{"total":24,"items":[{"citing_arxiv_id":"2605.12214","ref_index":32,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"A Runway to Dissipation of Angular Momentum via Worldline Quantum Field Theory","primary_cat":"hep-th","submitted_at":"2026-05-12T14:51:06+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The authors introduce static correlators in worldline QFT to compute angular momentum dissipation in black hole scattering, reproducing the known O(G^3) flux and extending the approach to electromagnetism at O(α^3).","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"tegration on all internal momenta and frequencies which has now been exposed by the factorization of the diagram in eq. (22). By assumption (and diagrammatically signi- fied by the blue coloring), all frequencies and momenta are static and thus scale withω IR. After the diagram has been expanded in this limit one may however integrate over their full ranges again (as dictated by the method of regions [32, 109, 110]). 6 The static correlator depicted in eq. (23) does, by as- sumption, not depend on the dynamical scaleq. Its de- pendence on its only scaleω IR can thus be determined from dimensional analysis. The dimension of a general n-point correlator may easily be determined and, taking into account integrations on incoming momenta of fre- quencies, for the generic static correlator (23) we find:"},{"citing_arxiv_id":"2605.10635","ref_index":31,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Heavy-Quark Condensate and Vacuum Energy Anomalous Dimension at Five Loops","primary_cat":"hep-ph","submitted_at":"2026-05-11T14:24:17+00:00","verdict":"UNVERDICTED","verdict_confidence":"UNKNOWN","novelty_score":7.0,"formal_verification":"none","one_line_summary":"The heavy-quark condensate is computed at five-loop order in QCD with massive quarks, confirming the five-loop vacuum anomalous dimension.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"mass colourings of the four five-loop sector templates depicted in figure 1 as well as their subsectors that form when contracting propagator lines to a point. The scalar integrals can be reduced to a set of 142 master integrals by exploiting integration-by-parts relations [28]. 2 To this end, we employcrusher[30], a custom im- plementation of Laporta's algorithm [31], together withtinbox[32] for reduction over 2In [29] the reduction lead to 156 different integrals. However, this number could be further reduced through a more comprehensive integral symmetrisation. - 2 - Figure 1. The four distinct five-loop vacuum-type integral sectors with the maximum number of 12 propagators each. All our integrals can be mapped onto these or their sub-sectors."},{"citing_arxiv_id":"2605.06775","ref_index":1,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"SIRENA -- Sum-Integral REductioN Algorithm","primary_cat":"hep-ph","submitted_at":"2026-05-07T18:00:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"SIRENA automates IBP reduction of sum-integrals in finite-temperature QFT, reproduces known results to 3 loops, supplies new 3-loop fermionic reductions, and derives an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"Similar public tools that are optimized and adapted to the unique symmetry proper- ties of sum-integrals are lacking. Solution method:The program first identifies equivalence classes of sum-integrals via shift sym- metry relations and transforms sum-integrals into the representative of the class they belong to. As its main function, it then implements the Laporta algorithm [1] to identify linearly dependent relations between sum-integrals based on integration-by-parts identities at finite temperature [2], keeping track of bosonic-fermionic signatures of loop momenta. Following techniques analogous to those presented in [3], independent linearly-independent subsystems are parallelized, brought to a triangular form, and back substitution is applied to solve them as a function of the least"},{"citing_arxiv_id":"2604.27314","ref_index":42,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \\rightarrow Z H$","primary_cat":"hep-ph","submitted_at":"2026-04-30T01:55:45+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"230, 99 (2018), arXiv:1705.05610 [hep-ph]. [39] J. Klappert, F. Lange, P. Maierh¨ ofer, and J. Usovitsch, Comput. Phys. Commun.266, 108024 (2021), arXiv:2008.06494 [hep-ph]. [40] S. Laporta, Int. J. Mod. Phys. A 15, 5087 (2000), arXiv:hep-ph/0102033. [41] R. N. Lee, \"Presenting LiteRed: a tool for the Loop InTEgrals REDuction,\" (2012), arXiv:1212.2685 [hep-ph]. [42] R. N. Lee, J. Phys. Conf. Ser. 523, 012059 (2014), arXiv:1310.1145 [hep-ph]. [43] K.-T. Chen, Bull. Am. Math. Soc. 83, 831 (1977). [44] J. M. Henn, Phys. Rev. Lett. 110, 251601 (2013), arXiv:1304.1806 [hep-th]. [45] W. Magnus, Commun. Pure Appl. Math. 7, 649 (1954). [46] S. Blanes, F. Casas, J. Oteo, and J. Ros, Phys. Rept. 470, 151 (2009), arXiv:0810."},{"citing_arxiv_id":"2604.25739","ref_index":22,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Graphical Functions by Examples","primary_cat":"hep-th","submitted_at":"2026-04-28T15:05:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic computability.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"without divergences, and fully general dimensional regularization. Each of these regimes presents its own challenges, and different identities or analytic tools become available depending on the underlying QFT. In some cases, standard techniques such as integration-by-parts (IBP) identities, introduced in [21] and formalized in the Laporta approach [22], or parametric integration methods, as developed in [23], are advantageous and can be applied directly. The latter method exploits the linear reducibility of Feynman integrals in terms of hyperlogarithms, whenever such reducibility is present. It has been fully automated in theHyperIntpackage [24] forMAPLEand inHyperFORM[25] underFORM[26]. These tools provide an efficient framework for performing parametric integrations and expressing"},{"citing_arxiv_id":"2604.18516","ref_index":60,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Three loop QCD corrections to electroweak radiative parameters","primary_cat":"hep-ph","submitted_at":"2026-04-20T17:12:47+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Three-loop QCD corrections to electroweak radiative parameters Δρ, Δr, and Δκ are computed, yielding an updated W boson mass prediction relevant for FCC precision targets.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"Vicini, Phys. Rev. Lett.125, 232004 (2020), arXiv:2007.06518 [hep-ph] . [56] P. Nogueira, J. Comput. Phys.105, 279 (1993). [57] M. Tentyukov and J. A. M. Vermaseren, Com- put. Phys. Commun.181, 1419 (2010), arXiv:hep- ph/0702279 . 8 [58] F. V. Tkachov, Phys. Lett. B100, 65 (1981). [59] K. G. Chetyrkin and F. V. Tkachov, Nucl. Phys. B 192, 159 (1981). [60] S. Laporta, Int. J. Mod. Phys. A15, 5087 (2000), arXiv:hep-ph/0102033 . [61] P. Maierhöfer, J. Usovitsch, and P. Uwer, Comput. Phys. Commun.230, 99 (2018), arXiv:1705.05610 [hep-ph] . [62] J. Klappert, F. Lange, P. Maierhöfer, and J. Uso- vitsch, Comput. Phys. Commun.266, 108024 (2021), arXiv:2008.06494 [hep-ph] . [63] F. Lange, J. Usovitsch, and Z."},{"citing_arxiv_id":"2604.16251","ref_index":38,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Tensor decomposition of $e^+e^-\\to\\pi^+\\pi^-\\gamma$ to higher orders in the dimensional regulator","primary_cat":"hep-ph","submitted_at":"2026-04-17T17:11:49+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"First beyond-NLO tensor decomposition and higher-order analytic one-loop amplitudes for e+e- to pi+pi-gamma, paired with a fast numerical five-point integral evaluator.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"For simplicity, we construct massless mo- menta as follows p♭ i =p i −x i p4 , x i = p2 i 2pi ·p 4 fori= 1,2,3,5. , p♭ 4 =p 4 , (12) where(p ♭ i)2 = 0, and the momentum of the external pho- ton is chosen as the reference momentum for all mas- sive momenta. The explicit construction of all polarised amplitudes is carried out with the aid ofs@M[37] and SpinorsExtras[38]. Because the form factors exhibit a dependence on Gram determinants, already at tree level, the polarised amplitudes are organised such that these denominators cancel, thereby ensuring numerical stability. To achieve this, the polarised amplitudes are constructed as: A(L) h = Φh ˜A(L) h ,(13) whereΦ h encodes the phase dependence on the polarisa-"},{"citing_arxiv_id":"2604.14741","ref_index":85,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"The OPE Approach to Renormalization: Operator Mixing","primary_cat":"hep-th","submitted_at":"2026-04-16T07:53:59+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"Lett. B100(1981) 65. [83] K.G. Chetyrkin and F.V. Tkachov,Integration by parts: The algorithm to calculate β-functions in 4 loops,Nucl. Phys. B192(1981) 159. [84] S.E. Derkachov and A.N. Manashov,The Simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion,Nucl. Phys. B522(1998) 301 [hep-th/9710015]. [85] S. Laporta,High-precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A15(2000) 5087 [hep-ph/0102033]. [86] A.V. Smirnov and F.S. Chukharev,FIRE6: Feynman Integral REduction with modular arithmetic,Comput. Phys. Commun.247(2020) 106877 [1901.07808]. [87] W. Cao, F. Herzog, T. Melia and J.R. Nepveu,Renormalization and non-renormalization of"},{"citing_arxiv_id":"2604.13464","ref_index":63,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion","primary_cat":"hep-th","submitted_at":"2026-04-15T04:34:17+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"Li,On the seven-loop renormalization of Gross-Neveu model,JHEP06(2025) 134, [arXiv:2504.00713]. [61] F. V. Tkachov,A theorem on analytical calculability of 4-loop renormalization group functions,Phys. Lett. B 100(1981) 65-68. [62] K. G. Chetyrkin and F. V. Tkachov,Integration by parts: The algorithm to calculateβ-functions in 4 loops, Nucl. Phys. B192(1981) 159-204. [63] S. Laporta,High-precision calculation of multiloop Feynman integrals by difference equations,Int. J. Mod. Phys. A15(2000) 5087-5159, [hep-ph/0102033]. [64] A. V. Smirnov,Algorithm FIRE - Feynman Integral REduction,JHEP10(2008) 107, [arXiv:0807.3243]. [65] P. Maierh¨ ofer, J. Usovitsch, and P. Uwer,Kira-A Feynman integral reduction program,Comput. Phys."},{"citing_arxiv_id":"2604.09810","ref_index":2,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Feynman integral reduction by covariant differentiation","primary_cat":"hep-ph","submitted_at":"2026-04-10T18:34:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"that are rational functions of Lorentz-invariants such as masses and scalar products of ex- ternal momenta. The number of master integrals is finite [3-5], and they can be computed systematically using the method of differential equations [6-8]. The main task is then to find the above mentioned coefficients, which is usually done by a well-established but relatively complex algorithm [2] that has been implemented in various computer codes [9-21]. Even for quite simple cases, this algorithm needs significant computing time, and it is therefore interesting to explore alternatives [22-29]. The aim of the present paper is to develop a novel way of reducing Feynman integrals to linear combinations of master integrals. It is based on a differential operator (or covariant"},{"citing_arxiv_id":"2604.09534","ref_index":53,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"The four-loop non-singlet splitting functions in QCD","primary_cat":"hep-ph","submitted_at":"2026-04-10T17:52:46+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"Schneider, The 3-loop pure singlet heavy flavor contributions to the structure func- tionF 2(x, Q2)and the anomalous dimension, Nucl. Phys. B890, 48 (2014), arXiv:1409.1135 [hep-ph]. [52] K. G. Chetyrkin, A. L. Kataev, and F. V. Tkachov, New Approach to Evaluation of Multiloop Feynman Integrals: The Gegenbauer Polynomial x Space Technique, Nucl. Phys. B174, 345 (1980). [53] S. Laporta, High precision calculation of multiloop Feyn- man integrals by difference equations, Int. J. Mod. Phys. A15, 5087 (2000), arXiv:hep-ph/0102033. [54] A. von Manteuffel and C. Studerus, Reduze 2 - Distributed Feynman Integral Reduction, (2012), arXiv:1201.4330 [hep-ph]. [55] A. von Manteuffel and R. M. Schabinger, A novel ap- proach to integration by parts reduction, Phys."},{"citing_arxiv_id":"2604.05034","ref_index":13,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Learning to Unscramble Feynman Loop Integrals with SAILIR","primary_cat":"hep-ph","submitted_at":"2026-04-06T18:00:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"A self-supervised transformer learns to unscramble Feynman integrals for online IBP reduction, delivering bounded memory use on complex two-loop topologies while matching Kira's speed on the hardest cases tested.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"in C++,\" Comput. Phys. Commun.181, 1293 (2010), arXiv:0912.2546 [physics.comp-ph]. [11] A. von Manteuffel and C. Studerus, \"Reduze 2 - Distributed Feynman Integral Reduction,\" (2012), arXiv:1201.4330 [hep-ph]. [12] R. N. Lee, \"LiteRed 1.4: a powerful tool for reduction of multiloop integrals,\" J. Phys. Conf. Ser.523, 012059 (2014), arXiv:1310.1145 [hep-ph]. [13] P. Kant, \"Finding linear dependencies in integration-by- parts equations: A Monte Carlo approach,\" Comput. Phys. Commun.185, 1473 (2014), arXiv:1309.7287 [hep- ph]. [14] A. von Manteuffel and R. M. Schabinger, \"A novel ap- proach to integration by parts reduction,\" Phys. Lett. B 744, 101 (2015), arXiv:1406.4513 [hep-ph]. [15] T. Peraro, \"FiniteFlow: multivariate functional recon-"},{"citing_arxiv_id":"2604.05025","ref_index":10,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Feynman integral reduction with intersection theory made simple","primary_cat":"hep-th","submitted_at":"2026-04-06T18:00:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Branch representation reduces the variable count for intersection-theory-based Feynman integral reduction to at most 3L-3 for L-loop integrals regardless of leg number.","context_count":1,"top_context_role":"other","top_context_polarity":"unclear","context_text":"indispensable component in the numerical evaluation of Feynman integrals through techniques such as the auxil- iary mass flow method [7]. In the IBP reduction procedure, one must generate and subsequently solve a large system of linear equa- tions, typically employing the Laporta algorithm [8, 9]. Several well-developed program packages have been cre- ated for this purpose, includingFIRE[10],Reduze[11], LiteRed[12], andKira[13, 14]. The computational complexity of the linear system escalates considerably as either the number of loops or the number of exter- nal legs increases. For cutting-edge problems in high- precision perturbation theory, solving these linear sys- tems demands substantial computational resources and has emerged as a significant bottleneck."},{"citing_arxiv_id":"2603.15751","ref_index":33,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"The photon-energy spectrum in $B\\to X_s\\gamma$ to N$^3$LO: light-fermion and large-$N_{\\rm c}$ corrections","primary_cat":"hep-ph","submitted_at":"2026-03-16T18:00:08+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"N3LO calculation of the B to Xs gamma photon spectrum including complete light-fermion corrections, two massive fermion loops, and large-Nc terms, with improved results in kinetic and MSR mass schemes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2603.11164","ref_index":38,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories","primary_cat":"hep-th","submitted_at":"2026-03-11T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A permutation-equivariant transformer trained on self-supervised oracle trajectories from scrambled expressions achieves near-perfect simplification rates for dilogarithms and 100% success on 5-point gluon scattering amplitudes with over 200 terms.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2601.08252","ref_index":6,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Resumming Scattering Amplitudes for Waveforms","primary_cat":"hep-th","submitted_at":"2026-01-13T06:19:05+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A new projector-based formalism determines effective potentials from perturbative amplitudes and resums them to compute non-perturbative gravitational waveforms for generic two-body trajectories.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2512.21210","ref_index":9,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics","primary_cat":"hep-th","submitted_at":"2025-12-24T14:49:21+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Twisted Feynman integrals are introduced with graded Symanzik polynomials, classified as exponential periods, and shown to have geometry not inferable from generalized Baikov leading singularities.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, \"One loop n point gauge theory amplitudes, unitarity and collinear limits,\"Nucl. Phys. B425(1994) 217-260, arXiv:hep-ph/9403226. [8] Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, \"Fusing gauge theory tree amplitudes into loop amplitudes,\"Nucl. Phys. B435(1995) 59-101, arXiv:hep-ph/9409265. [9] S. Laporta, \"High-precision calculation of multiloop Feynman integrals by difference equations,\"Int. J. Mod. Phys. A15(2000) 5087-5159,arXiv:hep-ph/0102033. [10] G. Ossola, C. G. Papadopoulos, and R. Pittau, \"Reducing full one-loop amplitudes to scalar integrals at the integrand level,\"Nucl. Phys. B763(2007) 147-169, arXiv:hep-ph/0609007. [11] J. M."},{"citing_arxiv_id":"2511.15381","ref_index":22,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"New algorithms for Feynman integral reduction and $\\varepsilon$-factorised differential equations","primary_cat":"hep-th","submitted_at":"2025-11-19T12:16:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2511.11424","ref_index":100,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Double virtual QCD corrections to $t\\bar{t}+$jet production at the LHC","primary_cat":"hep-ph","submitted_at":"2025-11-14T15:52:56+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"F(L2)h3h4h5 x = 4X i,j=1 h ˜F(L1)h3h4h5 x;i i∗ Ω−1\u0001 ij ˜F(L2)h3h4h5 x;j ,(3.20) where we sum over the massive top polarisations. Our representation for the amplitude makes the inclusion of top-quark decays within the narrow-width approximation straightforward: the decay amplitude can be directly attached to the massive spinor structures in eq. (3.5) [100, 101]. We compute analytically the contracted helicity finite remainders˜F(L)h3h4h5 x;i for the indepen- dent helicity configurations with the same framework successfully employed in a number of two-loop five-point amplitude calculations [50, 58, 59], combining Feynman diagrams, four-dimensional pro- jectors, integration-by-part (IBP) reduction, special function bases and finite-field arithmetic."},{"citing_arxiv_id":"2505.10406","ref_index":55,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"One-loop amplitudes for $t\\bar{t}j$ and $t\\bar{t}\\gamma$ productions at the LHC through $\\mathcal{O}(\\epsilon^2)$","primary_cat":"hep-ph","submitted_at":"2025-05-15T15:28:36+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2504.06689","ref_index":43,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist","primary_cat":"hep-ph","submitted_at":"2025-04-09T08:50:05+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"Multi-loop Collider Phenomenology: A Snowmass 2021 White Paper, Comput. Softw. Big Sci.6(2022) no. 1, 14,arXiv:2204.04200 [hep-ph]. 8 [41] F. V. Tkachov,A theorem on analytical calculability of 4-loop renormalization group functions, Phys. Lett. B100(1981) 65-68. 8 [42] K. G. Chetyrkin and F. V. Tkachov,Integration by parts: The algorithm to calculate β-functions in 4 loops, Nucl. Phys. B192(1981) 159-204. 8 [43] S. Laporta,High-precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A15(2000) 5087-5159,arXiv:hep-ph/0102033. 8 [44] T. Gehrmann and E. Remiddi,Differential equations for two-loop four-point functions, Nucl. Phys. B580(2000) 485-518,arXiv:hep-ph/9912329. 8 [45] O. V. Tarasov,Connection between Feynman integrals having different values of the"},{"citing_arxiv_id":"2411.11846","ref_index":74,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Emergence of Calabi-Yau manifolds in high-precision black hole scattering","primary_cat":"hep-th","submitted_at":"2024-11-18T18:59:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"At 5PM-1SF order, Calabi-Yau three-fold periods emerge in radiation-reacted observables for classical black hole scattering computed with worldline QFT and advanced IBP/DE methods.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2008.06494","ref_index":31,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Integral Reduction with Kira 2.0 and Finite Field Methods","primary_cat":"hep-ph","submitted_at":"2020-08-14T17:58:33+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"1906.11862","ref_index":26,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons","primary_cat":"hep-ph","submitted_at":"2019-06-27T18:24:17+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}