Next-to-leading Order Research Articles

A phenomenological analysis of LHC neutrino scattering at NLO accuracy matched to parton showers

AbstractWe perform a detailed phenomenological study of high-energy neutrino deep inelastic scattering (DIS) focused on LHC far-forward experiments such as FASER$$\nu $$ ν and SND@LHC. To this aim, we parametrise the neutrino fluxes reaching these LHC far-forward experiments in terms of ‘neutrino PDFs’ encoding their energy and rapidity dependence by means of the LHAPDF framework. We integrate these neutrino PDFs in the recently developed POWHEG-BOX-RES implementation of neutrino-induced DIS to produce predictions accurate at next-to-leading order (NLO) in the QCD coupling matched to parton showers (PS) with Pythia8. We present NLO+PS predictions for final-state distributions within the acceptance for FASER$$\nu $$ ν and SND@LHC as well as for two experiments of the proposed Forward Physics Facility (FPF), FASER$$\nu $$ ν 2 and FLArE. We quantify the impact of NLO QCD corrections, of the parton showering and hadronisation settings in Pythia8, of the QED shower, and of the incoming neutrino flavour for the description of these observables, and compare our predictions with the GENIE neutrino event generator. Our work demonstrates the relevance of modern higher-order event generators to achieve the key scientific targets of the LHC neutrino experiments.

QCD corrections at subleading power for inclusive nonleptonic b→cu¯d decays

In this paper we compute the next-to-leading order (NLO) QCD corrections for the inclusive nonleptonic decay rates of B hadrons at subleading power of the heavy quark expansion. In particular, we discuss the coefficient of the chromomagnetic moment parameter μG, which has a large uncertainty at leading order due to its dependence on the renormalization scale. We find that the renormalization-scale dependence of this coefficient is significantly reduced, thereby reducing the theoretical uncertainty of the coefficient and, consequently, the rates. The sign of the coefficient becomes stable, and we estimate that the NLO corrections will increase the decay rates by around 2%. Published by the American Physical Society 2024

Exclusive vector-quarkonium photoproduction at NLO in αs in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation

We perform the first complete one-loop study of exclusive photoproduction of vector quarkonia off protons in Collinear Factorisation (CF) including the scale evolution of the Generalised Parton Distributions (GPDs). We confirm the perturbative instability of the cross section at high photon-proton-collision energies (Wγp) at Next-to-Leading Order (NLO) in αs and solve this issue by resumming higher-order QCD corrections, which are enhanced by a logarithm of the parton energies, using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA) matched to CF. Our NLO CF ⊕ DLA HEF results are in agreement with the latest HERA data, show a smaller sensitivity to the factorisation and renormalisation scales compared to Born-order results. Quark-induced channels via interference with gluon ones are found to contribute at most 20% of the cross section for Wγp>100 GeV. Our results also show that such exclusive cross sections cannot be accurately obtained from the square of usual Parton Distribution Functions (PDFs) and clearly illustrate the importance of quarkonium exclusive photoproduction to advance our understanding of the 3D content of the nucleon in terms of gluons. Our work provides an important step towards a correct interpretation of present and future experimental data collected at HERA, the EIC, the LHC and future experiments.

Effective field theory descriptions of Higgs boson pair production

Higgs boson pair production is traditionally considered to be of particular interest for a measurement of the trilinear Higgs self-coupling. Yet it can offer insights into other couplings as well, since – in an effective field theory (EFT) parameterisation of potential new physics – both the production cross section and kinematical properties of the Higgs boson pair depend on various other Wilson coefficients of EFT operators. This note summarises the ongoing efforts related to the development of EFT tools for Higgs boson pair production in gluon fusion, and provides recommendations for the use of distinct EFT parameterisations in the Higgs boson pair production process. This document also outlines where further efforts are needed and provides a detailed analysis of theoretical uncertainties. Additionally, benchmark scenarios are updated. We also re-derive a parameterisation of the next-to-leading order (NLO) QCD corrections in terms of the EFT Wilson coefficients both for the total cross section and the distribution in the invariant mass of the Higgs boson pair, providing for the first time also the covariance matrix. A reweighting procedure making use of the newly derived coefficients is validated, which can be used to significantly speed up experimental analyses.

Asymmetries in invisible dark matter mediator production associated with tt¯ final states

In this paper, we propose two sets of different CP-sensitive observables inspired by the Higgs production in association with the top quark. We employ a dark matter simplified model that couples a scalar mediator with top quarks. The reconstruction of the kinematic variables is presented at next to leading order (NLO) accuracy for events associated with this massive scalar particle, which is assumed to be vanishing to invisible decays in a detector such as ATLAS. We build these observables by taking advantage of the similarity between the scalar coupling with the top quark and the factorization theorem in the total scattering amplitude, in order to represent the basis in which the phase space is parametrized. A twofold approach employs the direct implementation of the four-momentum phase space measure in building CP sensitive observables such as b2 for the Higgs, and the spin polarization of the top-quark decays in the narrow width approximation for the employed model. We studied the asymmetries of these distributions to test for any improvement in increasing the exclusion region for the gu33S−gu33P parameters associated with this vanishing scalar particle. We have found no significant effect in the exclusion limits by using the forward-backward asymmetry distributions and the full-shaped ones. Considering the case of an invisible mediator with mass of 10−2 GeV for a luminosity of 300 fb−1 expected at the end of Run 3, the best limits for gu33S and gu33P at NLO accuracy were obtained using the variables b˜2y^ and b2 respectively, with corresponding limits set to [−0.0425,0.0425] and [−0.83,0.83] at 68% CL. Published by the American Physical Society 2024

HighTEA: high energy theory event analyser

We introduce HighTEA, a new paradigm for deploying fully-differential next-to-next-to leading order (NNLO) calculations for collider observables. In principle, any infrared safe observable can be computed and, with very few restrictions, the user has complete freedom in defining their calculation’s setup. For example, one can compute generic n-dimensional distributions, can define kinematic variables and factorization/renormalization scales, and can modify the strong coupling and parton distributions. HighTEA operates on the principle of analyzing precomputed events. It has all the required hardware and software infrastructure such that users only need to request their calculation via the internet before receiving the results, typically within minutes, in the form of a histogram. No specialized knowledge or computing infrastructure is required to fully utilize HighTEA, which could be used by both experts in particle physics and the general public. The current focus is on all classes of Large Hadron Collider (LHC) processes. Extensions beyond NNLO, or to e + e − colliders, are natural next steps.

Release note: VBFNLO 3.0

Vbfnlo is a flexible parton level Monte Carlo program for the simulation of vector boson fusion (VBF), QCD-induced single and double vector boson production plus two jets, and double and triple vector boson production (plus jet) in hadronic collisions at next-to-leading order (NLO) in the strong coupling constant, as well as Higgs boson plus two and three jet production via gluon fusion at the one-loop level. For the new version – Version 3.0 – several major enhancements have been included. An interface according to the Binoth Les Houches Accord (BLHA) has been added for all VBF and di/tri-boson processes including fully leptonic decays. For all dimension-8 operators affecting vector boson scattering (VBS) processes, a modified T-matrix unitarization procedure has been implemented. Several new production processes have been added, namely the VBS Zγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z\\gamma jj$$\\end{document} and γγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\gamma jj$$\\end{document} processes at NLO, γγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\gamma jj $$\\end{document}, WWj and ZZj production at NLO including the loop-induced gluon-fusion contributions and the gluon-fusion one-loop induced Φjjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi jjj$$\\end{document} (Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document} is a CP-even or CP-odd scalar boson) process at LO, retaining the full top-mass dependence. Finally, the code has been parallelized using Openmpi.

New renormalization scheme in the two Higgs doublet models

We propose a new renormalization scheme in the two Higgs doublet models with a softly-broken Z2 symmetry and CP-conservation in the Higgs sector. In this scheme, counterterms for mixing angles of the Higgs bosons are determined by using the decay rates of the discovered Higgs boson h, i.e., h→τ+τ− and h→ZZ⁎→Zℓ+ℓ− at next leading order (NLO) instead of using the renormalized two-point functions which are adopted in the previous scheme. We require that the decay rates at NLO are determined to be the corresponding predictions at NLO in the Standard Model (SM) times square of the scaling factor which describes the deviation of h couplings at tree level from the SM value. The mixing angles then maintain the meaning of the “alignmentness”, i.e., how the properties of h are close to the SM predictions, while they lose such meaning in the previous scheme. We compare the predictions of the decay rates at NLO given in the new scheme and those in the previous scheme.

Next-to-leading-order electroweak correction to H→Z0γ

Inspired by the recent observation of the Higgs boson radiative decay into Z0 by and Collaborations, we investigate the next-to-leading-order (NLO) electroweak correction to this rare decay process in Standard Model (SM). Implementing the on shell renormalization scheme, we find that the magnitude of the NLO electroweak correction may reach 7% of the leading-order (LO) prediction, much more significant than that of the NLO QCD correction, which is merely about 0.3%. After incorporating the O(α) correction, the predicted partial width from various α schemes tend to converge to each other. Including both NLO electroweak and QCD corrections, the SM prediction for the branching fraction shifts from the LO value of (1.40–1.71)×10−3 to (1.55±0.06)×10−3, considerably lower than the measured value Bexp[H→Z0γ]=(3.4±1.1)×10−3. Resolving this discrepancy clearly calls for further theoretical investigations, and, more importantly, experimental efforts from and the prospective Higgs factories such as and . Published by the American Physical Society 2024

Unveiling desert region in inert doublet model assisted by Peccei-Quinn symmetry

The Inert Higgs Doublet model (IDM), assisted by Peccei-Quinn (PQ) symmetry, offers a simple but natural framework of a dark sector that accommodates Weakly Interacting Massive Particle (WIMP) and axion as dark matter components. Spontaneous breaking of U(1)PQ symmetry, which was originally proposed as an elegant solution to the strong charge-parity (CP) problem, also ensures the stability of WIMP through a residual ℤ2 symmetry. Interestingly, additional fields necessitated by PQ symmetry further enrich the dark sector. These include a scalar field proprietor for axion DM and a vector-like quark (VLQ) that acts as a portal for the dark sector through Yukawa interactions. Moreover, this combination of the axion and WIMP components satisfies the observed DM relic density and reopens the phenomenologically exciting region of the IDM parameter space where the WIMP mass falls between 100 - 550 GeV. We investigate the model-independent pair production of VLQs exploring this region at the Large Hadron Collider (LHC), incorporating the effects of next-to-leading order (NLO) QCD corrections. After production, each VLQ decays into a top or bottom quark accompanied by an inert scalar, a consequence of the residual ℤ2 symmetry. Utilising relevant observables with a leptonic search channel and employing multivariate analysis, we demonstrate the ability of this analysis to exclude a significant portion of the parameter space with an integrated luminosity of 300 fb−1.

Studies of Z boson decay into double ϒ mesons at the NLO QCD accuracy

In this paper, we employ the nonrelativistic quantum chromodynamics (QCD) factorization to conduct a comprehensive examination of the Z boson decay into a pair of ϒ mesons, achieving accuracy at the next-to-leading-order (NLO) in αs. Our calculations demonstrate that the quantum electrodynamics (QED) diagrams are indispensable in comparison to the pure QCD diagrams, and the implementation of QCD corrections markedly enhances the QCD results, whereas it substantially diminishes the QED results. To ensure consistency with the experimental methodology, we have taken into account the feed-down transitions originating from higher excited states, which exhibit significant relevance. Combining all the contributions, we arrive at the NLO prediction of BZ→ϒ(nS)+ϒ(mS)∼10−11, which is notably lower than the upper limits set by CMS. Published by the American Physical Society 2024

Two-loop electroweak corrections to the Higgs boson rare decay process H→Zγ

Recently, the ATLAS and CMS collaborations jointly announced the first evidence of the rare Higgs boson decay channel H→Zγ, with a ratio of 2.2±0.7 times the leading order standard model (SM) prediction. In order to face this challenge, it is urgent to produce an even more accurate calculation within the SM. To this end, we calculate in this paper the next-to-leading order (NLO) electroweak (EW) corrections to the H→Zγ process, in which the NLO quantum chromodynamics (QCD) corrections were found tiny. Our calculation finds that the inclusion of NLO EW corrections greatly enhances the prediction reliability. To tame the theoretical uncertainty, we adopt five different renormalization schemes. Combining our result with previous NLO QCD corrections and the signal-background interference, we conclude that the excess in H→Zγ cannot be explained within the SM. In fact, the incompatibility between the SM prediction and the LHC measurement of the concerned process is exacerbated upon considering the higher order EW corrections, which implies that something beyond the SM could be involved. Published by the American Physical Society 2024

Tritium β decay and proton-proton fusion in pionless effective field theory

The Gamow-Teller and Fermi matrix elements, 〈GT〉 and 〈F〉, respectively, for tritium β decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb interactions and isospin violation giving the leading order predictions 〈GT〉0=0.9807 and 〈F〉0=1. Using an experimentally determined value for the tritium β decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding L1,A=6.01±2.08fm3 at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. The impact of L1,A on proton-proton fusion is also discussed. Finally, the consequences of Wigner-SU(4) spin-isospin symmetry are considered for the Gamow-Teller matrix element. Published by the American Physical Society 2024

Measurement of multijet azimuthal correlations and determination of the strong coupling in proton-proton collisions at s=13TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=13\\,\ ext {Te}\\hspace{-.08em}\ ext {V} $$\\end{document}

A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_{\ extrm{T}}$$\\end{document}. This observable is measured in multijet events over the range of pT=360\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_{\ extrm{T}} = 360$$\\end{document}–3170GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3170\\,\ ext {Ge}\\hspace{-.08em}\ ext {V} $$\\end{document} based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ ext {Te}\\hspace{-.08em}\ ext {V}$$\\end{document}, corresponding to an integrated luminosity of 134fb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ ext {fb}^{-1}$$\\end{document}. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is αS(mZ)=0.1177±0.0013(exp)-0.0073+0.0116(theo)=0.1177-0.0074+0.0117\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _\ extrm{S} (m_{{\ extrm{Z}}}) =0.1177 \\pm 0.0013\\, \ ext {(exp)} _{-0.0073}^{+0.0116} \\,\ ext {(theo)} = 0.1177_{-0.0074}^{+0.0117}$$\\end{document}, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of αS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _\ extrm{S}$$\\end{document} in the TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ ext {Te}\\hspace{-.08em}\ ext {V}$$\\end{document} region shows no deviation from the expected NLO pQCD behaviour.

Bayesian method for fitting the low-energy constants in chiral perturbation theory

The values of the low-energy constants (LECs) are very important in the chiral perturbation theory. This paper adopts a Bayesian method with the truncation errors to globally fit eight next-to-leading order (NLO) LECs Lir and next-to-next-leading order (NNLO) LECs Cir. With the estimation of the truncation errors, the fitting results of Lir in the NLO and NNLO are very close. The posterior distributions of Cir indicate the boundary-dependent relations of these Cir. Ten Cir are weakly dependent on the boundaries and their values are reliable. The other Cir are required more experimental data to constrain their boundaries. Some linear combinations of Cir are also fitted with more reliable posterior distributions. If one knows some more precise values of Cir, some other Cir can be obtained by these values. With these fitting LECs, most observables provide a good convergence, except for the πK scattering lengths a03/2 and a01/2. An example is also introduced to test the improvement of the method. All the computations indicate that considering the truncation errors can improve the global fit greatly, and more prior information can obtain better fitting results. This fitting method can be extended to the other effective field theories and the perturbation theory.

Higgs interference effects in top-quark pair production in the 1HSM

We present a next-to-leading-order (NLO) study of the process pp (→ {h1, h2}) →tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} + X in the 1-Higgs-singlet extension of the Standard Model with an additional heavy Higgs boson h2 that mixes with the light Higgs boson h1. This process is subject to large interference effects between loop-induced Higgs-mediated amplitudes and the QCD continuum background which tend to overcompensate any resonance contributions. A reliable modelling of the resulting top-pair invariant mass shapes requires the inclusion of higher-order QCD corrections, which are presented here. The computation of these NLO corrections is exact in all contributions but in the class of non-factorisable two-loop diagrams which are included in an approximate way such that all infrared singular limits are preserved. We present numerical results for several benchmark points with heavy Higgs masses in the range 700–3000 GeV considering the production of stable top quarks. We find that the interference effects dominate the BSM signal yielding sharp dip structures instead of resonance peaks. The significance and excludability of the BSM effect is explored for the LHC Run 2, Run 3 and HL-LHC.

NLO thermal corrections to dark matter annihilation cross sections: A novel approach

Dark matter relic density has been increasingly accurately measured by successive generations of experiments. The Boltzmann equation determines the yields using the dark matter annihilation cross section as one of the inputs; the accurate computation of the latter including thermal contributions thus assumes importance. We report here the next-to-leading-order (NLO) thermal corrections to the cross sections for (Majorana) dark matter annihilation of standard model fermions, χχ→ff¯, via charged scalars. We use a novel approach, utilizing the technique of Grammer and Yennie, extended to thermal field theories, where the cancellation of soft infrared divergences occurs naturally. We present the NLO thermal cross sections in full detail both for the relativistic case and in the nonrelativistic limit. Our independent calculation verifies earlier results where the leading contribution at order O(T2) was shown to be proportional to the square of the fermion mass in the nonrelativistic limit, just as at leading order. We find that the O(T4) contributions have the same dependence on the fermion mass as well. Published by the American Physical Society 2024

Pseudoscalar Higgs plus jet production at Next-to-Next-to-Leading Order in QCD

We present a calculation of pseudoscalar Higgs production in association with a jet at Next-to-Next-to Leading Order (NNLO) accuracy in QCD. We work in an effective field theory in which mt → ∞ resulting in effective operators which couple the pseudoscalar to gluons and (massless) quarks. We have calculated all of the relevant amplitudes for the two-loop, one-loop and tree-level contributions. As a cross-check of our calculation we have re-calculated all of the scalar Higgs plus parton amplitudes and perform a detailed comparison to the literature. In order to regulate the infra-red singularities present at this order we employ the N-jettiness slicing method. In addition to a detailed validation of our calculation at this order we investigate LHC phenomenology for a selection of pseudoscalar Higgs masses. Our results are implemented into the parton-level Monte Carlo code MCFM.

One-loop five-parton amplitudes in the NMRK limit

We analyse the real part of one-loop five-parton amplitudes in the next-to-multi-Regge kinematic (NMRK) limit, to leading power, and to finite order in the dimensional regularisation parameter. To leading logarithmic (LL) accuracy, it is known that five-parton amplitudes in this limit are given to all-orders by a single factorised expression, in which the pair of partons which are not well-separated in rapidity are described by a two-parton emission vertex. In this study, we investigate the one-loop amplitudes at next-to-leading logarithmic (NLL) accuracy, and find that is has a more complex structure. In particular, it is found that the purely gluonic amplitudes are compatible with an analogous factorisation of individual colour structures. From the one-loop amplitudes we extract one-loop two-parton emission vertices, which are functions of a subset of the momenta of the amplitude. In the multi-Regge kinematic (MRK) limit, the vertices themselves factorise into the known one-loop single-parton emission vertices and Lipatov vertex, with rapidity dependence governed by the one-loop gluon Regge trajectory, as required by compatibility with the known MRK limit of amplitudes. The one-loop two-parton emission vertices are necessary ingredients for the construction of the next-to-next-to leading order (NNLO) jet impact factors in the BFKL framework.

A simple dirac prescription for two-loop anomalous dimension matrices

A novel method to treat effects from evanescent operators in next-to-leading order (NLO) computations is introduced. The approach allows, besides further simplifications, to discard evanescent-to-physical mixing contributions in NLO calculations. The method is independent of the treatments of γ5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _5$$\\end{document} and can therefore be combined with different renormalization schemes. We illustrate the utility of this result by reproducing literature results of two-loop anomalous dimension matrices for both |ΔF|=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\Delta F| = 1$$\\end{document} and |ΔF|=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\Delta F| = 2$$\\end{document} transitions.