Separation of left-handed and anomalous right-handed vector operators contributions into the Wtb vertex for single and double resonant top quark production processes using a neural network

A. Markina; A. Zaborenko; D. Gorin; E. Abasov; E. Boos; G. Vorotnikov; L. Dudko; M. Perfilov; O. Vasilevskii; P. Volkov

REVIEW 4 major objections 4 minor 22 references

Separation of left-handed and anomalous right-handed vector operators contributions into the Wtb vertex for single and double resonant top quark production processes using a neural network

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Splitting top quark events by resonance class tightens the bound on an anomalous Wtb coupling from 0.21 to 0.17.

desk verdict The NN separation itself looks plausible, but the reported 0.21→0.17 sensitivity gain is confounded by an unvalidated change in signal-scaling assumptions and a statistical derivation that is not reproducible as written. read the letter →

arxiv 2412.02468 v1 pith:YVBGAJO3 submitted 2024-12-03 hep-ph

E. Abasov , E. Boos , V. Bunichev , L. Dudko , D. Gorin , A. Markina , M. Perfilov , O. Vasilevskii

show 3 more authors

P. Volkov G. Vorotnikov A. Zaborenko

This is my paper · ORCID

classification hep-ph

keywords topquarkWtbvertexanomalouscouplingseffectivefieldtheoryneuralnetworksingleproductionpairLHC

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that sensitivity to an anomalous right-handed vector coupling at the Wtb vertex is improved by first splitting top quark production events into single-resonant and double-resonant classes with a neural network, then running a separate classifier inside each class. The two classes depend on the anomalous coupling differently, so analyzing them separately gives a tighter expected upper limit on the coupling magnitude |f_R^V|: below 0.17 with the split versus 0.21 without it. This matters because searches for new physics in the top quark sector may be able to use event topology rather than diagram removal to separate contributions, and single-resonant production, though smaller, is more sensitive to right-handed couplings. The paper also presents a statistical model based on asymptotic likelihood formulas to convert the neural network outputs into constraints.

What carries the argument

The machinery is a two-level deep neural network architecture. The first-level network separates events into double resonant (ttbar) and single resonant (tWb) production based on kinematic observables; the second level consists of two separately trained networks, one for each production class, that discriminate between the left-handed vector operator (SM) and the anomalous right-handed vector operator (RV). The statistical engine is an asymptotic Poisson likelihood with profiled background normalization, using Wilks and Wald formulas and Asimov data to derive one-sided 95% CL limits on the coupling f_R^V. The Wtb vertex is the interaction of the top quark, the W boson, and the bottom quark.

What would settle it

Compute the expected upper limit on f_R^V using a full event generator at several fixed values of f_R^V (for example 0, 0.1, 0.2, 0.3) without assuming a power-law scaling, and compare the single-resonant and double-resonant signal rates; if the single-resonant rate does not scale approximately as f_R^$V^{4}$, the reported 0.17 versus 0.21 comparison will not reproduce.

Watch

Extended reading notes

Core claim

The central claim is that a two-stage neural network analysis of pp -> l nu b bbar q qbar' events with a tWb final state can separate the contributions of the left-handed vector operator (SM-like) and the anomalous right-handed vector operator at the Wtb vertex more effectively when single and double resonant top quark production are treated as separate classes. A first-level network classifies each event as double resonant (ttbar) or single resonant (tWb); two second-level networks then discriminate LV from RV events in each class. Using a Poisson likelihood with a nuisance parameter for background normalization and Asimov data, the expected 95% CL upper limit on |f_R^V| improves from 0.21 for the combined phase space to 0.17 when the phase space is split, assuming the single-resonant signal rate scales as f_R^$V^{4}$ and the double-resonant rate as f_R^$V^{2}$.

Load-bearing premise

The whole comparison rests on the assumed rate scaling for the anomalous right-handed coupling: the single-resonant class is taken to grow as f_R^$V^{4}$ and the double-resonant class as f_R^$V^{2}$, a dependence cited from reference [22] and not validated here; if that scaling is wrong, the quoted limits and the size of the splitting gain change.

Editorial extensions

If this is right

A combined analysis of single and double resonant top quark events, without removing diagrams from the gauge-invariant set, can yield a stricter constraint on the anomalous right-handed vector operator than analyzing the full tWb final state as one class.
The two neural network levels provide separable discriminators that can be reused for event classification in experimental analyses of top quark final states.
The statistical procedure, with a Poisson likelihood and a profiled nuisance parameter, gives a practical route from classifier outputs to 95% CL upper limits on anomalous couplings.
Separate limits can be quoted for the double-resonant and single-resonant phase space regions, reflecting their different sensitivities to anomalous right-handed couplings.
The method offers a way to account for interference between single and double resonant production by classifying events rather than by removing part of the matrix element set.

Reading between the lines

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

The size of the gain (0.21 to 0.17) depends on the assumed f_R^V^4 scaling of the single-resonant signal; if a full matrix-element calculation shows a different scaling, the gain from splitting could shrink or vanish.
The same two-stage separation could be applied to tensor operators at the Wtb vertex, where single-resonant production is also expected to be the more sensitive class.
A direct cross-check would be to generate Monte-Carlo samples at several f_R^V values and fit the signal strength in each class, rather than relying on the cited f_R^V^2 and f_R^V^4 power-law dependencies.
If the splitting gain persists under realistic systematic uncertainties, the approach could become a standard way to structure searches for anomalous top quark couplings at the LHC.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

The paper extends the authors' earlier work on separating single- and double-resonant tWb events with a neural network, adding a second level of classifiers that distinguish SM left-handed from anomalous right-handed vector Wtb couplings within each event class. That is a genuine, modest extension: the plots in Sec. 3 show the two classes separate well for both the ttbar-like and single-resonant phase space regions, and the authors are careful to use the full gauge-invariant diagram set rather than removing diagrams. The two-stage design is sensible and the MC training setup is described in enough detail to reproduce the shapes in principle.

The soft spots are concentrated in Sec. 4. The central comparison, 0.21 without splitting vs 0.17 with splitting, changes two things at once: the phase-space split and the assumed dependence of the signal rate on f_R^V. The unsplit limit uses mu = f_R^V^2 for the whole tWb sample, while the split analysis uses mu = f_R^V^2 for the ttbar region and mu = f_R^V^4 for the single-resonant region. If the full tWb sample is a mixture of both diagram classes, its cross section is not purely quadratic in f_R^V, so the two limits are not directly comparable. The f^4 scaling is asserted from ref [22] without derivation or cross-check here, and the 0.9 threshold on the first-level NN that defines the split is not justified. If the true scaling differs, the size of the gain—and perhaps its sign—would change.

The statistical model itself is hard to follow, and not just in the usual phenomenological shorthand. Some formulas appear garbled: Eq. (8) with the defined S1 would give an imaginary Z, the derivative in Eq. (5) does not look right, and quantities like delta_i and tau are introduced in a way that leaves the reader guessing. No yields, bin counts, or luminosity are given, so the quoted limits are not reproducible from the text. That is a real problem for a paper whose main result is a pair of numbers.

What the paper does well is the phenomenological setup and the demonstration that operator-level separation within single/double resonant classes is feasible. That part earns attention. But the quantitative claim needs a clean statistical derivation, a validated or at least defended scaling assumption, and a matched comparison where only the splitting changes.

For a top-quark EFT audience, this is worth a serious referee, but heavy revision is required before the limits can be believed. I would not cite it in its current form.

Referee Report

4 major / 4 minor

Summary. The paper proposes a neural-network-based strategy for separating single- and double-resonant top quark production in the tWb final state, and then applying dedicated second-level classifiers to distinguish Standard Model left-handed from anomalous right-handed vector Wtb couplings in each phase-space class. The authors report that this splitting improves the expected 95% CL constraint on the anomalous right-handed vector coupling from |f_R^V| < 0.21 (unsplit) to |f_R^V| < 0.17 (split), using a simplified likelihood-based statistical model with a 20% systematic uncertainty. The central quantitative claim is therefore that phase-space separation of the two resonance topologies increases sensitivity to this anomalous coupling.

Significance. If the claimed improvement is genuine, the approach would be useful because it avoids the common practice of removing part of the diagram set to separate single- and double-resonant contributions, instead using neural networks to classify events and treating the interference as smeared across classes. The paper also uses a complete gauge-invariant set of diagrams and provides Monte Carlo distributions showing that the second-level classifiers achieve visible separation between left- and right-handed vector operator hypotheses. However, the statistical derivation in Section 4 is not internally consistent, the numerical limits are not reproducible from the given information, and the reported improvement may be an artifact of the assumed f_R^V scaling rather than of the neural-network split. The potential significance is therefore not yet established by the manuscript as written.

major comments (4)

[Section 4, Eqs. (4)–(8)] The statistical model is internally inconsistent. In Eq. (4) the Poisson term is printed as n_i · ln( (μ s_i + b_i)/n_i! ) − μ s_i − b_i, which is missing the exponent n_i in the numerator and is not a valid log-likelihood. Eq. (5) mixes i and j indices and the derivative with respect to b_j is incorrect: the control-region derivative should be m_j/b_j − τ, not m_j/(τ b_j) − τ. In Eq. (8), the significance Z is written as sqrt(2(S1 + S2)) using S1 and S2 from Eqs. (6)–(7), but with Asimov data n_i = b_i and b̂_i = b_i, S1 can be negative, so Z is not guaranteed real. Since the limits 0.21 and 0.17 are the central quantitative result, these formulas must be corrected and the calculation repeated.
[Section 4, paragraph after Eq. (8)] The comparison between the unsplit and split cases changes two assumptions at once. The unsplit limit uses μ = f_R^V^2 for the full tWb sample, while the split limit uses μ = f_R^V^2 for the double-resonant region and μ = f_R^V^4 for the single-resonant region, with the f^4 scaling asserted from reference [22] without derivation or validation. The full tWb sample contains both single- and double-resonant diagrams, so its cross-section dependence on f_R^V is not necessarily purely quadratic; the reported 0.21 → 0.17 improvement could therefore be driven by the assumed signal parameterization rather than by the neural-network phase-space split. The authors should test the split with a consistent scaling for both samples or provide a derivation of the appropriate scaling of the single-resonant region.
[Section 4, input values] The numerical limits are not reproducible as written. No yields s_i and b_i, no luminosity, no binning parameters N and M, and no value for the 20% systematic Δ are given. The quantities δ_i and τ are defined circularly: the text introduces δ_i = 1/sqrt(τ b_i) with τ = Δ^2 * Σ b_i, and later substitutes τ = 1/(δ_i^2 b_i). This leaves the normalization of the control region unspecified. The authors should provide the input histograms, binning, and either a public implementation or enough detail to reproduce the 0.21 and 0.17 numbers.
[Section 3, first-level NN threshold] The split between the double-resonant and single-resonant classes is defined by a fixed threshold of 0.9 on the first-level neural-network discriminator, but this threshold is not justified or optimized. The sensitivity result will depend on this arbitrary cut, and the paper should either scan the threshold or at least demonstrate that the qualitative conclusion is stable within a reasonable range.

minor comments (4)

[Figure 1] Several axis labels in Fig. 1 are garbled, e.g., 'cos(D,l)_RF(l,0' and 'cos(l,u)_RF(l,0', which makes it impossible to identify the plotted observables. Please fix the labels.
[Section 4] The notation 'tWb' is used both for the full final state (including double-resonant diagrams) and for the single-resonant phase-space region in the sentence 'for tWb- μ = f_R^V^4'. This is confusing and should be disambiguated, e.g., by calling the single-resonant region 'tW' or 'single-resonant'.
[General] There are numerous typographical and readability issues, such as 'splitted' instead of 'split', 'a object' instead of 'an object', and the phrase 'Wtb vertex into a Wtb vertex'. A thorough language edit is needed.
[References] Reference [15] is cited in the text as a source of high-level observables but appears to be about a different topic; please verify that the reference list matches the citations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the limits are computed from stated MC templates and an external f_R^V-scaling assumption; the f^4 input and statistical equations are correctness risks, not circular reductions.

full rationale

The paper's derivation chain is not circular. The first-level phase-space split is imported from the authors' prior paper [6], and the mu=f_R^V^2 / f_R^V^4 signal normalizations are taken from an external reference [22]; neither is fitted to the limit numbers being reported. The second-level networks are trained on MC benchmark samples (f_L^V=1, f_R^V=0 versus f_L^V=0, f_R^V=1), and the expected 95% CL limits are computed from an Asimov likelihood on those templates, so the 0.21->0.17 comparison is a stated sensitivity study rather than a fit renamed as a prediction. The split case does change both the phase-space division and the mu(f_R^V) parameterization at once, and the f^4 scaling for the NN-defined single-resonant class is asserted without derivation; also Eqs. (5) and (8) are internally inconsistent and the s_i,b_i yields are not given. These are serious reproducibility/correctness concerns, but they are not circular reductions because the output limits are not algebraically identical to the assumed scalings and the scaling reference is external. Self-citations [6,14,16] supply methodology, but the performance numbers are produced by the present MC/training pipeline, so no load-bearing self-citation chain makes the result tautological.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper rests on a chain of assumptions: the EFT framework, the correctness of the first-level NN separation, the signal-rate scalings taken from ref [22], and the Poisson likelihood with a flat 20% systematic. None of these are independently validated in this manuscript.

free parameters (5)

Flat systematic uncertainty Delta = 20%
Assumed in Section 4 for the integrated cross section; directly shifts the extracted limits.
First-level NN threshold = 0.9 on the DNN_tT_DR discriminator
Defines which events are called double resonant (DNN < 0.9) versus single resonant (DNN >= 0.9); no optimization or error is given, and the limits depend on this split.
Signal-strength scaling, double resonant region = mu = f_R^V^2
Taken from reference [22] without derivation; controls the limit in the double resonant class.
Signal-strength scaling, single resonant region = mu = f_R^V^4
Taken from reference [22]; this faster scaling is what makes splitting improve the expected limit.
Histogram binning N and M = not reported
The likelihood in Eq. (4) requires binning, but the bin counts are not stated.

assumptions (5)

domain assumption The dimension-6 operator basis of Buchmuller-Wyler / Grzadkowski et al. describes new physics at the Wtb vertex.
Used in Section 2 to define f_R^V in terms of Wilson coefficients; standard EFT framework.
domain assumption The interference between left- and right-handed vector amplitudes is negligible or absent.
Implicit in Section 4 where mu is set to f_R^V^2 or f_R^V^4 with no linear term; not stated or checked.
domain assumption The first-level NN from reference [6] separates single and double resonant events correctly.
All second-level analysis inherits this classification; not revalidated here.
standard math Asymptotic Wilks and Wald approximations are valid for the likelihood.
Used to derive Eq. (8) and the 95% CL limits.
domain assumption CompHEP Monte Carlo accurately simulates the tWb processes with the given operators.
All training and limit-setting use these events; no validation against data.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Separation of left-handed and anomalous right-handed vector operators contributions into the Wtb vertex for single and double resonant top quark production processes using a neural network." pith.science (2026). https://pith.science/paper/YVBGAJO3

@misc{pith2026241202468,
  author       = {Pith},
  title        = {Pith review of: Separation of left-handed and anomalous right-handed vector operators contributions into the Wtb vertex for single and double resonant top quark production processes using a neural network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YVBGAJO3}},
  note         = {Machine review of arXiv:2412.02468}
}

read the original abstract

The paper describes the application of deep neural networks for the searchdeviations from the Standard Model predictions at the Wtb vertex in the processes of single and double resonant top quark production with identical final state tWb. Monte-Carlo events preliminary classified by first level neural network as corresponding to single or double resonant top quark production are analyzed by two second level neural networks if there is a possible contribution of the anomalous right-handed vector operator into Wtb vertex or events are corresponded to the Standard Model. The second level neural networks are different for single and double resonant classes. The classes depend differently on anomalous contribution and such splitting leads to better sensitivity. The developed statistical model is used to set constraints on the anomalous right-handed vector operator at the Wtb vertex in different regions of phase space. It is demonstrated that the proposed method allows to increase the efficiency of a search for the anomalous contributions to the Wtb vertex.

Figures

Figures reproduced from arXiv: 2412.02468 by the authors.

**Figure 2.** The distribution of simulated events by the values of the neural network discriminator, distinguishing contributions from the left-handed and anomalous right-handed vector operators in the Wtb vertex for events classified by the previous neural network as double resonant top quark production events. 0.0 0.2 0.4 0.6 0.8 1.0 DNN_DR_LV_RV 0 5 10 15 20 25 30 35 40 45 −3 ×10 dN/N DNN_tT_DR>=0.9 tt_tW_LV tt_tW_RV [P… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

22 extracted references · 13 canonical work pages

[22]

Secondary particles spectra in the decay of a polarized top quark with anomalous $tWb$ coupling

M. Mohammadi Najafabadi, J. Phys. G 34 (2007), 39-46 doi:10.1088/0954-3899/34/1/003 [arXiv:hep-ph/0601155 [hep-ph]]

work page Pith review arXiv 2007
[1]

E. Boos, L. Dudko, P. Mandrik and S. Slabospitskii, Phys. Part. Nucl. 50 (2019) no.3, 231-258 doi:10.1134/S106377961903002X

work page doi:10.1134/s106377961903002x 2019
[2]

R. L. Workmanet al.[Particle Data Group], PTEP2022 (2022), 083C01 doi:10.1093/ptep/ptac097

doi:10.1093/ptep/ptac097 2022
[3]

Search for anomalous Wtb couplings and flavour-changing neutral currents in t-channel single top quark production in pp collisions at sqrt(s) = 7 and 8 TeV

V. Khachatryan et al. [CMS], JHEP 02 (2017), 028 doi:10.1007/JHEP02(2017)028 [arXiv:1610.03545 [hep-ex]]

work page Pith review arXiv 2017
[4]

A. M. Sirunyan et al. [CMS], Eur. Phys. J. C 79 (2019) no.11, 886 doi:10.1140/epjc/s10052-019-7387-y [arXiv:1903.11144 [hep-ex]]. 9

work page Pith review arXiv 2019
[5]

Baskakov, E

A. Baskakov, E. Boos, V. Bunichev, G. Vorotnikov, L. Dudko, I. Myagkov and M. Perfilov, EPJ Web Conf. 158 (2017), 04004 doi:10.1051/epjconf/201715804004

work page arXiv 2017
[6]

E. E. Boos, V. E. Bunichev, P. V. Volkov, L. V. Dudko and M. A. Perfilov, Moscow Univ. Phys. Bull. 78 (2023) no.6, 707-715 doi:10.3103/S0027134923060024

doi:10.3103/s0027134923060024 2023
[7]

Booset al.[CompHEP], Nucl

E. Booset al.[CompHEP], Nucl. Instrum. Meth. A534 (2004), 250-259 doi:10.1016/j.nima.2004.07.096 [arXiv:hep-ph/0403113 [hep-ph]]

arXiv 2004

Show all 22 references

[8]

Pukhov, E

A. Pukhov, E. Boos, M. Dubinin, V. Edneral, V. Ilyin, D. Kovalenko, A. Kryukov, V. Savrin, S. Shichanin and A. Semenov, [arXiv:hep- ph/9908288 [hep-ph]]
[9]

Abadi, A

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean and M. Devin,et al.[arXiv:1603.04467 [cs.DC]]

arXiv
[10]

Buchmuller and D

W. Buchmuller and D. Wyler, Nucl. Phys. B 268 (1986), 621-653 doi:10.1016/0550-3213(86)90262-2

1986 doi
[11]

Grzadkowski, Z

B. Grzadkowski, Z. Hioki, K. Ohkuma and J. Wudka, Nucl. Phys. B 689 (2004), 108-126 doi:10.1016/j.nuclphysb.2004.04.006 [arXiv:hep- ph/0310159 [hep-ph]]

2004
[12]

J. A. Aguilar-Saavedra, Nucl. Phys. B 821 (2009), 215-227 doi:10.1016/j.nuclphysb.2009.06.022 [arXiv:0904.2387 [hep-ph]]

2009 arXiv
[13]

J. A. Aguilar-Saavedra, PoS ICHEP2010 (2010), 378 doi:10.22323/1.120.0378 [arXiv:1008.3225 [hep-ph]]

2010 arXiv
[14]

E. E. Boos, V. E. Bunichev, L. V. Dudko and A. A. Markina, Phys. Atom. Nucl. 71 (2008) no.2, 388-393 doi:10.1134/s1063778808020191

2008 doi
[15]

Dudko, G

L. Dudko, G. Vorotnikov, P. Volkov, D. Ovchinnikov, M. Perfilov, A. Sh- porin and A. Chernoded, Int. J. Mod. Phys. A35 (2020) no.21, 2050119 doi:10.1142/S0217751X20501195 [arXiv:2002.09350 [hep-ph]]

2020 arXiv
[16]

E. E. Abasov, M. I. Belobrova, P. V. Volkov, G. A. Vorotnikov, L. V. Dudko, A. D. Zaborenko, M. A. Perfilov and E. S. Sivakova, Phys. Atom. Nucl. 85 (2022) no.6, 708-720 doi:10.1134/S1063778822060023

2022 doi
[17]

Cowan, K

G. Cowan, K. Cranmer, E. Gross and O. Vitells, Eur. Phys. J. C 71 (2011), 1554 [erratum: Eur. Phys. J. C 73 (2013), 2501] doi:10.1140/epjc/s10052-011-1554-0 [arXiv:1007.1727 [physics.data-an]]

2011 arXiv
[18]

M. J. Basso, J. Phys. G 49 (2022) no.2, 025001 doi:10.1088/1361- 6471/ac3dcd [arXiv:2102.04275 [physics.data-an]]. 10

2022 arXiv
[19]

Gorin, O

D. Gorin, O. Vasilevskii, L. Dudko, E. Abasov, Memoirs of the Faculty of Physics 49 (2024)

2024
[20]

S. S. Wilks, Annals Math. Statist. 9 (1938) no.1, 60-62 doi:10.1214/aoms/1177732360

1938
[21]

Wald, Transactions of the American Mathematical Society54, (1943), 426-482

A. Wald, Transactions of the American Mathematical Society54, (1943), 426-482

1943

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [22]

Secondary particles spectra in the decay of a polarized top quark with anomalous $tWb$ coupling

M. Mohammadi Najafabadi, J. Phys. G 34 (2007), 39-46 doi:10.1088/0954-3899/34/1/003 [arXiv:hep-ph/0601155 [hep-ph]]

work page Pith review arXiv 2007

[2] [1]

E. Boos, L. Dudko, P. Mandrik and S. Slabospitskii, Phys. Part. Nucl. 50 (2019) no.3, 231-258 doi:10.1134/S106377961903002X

work page doi:10.1134/s106377961903002x 2019

[3] [2]

R. L. Workmanet al.[Particle Data Group], PTEP2022 (2022), 083C01 doi:10.1093/ptep/ptac097

doi:10.1093/ptep/ptac097 2022

[4] [3]

Search for anomalous Wtb couplings and flavour-changing neutral currents in t-channel single top quark production in pp collisions at sqrt(s) = 7 and 8 TeV

V. Khachatryan et al. [CMS], JHEP 02 (2017), 028 doi:10.1007/JHEP02(2017)028 [arXiv:1610.03545 [hep-ex]]

work page Pith review arXiv 2017

[5] [4]

A. M. Sirunyan et al. [CMS], Eur. Phys. J. C 79 (2019) no.11, 886 doi:10.1140/epjc/s10052-019-7387-y [arXiv:1903.11144 [hep-ex]]. 9

work page Pith review arXiv 2019

[6] [5]

Baskakov, E

A. Baskakov, E. Boos, V. Bunichev, G. Vorotnikov, L. Dudko, I. Myagkov and M. Perfilov, EPJ Web Conf. 158 (2017), 04004 doi:10.1051/epjconf/201715804004

work page arXiv 2017

[7] [6]

E. E. Boos, V. E. Bunichev, P. V. Volkov, L. V. Dudko and M. A. Perfilov, Moscow Univ. Phys. Bull. 78 (2023) no.6, 707-715 doi:10.3103/S0027134923060024

doi:10.3103/s0027134923060024 2023

[8] [7]

Booset al.[CompHEP], Nucl

E. Booset al.[CompHEP], Nucl. Instrum. Meth. A534 (2004), 250-259 doi:10.1016/j.nima.2004.07.096 [arXiv:hep-ph/0403113 [hep-ph]]

arXiv 2004