A General Approach To Photon Radiation Off Fermions

Stefan Dittmaier

REVIEW

A General Approach To Photon Radiation Off Fermions

Stefan Dittmaier

High Energy Physics - Phenomenology · Submitted 23 Apr 1999 · 20 references

Pith's verdict: The paper that made massive-fermion dipole subtraction for photons usable; the derivation is solid, with one narrow corner — the mixed ia/ai case at positive P²ia — extended by asserted analytic continuation and never exercised numerically.

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arXiv IDhep-ph/9904440 (version 2)

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CitationStefan Dittmaier. "A General Approach To Photon Radiation Off Fermions." arXiv:hep-ph/9904440 (1999). https://pith.science/paper/3AX4P545

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Editor's note

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Bottom line: this is the paper that made massive-fermion dipole subtraction for photons usable, and it holds up. The genuinely new content is the finite-mass, helicity-resolved generalization of Catani–Seymour. The massless QCD version already existed, and Roth had the light-fermion case independently — the paper says so in footnote 2, and Roth's dissertation is listed as in preparation, so that limit's independent corroboration rests on an unpublished thesis at the time of writing. The massive case is Dittmaier's own, and it is the substance of the paper. Everything from Eq. (4.5) onward is his work, and it is done carefully: explicit momentum mappings, the phase-space splittings in Appendix B, closed-form integrated dipoles in Eqs. (4.10), (4.28), (4.34), (4.49), and the special cases in Appendix A. The numerical section is the right kind of validation — three processes covering ij, ia+ai, and ab, compared against phase-space slicing, with integration errors dropping by one to two orders of magnitude. The scope statement is honest: photons only, charged bosons called straightforward but not worked out, massless-parton QCD with dimensional regularization explicitly not covered. No code ships, which is normal for 1999 and not a real complaint. The one soft spot worth a referee's attention is the stress-test's: Appendix C.2 derives the mixed ia/ai endpoint integrals only for A = sqrt(-P̄²ia - m_i²) > 0, then covers the window 0 < P²ia < (m_a - m_i)² by 'analytic continuation in P²ia' with no demonstration. In that window γ goes imaginary and the b_k, c_k dilogarithm arguments leave the real axis; the paper asserts reality and iε-independence rather than showing it. None of the three examples hits that corner — e⁻γ has P²ia = t̃ < 0 — so the 'arbitrary mass' claim is checked where the closed form is easiest. Narrow, but real. On the reader's x0 worry: I agree with the stress-test that it does not land. The plus prescription of Eqs. (4.26)–(4.27) makes x0-independence structural; the residual risk is an algebra slip in G_endpoint, which Section 5 does test for the tested kinematics. This is a tool paper for people building NLO electroweak calculations, and it earned its place. Send it to referees.

Referee report

Significance

The result is a reusable, process-independent tool: once the auxiliary functions and mappings are implemented, any process with charged fermions and neutral bosons can be handled without singular numerical integration, and the paper supplies every ingredient needed to do so, including the massless limits that connect back to earlier work. The explicit disclosure that the ij auxiliary function carries an extra factor 1/(1−y_ij) relative to Ref. [5], and that this changes only a non-singular constant in the integrated counterpart, is exactly the kind of statement that makes a formalism reproducible. The closed forms are checked against the massless results of Section 3 and against an independent calculational route (slicing) in Section 5, and the paper states where the formalism stops: no collinear factorization for massless partons in dimensional regularization, and no explicit treatment of charged bosons. The derivation is carried through in enough detail (momentum mappings, phase-space splittings, reduction of the non-trivial integrals in Appendix C) that an independent implementation is feasible.

Major objections (1)

[Section 5, with Sections 4.2–4.3 and Appendix C.2] The numerical validation does not cover the massive mixed emitter/spectator case. Table 1 exercises the massive ij case (P²_ij = s > 0, m_t ≠ 0); Table 4 exercises the massive ab case (m_μ ≠ 0, √s = 500 MeV); but the only ia/ai application, e⁻γ → e⁻γ(γ) in Section 5.2, has m_a = m_i = m_e and P²_ia = t̃ = (k_γ − k'₂)² ≤ 0, while the high-energy variant takes m_e → 0. The closed forms (4.25), (4.28), (4.34) are therefore never tested where m_a ≠ m_i and 0 < P²_ia < (m_a − m_i)², which is precisely the region where the dilogarithm arguments b_k and c_k of (4.28) and (4.34) move and where the derivation of Appendix C.2 is least transparent. Since the abstract claims 'arbitrary mass and helicity configurations', the paper should either add one numerical check of the endpoint functions against a direct integration of the defining relation (4.27) at such a parameter point, or state explicitly which parameter regions the consistency checks of Section 6.3 actually covered.

Minor objections (11)

[Appendix C.2] The appendix states that the substitution used there requires A = √(−P̄²_ia − m_i²) > 0 and that this is 'in general not' guaranteed. Within the domain of applicability fixed by (4.13), however, A² = m_a² + m_γ² − P²_ia > 0 follows immediately, since P²_ia < (m_a − m_i)² ≤ m_a². Saying this explicitly would remove an apparent gap in the 'arbitrary mass' claim and would confine the analytic continuation in P²_ia to kinematics outside the physical domain.
[Section 4.2, Eq. (4.26)] The paper asserts that observables must not depend on x0 and that verifying this is a non-trivial check. The cancellation is in fact algebraic: the second and third terms of (4.30) combine to −∫_{x0}^{1} dx G(x) ∫dΦ̃(1)|M0(1)|² + Ḡ(x0) ∫dΦ̃(1)|M0(1)|², which vanishes identically by the definition (4.27) of Ḡ(x0). A two-line demonstration after (4.26) would turn an asserted check into a stated property.
[Section 4.2, Eqs. (4.26)–(4.28)] The symbol G^(sub) is used both for the x-dependent distribution G^(sub)(P², x) and for its x-integrated endpoint value Ḡ^(sub)(P², x0). The overbar that distinguishes them should be introduced once in words and used consistently, since the two objects enter the convolution of (4.30) in different ways.
[Table 1, √s = 1000 GeV row] The three slicing entries (0.1881 ± 0.0059, 0.184 ± 0.013, 0.191 ± 0.021) do not converge toward the dipole value 0.17431 ± 0.00059; the ΔE/E = 10⁻² entry is about 2.3σ high. A sentence on whether this is residual cut dependence or a statistical fluctuation would help, since the other three energies show clean convergence.
[Section 3.1, Ref. [11]] The consistency claim for the massless special case rests on a dissertation listed as 'in preparation'. Either the comparison should be documented in a citable form, or the sentence should be softened to indicate that the agreement was checked privately.
[Section 5.1] The statement that the subtraction functions of Ref. [13] and of this paper 'differ by a non-singular factor, leading to a different constant contribution in the integrated counterparts' would read better with an explicit note that both choices are equally valid and that the difference is a convention, so that the two sets of numbers are not in conflict.
[Section 2.3, Eq. (2.12)] It would be worth stating that charge conservation (2.1) guarantees at least two charged fermions whenever all other particles are neutral, so that the sum over f ≠ f' is never empty and the formalism is self-consistent within its stated scope.
[Section 2.2, Eq. (2.4)] The notation τκ_f for the helicity after emission should be defined in words; the summation convention over τ is stated, but the meaning of the product τκ_f is not.
[Section 6.4] The statement that 'the inclusion of charged bosons is completely straightforward' is plausible but not demonstrated; a sentence on which of the conditions (2.13)–(2.16) would change would make the scope statement concrete.
[Appendix D, Eq. (D.1)] The convention for the IR subtraction in the virtual amplitude, in particular the origin of the term linear in ln(m_μ/m_γ) outside the β-dependent bracket, should be stated so that the result can be combined with the real corrections of Section 5.3 without ambiguity.
[Throughout] A few typographical errors should be corrected: 'prodecure' in Section 4.2, 'calulation' in Section 5.2, and 'inital' in the heading of Appendix A.1.

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The paper

The paper claims

A general subtraction recipe removes soft- and collinear-photon singularities from any fermion process, with the singular integrals done once and for all in closed form.

The reading

Any precise prediction for a process with charged fermions has to include real photon emission, and that emission blows up in two places: when the photon energy goes to zero and when the photon is emitted along a light fermion's direction. The standard workaround, phase-space slicing, throws away a small soft or collinear region and computes it separately, which costs computer time and leaves a residual dependence on arbitrary cut parameters. This paper constructs a subtraction function that reproduces the full squared matrix element exactly in every one of those singular limits, so that the difference can be integrated numerically with no regulators at all, while the subtracted piece is integrated analytically over the photon phase space. The author carries this through for arbitrary fermion masses and helicities, keeping finite masses as the regulator for both infrared and collinear singularities rather than using dimensional regularization, and gives closed-form results for all four emitter/spectator configurations. Three worked examples show the resulting Monte Carlo integration errors falling by roughly an order of magnitude relative to slicing at equal statistics.

What carries the argument

The load-bearing object is the pair of auxiliary functions $g^{(sub)}_{ff',�tau}$ and their analytic photon-phase-space integrals $G^{(sub)}_{ff',�tau}$, together with the momentum mappings $�tilde��Phi_{0,ff'}$. The functions $g^{(sub)}$ are fixed only up to non-singular terms by the requirement that they reproduce the soft factor of Eq. (2.3) and the collinear splitting functions of Eq. (2.4); the specific choices in Section 4 are made so that the $z$ and $y$ integrations close. The mappings are constrained to preserve all mass-shell relations and to reduce to the correct limits, $�tilde p_i �to p_i+k$ for a final-state emitter and $�tilde p_a �to x_a p_a$ for an initial-state emitter, while leaving untouched spectator and beam momenta where possible. The finite-mass regularization scheme is what makes the collinear logarithms appear as explicit $�ln(m_f)$ terms in $G^{(sub)}$ rather than as $1/�epsilon$ poles, so the results can be combined directly with virtual corrections computed in the same scheme.

Extended reading notes

Core claim

The paper's claim is that the dipole subtraction formalism of Catani and Seymour, built for massless unpolarized QCD partons, extends to photon radiation off fermions of arbitrary mass and helicity, in a process-independent way. The construction is a sum over ordered pairs of charged fermions, $|M_{sub}|^2 = -Q_f Q_{f'} e^2 g^{(sub)}_{ff',�tau}(p_f,p_{f'},k)|M_0(�tilde��Phi_{0,ff'};�tau �kappa_f)|^2$, in which each term pairs an emitter with a spectator and each term carries a momentum mapping from the $(n+1)$-particle to the $n$-particle phase space. The auxiliary functions $g^{(sub)}$ are chosen to match the known soft limit and the known collinear splitting behaviour, with charge conservation used to avoid double-counting the infrared region across overlapping collinear terms. The author then integrates each $g^{(sub)}$ over the photonic part of phase space analytically, obtaining the closed-form $G^{(sub)}$ of Eqs. (4.10), (4.28), (4.34) and (4.49) for final-final, final-initial, initial-final and initial-initial emitter/spectator pairs, including the spin-flip pieces that vanish in the massless limit but must be retained here. For the mixed and initial-initial cases the analytic result is organized as a convolution over the energy fraction $x$ of the incoming fermion, with the $x�to 1$ singularity split off through a $[�dots]_+$ distribution so that the convolution itself can be evaluated with vanishing photon and fermion masses.

Load-bearing premise

For the mixed and initial-initial cases the construction introduces an arbitrary lower cutoff $x_0$ on the incoming fermion's energy fraction, and the paper asserts without proof that physical results do not depend on it, deferring that check to the numerics; if the endpoint terms $G^{(sub)}(P^2,x_0)$ did not cancel the $x_0$ dependence exactly, the convolutions would silently return cutoff-dependent answers.

Editorial extensions

If this is right

Real-photonic $O(�alpha)$ corrections to any process with charged fermions and neutral particles can be computed by Monte Carlo without a soft-photon cutoff or an angular collinearity cutoff, removing the need to scan for a plateau in auxiliary parameters.
Because the subtraction is process-independent and the $G^{(sub)}$ are given in closed form for arbitrary masses, the same code applies across the mass range from the electron to the top quark, and the massless limit is obtained by expansion rather than by a separate derivation.
For processes with only massive quarks as QCD partons, the same results carry over to gluon radiation by replacing $Q_q^2�alpha$ with $4�alpha_s/3$ and translating the infrared regulator into the dimensional-regularization pole.
Worked results are supplied for $�gamma�gamma �to t�bar t(�gamma)$, $e^-�gamma �to e^-�gamma(�gamma)$ and $�mu^+�mu^- �to �nu_e�bar�nu_e(�gamma)$, covering the final-final, mixed and initial-initial cases respectively.

Reading between the lines

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

The same machinery should apply to any neutral-boson-mediated process with many charged fermions, since the subtraction is a sum over emitter/spectator pairs and the pair sum is fixed by charge conservation; the practical bottleneck becomes the number of momentum mappings to implement, not new analytic integrals.
The treatment of cuts is the part most likely to be reused incorrectly: the paper argues that cuts applied to the subtraction function must be applied identically to its integrated counterpart, which for angular cuts means cutting the reconstructed angles of the reduced momenta rather than the original ones. That prescription, more than the algebra, is what a reimplementation has to get right.
Because the collinear logarithms are kept as explicit $�ln(m_f)$ terms, the formalism can be used to study the size of mass-singular initial-state corrections directly, which is the regime where electroweak corrections at future lepton colliders grow large; that is a natural next application the paper does not carry out.

Original abstract

Soft or collinear photon emission potentially poses numerical problems in the phase-space integration of radiative processes. In this paper, a general subtraction formalism is presented that removes such singularities from the integrand of the numerical integration and adds back the analytically integrated contributions that have been subtracted. The method is a generalization of the dipole formalism of Catani and Seymour, which was formulated for NLO QCD processes with massless unpolarized particles. The presented formalism allows for arbitrary mass and helicity configurations in processes with charged fermions and any other neutral particles. Particular attention is paid to the limit of small fermion masses, in which collinear singularities cause potentially large corrections. The actual application and the efficiency of the formalism are demonstrated by the discussion of photonic corrections to the processes \gamma \gamma --> t \bar t (\gamma), e^- \gamma --> e^- \gamma (\gamma), and \mu^+ \mu^- --> \nu_e \bar\nu_e (\gamma).

The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,043 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.75 · 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.

Soft or collinear photon emission potentially poses numerical problems in the phase-space integration of radiative processes. In this paper, a general subtraction formalism is presented that removes such singularities from the integrand of the numerical integration and adds back the analytically integrated contributions that have been subtracted. The method is a generalization of the dipole formalism of Catani and Seymour, which was formulated for NLO QCD processes with massless unpolarized particles. The presented formalism allows for arbitrary mass and helicity configurations in processes with charged fermions and any other neutral particles. Particular attention is paid to the limit of small fermion masses, in which collinear singularities cause potentially large corrections. The actual application and the efficiency of the formalism are demonstrated by the discussion of photonic corrections to the processes \gamma \gamma --> t \bar t (\gamma), e^- \gamma --> e^- \gamma (\gamma), and \mu^+ \mu^- --> \nu_e \bar\nu_e (\gamma).

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	Soft or collinear photon emission potentially poses numerical problems in the phase-space integration of radiative processes.	background 1.00	0.06	0.03	hedged possibility 0.98
s1	In this paper, a general subtraction formalism is presented that removes such singularities from the integrand of the numerical integration and adds back the analytically integrated contributions that have been subtracted.	contribution 0.75	0.94	0.59	asserted 1.00
s2	The method is a generalization of the dipole formalism of Catani and Seymour, which was formulated for NLO QCD processes with massless unpolarized particles.	background 0.73	0.11	0.06	asserted 1.00
s3	The presented formalism allows for arbitrary mass and helicity configurations in processes with charged fermions and any other neutral particles.	contribution 0.87	0.86	0.22	asserted 1.00
s4	Particular attention is paid to the limit of small fermion masses, in which collinear singularities cause potentially large corrections.	contribution 0.46	0.29	0.05	asserted 0.69
s5	The actual application and the efficiency of the formalism are demonstrated by the discussion of photonic corrections to the processes \gamma \gamma --> t \bar t (\gamma), e^- \gamma --> e^- \gamma (\gamma), and \mu^+ \mu^- --> \nu_e \bar\nu_e (\gamma).	contribution 0.56	0.93	0.17	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.62.

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.** Effective diagrams for the different emitter/spect

**Figure 2.** Definition of kinematical variables for d

Figures reproduced from arXiv:hep-ph/9904440 by the authors.

References

Works cited (20)

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S. Dittmaier, Phys. Rev. D59 (1999) 016007

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Complete NLO corrections to ${\rm W}^+{\rm W}^+$ scattering and its irreducible background at the LHC
hep-ph 2017-08 accept novelty 6.0 of 10

Complete NLO QCD and electroweak corrections to same-sign W scattering plus two jets shift the fiducial LHC cross section by -17%, mostly from a -13% electroweak Sudakov correction, and show signal and background are ...
Triple collinear emissions in parton showers
hep-ph 2017-05 accept novelty 6.0 of 10

A framework that folds triple-collinear 1-to-3 splitting functions into parton showers is constructed, validated against known NLO DGLAP kernels, and implemented in Pythia and Sherpa for the flavor-changing case.
NLO QCD+EW predictions for $2\ell2\nu$ diboson signatures at the LHC
hep-ph 2017-05 conditional novelty 6.0 of 10

Full NLO QCD plus electroweak predictions for pp to 2 leptons plus 2 neutrinos at 13 TeV, including photon-induced channels, with electroweak Sudakov corrections reaching tens of percent at TeV scales.
Automation of NLO QCD and EW corrections with Sherpa and Recola
hep-ph 2017-04 conditional novelty 6.0 of 10

A new software interface lets Sherpa call Recola for one-loop amplitudes, giving automated next-to-leading-order QCD and electroweak predictions for Standard Model LHC processes, validated against independent codes an...
Higgs production in association with off-shell top-antitop pairs at NLO EW and QCD at the LHC
hep-ph 2016-12 accept novelty 6.0 of 10

Full NLO electroweak corrections to off-shell ttH production at the LHC shift the total rate by +0.2 per cent but reach -8 to +15 per cent in specific kinematic regions, and the calculation is the first public NLO res...
NLO electroweak corrections to off-shell top-antitop production with leptonic decays at the LHC
hep-ph 2016-07 accept novelty 6.0 of 10

Full off-shell NLO electroweak corrections to pp to e+ nu mu- nubar b bbar at the 13 TeV LHC stay below 1 per cent inclusively but reach roughly 15 per cent at high transverse momentum.
Next-to-leading-order electroweak corrections to $pp \to W^+W^-\to$ 4 leptons at the LHC
hep-ph 2016-05 accept novelty 6.0 of 10

Full off-shell NLO electroweak corrections to pp to W+W- to 4 leptons are computed for the first time, and the double-pole approximation is shown to fail by more than 10% in TeV transverse-momentum tails.
NLO QCD+EW predictions for V+jets including off-shell vector-boson decays and multijet merging
hep-ph 2015-11 conditional novelty 6.0 of 10

The authors deliver NLO QCD+EW predictions for off-shell V+2 jet production at 13 TeV and an approximate scheme that injects electroweak corrections into MEPS@NLO multijet merging, agreeing with exact NLO EW at the fe...
Dominant mixed QCD-electroweak $\mathcal{O}(\alpha_s\alpha)$ corrections to Drell-Yan processes in the resonance region
hep-ph 2015-11 conditional novelty 6.0 of 10

The dominant mixed QCD-electroweak O(alpha_s alpha) corrections to resonant W and Z production are computed in pole approximation and shift the extracted W-boson mass by about -14 MeV for bare muons.
Mixed QCD-electroweak O(\alpha_s\alpha) corrections to Drell-Yan processes in the resonance region: pole approximation and non-factorizable corrections
hep-ph 2014-03 accept novelty 6.0 of 10

The non-factorizable mixed QCD-electroweak corrections to Drell-Yan production near the W/Z resonance are computed and found to be below 0.1%, so the corrections factorize for practical purposes.
Massive gauge boson pair production at the LHC: a next-to-leading order story
hep-ph 2013-07 accept novelty 6.0 of 10

Full NLO QCD+EW diboson predictions at the LHC, with a leading-logarithmic explanation of why gluon-quark and photon-quark induced corrections are large for W W and W Z but small for Z Z.
Electroweak corrections to W-boson pair production at the LHC
hep-ph 2012-08 conditional novelty 6.0 of 10

The first complete one-loop electroweak corrections to on-shell W-pair production at hadron colliders show photon-induced channels growing large at high energy while extra massive-boson radiation stays below about 5 percent.
NLO QCD corrections to off-shell top-antitop production with leptonic decays at hadron colliders
hep-ph 2012-07 accept novelty 6.0 of 10

Off-shell top-antitop production with leptonic decays is computed at NLO QCD including all non-resonant diagrams, and finite-width effects are shown to be sub-percent inclusively but large in exclusive tails.
Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK
hep-ph 2011-12 accept novelty 6.0 of 10

Fully differential NLO electroweak corrections to WH and ZH production with leptonic W/Z decays reach about -14% for boosted Higgs bosons at the LHC, exceeding PDF and scale uncertainties.
Numerical NLO QCD calculations
hep-ph 2010-10 conditional novelty 6.0 of 10

A complete algorithm for numerical one-loop QCD amplitudes, combining local subtraction terms with a Feynman-parameter contour deformation, checked on a three-point function up to nine propagators and on photon-to-qua...
NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results
hep-ph 2010-01 accept novelty 6.0 of 10

Full next-to-leading-order QCD predictions for top-antitop-bottom-antibottom production at the LHC, with a new dynamical scale that cuts the correction factor from about 1.8 to 1.24 and reduces scale uncertainty.
A proposal for a standard interface between Monte Carlo tools and one-loop programs
hep-ph 2010-01 accept novelty 6.0 of 10

The paper specifies a two-phase interface, an order file and a contract file for setup plus two function calls at run time, that lets any Monte Carlo generator request one-loop interference terms from any one-loop provider.
Electroweak corrections to W + jet hadroproduction including leptonic W-boson decays
hep-ph 2009-06 accept novelty 6.0 of 10

The authors deliver the first NLO electroweak calculation of W plus jet hadroproduction with the W boson treated off shell and decaying leptonically, finding corrections from a few percent up to roughly minus 30 perce...
Polarized QED splittings of massive fermions and dipole subtraction for non-collinear-safe observables
hep-ph 2008-02 accept novelty 6.0 of 10

The dipole subtraction formalism for photonic corrections is extended to four photon-fermion splitting configurations, with polarization, enabling stable next-to-leading-order calculations for observables that are not...
Single top production and decay at next-to-leading order
hep-ph 2004-08 conditional novelty 6.0 of 10

Single top production and its leptonic decay are computed together at next-to-leading order in QCD, with a new subtraction method for gluon radiation in the decay, and the resulting jet activity is compared against th...
Electroweak Radiative Corrections to Associated WH and ZH Production at Hadron Colliders
hep-ph 2003-06 accept novelty 6.0 of 10

Electroweak O(alpha) corrections reduce the associated WH and ZH production cross sections by 5 to 10 percent, and the updated NLO QCD plus electroweak prediction carries about 10 percent scale and under 5 percent PDF...
The Dipole Formalism for Next-to-Leading Order QCD Calculations with Massive Partons
hep-ph 2002-01 accept novelty 6.0 of 10

The authors give the complete dipole subtraction formulae needed to compute next-to-leading-order QCD corrections for processes with massive quarks, squarks and gluinos in the final state, with a quasi-collinear treat...
Electroweak radiative corrections to W-boson production at hadron colliders
hep-ph 2001-09 accept novelty 6.0 of 10

A complete one-loop electroweak calculation for W production at the Tevatron and LHC shows that resonance-pole approximations fail for high-transverse-momentum leptons.
Mixed QCD-EW corrections to the neutral-current Drell-Yan process
hep-ph 2024-12 accept novelty 5.0 of 10

Exact mixed QCD-EW corrections at order alpha_s alpha to neutral-current Drell-Yan production are computed and applied to distributions, the forward-backward asymmetry, and dressed leptons.
NLO QCD corrections to off-shell top-antitop production with leptonic decays in association with a Higgs boson at the LHC
hep-ph 2015-06 accept novelty 5.0 of 10

Full off-shell NLO QCD prediction for pp to e+ nu mu- nubar b bbar H at 13 TeV, giving a K factor of about 1.17 and showing that a dynamical scale choice stabilises high-energy tails.
QCD NLO and EW NLO corrections to $t\bar{t}H$ production with top quark decays at hadron collider
hep-ph 2014-07 conditional novelty 5.0 of 10

Adding electroweak NLO corrections to ttH production leaves the total rate nearly unchanged (about minus one percent) but shifts the high-transverse-momentum and high-invariant-mass tails by up to ten percent, compara...
Radiative corrections to the neutral-current Drell-Yan process in the Standard Model and its minimal supersymmetric extension
hep-ph 2009-11 accept novelty 5.0 of 10

Complete NLO electroweak plus QCD corrections to neutral-current Drell-Yan are presented for the Standard Model and the MSSM, with three gauge-invariant treatments of the Z resonance and a consistent treatment of phot...
Event generation with SHERPA 1.1
hep-ph 2008-11 accept novelty 5.0 of 10

SHERPA 1.1 integrates tree-level matrix elements, CKKW merging, cluster hadronisation, hadron decays, and YFS QED radiation into one validated event generator for lepton and hadron collisions.
Standard Model Handles and Candles Working Group: Tools and Jets Summary Report
hep-ph 2008-03 accept novelty 5.0 of 10

Three electroweak Z-boson generators agree on the NLO correction to within about two per mille, and jet-radius choice matters more than jet-algorithm choice for heavy-resonance mass reconstruction.
Radiative corrections to the semileptonic and hadronic Higgs-boson decays H -> W W/Z Z -> 4 fermions
hep-ph 2006-11 accept novelty 5.0 of 10

Complete NLO electroweak plus QCD corrections to H -> WW/ZZ -> 4 fermion decays with semileptonic and hadronic final states, with QCD corrections dominated by the alpha_s/pi and 2 alpha_s/pi factors from hadronic gaug...
NLO QCD and EW corrections to semileptonic vector-boson scattering at the LHC
hep-ph 2026-06 unverdicted novelty 4.0 of 10

NLO QCD and EW corrections computed for semileptonic vector-boson scattering in two fiducial regions at the LHC.
HAWK 2.0: A Monte Carlo program for Higgs production in vector-boson fusion and Higgs strahlung at hadron colliders
hep-ph 2014-12 accept novelty 4.0 of 10

HAWK 2.0 releases, with full user documentation, a Monte Carlo integrator that supplies NLO QCD and electroweak predictions for Higgs production via vector-boson fusion and Higgs strahlung at hadron colliders.
Electroweak Radiative Corrections for Collider Physics
hep-ph 2019-12 accept novelty 3.0 of 10

A comprehensive review that unifies the concepts and tools of electroweak radiative corrections, from renormalization and one-loop methods to infrared subtraction and unstable-particle treatments, for collider phenomenology.
Effects of bottom quark induced processes on polarized $W^+W^-$ production at the LHC at NLO
hep-ph 2025-05 conditional novelty 2.0 of 10

Bottom-quark induced processes at NLO QCD+EW increase the doubly-longitudinal W+W- polarization fraction by about 7.6% with a jet veto and 10.5% without, after on-shell top-quark subtraction.
Feynman Integrals
hep-th 2022-01 accept novelty 2.0 of 10

A self-contained graduate course assembling the modern methods for computing Feynman integrals, from graph polynomials and differential equations through symbols, cluster algebras, elliptic curves and motives.

How later papers used it

114 later papers cite it

Evidence: some. 98 of the citing papers share no author with it, and 77 of those carry a confident label from Pith's citation classifier.

Pith read 8 of the 214 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

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 91 papers with this label

Employed the dipole-subtraction method for QCD and its extension to QED from this paper to handle the associated IR divergences.

Complete NLO corrections to ${\rm W}^+{\rm W}^+$ scattering and its irreducible background at the LHC (2017) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

111 arXiv papers cite this in 211 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 · 70 sentences without a confident label

Builds on it 3 papers

To this end, based on the results presented in Refs. [ref] , the implementation of the Catani–Seymour dipole-subtraction formalism has been extended to account for QED corrections [ref] .

Automation of NLO QCD and EW corrections with Sherpa and Recola · The framework · 0.92
In this paper, we have presented an extension of the dipole subtraction formalism introduced in Refs. [ref] to massive initial-state particles for NLO (SUSY)-QCD calculations which allows the analytic cancellation of infrared singularities between the virtual and real corrections.

The dipole formalism for massive initial-state particles and its application to dark matter calculations · Summary and outlook · 0.98
The dipole splitting functions of [ref] have been generalised further in [ref] to incorporate also polarisation.

Soft Photon Radiation in Particle Decays in SHERPA · Approximations for real emission matrix elements · 0.92

Uses its method or tool 88 papers

It is based on the ACOT massive factorization theorem [ref] and massive dipole subtraction method (DSM) [ref] , which however had to be reformulated in order to match with the former.

Fully massive Scheme for Jet Production in DIS · Introduction · 0.89
The results presented here were produced using the parton-level Monte Carlo program [ref] , in which the subtraction of IR divergences in the real radiation is realised with the Catani–Seymour dipole formalism [ref] .

NLO QCD and EW corrections to semileptonic vector-boson scattering at the LHC · Details and validation of the calculation · 1.00
We perform the subtraction of IR divergences in the Catani–Seymour (CS) dipole formalism [ref] .

NLO EW and QCD corrections to polarized ZZ production in the four-charged-lepton channel at the LHC · Calculation details · 1.00

Compares with it 1 paper

Furthermore we define for brevity [equation] The contribution from the collinear integral is simpler and we find [equation] The results in dimensional regularization can be compared with the results in mass regularization given in Eq. (4.10) of [ref] .

Photon Radiation with MadDipole · Final-final $f→f+γ$ dipole in dimensional regularization · 0.99

Cites it as background 5 papers

The factorization properties of such amplitudes are well-known [ref] .

Final-state QED Multipole Radiation in Antenna Parton Showers · Emission kernel · 0.87
Various general NLO subtraction schemes have been proposed (see [ref] ), and several (semi)automated implementations are available [ref] .

An alternative subtraction scheme for next-to-leading order QCD calculations · Introduction · 0.93
The various methods that were proposed in the literature can be broadly classified into two types: the phase-space-slicing [ref] and the subtraction formalisms [ref] .

Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay · Introduction · 0.90

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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