{"total":15,"items":[{"citing_arxiv_id":"2605.29789","ref_index":39,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Magic Relations and Critical Varieties of Feynman Integrals","primary_cat":"hep-th","submitted_at":"2026-05-28T11:40:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.13256","ref_index":21,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Factorization of denominators as a `fuel' for Feynman integral reduction","primary_cat":"hep-ph","submitted_at":"2026-05-13T09:39:49+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Algorithms that factor denominators in IBP coefficients inside the FUEL interface reduce reconstruction cost and improve robustness of large-scale Feynman integral reductions.","context_count":1,"top_context_role":"baseline","top_context_polarity":"baseline","context_text":"to represent all integrals belonging to a given family (defined by a particular set of propagators) in terms of a finite set of simpler integrals known as master integrals. Normally, a reduction means combining IBP identities in nontrivial ways. A systematic procedure for this is the so-called Laporta algorithm [20]. Several public implementations of this algorithm exist, includingAIR[2],Reduze[40, 25],LiteRed[21, 22],FIRE[35, 36, 37, 38, 39], andKira [19, 20, 21, 22, 23, 24]. There are two competitive approaches to Feynman integral reduction, a classical one when one directly solves the system of equations and an alternative one with the modular approach when reduction is performed multiple times for fixed values of kinematic invariants and then a reconstruc-"},{"citing_arxiv_id":"2605.09541","ref_index":21,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"An Algorithm for the Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions","primary_cat":"hep-ph","submitted_at":"2026-05-10T13:53:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A new generating-function framework turns IBP relations into differential equations in a non-commutative algebra, yielding an iterative algorithm that derives symbolic reduction rules and checks completeness for topologies such as the sunset and double-box diagrams.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"arXiv:hep-ph/0404258, doi:10.1088/1126-6708/2004/07/046. [19] A. V. Smirnov. Algorithm fire - feynman integral reduction. JHEP, 10:107, 2008. arXiv:0807.3243, doi:10.1088/1126-6708/2008/10/107. [20] C. Studerus. Reduze - feynman integral reduction in c++. Comput. Phys. Commun. , 181:1293-1300, 2010. arXiv:0912.2546, doi:10.1016/j.cpc.2010.03.012. [21] R. N. Lee. Presenting litered: a tool for the loop integrals reduction. 2012. arXiv:1212.2685. [22] Roman N. Lee. Litered 1.4: a powerful tool for reduction of multiloop integrals. J. Phys. Conf. Ser. , 523:012059, 2014. doi:10.1088/1742-6596/523/1/012059. [23] Christoph Dlapa, Gregor Kälin, Zhengwen Liu, and Rafael A. Porto. Nonlocal-in-time tail"},{"citing_arxiv_id":"2605.06775","ref_index":82,"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":"background","top_context_polarity":"background","context_text":"the analysis of cosmological PTs to high loop orders [40, 53, 78], where analogous sum- integral structures arise. As acknowledged in the aforementioned works, the conceptual framework underlying these techniques closely parallels that of regular Feynman integrals, where they have been automated in a series of public computer algebra packages (Air[79],FIRE7[80], Reduze2[81],LiteRed[82] andKira3[83]) 1. The main diverging point is the evaluation of MSI, where the Matsubara sum prevents the extension of the known techniques at zero temperature, and has so far forced the study of solutions on a case-by-case basis (see [72] 1See [84] and references therein for a thorough review on the development and historical versions of these packages."},{"citing_arxiv_id":"2604.27314","ref_index":43,"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":"However, obtaining analytic solutions to such multivariable systems of differential equations is, in general, a highly nontrivial task. If there exists a basis ⃗ g(⃗ x, ϵ) in which the differential equations can be cast into a canonical (or ϵ-factorized) form, d⃗ g(⃗ x, ϵ) = ϵ dA (⃗ x) ⃗ g(⃗ x, ϵ) , (9) the system simplifies considerably, and its solution can be written in terms of Chen's iterated integrals [43], ⃗ g(⃗ x, ϵ) = P exp \u0010 ϵ Z γ dA \u0011 ⃗ g(⃗ x0, ϵ) , (10) 6 where P denotes the path-ordering operator, and γ is an integration path connecting ⃗ x0 to ⃗ x. This approach is known as the canonical differential-equations method [44], and the corresponding set of MIs is referred to as a canonical basis. Several approaches have been developed for constructing a canonical basis, including the Magnus expansion [45-47], d log"},{"citing_arxiv_id":"2604.19232","ref_index":96,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Progress on the soft anomalous dimension in QCD","primary_cat":"hep-ph","submitted_at":"2026-04-21T08:36:24+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A lightcone-expansion strategy using Wilson-line correlators and the Method of Regions yields the three-loop soft anomalous dimension for QCD amplitudes with one massive colored particle and arbitrary massless ones.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"are hard, while the green, orange and brown gluons are collinear to the𝑖,𝑗and𝑘directions, respectively. The blob represents all the possible ways in which the four gluons connect through a single 4-gluon vertex or two 3-gluon vertices. Weusethemethodofdifferentialequationtocomputetheregionintegrals. Usingthepackages AmpRed[89],Kira[93-95] andLiteRed[96, 97], we derive the differential equation for a subset of the regions of one channel, obtaining the rest by permutations. In addition to the singularities at𝑟 𝑢𝑣𝑄 → {0,1,∞}(represented by the physical alphabet in Eq. (37) below), the differential equations display singularities also atΔ1 →0andΔ 2 →0, where Δ1 =𝜅(𝑟 𝑖 𝑗𝑄 , 𝑟𝑖𝑘𝑄 , 𝑟 𝑗 𝑘𝑄),Δ 2 = Δ 1 +4𝑟 𝑖 𝑗𝑄𝑟 𝑗 𝑘𝑄𝑟𝑖𝑘𝑄 , (30)"},{"citing_arxiv_id":"2604.18516","ref_index":64,"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":"by in-houseFORM[57] routines, which translates the di- agrams into Feynman amplitudes and performs the Dirac, Lorentz, and color algebra. The resulting expressions con- sist of∼ O(10 4)scalar Feynman integrals. We employ the standard method of Integration-By-Parts (IBP) reduction [58-60]toreducethescalarintegralsto94MasterIntegrals (MIs). We have utilized the public codesKira[61-63] and LiteRed[64, 65] to perform the IBP reduction. The primary task lies in the evaluation of the three- loop two-point MIs at the kinematic scalesq 2 = 0and q2 =m 2 V (whereV∈ {Z, W}). From two-loop onward, the analytic structure of the MIs becomes complex, fre- quently involving elliptic multiple polylogarithms. Hence, we solve the MIs using a system of differential equations"},{"citing_arxiv_id":"2604.16251","ref_index":41,"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":"Integration-by-parts identities [46-48] are used to re- duce the integrals that appear in the form factors into a minimal set of master integrals that obey a canonical system of differential equations [49], which were obtained by studying their leading and Landau singularities [50]. We opt to useLiteRed[51] to generate IBP relations among integrals and master integrals, and then employ FiniteFlow[41] to solve over finite fields the resulting linear systems of integrals in terms of master integrals. Since in this work we are interested in calculating the form factors up toO(ϵ 2)we calculate master integrals up to transcendental weight four. We note that the master integrals corresponding to the pentagon family shown in Fig. 2b were recently evaluated in [21], together"},{"citing_arxiv_id":"2604.09810","ref_index":12,"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":"background","top_context_polarity":"background","context_text":"[9] C. Anastasiou and A. Lazopoulos,Automatic integral reduction for higher order perturbative calculations,JHEP07(2004) 046 [hep-ph/0404258]. [10] C. Studerus,Reduze - Feynman integral reduction in C++,Comput. Phys. Commun. 181(2010) 1293 [0912.2546]. [11] A. von Manteuffel and C. Studerus,Reduze 2 - Distributed Feynman Integral Reduction,1201.4330. [12] R. N. Lee,Presenting LiteRed: a tool for the Loop InTEgrals REDuction,1212.2685. [13] R. N. Lee,LiteRed 1.4: a powerful tool for reduction of multiloop integrals,J. Phys. Conf. Ser.523(2014) 012059 [1310.1145]. [14] A. V. Smirnov,Algorithm FIRE - Feynman Integral REduction,JHEP10(2008) 107 [0807.3243]. [15] A. V. Smirnov and V. A. Smirnov,FIRE4, LiteRed and accompanying tools to solve"},{"citing_arxiv_id":"2604.08332","ref_index":19,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Discrete symmetries of Feynman integrals","primary_cat":"hep-th","submitted_at":"2026-04-09T15:06:06+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"There is a natural filtration bysectors, coming from the set of propagators that are raised to positive powers. Understanding the symmetries of the family allows one to relate integrals from different sectors to each other [18-20]. This may speed up the solution of the IBP system, and various public tools for IBP reduction try to exploit symmetries [19, 21-30]. These symmetries, however, are often determined in a heuristic manner, and their structure is still relatively poorly understood. For example, it was recently observed that there are symmetries between sectors that require kinematics-dependent transformations [20], and these symmetries had not been considered by IBP reduction codes so far."},{"citing_arxiv_id":"2603.15751","ref_index":51,"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":"2602.06947","ref_index":135,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"The gravitational Compton amplitude at third post-Minkowskian order","primary_cat":"hep-th","submitted_at":"2026-02-06T18:44:09+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"ph]. [132] R. N. Lee, (2012), arXiv:1212.2685 [hep-ph]. [133] R. N. Lee,Proceedings, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2013), J. Phys. Conf. Ser. 523, 012059 (2014), arXiv:1310.1145 [hep-ph]. [134] SinceK 3 =K 2 andK 6 =K 5, our master integral basis is, in principle, overdetermined. [135] Z. Bern, L. J. Dixon, and D. A. Kosower, Nucl. Phys. B412, 751 (1994), arXiv:hep-ph/9306240. [136] E.Remiddi,NuovoCim.A110,1435(1997),arXiv:hep- th/9711188. [137] J. M. Henn, Phys. Rev. Lett.110, 251601 (2013), arXiv:1304.1806 [hep-th]. [138] R. A. Matzner and M. P. Ryan, Phys. Rev. D16, 1636 (1977). [139] S. R. Dolan, Class. Quant. Grav.25, 235002 (2008),"},{"citing_arxiv_id":"2504.06689","ref_index":53,"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":"The use of integration-by-parts (IBP) identities [41-43], Lorenz invariance (LI) [44], and dimension shift relations [45,46] remains a critically important technique in modern loop cal- culations, but also presents a major bottleneck. Several efficient codes exist to facilitate their use, including:Air[47],Fire[48-51] (recently updated in Ref. [52]),LiteRed[53,54],Re- duze[55,56], andKira[57-59]. TheBladereduction package [60] aims to reduce the total time to obtain a reduction by generating block-triangular IBP systems, which can be orders of magnitude smaller than traditional tools. TheNeatIBPtool [61] uses syzygy and module intersection techniques to provide IBP systems in which the propagator degrees are limited."},{"citing_arxiv_id":"2001.04407","ref_index":27,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"FeynCalc 9.3: New features and improvements","primary_cat":"hep-ph","submitted_at":"2020-01-13T17:17:50+00:00","verdict":"ACCEPT","verdict_confidence":"MODERATE","novelty_score":3.0,"formal_verification":"none","one_line_summary":"FeynCalc 9.3 adds improved interoperability, UV divergence extraction, Majorana fermion support, and explicit Dirac index handling to the existing symbolic QFT package.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"1906.11862","ref_index":39,"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}