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New features of FORM
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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.
Forward citations
Cited by 38 Pith papers
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Probing Heavy-Quark Spin Symmetry in Double $J/\psi$ Hadroproduction
A complete O(alpha_s^5) NRQCD calculation for prompt J/psi pair hadroproduction finds LHC data fix one combination of color-octet LDMEs, yielding a set that tests heavy-quark spin symmetry via eta_c data.
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Analytic two-loop amplitudes for $q\bar{q}\to \gamma \gamma$ and $gg \to \gamma \gamma$ mediated by a heavy-quark loop
The two-loop amplitudes for q qbar -> gamma gamma and gg -> gamma gamma with a heavy-quark loop are computed analytically in terms of elliptic iterated integrals, with validated fast series expansions for numerical ev...
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Investigating the universality of five-point QCD scattering amplitudes at high energy
First extraction of the two-loop universal central-emission vertex in QCD and in N=4 super Yang-Mills from the multi-Regge limit of five-point amplitudes.
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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.
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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.
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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 s...
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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.
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Radiative return at NLOPS accuracy
First implementation of NLO corrections matched to a parton shower for the radiative processes e+e−→π+π−γ and e+e−→μ+μ−γ, including ISR, FSR and their interference.
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One-loop matching of the LEFT to the QCD gradient flow
All one-loop matching coefficients connecting the full baryon- and lepton-number-conserving low-energy effective field theory up to dimension six to the QCD gradient flow are computed.
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$B$-meson decay width up to $1/m_b^3$ corrections within and beyond the Standard Model
Complete analytic HQE matching coefficients for B-meson decay widths up to 1/m_b^3 are derived for generic new-physics operators, including previously missing weak-annihilation terms.
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Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops
First five-loop renormalization group functions for the O(N) Gross-Neveu-Yukawa model, yielding refined, resummed critical exponent estimates for N=1, 2, and 5.
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Cosmological phase transitions without high-temperature expansions
A hard-soft split combined with a finite-temperature Loop-Tree Duality method computes the resummed 4d thermal effective potential without high-temperature expansions, demonstrated in a scalar-Yukawa model.
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Two-loop helicity amplitudes for diphoton production with massive quark loop
Two-loop helicity amplitudes for diphoton production with a massive top quark loop are computed, providing new analytic results for gluon fusion and benchmark numbers for both channels.
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Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks
Spectral lattice artifacts for unrooted staggered quarks scale as a^2 [2 b0 gbar^2(1/a)]^gamma, with the smallest exponents near -0.3 for N_f=0,4 and near -0.9 and -2.6 for N_f=8,12.
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Catalogues of Cosmologically Self-Consistent Hadronic QCD Axion Models
Hadronic axion models with d=6 and d=7 heavy-quark decay operators can produce two new cosmologically viable 'islands' at f_a ~ 10^12 and 10^14 GeV, extending the post-inflationary axion search window.
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HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model
HQET sum rules yield the first four-quark bag parameters for B-meson lifetimes with beyond-standard-model operators, plus updated standard-model results.
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Renormalization-group equations of the LEFT at two loops: dimension-five effects
The complete two-loop renormalization-group equations for the dimension-five LEFT sector, derived in a chirally symmetric scheme, with two methods that avoid gauge-variant nuisance operators.
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The Ramanujan Challenge For AI
A benchmark of new continued fractions, recurrences, series and integrals for classical constants, split into encrypted-proof problems and open conjectures for testing AI mathematical reasoning.
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Heavy Jet Mass in Hadronic Higgs Decays
Heavy jet mass in hadronic Higgs decays is predicted at N³LL′ (dijet) plus NNLL (Sudakov shoulder) plus NNLO, with new analytic trijet-region logarithms for H→gg and H→q̄q.
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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 re...
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Top-associated Higgs-boson production using perturbative fragmentation functions at next-to-leading-order
Perturbative fragmentation functions reproduce the leading top-mass dependence of the exact NLO ttH cross section in the hybrid prescription at LHC energies.
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Fast evaluation of Feynman integrals for Monte Carlo generators
A new numerical integrator evaluates one- and two-loop five-point Feynman integrals with complex masses in milliseconds, using variable-by-variable integration and a new branch-cut prescription.
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Effect of anomalous $HHH$ coupling on the decay $H\rightarrow Z\,Z^*\rightarrow$ 4 charged leptons
The H to 4 lepton partial width shifts by up to about 6 percent at one loop when the Higgs trilinear coupling is anomalous, offering a new observable for the Higgs self-coupling.
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Double Higgs Production in Vector Boson Fusion at NLO QCD in HEFT
Full NLO QCD predictions for pp -> hhjj production in VBF with HEFT couplings cλ, cV, c2V, including non-factorising and Higgs-strahlung diagrams, show that some allowed coupling combinations reshape key observables.
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Boundary Curvature Scalars on Conformally Compact Manifolds
Five CC boundary curvature scalars are constructed explicitly, yielding conformal invariants, singular Yamabe expansion coefficients, and Dirichlet-to-Neumann maps.
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T-odd observables from anomalous $tbW$ couplings in single-top W associated production at the LHC
T-odd observables in pp to tW- X are predicted to depend only on Im f2R among anomalous tbW couplings, with projected 1-sigma limits near 10^-2 at the LHC.
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Four loop renormalization of QCD in the Curci-Ferrari gauge
The four-loop renormalization of QCD in the Curci-Ferrari gauge is completed, reproducing the known beta function via a Slavnov-Taylor identity and giving new five-loop results in the mMOM scheme.
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Triple real-emission contribution to the zero-jettiness soft function at N3LO in QCD
The paper provides the technical derivation and cross-checks of the triple-real-emission piece of the N3LO zero-jettiness soft function, confirming the result announced in arXiv:2409.11042.
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$e^+ e^- \to \mu^+ \mu^-$ in the Asymptotically Safe Standard Model
Using reconstructed timelike graviton spectral functions, the authors find that the e+e- to mu+mu- cross-section in the asymptotically safe Standard Model falls as 1/s in the ultraviolet and is compatible with unitarity.
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Four loop Green's functions involving the $n$ $=$ $2$ moment of the Wilson operator
Four-loop MSbar expressions are computed for all single-scale quark two-point Green's functions with a second-moment twist-2 Wilson operator insertion, including operator mixing and operator correlation functions.
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Next-to-leading order QCD corrections to $Z\to q\bar{q}\gamma$, $q\bar{q}\gamma\gamma$
NLO QCD corrections reduce the predicted widths of Z to two jets plus one photon by 6.03% and to two jets plus two photons by 12.39%.
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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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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.
- IBIS: Inverse BInomial sum Solver
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