] , by default, in our numerical analysis the mass of the $b$-quark is expressed in the kinetic scheme [ref] fixing the cut-off scale $μ^cut = 1$GeV, while we adopt the $MS$ scheme for the charm quark mass [ref] , i.e. [equation] [equation] In order to understand the size of each of the contributions to the HQE, in the following we show the partial decomposition for all the five observables considered.

Disintegration of beauty: a precision study · Numerical analysis and results · 0.82
In analyzing the lifetime ratio, input parameters including the heavy-quark mass and power correction parameters in the heavy quark effective theory (HQET) are adopted from Ref. [ref] in the kinetic scheme [ref] .

$B_{(s)}\to D_{(s)}^{(*)}M$ decays in the presence of final-state interaction · Numerical results · 0.95

Compares with it 1 paper

Comparing with the usual HQET kinetic mass, implemented in HQE applications through [ref] [equation] we note that the first two terms agree, aside from the ambiguous leading power in $μ$.

Extending the Kinetic Mass to Higher Orders in $1/m_Q$ · The extended kinetic mass · 1.00

Cites it as support 1 paper

However, QCD corrections to the semi-leptonic rates exhibit a bad convergence also in the $MS$ scheme [ref] .

The Kinetic Heavy Quark Mass to Three Loops · Introduction · 0.96

Cites it as background 11 papers

The kinetic scheme for the mass of a heavy quark, $m_Q^kin$, was introduced in [ref] to resum in the semileptonic rate the $(n α_s)^k$-enhanced terms via a suitable short-distance definition.

On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks · Why the kinetic mass? · 0.87
In Ref. [ref] (see also Ref. [ref] ) the kinetic mass has been defined via its relation to the pole mass $m^OS$ through [equation] where the ellipses stand for contributions from higher dimensional operators.

The Kinetic Heavy Quark Mass to Three Loops · Introduction · 0.92
To this end, other schemes have been identified, such as the potential-subtracted mass [ref] or the kinetic mass [ref] , which can be used at scales $μ≤m_Q$, as well as schemes which can be used at all scales [ref] .

Extending the Kinetic Mass to Higher Orders in $1/m_Q$ · Introduction · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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