Matching QCD and HQET heavy--light currents at two loops and beyond

A.G.Grozin; D.J.Broadhurst

REVIEW

Matching QCD and HQET heavy--light currents at two loops and beyond

D.J.Broadhurst, A.G.Grozin

High Energy Physics - Phenomenology · Submitted 6 Oct 1994 · 34 references

Pith's verdict: A solid, well-checked two-loop matching calculation that gives one formula for all heavy-light currents; the only real gap is the unbenchmarked tensor anomalous dimension, and that gap is small.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9410240 (version 2)

Pith IDCYIHSWLW, Pith's permanent record of this paper and its review

CitationA.G.Grozin, D.J.Broadhurst. "Matching QCD and HQET heavy--light currents at two loops and beyond." arXiv:hep-ph/9410240 (1994). https://pith.science/paper/CYIHSWLW

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

Significance

If correct, this is the general two-loop matching formula for heavy-light currents in HQET, extending the one-loop Eichten–Hill result to all Dirac structures in a single expression. The numerical two-loop corrections to f_B*/f_B and related ratios are of direct phenomenological interest for lattice and sum-rule extractions of decay constants, and the paper is careful to state that the two-loop correction is comparable in size to the one-loop one. The all-order large-β0 analysis is a useful model calculation, and the demonstration that infrared- and ultraviolet-renormalon ambiguities cancel in (4.11)–(4.14) provides a consistency check on the 1/m expansion that goes beyond what was previously available. The paper also corrects a factor CF omission in Equation (17) of [11] for the finite light-quark-mass effects.

Minor objections (8)

[§2.3, Eq. (2.18)] The n=2 tensor anomalous dimension has no external benchmark, and the paper acknowledges that it 'appears to be absent from the literature'. The general formula (2.17) is derived for arbitrary n and checked at n=0,1,3,4, so the n=2 result is supported by the general derivation rather than fitted; nevertheless, an independent massless-QCD calculation, which the authors themselves describe as straightforward, would strengthen the claim and is worth stating explicitly as a future check.
[§2.2, Eq. (2.17)] The text should clarify that the 't Hooft–Veltman and naively anticommuting γ5 prescriptions correspond to different values of n (n=3 versus n=1 for the axial current, n=4 versus n=0 for the pseudoscalar), and that the single formula (2.17) is evaluated at those different n values. The present sentence, 'with a check being provided by the absence of the signature η', is terse and may leave readers unsure how one polynomial can describe both prescriptions.
[Table 1] The caption states that the two-loop coefficients are sums of three terms (quenched, light-quark loop, heavy-quark loop), but the table entries do not label which term is which; a reader has to infer that the final constant in each entry is the heavy-quark contribution. Labelling the three terms explicitly, or adding a footnote, would make the table self-contained.
[§3.2, Eq. (3.18)] The 1/m correction is written as (1/m_b)(2/3 Λ̄ − 8G_2(m_b)), but the sign and normalization of G_2 are not defined in the paper; the reader has to consult [13,14]. A one-line definition of G_2 and of the sign convention would help.
[§4.1, Eq. (4.6)] The derivation of the all-order matching coefficient is sketched, and the reader is asked to trust the combinatoric identities of [29,30]. Since these are cited published results this is acceptable, but a brief summary of the identities that convert the 1/ε poles into the Taylor coefficients of F(ε,0) and F(0,u) would make the section more readable.
[§2.1, Eq. (2.4)] The HQET on-shell wave-function renormalization constant exhibits non-uniformity as m_i → 0, and the notation ∑_{m_i>0} is used to encode this. The surrounding discussion explains the origin, but the notation itself could be defined more explicitly at the point of use.
[Abstract and §3.2] The value Δ_c = 0.18 ± 0.01 is quoted in the abstract and in (3.18), but the derivation from m_c/m_b = 0.28 ± 0.03 is only sketched. A short explicit evaluation of Δ_2 and Δ_3 at the relevant mass ratio, or a pointer to the relevant line of Appendix A, would make the number reproducible without effort.
[§3.2, Eq. (3.12)] The observation that f_B*/f_B is 'numerically very close to (m(m)/m)^{1/2}' is interesting but not derived. If there is a structural reason for the closeness, it would be worth stating; if it is accidental, saying so would avoid over-interpretation.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Heavy-light quark currents are matched between QCD and the static-quark effective theory at two loops, with one formula covering every current of the allowed Dirac structure.

The reading

At a heavy-quark mass shell, QCD and the static-quark effective theory must describe the same heavy-light current up to a matching coefficient. This paper computes that coefficient to two loops and leading order in $1/m$ for every current whose Dirac matrix satisfies the paper's commutation condition, and gives the answer as one formula depending on the number of antisymmetrized gamma matrices and a sign. The practical payoff is a two-loop correction to ratios of B-meson decay constants that does not require the unknown three-loop anomalous dimension of the HQET current. The authors also extract a general two-loop anomalous-dimension formula for the QCD current, including a tensor-current case they say was missing, and study the all-order large-flavour limit to show how infrared and ultraviolet renormalon ambiguities cancel in physical ratios.

What carries the argument

The carrying mechanism is a reduction of any two-loop vertex diagram to a fourth-order polynomial in $h$, the parameter that encodes how the Dirac matrix contracts with itself. Instead of evaluating traces with complicated antisymmetrized gamma matrices, the authors take five double traces on the light- and heavy-quark lines, invert once, and read off the coefficients of $h^k$. The QCD current renormalization constant $Z_J$ is not computed independently: a minimal ansatz is fixed by requiring finiteness of the matching equation (1.4), then checked against known anomalous dimensions. Finite light-quark masses enter through three dilogarithmic integrals $Delta_k(r)$ defined and expanded in Appendix A. For the all-order large-$beta_0$ analysis, a master multinomial $F(varepsilon,u)$ encodes both the $varepsilon$-dependence that gives anomalous dimensions and the $u$-dependence that gives renormalon singularities.

Extended reading notes

Core claim

The central claim is Eq. (2.19): for $Gamma=gamma^{[mu_1}cdotsgamma^{mu_n]}$ obeying $gamma^0Gamma=sigmagamma^0$ and $gamma^muGammagamma_mu=2sigma hGamma$, with $h=eta(n-2+varepsilon)$ and $eta=-sigma(-1)^n$, the matching coefficient $C_Gamma(m)$ has a single two-loop expression whose coefficients $a_F$, $a_A$, and $a_f$, plus the finite-mass correction $Delta_J(r)$, are given in Eqs. (2.20)–(2.22). The one-loop term reproduces the earlier result of [1], and the two-loop term is checked against known anomalous dimensions for the scalar, vector, axial, and pseudoscalar currents. The tensor-current anomalous dimension at $n=2$, Eq. (2.18), is presented as new and appears to have no prior literature value. For the ratio $f_{B^*}/f_B$, the same machinery gives $K_b=6.37+Delta_c$ with $Delta_c=0.18pm0.01$ for $N_l=4$ and $m_c/m_b=0.28pm0.03$.

Load-bearing premise

The matching formula rests on a minimal ansatz for the QCD current renormalization constant, with its coefficients fixed only by finiteness of the matching equation and checked against known scalar, vector, axial, and pseudoscalar cases; the new tensor-current anomalous dimension has no independent external benchmark.

Editorial extensions

If this is right

For any heavy-light current satisfying the paper's condition, the two-loop matching coefficient can be read from one formula instead of being recomputed diagram by diagram.
At $alpha_s(m_b)=0.215pm0.018$, the two-loop term in $f_{B^*}/f_B$ is about $-(3.1pm0.5)%$, comparable to the one-loop $-(4.6pm0.4)%$, and the paper's combined estimate is $f_{B^*}/f_B=1.00pm0.04$.
Ratios of matching coefficients are independent of the three-loop HQET current anomalous dimension, so decay-constant ratios can be predicted more cleanly than individual decay constants.
The tensor-current anomalous dimension Eq. (2.18) supplies the QCD evolution needed for $f_{B^*}^T$ once the corresponding HQET matrix element is known.
In the large-$beta_0$ limit, the master formula yields all-order anomalous dimensions and matching coefficients, and the residue at $u=1/2$ shows that the infrared renormalon ambiguity is cancelled by ultraviolet ambiguities in the pole mass and the $1/m$ matrix elements.

Reading between the lines

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

Because the tensor-current anomalous dimension is new and unbenchmarked, an external massless-QCD calculation of that entry would be the cleanest test of the ansatz used for the QCD current renormalization.
If naive non-abelianization continues to work at the 30% level in other heavy-light observables, it offers a cheap way to estimate missing higher orders where exact multi-loop matching is impractical.
The renormalon cancellation pattern suggests a practical consistency check for future $1/m$ expansions: any new higher-dimension operator that mixes with the pole mass should carry an ultraviolet ambiguity matching the corresponding infrared residue in the matching coefficient.
The single formula could be used to generate matching coefficients for currents not tabulated here, since only $n$ and $eta$ are needed.

Original abstract

Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}\gamma^{[\mu_1}\ldots\gamma^{\mu_n]}q$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on $\gamma_5$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}^2/\pi^2 +{\rm O}(\alpha_{\rm s}^3,1/m_b)$ is \[K_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c\] with $N_l=4$ light flavours, and a correction, $\Delta_c=0.18\pm0.01$, that takes account of the non--zero ratio $m_c/m_b=0.28\pm0.03$. Fastest apparent convergence would entail $\alpha_{\rm s}(\mu)$ at $\mu=370$~MeV. ``Naive non--abelianization'' of large--$N_l$ results, via $N_l\to N_l-\frac{33}{2}$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large $\beta_0=11-\frac23N_l$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.

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, 7,399 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.51 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.61 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}\gamma^{[\mu_1}\ldots\gamma^{\mu_n]}q$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on $\gamma_5$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}^2/\pi^2 +{\rm O}(\alpha_{\rm s}^3,1/m_b)$ is \[K_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c\] with $N_l=4$ light flavours, and a correction, $\Delta_c=0.18\pm0.01$, that takes account of the non--zero ratio $m_c/m_b=0.28\pm0.03$. Fastest apparent convergence would entail $\alpha_{\rm s}(\mu)$ at $\mu=370$~MeV. ``Naive non--abelianization'' of large--$N_l$ results, via $N_l\to N_l-\frac{33}{2}$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large $\beta_0=11-\frac23N_l$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.

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	Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$.	contribution 0.94	0.91	0.50	asserted 1.00
s1	A single formula applies to all current matchings.	result 0.52	0.85	0.17	asserted 1.00
s2	As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}\gamma^{[\mu_1}\ldots\gamma^{\mu_n]}q$ is obtained, yielding a new result for the tensor current.	result 0.79	0.95	0.19	asserted 1.00
s3	The dependence of matching coefficients on $\gamma_5$ prescriptions is elucidated.	result 0.55	0.88	0.04	asserted 1.00
s4	Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents.	result 0.84	0.91	0.09	asserted 1.00
s5	The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}^2/\pi^2 +{\rm O}(\alpha_{\rm s}^3,1/m_b)$ is \[K_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c\] with $N_l=4$ light flavours, and a correction, $\Delta_c=0.18\pm0.01$, that takes account of the non--zero ratio $m_c/m_b=0.28\pm0.03$.	result 1.00	0.92	0.29	asserted 1.00
s6	Fastest apparent convergence would entail $\alpha_{\rm s}(\mu)$ at $\mu=370$~MeV. ``Naive non--abelianization'' of large--$N_l$ results, via $N_l\to N_l-\frac{33}{2}$, gives reasonable approximations to exact two--loop results.	result 0.65	0.72	0.05	asserted 0.62
s7	All--order results for anomalous dimensions and matching coefficients are obtained at large $\beta_0=11-\frac23N_l$.	result 0.78	0.92	0.14	asserted 1.00
s8	Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.	result 0.95	0.89	0.11	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 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.** One– and two–loop diagrams for the proper vertex

Figures reproduced from arXiv:hep-ph/9410240 by the authors.

References

Works cited (34)

[11]

N. Gray, D. J. Broadhurst, W. Grafe, and K. Schilcher, Z. Phys. C48 (1990) 673

View on Pith 1990
[1]

E. Eichten and B. Hill, Phys. Lett. B234 (1990) 511

View on Pith 1990
[2]

B. Grinstein, Nucl. Phys. B339 (1990) 253; H. Georgi, Phys. Lett. B240 (1990) 447

View on Pith 1990
[3]

M. Neubert, Phys. Reports 245 (1994) 259

View on Pith 1994
[4]

M. Golden and B. Hill, Phys. Lett. B254 (1991) 225

View on Pith 1991
[5]

M. Neubert, Phys. Rev. D49 (1994) 1542

View on Pith 1994
[6]

M. B. Voloshin and M. A. Shifman, Sov. J. Nucl. Phys. 45 (1987) 292

View on Pith 1987
[7]

H. D. Politzer and M. B. Wise, Phys. Lett. B206 (1988) 681; B208 (1988) 504

View on Pith 1988
[8]

X. Ji and M. J. Musolf, Phys. Lett. B257 (1991) 409

View on Pith 1991
[9]

D. J. Broadhurst and A. G. Grozin, Phys. Lett. B267 (1991) 105

View on Pith 1991
[10]

V. Gim´ enez,Nucl. Phys. B375 (1992) 582

View on Pith 1992
[12]

D. J. Broadhurst, N. Gray, and K. Schilcher, Z. Phys. C52 (1991) 111

View on Pith 1991
[13]

M. Neubert, Phys. Rev. D46 (1992) 1076

View on Pith 1992
[14]

P. Ball, Nucl. Phys. B421 (1994) 593

View on Pith 1994
[15]

M. Beneke and V. M. Braun, Nucl. Phys. B426 (1994) 301

View on Pith 1994
[16]

I. I. Bigi, M. A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Phys. Rev. D50 (1994) 2234

View on Pith 1994
[17]

M. Neubert and C. T. Sachrajda, CERN–TH.7312/94 (July 1994 ), hep–ph/9407394

View on Pith 1994
[18]

D. J. Broadhurst, Z. Phys. C47 (1990) 115

View on Pith 1990
[19]

D. J. Broadhurst, Z. Phys. C54 (1992) 599

View on Pith 1992
[20]

A. C. Hearn, REDUCE user’s manual, version 3.5, Rand publication CP78 (1993)

View on Pith 1993
[21]

R. Tarrach, Nucl. Phys. B183 (1981) 384

View on Pith 1981
[22]

T. L. Trueman, Phys. Lett. B88 (1979) 331

View on Pith 1979
[23]

S. A. Larin, Proc. 7 int. seminar Quarks–92, ed. D. Yu Grigoriev , V. A. Matveev, V. A. Rubakov, and P. G. Tinyakov, World Scientiﬁc (1993), p. 201; NIKHEF–H/92–18 (1992), hep–ph/9302240

View on Pith 1993
[24]

S. A. Larin and J. A. M. Vermaseren, Phys. Lett. B259 (1991) 345; S. A. Larin, Phys. Lett. B303 (1993) 113. 24

View on Pith 1991
[25]

S. G. Gorishny and S. A. Larin, Phys. Lett. B172 (1986) 109

View on Pith 1986
[26]

D. J. Broadhurst and A. L. Kataev, Phys. Lett. B315 (1993) 179

View on Pith 1993
[27]

D. J. Broadhurst and A. G. Grozin, Phys. Lett. B274 (1992) 421

View on Pith 1992
[28]

Particle Data Group, Phys. Rev. D50 (1994) 1173

View on Pith 1994
[29]

A. Palanques–Mestre and P. Pascual, Comm. Math. Phys. 95 (1984) 277

View on Pith 1984
[30]

D. J. Broadhurst, Z. Phys. C58 (1993) 339

View on Pith 1993
[31]

M. Beneke, Nucl. Phys. B405 (1993) 424

View on Pith 1993
[32]

A. H. Mueller, in QCD 20 years later, ed. P. M. Zerwas and H. A. Kastrup, World Scientiﬁc (1993), v. 1, p. 162

View on Pith 1993
[33]

J. A. Gracey, Mod. Phys. Lett. A7 (1992) 1945

View on Pith 1992
[34]

M. Beneke, UM–TH–94–31 (August 1994), hep–ph/9408380. 25 This figure "fig1-1.png" is available in "png" format from: http://arxiv.org/ps/hep-ph/9410240v2

View on Pith Pith review arXiv 1994

Forward citations

Cited by 26 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Heavy-quark expansion at leading power for local QCD operators in gradient flow
hep-ph 2026-09 accept novelty 7.0 of 10

Mass-dependent matching coefficients for flowed QCD heavy-light currents to HQET are computed at one loop, enabling more accurate lattice calculations of heavy-quark observables.
Magnetic susceptibility of QCD matter and its decomposition from the lattice
hep-lat 2020-04 conditional novelty 7.0 of 10

Continuum-extrapolated lattice QCD gives a magnetic susceptibility that is negative below roughly 150 MeV and positive above, and its decomposition shows the orbital term, not the spin term, driving the paramagnetism.
The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
hep-ph 2015-10 accept novelty 7.0 of 10

The authors compute the angle-dependent cusp anomalous dimension to three loops in QCD and supersymmetric Yang-Mills theories, and show it takes a universal form when expressed in terms of an effective coupling set by...
Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
hep-ph 2005-11 conditional novelty 7.0 of 10

The paper completes the O(alpha_s^4) calculation of the absorptive scalar quark correlator and applies it to Higgs decay and light-quark mass bounds.
SCET sum rules for $B\to D_1(2420)$ and $B\to D_1'(2430)$ form factors at next-to-leading order
hep-ph 2026-07 conditional novelty 6.0 of 10

First O(αs) SCET light-cone sum rules for B o D1 and B o D1' form factors yield R(D1)=0.070+0.028-0.018 and R(D1')=0.159+0.032-0.025.

Show 21 more citing papers

$\bar{B}_{s,d}^{0} \to J/\psi \mu^{+}\mu^{-}$ Decays in QCD Factorization
hep-ph 2025-10 unverdicted novelty 6.0 of 10

Computes branching ratios of order 10^{-10} for Bs and 10^{-11} for Bd decays after NLO vertex corrections in QCD factorization, plus dimuon distributions and J/psi polarization.
Lattice continuum-limit study of nucleon quasi-PDFs
hep-lat 2020-11 accept novelty 6.0 of 10

Extrapolating nucleon quasi-PDF lattice data from three lattice spacings to the continuum shifts the small-x antiquark distribution positive, bringing it into qualitative agreement with global PDF fits.
Asymptotic behavior of cutoff effects in Yang-Mills theory and in Wilson's lattice QCD
hep-lat 2019-12 conditional novelty 6.0 of 10

The leading logarithmic corrections to lattice cutoff effects in Yang-Mills theory have small positive anomalous dimensions (gamma-hat-1 = 7/11, gamma-hat-2 = 63/55), so discretization errors vanish slightly faster th...
Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
hep-ph 2019-02 accept novelty 6.0 of 10

Small-angle four-loop QCD calculations confirm a conjecture for the full angle dependence of five fermionic color structures but disprove it for the two structures that receive fermion-box contributions.
Four-loop cusp anomalous dimension in QED
hep-ph 2018-05 accept novelty 6.0 of 10

The four-loop C_F^3 T_F n_l and five-loop C_F^4 T_F n_l terms in the HQET field and cusp anomalous dimensions are computed analytically, exactly in the cusp angle, and cross-checked against independent numerical results.
$\Lambda_c \to N$ form factors from lattice QCD and phenomenology of $\Lambda_c \to n \ell^+ \nu_\ell$ and $\Lambda_c \to p \mu^+ \mu^-$ decays
hep-lat 2017-12 conditional novelty 6.0 of 10

Lattice QCD fixes the Lambda_c to nucleon vector, axial and tensor form factors, giving Lambda_c to n lepton neutrino rates about 1.4 to 2 times higher than earlier quark-model and sum-rule estimates.
$\Lambda_b \to \Lambda \ell^+ \ell^-$ form factors, differential branching fraction, and angular observables from lattice QCD with relativistic $b$ quarks
hep-lat 2016-02 conditional novelty 6.0 of 10

A lattice QCD calculation at the physical bottom-quark mass yields all ten Lambda_b to Lambda form factors and Standard-Model predictions for the Lambda_b to Lambda mu mu differential rate and angular observables.
Exclusive Radiative Higgs Decays as Probes of Light-Quark Yukawa Couplings
hep-ph 2015-05 accept novelty 6.0 of 10

Next-to-leading-order QCD factorization plus a ratio to h to gamma gamma turns rare h to V gamma decays into a quantitatively controlled probe of the charm, bottom and strange Yukawa couplings.
B-meson decay constants: a more complete picture from full lattice QCD
hep-lat 2015-03 accept novelty 6.0 of 10

Lattice QCD gives f_B*/f_B = 0.941(26), f_B*_s/f_B_s = 0.953(23) and f_B*_c/f_B_c = 0.988(27), so the vector decay constant sits below the pseudoscalar one for b-light mesons and approaches it as the lighter quark get...
Isospin breaking in the nucleon mass and the sensitivity of beta decays to new physics
hep-ph 2013-09 accept novelty 6.0 of 10

The scalar nucleon charge is fixed at g_S = 1.02(11) from the pure-QCD nucleon mass splitting, tightening the bound on non-standard scalar beta-decay couplings to epsilon_S = 0.0012(23) at 90% CL.
Two-loop Corrections to the B to pi Form Factor from QCD Sum Rules on the Light-Cone and |V(ub)|
hep-ph 2012-03 accept novelty 6.0 of 10

The O(alpha_s^2 beta_0) leading-twist correction to f+(0) moves the light-cone sum rule prediction by only about 2 percent, confirming that the large two-loop correction to fB cancels in the ratio fB f+(0) / fB.
Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC
hep-ph 2011-10 accept novelty 6.0 of 10

Current bounds on scalar and tensor weak interactions come from nuclear 0+ to 0+ decays and radiative pion decay, and future neutron-decay and LHC measurements should compete once lattice QCD pins the nucleon scalar a...
Heavy-to-light currents at NNLO in SCET and semi-inclusive anti-B ---> X(s) l+ l- decay
hep-ph 2010-07 conditional novelty 6.0 of 10

Two-loop matching coefficients for the full Dirac basis of heavy-to-light currents in SCET shift the predicted forward-backward asymmetry zero in semi-inclusive B to X_s lepton-pair decay to q_0^2 = 3.34 GeV^2 at an i...
NNLO vertex corrections in charmless hadronic B decays: Real part
hep-ph 2009-02 accept novelty 6.0 of 10

The real parts of the two-loop vertex corrections for charmless B decays are computed, completing the NNLO topological tree amplitudes and showing no perturbative enhancement of the colour-suppressed amplitude.
Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
hep-ph 2003-06 accept novelty 6.0 of 10

The three-loop mixing of four-quark operators into the semileptonic operators Q9 and Q10 is computed, supplying a missing ingredient for next-to-next-to-leading-order predictions of B to Xs lepton-pair decays.
Optimization of perturbation series in QCD for physical quantities using the renormalization group: necessary conditions and partial results
hep-ph 2026-06 unverdicted novelty 5.5 of 10

Hierarchy filters on RG scale-shift parameters {Δ_i} delimit admissible optimizations of truncated pQCD series for C_Bjp and D_NS; only selected literature schemes survive.
Correlator of heavy-light quark currents in HQET in the large $\beta_0$ limit
hep-ph 2026-03 unverdicted novelty 5.0 of 10

The perturbative heavy-light current correlator in HQET is computed to O(m_q²) at leading order in 1/β₀, and its UV/IR renormalon poles are mapped.
Power corrections in the determination of heavy meson LCDAs: A renormalon-based estimation
hep-ph 2025-05 conditional novelty 5.0 of 10

Using the renormalon model, the paper estimates that power corrections to the QCD-to-HQET light-cone distribution amplitude matching are around 22% for the D meson and 7% for the B meson in the peak region.
Non-standard Charged Current Interactions: beta decays versus the LHC
hep-ph 2012-10 accept novelty 5.0 of 10

Within an effective field theory, LHC data already beat beta decay for right-handed neutrino charged-current couplings, while beta decay remains best for left-handed vector and pseudoscalar couplings.
Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions
hep-lat 2010-03 conditional novelty 5.0 of 10

Lattice QCD with domain wall fermions yields a quark-mass-independent momentum-to-helicity ratio agreeing with experiment, plus renormalized moments that trend toward experiment at the lightest simulated quark mass.
Beta Decays and Non-Standard Interactions in the LHC Era
hep-ph 2013-03 accept novelty 2.0 of 10

Precision beta-decay and light-meson measurements probe non-standard charged-current interactions at scales of 7 to 11 TeV and remain complementary to direct LHC searches.

How the literature uses it

52 arXiv papers cite this in 92 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 · 64 sentences without a confident label

Uses its method or tool 5 papers

Then, through the procedure known as naive non-abelianization [ref] , in which the fermionic contribution to the QCD beta function is replaced by the full one-loop beta function coefficient ($β_1$ in our notation), a set of non-abelian terms is effectively introduced, generating a realistic result to all orders in $α_s$.

Higher-order QCD corrections to $H\to b\bar b$ from rational approximants · A proof of concept in the large-beta0 limit · 0.97
The tensor-current evolution function $U_T$ is obtained from [ref] using the two-loop anomalous dimension [ref] [equation]

SCET sum rules for $B\to D_1(2420)$ and $B\to D_1'(2430)$ form factors at next-to-leading order · Renormalization-group improvement · 0.84
* Running to 2 GeV with two loop anomalous dimensions [31] [ref] .

Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions · Formulation · 0.97

Uses its data or values 5 papers

After isolating the factor ([ref]), we may use explicit two-loop results extracted [ref] from the literature [ref] to compute the remaining components of the factorization formula through two-loop order:

The Fermi function and the neutron's lifetime · Factorization and small mass expansion · 0.94
For these [ref] , [equation] In order to derive the $𝒪(^3)$ terms of $γ̃$ in <ref>, we also need the terms at $^3$ [ref] : [equation] Recall that the vector current does not require renormalization, and the scalar current renormalizes with $Z_S≡Z_m$.

Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD · Renormalization constants · 0.87
The second quantity entering the expression for the hard function is the matching coefficient $K_F(m_b,μ)$ defined in relation [ref], which has been calculated at two-loop order in [ref] .

Factorization and Sudakov Resummation in Leptonic Radiative $B$ Decay -- A Reappraisal · Matching conditions · 0.88

Compares with it 5 papers

Numerically, ([ref]) gives [equation] Comparing this series with ([ref]) we see that naive nonabelianization [ref] works rather well up to the N$^3$LL level.

Anomalous dimension of the heavy-light quark current in HQET up to four loops · The ratio $f_B/f_D$ · 0.96
After specifying the color factors to QCD with $N_c=3$ we obtain for $ε=0$ [equation] In Landau gauge ($ξ^(n_f)=1$) at $n_l=4$ this gives [equation] while the naive nonabelianization [ref] (large $β_0$ limit) predicts [ref] [equation] The comparison to Eq. ([ref]) shows that up to four loops these predictions are rather good.

Matching the heavy-quark fields in QCD and HQET at four loops · The QCD and HQET heavy-quark fields · 0.89
Multiplying the leading $m^0$ term in the HQET spectral density ([ref]) by the corresponding matching coefficients [ref] , we reproduce the leading $δ^0$ terms in the 3-loop QCD spectral densities (10), (14) in [ref] .

Correlators of heavy-light quark currents in HQET: OPE at three loops · Perturbative contribution · 0.81

Cites it as background 10 papers

The calculation has been done for quark bilinears at one-loop [ref] and two-loop [ref] levels, and for the $ΔB=2$ four-quark operator at one-loop [ref] .

One-loop operator matching in the static heavy and domain-wall light quark system with O(a) improvement · Matching procedure · 0.92
Such corrections are usually referred to as “large-$β_0$” (or “BLM” [ref] ) corrections, see also [ref] .

On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks · BLM corrections to four loops · 0.94
At the leading large $β_0$ order ($b = β_0 α_s/(4π) ∼1$, $1/β_0 ≪1$, see, e. g., chapter 8 in [ref] ) we have [ref] [equation] At $n_f=4$, [equation] This approximation usually works rather well for matching coefficients and other renormalized matrix elements (which usually contain renormalons), but absolutely does not work for anomalous dimensions.

Anomalous dimension of the heavy-light quark current in HQET up to four loops · Result · 0.83

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.

[1] [11]

N. Gray, D. J. Broadhurst, W. Grafe, and K. Schilcher, Z. Phys. C48 (1990) 673

View on Pith 1990

[2] [1]

E. Eichten and B. Hill, Phys. Lett. B234 (1990) 511

View on Pith 1990

[3] [2]

B. Grinstein, Nucl. Phys. B339 (1990) 253; H. Georgi, Phys. Lett. B240 (1990) 447

View on Pith 1990

[4] [3]

M. Neubert, Phys. Reports 245 (1994) 259

View on Pith 1994

[5] [4]

M. Golden and B. Hill, Phys. Lett. B254 (1991) 225

View on Pith 1991

[6] [5]

M. Neubert, Phys. Rev. D49 (1994) 1542

View on Pith 1994

[7] [6]

M. B. Voloshin and M. A. Shifman, Sov. J. Nucl. Phys. 45 (1987) 292

View on Pith 1987

[8] [7]

H. D. Politzer and M. B. Wise, Phys. Lett. B206 (1988) 681; B208 (1988) 504

View on Pith 1988

[9] [8]

X. Ji and M. J. Musolf, Phys. Lett. B257 (1991) 409

View on Pith 1991

[10] [9]

D. J. Broadhurst and A. G. Grozin, Phys. Lett. B267 (1991) 105

View on Pith 1991

[11] [10]

V. Gim´ enez,Nucl. Phys. B375 (1992) 582

View on Pith 1992

[12] [12]

D. J. Broadhurst, N. Gray, and K. Schilcher, Z. Phys. C52 (1991) 111

View on Pith 1991

[13] [13]

M. Neubert, Phys. Rev. D46 (1992) 1076

View on Pith 1992

[14] [14]

P. Ball, Nucl. Phys. B421 (1994) 593

View on Pith 1994

[15] [15]

M. Beneke and V. M. Braun, Nucl. Phys. B426 (1994) 301

View on Pith 1994

[16] [16]

I. I. Bigi, M. A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Phys. Rev. D50 (1994) 2234

View on Pith 1994

[17] [17]

M. Neubert and C. T. Sachrajda, CERN–TH.7312/94 (July 1994 ), hep–ph/9407394

View on Pith 1994

[18] [18]

D. J. Broadhurst, Z. Phys. C47 (1990) 115

View on Pith 1990

[19] [19]

D. J. Broadhurst, Z. Phys. C54 (1992) 599

View on Pith 1992

[20] [20]

A. C. Hearn, REDUCE user’s manual, version 3.5, Rand publication CP78 (1993)

View on Pith 1993

[21] [21]

R. Tarrach, Nucl. Phys. B183 (1981) 384

View on Pith 1981

[22] [22]

T. L. Trueman, Phys. Lett. B88 (1979) 331

View on Pith 1979

[23] [23]

S. A. Larin, Proc. 7 int. seminar Quarks–92, ed. D. Yu Grigoriev , V. A. Matveev, V. A. Rubakov, and P. G. Tinyakov, World Scientiﬁc (1993), p. 201; NIKHEF–H/92–18 (1992), hep–ph/9302240

View on Pith 1993

[24] [24]

S. A. Larin and J. A. M. Vermaseren, Phys. Lett. B259 (1991) 345; S. A. Larin, Phys. Lett. B303 (1993) 113. 24

View on Pith 1991

[25] [25]

S. G. Gorishny and S. A. Larin, Phys. Lett. B172 (1986) 109

View on Pith 1986

[26] [26]

D. J. Broadhurst and A. L. Kataev, Phys. Lett. B315 (1993) 179

View on Pith 1993

[27] [27]

D. J. Broadhurst and A. G. Grozin, Phys. Lett. B274 (1992) 421

View on Pith 1992

[28] [28]

Particle Data Group, Phys. Rev. D50 (1994) 1173

View on Pith 1994

[29] [29]

A. Palanques–Mestre and P. Pascual, Comm. Math. Phys. 95 (1984) 277

View on Pith 1984

[30] [30]

D. J. Broadhurst, Z. Phys. C58 (1993) 339

View on Pith 1993

[31] [31]

M. Beneke, Nucl. Phys. B405 (1993) 424

View on Pith 1993

[32] [32]

A. H. Mueller, in QCD 20 years later, ed. P. M. Zerwas and H. A. Kastrup, World Scientiﬁc (1993), v. 1, p. 162

View on Pith 1993

[33] [33]

J. A. Gracey, Mod. Phys. Lett. A7 (1992) 1945

View on Pith 1992

[34] [34]

M. Beneke, UM–TH–94–31 (August 1994), hep–ph/9408380. 25 This figure "fig1-1.png" is available in "png" format from: http://arxiv.org/ps/hep-ph/9410240v2

View on Pith Pith review arXiv 1994