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.
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abstract
Version 3 of FORM is introduced. It contains many new features that are inspired by current developments in the methodology of computations in quantum field theory. A number of these features is discussed in combination with examples. In addition the distribution contains a number of general purpose packages. These are described shortly.
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UNVERDICTED 20representative citing papers
First complete two-loop calculation of electron EDM and LFV decay rates μ→eγ, τ→e/μγ in the unconstrained 2HDM with general Yukawas and phases, with public Python code.
The anomalous dimension of |ΔS|=1 current-current operators is calculated analytically at NNNLO in QCD, with basis transformation rules provided.
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
Computes three-loop renormalization constants and pure-singlet axial-vector form factor contributions for SU(N)×U(1) using form factors and IR divergence universality.
Computes two-loop jet functions for N=4,5,6 projected energy correlators enabling NNLL collinear resummation matched to NLO in e+e- and Higgs-to-gluons processes, with non-perturbative corrections from two universal soft matrix elements.
The heavy-quark condensate is computed at five-loop order in QCD with massive quarks, confirming the five-loop vacuum anomalous dimension.
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new small-x logarithmic structure.
The zeta(3)-proportional contribution to the four-loop twist-two gluon anomalous dimension gamma_gg^(3)(N) is constructed in analytic form from low-N moments via the LLL algorithm together with reciprocity and supersymmetric constraints.
N³LO QCD predictions for photon-pair production are presented, demonstrating perturbative convergence.
Three-loop renormalization constants and anomalous dimensions are derived analytically for three-quark operators with derivatives in QCD, confirming prior N=0 results and enabling lattice matching.
FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.
SCET factorization confirms the double-logarithmic resummation for B_c to eta_c form factors up to three loops and derives the iterative structure from RG equations of light-cone distribution amplitudes with cutoff regularization.
A unified Lagrangian framework connects supersymmetric and non-supersymmetric scalar-fermion theories and supplies Ward identities that simplify computations of anomalous dimensions in the non-supersymmetric case.
Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.
Tau weak dipole moments already rank among the leading probes of tau dipole operators and will become dominant at FCC-ee and HL-LHC.
Perturbative fragmentation functions approximate ttH production at NLO and yield reliable results in the hybrid prescription at LHC energies.
Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.
Historical review tracing the evolution of precision perturbative QCD calculations and tools between 1976 and 2000.
citing papers explorer
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Emergence of Calabi-Yau manifolds in high-precision black hole scattering
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.
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Electron EDM and $\Gamma(\mu \to e \gamma)$ in the 2HDM
First complete two-loop calculation of electron EDM and LFV decay rates μ→eγ, τ→e/μγ in the unconstrained 2HDM with general Yukawas and phases, with public Python code.
-
Four-loop QCD mixing of current-current operators
The anomalous dimension of |ΔS|=1 current-current operators is calculated analytically at NNNLO in QCD, with basis transformation rules provided.
-
The four-loop non-singlet splitting functions in QCD
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
-
Renormalization of axial anomaly in SU(N)$\times$U(1)
Computes three-loop renormalization constants and pure-singlet axial-vector form factor contributions for SU(N)×U(1) using form factors and IR divergence universality.
-
Projected Energy Correlators: Two-Loop Jet Functions and NNLL Resummation
Computes two-loop jet functions for N=4,5,6 projected energy correlators enabling NNLL collinear resummation matched to NLO in e+e- and Higgs-to-gluons processes, with non-perturbative corrections from two universal soft matrix elements.
-
Heavy-Quark Condensate and Vacuum Energy Anomalous Dimension at Five Loops
The heavy-quark condensate is computed at five-loop order in QCD with massive quarks, confirming the five-loop vacuum anomalous dimension.
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All-loop four-quark Bethe-Salpeter kernel
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
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Properties and implications of the four-loop non-singlet splitting functions in QCD
Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new small-x logarithmic structure.
-
Four-Loop Gluon Anomalous Dimension of General Lorentz Spin: Transcendental Part
The zeta(3)-proportional contribution to the four-loop twist-two gluon anomalous dimension gamma_gg^(3)(N) is constructed in analytic form from low-N moments via the LLL algorithm together with reciprocity and supersymmetric constraints.
-
Next-to-next-to-next-to-leading order QCD corrections to photon-pair production
N³LO QCD predictions for photon-pair production are presented, demonstrating perturbative convergence.
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Renormalization of three-quark operators with up to two derivatives at three loops
Three-loop renormalization constants and anomalous dimensions are derived analytically for three-quark operators with derivatives in QCD, confirming prior N=0 results and enabling lattice matching.
-
FunKit: A computer algebra toolkit for functional approaches
FunKit is a computer algebra toolkit that automates derivation of functional equations such as Dyson-Schwinger and functional RG from arbitrary master equations, with tracing via FORM and export to numerical code.
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$B_c \to \eta_c$ form factors at large recoil: SCET analysis and a three-loop consistency check
SCET factorization confirms the double-logarithmic resummation for B_c to eta_c form factors up to three loops and derives the iterative structure from RG equations of light-cone distribution amplitudes with cutoff regularization.
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Connecting Supersymmetry to Non-Supersymmetric theories: the Gross-Neveu-Yukawa example
A unified Lagrangian framework connects supersymmetric and non-supersymmetric scalar-fermion theories and supplies Ward identities that simplify computations of anomalous dimensions in the non-supersymmetric case.
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Tracing Transcendentality in Protected Correlators of N=4 SYM
Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.
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Current and future constraints on heavy New Physics from $\tau$ weak dipole moments
Tau weak dipole moments already rank among the leading probes of tau dipole operators and will become dominant at FCC-ee and HL-LHC.
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Top-associated Higgs-boson production using perturbative fragmentation functions at next-to-leading-order
Perturbative fragmentation functions approximate ttH production at NLO and yield reliable results in the hybrid prescription at LHC energies.
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Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations
Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.
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Perturbative QCD as a quantitative tool in the years 1976-2000
Historical review tracing the evolution of precision perturbative QCD calculations and tools between 1976 and 2000.