Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production

Anton V. Konychev; Pavel M. Nadolsky

REVIEW

Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production

Anton V. Konychev, Pavel M. Nadolsky

High Energy Physics - Phenomenology · Submitted 23 Jun 2005 · 15 references

Pith's verdict: A real, useful revision of the b_* model — the Z-mass nonperturbative correction drops to about a third of BLNY — but the abstract's 'closely agrees' is stated at a precision the quoted errors don't support.

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arXiv IDhep-ph/0506225 (version 3)

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CitationAnton V. Konychev, Pavel M. Nadolsky. "Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production." arXiv:hep-ph/0506225 (2005). https://pith.science/paper/XZLOM6GG

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Editor's note

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The thing worth your time here is the model change, not the headline. Konychev and Nadolsky raise the b_* cutoff from BLNY's 0.5 GeV^-1 to about 1.5 GeV^-1 and, because that pushes past b0/Qini ~ 0.86 GeV^-1, replace mu_F = C3/b_* with C3/b_*(b, b0/Qini) so the CTEQ6 starting scale is never undershot. That single move drops chi2 from roughly 140 to 125 across 98 points and five experiments, and pulls the fitted nonperturbative correction at M_Z down to a(M_Z) = 0.85 +/- 0.10 GeV^2, against BLNY's 2.7. That is a substantive, checkable result and it matters for the M_W program they motivate. The per-Q-bin scan in Fig. 1 is the part I trust most: each bin is fitted independently, so the near-linear ln Q behaviour there is not put in by hand. The b^{2-beta} shape test with |beta| < 0.5 is a sensible sanity check, and the authors are upfront that a3 is small enough to drop (chi2 up by ~5) whereas BLNY needed it badly (chi2 up by >200). Credit for that candour. Now the soft spots, which are about precision rather than existence. Eq. (5) writes F_NP as b^2(a1 + a2 ln Q + ...) because RG invariance demands it, so 'found to follow universal quasi-linear dependence' is partly a restatement of the ansatz; the empirical content is the size of a2 and the smallness of a3. The quoted +/-0.018 on a2 is statistical only, and their own C3 = b0 versus 2b0 comparison moves a2 from 0.184 to 0.158 — a shift comparable to the error, and the low-Q chi2 improves by 14 units with the larger scale. The renormalon estimate they compare to carries +0.12/-0.09, so 'closely agrees' is doing more work than the numbers bear. bmax = 1.5 GeV^-1 is also picked at the chi2 minimum on the same data. And the stability argument for the mu_F prescription, plus the error propagation, live in Ref. [15], listed as in preparation — that is load-bearing and cannot be checked here. None of this breaks the qualitative claim. It is a solid phenomenology paper with an overstated abstract. Worth a referee, and worth citing if you work on qT resummation or M_W systematics.

Referee report

Significance

If it holds, the result matters well beyond the fitting exercise: the nonperturbative recoil model is the dominant theory uncertainty in the extraction of M_W at the Tevatron and LHC, and a reduction of a(M_Z) from the BLNY 2.7 GeV^2 to about 0.85 GeV^2 would materially shrink that error. The paper earns credit for several things done right. The per-Q-bin extraction of a(Q) in Fig. 1 is a genuine empirical test of the ln Q dependence that does not impose linearity by construction, and it is the strongest evidence in the letter. The b^{2-beta} shape test, the bmax scan, the explicit C3 = b0 versus 2 b0 comparison, and the side-by-side confrontation with the Qiu-Zhang parametrization in Fig. 4(b) are all appropriate and candid. The prediction a(M_Z) ~ 0.85 GeV^2 is falsifiable with Run-2 Z data, and the paper states plainly where the fit is weakest (the two E605 outliers, the low-Q scale dependence). The qualitative claim is robust; the quantitative precision claim in the abstract is where the work remains incomplete.

Major objections (3)

[Factorization-scale prescription, paragraph preceding 'We perform a series of fits'] The operating point bmax = 1.5 GeV^-1 lies above b0/Qini ~ 0.86 GeV^-1, so the entire improvement reported here (chi-squared from roughly 140 to 125) and the quoted a2 are produced in the regime where the modified scale mu_F = C3/b_*(b, b0/Qini) is required. The text asserts that this prescription 'preserves correct resummation of the large logarithms and is numerically stable up to bmax ~ 3 GeV^-1', but the demonstration is deferred to Ref. [15], which is listed as 'in preparation'. A reader cannot check from this letter that the resummation is preserved, and the central quantitative result depends on that unverified step. Please either sketch the argument in this manuscript (even two or three sentences identifying which logarithms are protected and why the substitution bmax -> b0/Qini in mu_F does not spoil them) or replace the citation with a published reference that contains it.
[Best-fit parameters paragraph and Abstract, sentence [abstract:s2]] The uncertainties quoted on a1, a2, a3 are statistical only, while the paper's own Fig. 2 shows that changing C3 from b0 to 2 b0 moves a2 from 0.184 +/- 0.018 to 0.158 +/- 0.023 GeV^2, a shift of about 1.4 sigma that is comparable to the quoted error, and improves chi-squared for the low-Q data by 14 units. The abstract's 'closely agrees with an estimate from the infrared renormalon analysis' is therefore stated at a precision the error budget does not support. Two fixes are needed: fold the C3 variation into the quoted uncertainty (or quote it explicitly as a separate systematic alongside the statistical error), and soften the abstract, since the renormalon band 0.19 (+0.12/-0.09) GeV^2 is itself wide enough that both 0.158 and 0.184 sit comfortably inside it. The informative content of the comparison is the sign and rough magnitude of the slope and the smallness of a3, not a sharp numerical coincidence, and the text should say so.
[Fig. 1 and the per-bin universality test] Fig. 1 is the paper's cleanest evidence for universality, because the per-bin a(Q) extraction does not impose ln Q linearity, and the text is right to lean on it. Two things weaken it as presented. First, the overall normalizations are fixed at their global best-fit values before the Delta chi-squared = 1 error bars are computed, so the vertical bars do not include normalization uncertainty; please state this explicitly and, if feasible, show the effect of letting the normalization float within its experimental error. Second, the per-bin fit uses the same W_LP(b) with bmax = 1.5 GeV^-1, so the test is not independent of the cutoff choice, yet the text asserts linearity holds 'for bmax = 1-2 GeV^-1' while displaying only one value. Adding a(Q) for bmax = 1.0 and 2.0 GeV^-1 as additional panels or as a small table would substantiate the claim that the linearity is not an artifact of the chosen cutoff.

Minor objections (7)

[Paragraph quoting a(M_Z) = 0.85 +/- 0.10 GeV^2] The value a(M_Z) is not directly fitted but derived from {a1, a2, a3}; please state the x1, x2 (or the value of the a3 ln[100 x1 x2] term) used in the conversion, so that a reader can reproduce 0.85 +/- 0.10 from the quoted parameters.
[Paragraph following Fig. 1, b^{2-beta} shape test] The statement that each data set prefers F_NP = a(Q) b^{2-beta} with |beta| < 0.5 is given without numbers. Please quote the fitted beta and its error for each of the five experiments, in the text or in a small table.
[Fig. 2] The bmax and C3 dependence of chi-squared, a1, a2 and a3 is currently readable only off a four-panel plot. A compact table of {chi-squared, a1, a2, a3} versus bmax for both C3 values would make the stability argument much easier to check.
[Eq. (5) and the parametrization of a(Q)] The identification phi(x) = ln(x/0.1) is made only in the paragraph after Fig. 2, well after Eq. (5) introduces phi(x) as an unspecified dimensionless function. Define it at Eq. (5) so the two parametrizations can be matched immediately.
[Discussion of the two E605 outliers] The two outlier points are described only in words ('the first point in the second Q bin and fifth point in the fifth Q bin'). Since they contribute 15-25 units of chi-squared at every bmax and the claim chi-squared/d.o.f. ~ 1 depends on removing them, please identify them by (Q, qT) in a table or figure so the reader can verify the exclusion is reasonable.
[Title and scope] The manuscript title says 'vector boson production' while the abstract and the surrounding literature say 'gauge boson production', and no W data are used despite W production being the case of greatest practical interest for M_W. Please reconcile the title and state explicitly whether the Z/Drell-Yan result is expected to transfer to W production unchanged, or whether a separate check is needed.
[Paragraph on the a3 = 0 fit] The statement that chi-squared increases by about 5 when a3 is set to zero should be accompanied by the number of degrees of freedom and the resulting chi-squared/d.o.f. for both fits, so the reader can judge whether a3 is meaningfully constrained.

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The paper

The paper claims

One nonperturbative function is enough to fit Drell-Yan and Z data

The reading

Transverse-momentum distributions of Drell-Yan pairs and $Z$ bosons are predicted by a resummation that splits into a computable short-distance part and a nonperturbative function $F_{NP}(b,Q)$ that has to be extracted from data. The authors argue that the standard $b_*$ prescription, which freezes the perturbative form factor at $b_{max}=0.5$ GeV$^{-1}$, cuts off the perturbative region too early, and that raising $b_{max}$ to $1$-$2$ GeV$^{-1}$ lets the known short-distance calculation carry more of the answer. With that single change, a global fit to 98 fixed-target Drell-Yan and Tevatron $Z$ data points returns a nonperturbative function whose coefficient of $b^2$ grows almost linearly with $a_2 = 0.184$ GeV$^2$ per unit $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2 = 0.184$ GeV$^2$ per unit of $a_2$.

What carries the argument

The carrying device is the $b_*$ model with a raised cutoff: $b_* = b(1+b^2/b_{max}^2)^{-1/2}$, so that the leading-power form factor is the exact perturbative one, $W_{LP}(b) = W_{pert}(b_*)$, for $b$ up to roughly $b_{max}$ and only saturates beyond it. The full form factor is written $W(b) = W_{LP}(b)e^{-F_{NP}(b,Q)}$, which isolates the power-suppressed terms in the exponent while keeping the logarithmic terms in the perturbative piece. Because the choice of factorization scale $a_2 = 0.184$ GeV$^2$ is tied to $b_*$, the authors also prescribe $a_2 = C_3/b_*(b, b_0/Q_{ini})$ once $b_{max}$ exceeds $b_0/Q_{ini} = 0.86$ GeV$^{-1}$, so that the CTEQ6M densities are never evaluated below their starting scale.

Extended reading notes

Core claim

The paper's central claim is that the nonperturbative function of Collins-Soper-Sterman resummation, $F_{NP}(b,Q)$, is universal across Drell-Yan and $Z$ production and depends quasi-linearly on $a_2 = 0.184$ GeV$^2$ per unit of $a_2$.

Load-bearing premise

The functional form $F_{NP}=b^2(a_1+a_2a_2 = 0.184$ GeV$^2$.

Editorial extensions

If this is right

The same nonperturbative function, with its fitted $a_2 = 0.184\pm0.018$ GeV$^2$, describes fixed-target Drell-Yan data near $Q\approx5$-$10$ GeV and Tevatron $Z$ data at $Q=M_Z$ without retuning.
The nonperturbative correction at the $Z$ pole, $a(M_Z) = 0.85\pm0.10$ GeV$^2$, is about a third of the $2.7$ GeV$^2$ assumed in the earlier fit, which shrinks a leading theory uncertainty in the extraction of the $W$ mass.
The fitted slope agrees numerically with the infrared-renormalon estimate of $0.19^{+0.12}_{-0.09}$ GeV$^2$, giving the soft-gluon interpretation of the dominant nonperturbative term direct empirical support.
The coefficient $a_3$ that measures departure from pure $\ln Q$ dependence comes out below $0.05$ GeV$^2$, so the quasi-linear form is preferred by the data once the leading-power piece is modelled with a larger $b_{max}$.
The quality of the fit is flat for $b_{max}$ between $1$ and $2$ GeV$^{-1}$ and degrades outside that window, which localizes where the perturbative and nonperturbative regions may be joined.

Reading between the lines

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

If the slope really is the renormalon slope, then the same two-parameter description should carry over to $W$ production at the LHC without new fitting, which is a sharp test the paper does not perform here.
The dependence on the factorization-scale parameter $C_3$ (from $0.184$ to $0.158$ GeV$^2$) is comparable to the quoted statistical error, so an extraction with higher-order coefficient functions would be the natural way to tell whether the renormalon agreement is coincidence or content.
The paper notes that two E605 points contribute $15$-$25$ units of $\chi^2$ at any $b_{max}$ and that $\chi^2/\mathrm{d.o.f.}\approx1$ follows if they are dropped; a reader should treat the absolute fit quality as partly hostage to those two points rather than to the model.
Because the linear $\ln Q$ form is imposed by renormalization-group invariance rather than discovered, the genuinely empirical statements are the magnitude of $a_2$ and the smallness of $a_3$; a future fit that leaves the $Q$ dependence free would be the cleanest confirmation of universality.

Original abstract

We revise the $b_*$ model for the Collins-Soper-Sterman resummed form factor to improve description of the leading-power contribution at nearly nonperturbative impact parameters. This revision leads to excellent agreement of the transverse momentum resummation with the data in a global analysis of Drell-Yan lepton pair and Z boson production. The nonperturbative contributions are found to follow universal quasi-linear dependence on the logarithm of the heavy boson invariant mass, which closely agrees with an estimate from the infrared renormalon analysis.

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, 3,006 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.70 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We revise the $b_*$ model for the Collins-Soper-Sterman resummed form factor to improve description of the leading-power contribution at nearly nonperturbative impact parameters. This revision leads to excellent agreement of the transverse momentum resummation with the data in a global analysis of Drell-Yan lepton pair and Z boson production. The nonperturbative contributions are found to follow universal quasi-linear dependence on the logarithm of the heavy boson invariant mass, which closely agrees with an estimate from the infrared renormalon analysis.

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	We revise the $b_*$ model for the Collins-Soper-Sterman resummed form factor to improve description of the leading-power contribution at nearly nonperturbative impact parameters.	contribution 0.74	0.93	0.09	asserted 0.96
s1	This revision leads to excellent agreement of the transverse momentum resummation with the data in a global analysis of Drell-Yan lepton pair and Z boson production.	result 0.99	0.87	0.28	asserted 1.00
s2	The nonperturbative contributions are found to follow universal quasi-linear dependence on the logarithm of the heavy boson invariant mass, which closely agrees with an estimate from the infrared renormalon analysis.	result 0.97	0.93	0.64	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.54 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

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.** The best-fit values of a(Q) obtained in independent scans of χ 2 for the contributing experiments. The vertical error bars correspond to the increase of χ 2 by unity above its minimum in each Q bin. The slope of the line is equal to the central-value prediction from the renormalon analysis [11]. exception of the CDF Run-1 normalization (rescaled down by 7%). To test the universality of FNP , we individually examine each bin of Q. We choose FNP = a(Q)b 2 and independently fit it to each of the 5 experimental data sets to determine the most plausible normalization in each experiment.…

**Figure 2.** The best-fit χ 2 and coefficients a1, a2, and a3 in FNP (b, Q) for different values of bmax, C3 = b0 (stars) and C3 = 2b0 (squares). The size of the symbols approximately corresponds to 1σ errors for the shown parameters. To further explore the issue, we simultaneously fit our model to all the data. We parametrize a(Q) as a(Q) ≡ a1+a2ln [Q/(3.2 GeV)]+a3ln [100x1x2] . This parametrization coincides with the BLNY form [9], if the parameters are renamed as {g1, g2, g1g3}(BLNY) → {a1, a2, a3}(here). It agrees with the generic form of FNP (b, Q) in Eq. (5), if one identifies φ(x) =…

**Figure 3.** Differences between the measured (Data) and theoretic

**Figure 4.** The best-fit form factors bWf(b) in (a) Tevatron Run-2 Z boson production; (b) E605 experiment. In the E605 case, bWf(b) are divided by the best-fit normalizations Nf it for the E605 data, and the form factor in the Qiu-Zhang parametrization [12] for b QZ max = 0.3 GeV−1 is also shown. renormalon analysis estimate. The coefficient a3, which parametrizes deviations from the linear ln Q dependence, is considerably smaller (< 0.05) than both a1 and a2 (∼ 0.2). A reasonable quality of the fit is retained if a3 is set to zero by hand: χ 2 increases by ≈ 5 in such a fit above its…

Figures reproduced from arXiv:hep-ph/0506225 by the authors.

References

Works cited (15)

[15]

A. Konychev, P. M. Nadolsky, in preparation. 14

View on Pith
[1]

Yu. L. Dokshitzer, D. I. D’yakonov, S. I. Troyan, Phys. Le tt. B79, 269 (1978); G. Parisi, R. Petronzio, Nucl. Phys. B154, 427 (1979)

View on Pith 1978
[2]

J. C. Collins, D. E. Soper, Nucl. Phys. B193, 381 (1981); B213, 545(E) (1983)

View on Pith 1981
[3]

J. C. Collins, D. E. Soper, Nucl. Phys. B197, 446 (1982)

View on Pith 1982
[4]

J. C. Collins, D. E. Soper, and G. Sterman, Nucl. Phys. B250, 199 (1985)

View on Pith 1985
[5]

J. C. Collins, A. Metz, Phys. Rev. Lett. 93, 252001 (2004)

View on Pith 2004
[6]

X. Ji, J.-P. Ma, and F. Yuan, Phys. Lett., B597, 299 (2004); Phys. Rev. D71, 034005 (2005)

View on Pith 2004
[7]

P. M. Nadolsky, hep-ph/0412146

View on Pith Pith review arXiv
[8]

C. Davies, B. Webber, W. Stirling, Nucl. Phys. B256, 413 (1985); G. A. Ladinsky, C.-P. Yuan, Phys. Rev. D 50, R4239 (1994); F. Landry, R. Brock, G. Ladinsky, C.-P. Yuan, ibid. 63, 013004 (2001); R. K. Ellis, D. A. Ross, S. Veseli, Nucl. Phys. B503, 309 (1997)

View on Pith 1985
[9]

F. Landry, R. Brock, P. Nadolsky, C.-P. Yuan, Phys. Rev. D 67, 073016 (2003)

View on Pith 2003
[10]

G. P. Korchemsky, G. Sterman, Nucl. Phys. B437, 415 (1995)

View on Pith 1995
[11]

S. Tafat, JHEP 05, 004 (2001). 13

View on Pith 2001
[12]

J.-W. Qiu, X.-F. Zhang, Phys. Rev. Lett. 86, 2724 (2001); Phys. Rev. D 63, 114011 (2001); E. L. Berger, J.-W. Qiu, Phys. Rev. D 67, 034026 (2003)

View on Pith 2001
[13]

A. Kulesza, G. Sterman, and W. Vogelsang, Phys. Rev. D 66, 014011 (2002)

View on Pith 2002
[14]

J. Pumplin et al., JHEP 0207, 012 (2002)

View on Pith 2002

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A global fit with QCD evolution extracts quark Sivers functions from SIDIS data and predicts few-percent Drell-Yan and W asymmetries whose sign is expected to flip relative to SIDIS.
Limits on TMD Evolution From Semi-Inclusive Deep Inelastic Scattering at Moderate $Q$
hep-ph 2014-01 conditional novelty 5.0 of 10

At momentum transfers of a few GeV, the coordinate-space region dominating semi-inclusive deep inelastic scattering extends to transverse distances of several GeV^-1, so the nonperturbative part of the Collins-Soper k...
Model Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL
hep-ph 2012-08 conditional novelty 5.0 of 10

The authors derive an NNLL resummation of the TMD evolution kernel that is parameter-free in the perturbative region and matches the CSS approach when the running coupling is treated consistently.
TMD Parton Distribution and Fragmentation Functions with QCD Evolution
hep-ph 2011-01 conditional novelty 5.0 of 10

Starting from existing fits and the Collins-Soper-Sterman formalism, the authors produce evolved transverse-momentum-dependent quark distributions and fragmentation functions and show that QCD evolution suppresses the...
Resummation for Polarized Semi-Inclusive Deep-Inelastic Scattering at Small Transverse Momentum
hep-ph 2006-02 accept novelty 5.0 of 10

The authors derive NLL-resummed cross sections for five polarized SIDIS channels and find numerically that resummation and non-perturbative effects largely cancel in the longitudinal double-spin asymmetry.
Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
hep-ph 2005-08 accept novelty 5.0 of 10

A unitarity-constrained b-space resummation formalism predicts the Higgs boson transverse-momentum spectrum at the LHC at NNLL+NLO accuracy with roughly 10% perturbative uncertainty over small and intermediate momenta.
Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC
hep-ph 2019-09 conditional novelty 4.0 of 10

Adding TMD evolution to quarkonium-pair production reduces the gluon-polarization azimuthal asymmetries to 5-10%, still measurable at the LHC.
TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions
hep-ph 2014-08 conditional novelty 4.0 of 10

The paper releases TMDlib, a C++ library plus web plotter that place several published transverse-momentum-dependent parton distribution fits behind a single callable interface.
Large-Momentum Effective Theory
hep-ph 2020-04 accept novelty 3.0 of 10

LaMET lets lattice QCD compute x-dependent parton distributions, GPDs, and TMDs from proton matrix elements at finite boost, matched to light-front quantities through effective field theory.
Recent Advances in Transverse-Momentum--Dependent Distributions in Lattice QCD
hep-lat 2026-10 accept novelty 2.0 of 10

A review of lattice QCD progress in computing TMDs via LaMET, covering the Collins-Soper kernel, soft functions, and TMDPDFs.

How the literature uses it

44 arXiv papers cite this in 72 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 · 42 sentences without a confident label

Contests it 1 paper

This suggests the following hypothesis: The fits in Refs. [ref] determine $g_K$ and $g_j/H$ in a range of relatively low $b$, say between about 0.5 and $[2]GeV^-1$, but their extrapolation to larger $b$ is wrong.

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel · Fits to Drell-Yan data with CSS formalism · contest 0.75

Uses its method or tool 3 papers

To account for non-perturbative effects that dominate at large impact parameters $b$, we introduce a non-perturbative Sudakov form factor, $S_NP$ [ref] .

Resummed azimuthal decorrelation and transverse momentum imbalance of dijets at the LHC · Azimuthal decorrelation · 0.94
At leading order of $C_a/i$, the evolved TMD reduces to [equation] where the Sudakov factor is [ref] [equation] The functions $A$ and $B$ have a perturbative expansions of the form [equation] To NLL accuracy, one has [ref] [equation] Following Refs. [ref] , the non-perturbative Sudakov factor in Eq. ([ref]) is modeled as [equation] with $g_2$ a free parameter.

Transvese momentum dependent parton distributions of pion at leading twist · The generalized Boer-Mulders shift · 0.87
However, in the integration, we encounter an issues in the region where $μ_b ∼Λ_QCD$, which is avoided using the $b_*$-prescription [ref] .

Precision three-dimensional imaging of nuclei using recoil-free jets · Parameterization · 0.90

Uses its data or values 5 papers

[equation] In this work, the universality of the CSS kernel is tested by verifying that the observables are well described across several resolution parameters $R$, grooming settings, and intervals with the same parameters in $g_K(b_⊥;b_⊥^max)$ corresponding to $b_⊥^max = 1.5 (GeV/c)^-1$ and $g_2(b_⊥^max) = 0.18$ from a global data analysis to Drell–Yan lepton pair and Z$^0$-boson production [ref] .

Measurement of the angle between jet axes in pp collisions at $\sqrt{s} = 5.02$ TeV · Comparison to analytical calculations · 0.92
The analysis in Ref. [ref] has found that $b_max = 1.5$ GeV$^-1$ is preferred, and the parameters for the BLNY fit in Eq. ([ref]) become $g_1 = 0.201$ GeV$^2$, $g_2 = 0.184$ GeV$^2$ and $g_3 = -0.129$.

TMD Parton Distribution and Fragmentation Functions with QCD Evolution · TMD PDFs · 0.89
This justifies the use of the following expression: [equation] employed and fitted to data in Ref. [ref] (BLNY in the following) and in Ref. [ref] (KN) where they found, respectively, a value of $g_2 = 0.68 GeV^2$, with $b_max = 0.5 GeV^-1$, and a value of $g_2 = 0.18 GeV^2$, with $b_max = 1.5 GeV^-1$.

Transverse $\Lambda$ polarization in $e^+e^-$ processes within a TMD factorization approach and the polarizing fragmentation function · $g_K(b_T;b_max)$ · 0.88

Compares with it 1 paper

By contrast, the Drell-Yan fits in Refs. [ref] give results in terms of the TMD factorization formula in the particular CSS1 form given in Eq. ([ref]).

Connecting Different TMD Factorization Formalisms in QCD · TMD functions from fits with CSS1 · 0.88

Cites it as support 1 paper

Confirmations are given both at perturbative level (the coefficients of perturbative expansion are known up to four loops [ref] , and also in the non-perturbative regime, where both phenomenological extractions [ref] and lattice computations [ref] agree on considering $g_K$ as a positive-definite monotonically increasing function of $b_T$.

Full treatment of the thrust distribution in single inclusive $e^+ e^- \to h \, X$ processes · Rapidity regulator as a function of thrust · 0.96

Cites it as background 15 papers

The original CSS formula [ref] , as used in the fits in [ref] , was obtained starting from a TMD factorization formula, using the specific definitions of TMD parton densities that had been given by Collins and Soper (CS) [ref] .

Connecting Different TMD Factorization Formalisms in QCD · Original CSS formalism · 0.83
In previous work on CSS resummation, the $b_*$-prescription was introduced along with non-perturbative Sudakov factors, which were modeled through various functional forms and obtained by fitting to experimental data [ref] .

QCD resummation of dijet azimuthal decorrelations in pp and pA collisions · Parameterization · 0.99
The presence, at low lepton-pair transverse momenta, of large logarithmically enhanced QCD corrections and the role, in the same kinematic region, of non-perturbative effects have been discussed in Refs. [ref] , but the dependence of the resulting model on the acceptance cuts has never been investigated in detail and will deserve a dedicated study.

Prospects for improving the LHC W boson mass measurement with forward muons · Uncertainties stemming from the modelling · 0.94

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] [15]

A. Konychev, P. M. Nadolsky, in preparation. 14

View on Pith

[2] [1]

Yu. L. Dokshitzer, D. I. D’yakonov, S. I. Troyan, Phys. Le tt. B79, 269 (1978); G. Parisi, R. Petronzio, Nucl. Phys. B154, 427 (1979)

View on Pith 1978

[3] [2]

J. C. Collins, D. E. Soper, Nucl. Phys. B193, 381 (1981); B213, 545(E) (1983)

View on Pith 1981

[4] [3]

J. C. Collins, D. E. Soper, Nucl. Phys. B197, 446 (1982)

View on Pith 1982

[5] [4]

J. C. Collins, D. E. Soper, and G. Sterman, Nucl. Phys. B250, 199 (1985)

View on Pith 1985

[6] [5]

J. C. Collins, A. Metz, Phys. Rev. Lett. 93, 252001 (2004)

View on Pith 2004

[7] [6]

X. Ji, J.-P. Ma, and F. Yuan, Phys. Lett., B597, 299 (2004); Phys. Rev. D71, 034005 (2005)

View on Pith 2004

[8] [7]

P. M. Nadolsky, hep-ph/0412146

View on Pith Pith review arXiv

[9] [8]

C. Davies, B. Webber, W. Stirling, Nucl. Phys. B256, 413 (1985); G. A. Ladinsky, C.-P. Yuan, Phys. Rev. D 50, R4239 (1994); F. Landry, R. Brock, G. Ladinsky, C.-P. Yuan, ibid. 63, 013004 (2001); R. K. Ellis, D. A. Ross, S. Veseli, Nucl. Phys. B503, 309 (1997)

View on Pith 1985

[10] [9]

F. Landry, R. Brock, P. Nadolsky, C.-P. Yuan, Phys. Rev. D 67, 073016 (2003)

View on Pith 2003

[11] [10]

G. P. Korchemsky, G. Sterman, Nucl. Phys. B437, 415 (1995)

View on Pith 1995

[12] [11]

S. Tafat, JHEP 05, 004 (2001). 13

View on Pith 2001

[13] [12]

J.-W. Qiu, X.-F. Zhang, Phys. Rev. Lett. 86, 2724 (2001); Phys. Rev. D 63, 114011 (2001); E. L. Berger, J.-W. Qiu, Phys. Rev. D 67, 034026 (2003)

View on Pith 2001

[14] [13]

A. Kulesza, G. Sterman, and W. Vogelsang, Phys. Rev. D 66, 014011 (2002)

View on Pith 2002

[15] [14]

J. Pumplin et al., JHEP 0207, 012 (2002)

View on Pith 2002