We compute the three-loop QCD corrections to the massive quark-anti-quark-photon form factors $F_1$ and $F_2$ involving a closed loop of massless fermions. This subset is gauge invariant and contains both planar and non-planar contributions. We perform the reduction using FIRE and compute the master integrals with the help of differential equations. Our analytic results can be expressed in terms of Goncharov polylogarithms. We provide analytic results for all master integrals which are not present in the large-$N_c$ calculation considered in Refs. [1,2].
We present a new variant of the spinor techniques for calculating the amplitudes of processes involving massive fermions with arbitrary polarization. It is relatively simple and leads to basic spinor products. Our procedure is not more complex than CALCUL spinor techniques for massless fermions. We obtain spinor Chisholm identities for massive fermions. As an illustration, expressions are given for the amplitudes of electron-positron annihilation into fermions-pairs for several polarizations.
We compute the eighth-order fermionic corrections involving two and three closed massless fermion loops to the anomalous magnetic moment of the muon. The required four-loop on-shell integrals are classified and explicit analytical results for the master integrals are presented. As further applications we compute the corresponding four-loop QCD corrections to the mass and wave function renormalization constants for a massive quark in the on-shell scheme.
In the work we have considered the reduction techniques matrix element of the reaction interaction of elementary particles for massive fermions to spinor products . The our procedure is not more complex than CALCUL spinor techniques for massless fermions. It is relatively simple and leads to basic spinor products with any polarizationod fermions. Also obtained spinor Chisholm identities for massive fermions.
We derive a systematic procedure of computing the vacuum functional and fermion condensate of the massive Schwinger model via a perturbative expansion in the fermion mass. We compute numerical results for the first nontrivial order.
We present an extension of the antenna subtraction formalism at NLO to include massive final state fermions. The basic ingredients to the subtraction terms, the NLO massive final-final antenna functions are derived and integrated over the corresponding factorised phase space. Those antenna functions account for all soft, collinear and quasi-collinear limits of the QCD matrix elements involving massive fermions in the final state.
In this proceeding, we highlight the computation of leading fermionic three-loop corrections to electroweak precision observables (EWPOs) accomplished recently. We summarize the numerical analysis and provide an outlook.
The recent evaluation of the parametrically dominant next-to-next-to-leading order corrections to four-fermion production near the W-pair threshold in the framework of unstable-particle effective theory is briefly summarized.
We describe the analytic calculation of the fermionic two-loop QCD corrections to the heavy-quark pair production process in the quark-antiquark channel.
We compute the three-loop QCD corrections to the massive quark form factors with external vector, axial-vector, scalar and pseudo-scalar currents. All corrections with closed loops of massless fermions are included. The non-fermionic part is computed in the large-$N_c$ limit, where only planar Feynman diagrams contribute.
We reemphasize the importance of discriminating fermion-loop and bosonic electroweak corrections in the analysis of electroweak precision data. Most recent data are indeed precise enough to require corrections beyond (trivial) fermion loops. An analysis of these data in terms of the observables $Δx \equiv ε_{N1} - ε_{N2}$, $Δy \equiv - ε_{N2}$ and $ε\equiv - ε_{N3}$ identifies the required additional corrections as vertex corrections at the $W^\pm f\bar f^\prime$ and $Z^0 f\bar f$ vertices. Standard-model values for these corrections are consistent with the experimental data.
A summary of recent work related to the calculation of loop quantum gravity induced corrections to standard particle (photons and spin 1/2 fermions) dynamics in flat space is presented. Stringent bounds upon the parameters characterizing the corrections in the fermionic sector, arising from already known clock-comparison experiments, are reviewed.
Tensor reduction is important for multi-loop amplitude calculation. And the projection method is one of the most popular approaches for tensor reduction. However, projection method could be problematic for amplitude with massive fermions due to the inconsistency between helicity and chirality. We propose an approach to extend the projection method to reduce the loop amplitude containing fermion chain with two massive spinors. The extension is achieved by decomposing one of the massive spinors into two specific massless spinors, "null spinor" and "reference spinor". Then the extended projection…
Recently the two-loop next-to-leading logarithmic (NLL) virtual corrections to arbitrary processes with massless external fermions have been calculated. Within the spontaneously broken electroweak theory the one- and two-loop mass singularities have been derived to NLL accuracy and expressed as universal correction factors depending only on the quantum numbers of the external particles. This talk summarizes the results for massless fermionic processes and presents new aspects arising in the extension of the corresponding loop calculations to massive external fermions. As a preliminary result, …
The structure of the double-pole approximation for the O(alpha) corrections to e^+e^- -> WW -> 4 fermions is described, and some results are presented. Moreover, results on full tree-level predictions for $e^+e^- -> WW -> 4 fermions + gamma are given.
The one-loop fermionic contribution to the probability of an instanton transition with fermion number violation is calculated in the chiral Abelian Higgs model in 1+1 dimensions, where the fermions have a Yukawa coupling to the scalar field. The dependence of the determinant on fermionic, scalar and vector mass is determined. We show in detail how to renormalize the fermionic determinant in partial wave analysis, which is convenient for computations.
The complete two-loop electroweak fermionic corrections to the effective leptonic weak mixing angle, sin^2(theta_eff), are now available. Here we shortly present the methods applied and illustrate the implications on indirect prediction for the Higgs boson mass within the standard model.
We studied the $m=0$ limit of different components of Wigner functions for massive fermions. Comparing with the chiral kinetic theory, we separated the vanishing part and non-vanishing part for vector and axial vector components, up to the first order of $\hbar$. Then we discussed the possible physical meaning of the vanishing and non-vanishing parts, and their different behavior at thermal equilibrium.
Analytic formulae are derived for the complete photon energy spectrum due to QED corrections to fermion pair production in case of a limited angular acceptance for the final state fermions. After a numerical integration over the energy of non-observed photons, this corresponds to typical experimental conditions at LEP/SLC.
One-loop radiative corrections to the charged Higgs coupling to two fermions and to the charged Higgs fermionic decay are studied. A renormalization scheme is proposed including the definition of the parameter $\tanβ$ through the coupling of the CP-odd Higgs boson to a charged lepton pair. Loops including top and bottom quarks and squarks are considered using the unitary gauge. Large corrections to the coupling are found when there is a substantial mixing in the squark mass matrix, but these corrections are suprress in the decay rate. Interesting applications to rare processes are discussed.
The dynamical evolution of spin of a massive probe fermion in a massless hot QED plasma at local equilibrium is investigated through the quantum kinetic theory. We consider the massive probe fermion undergoing 2-by-2 Coulomb scattering with the massless fermions in the medium. The axial kinetic equation is derived including the collision terms to the first order of gradients and leading logarithmic order of the coupling. The collision terms are vanishing at global equilibrium, around which the relaxation time can be extracted as an operator. We further decompose the axial kinetic equation into…
The explicit exact expressions of QED lowest-order radiative corrections to the two polarized identical fermion scattering are presented in covariant form. Polarization effects are treated in detail. The infrared divergence from the real photon emission is extracted by covariant approach. Some numerical results for Møller scattering are given.
The two-loop massive operator matrix elements for the fermionic local twist--2 operators with external massive fermion lines in Quantum Electrodynamics (QED) are calculated up to the constant terms in the dimensional parameter $ε= D - 4$. We investigate the hypothesis of Ref. \cite{BBN} that the 2--loop QED initial state corrections to $e^+e^-$ annihilation into a virtual neutral gauge boson, except power corrections of $O((m_f^2/s)^k), k \geq 1$, can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell-Yan process.
We examine QED$_{1+1}$ (the massive Schwinger model) to extend existing perturbation results in $m_f/m_b$, and compare our results with lattice and DLCQ calculations. (Based on a talk presented by J.P. Vary at ``Theory of Hadrons and Light-Front QCD'', Polona Zgorzelisko, Poland, August 1994.)
Contributions of fermions to the mass of the scalar glueball $0^{++}$ are calculated at two-loop level in the framework of QCD sum rules. It obviously changes the coefficients in the operator product expansion (OPE) and shifts the mass of glueball.
We give some details of the recently completed calculation of the full two-loop fermionic corrections to the effective leptonic weak mixing angle. Among others, we describe the C++ library DiaGen/IdSolver, which was used to reduce the two-loop light fermion vertex diagrams to linear combinations of master integrals with rational function coefficients.
We study chiral symmetry breaking in $\rm QED_3$ with $N_f$ flavors of four-component fermions. A closed system of Schwinger-Dyson equations for fermion and photon propagators and the full fermion-photon vertex is proposed, which is consistent with the Ward-Takahashi identity. A simplified version of that set of equations is reduced (in nonlocal gauge) to the equation for a dynamical fermion mass function, where the one-loop vacuum polarization with dynamically massive fermions has been taken into account. The linearized equation for the fermion mass function is analyzed in real space. The ana…
The motion equation with nonzero mass, invariant for weak isospin transformation, can be obtained from the Dirac equation by the adding of the Clifford pentad fifth element. The motion equation of the SU(2) Yang-Mills field components is similar to the Klein-Gordon equation with the nonzero mass.
We describe an application of generalised unitarity to the computation of one-loop amplitudes with massive external fermions. We present analytic results for the cut-constructible parts of the leading colour contributions to the all-plus helicity configuration of the $t\bar{t}gg$ amplitude. Using a special choice for the helicity basis of the massive fermions we are able to obtain extremely compact analytic expressions. In particular we describe how one can fix the divergent contributions from tadpole and wave-function renormalisation using universal UV and IR behaviour.
We present an analytical calculation of additional real or virtual radiation of the light fermion pair in the fermionic decay of the Higgs boson $ H \to f_1\bar f_1$ for arbitrary ratios of the Higgs boson mass to the $f_1$ fermion mass. This result gives us a value of the $O(N_f α_s^2)$ radiative correction to the inclusive decay rate $ H \to f_1\bar f_1$. Using this result in the framework of the Brodsky-Mackenzie-Lepage scheme, we discuss the scale setting in the one-loop QCD correction to the decay width $ H \to f_1\bar f_1$ for arbitrary relation between the Higgs boson and fermion masses…
We calculate the full set of the two-loop master integrals for heavy-to-light form factors of two different massive fermions for arbitrary momentum transfer in NNLO QCD or QED corrections. These integrals allow to determine the two-loop QCD or QED corrections to the amplitudes for heavy-to-light form factors of two massive fermions in a full analytical way, without any approximations. The analytical results of the master integrals are derived using the method of differential equations, along with a proper choosing of canonical basis for the master integrals. All the results of master integrals…
We study the QCD scattering amplitudes for \bar{q}q \to gg and \bar{q}q \to ggg where q is a massive fermion. Using a particular choice of massive fermion spinor we are able to derive very compact expressions for the partial spin amplitudes for the 2 \to 2 process. We then investigate the corresponding 2 \to 3 amplitudes using the BCFW recursion technique. For the helicity conserving partial amplitudes we again derive very compact expressions, but were unable to treat the helicity-flip amplitudes recursively, except for the case where all the gluon helicities are the same. We therefore evaluat…
We calculate the two--loop electroweak corrections to the fermionic decay width of the Higgs boson at leading order in $m_{H}$. The sum of one--loop and two--loop radiative corrections turns out to be at 6% level over the whole range of $m_{H}$ where the perturbation theory is supposed to be a sensible approximation. We show that the perturbative approach breaks down at $m_{H} \sim$ 1.4 TeV, and address the question of its relevance beyond this limit.
$Z \to γγ$ decay amplitude is considered and proven to be zero due to properties of polarization vectors and Bose statistics. Triangular diagrams for a pseudoscalar $\to γγ$ and $Z \to γγ$ processes with massive fermions in the loop are explicitely calculated. In the Standard Model axial anomaly vanishes in the sum of these diagrams as Z boson is mixed with one of the Goldstone bosons.
Low- and intermediate mass Higgs bosons decay preferably into fermion pairs. The one-loop electroweak corrections to the respective decay rates are dominated by a flavour-independent term of ${\cal O}(G_Fm_t^2)$. We calculate the two-loop gluon correction to this term. It turns out that this correction screens the leading high-$m_t$ behaviour of the one-loop result by roughly 10\%. We also present the two-loop QCD correction to the contribution induced by a pair of fourth-generation quarks with arbitrary masses. As expected, the inclusion of the QCD correction considerably reduces the renormal…
We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses me, mf and the Mandelstam invariants s,t,u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales me^2 << mf^2 << s,t,u. The numerical result is combined with the available non-fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions.
We calculate the parametrically dominant next-to-next-to-leading order corrections to four-fermion production e^- e^+ -> mu^- nubar_mu u dbar + X at centre-of-mass energies near the W-pair production threshold employing the method of unstable-particle effective theory. In total the correction is small, leading to a shift of 3 MeV in the W-mass measurement. We also discuss the implementation of realistic cuts and provide a result for the interference of single-Coulomb and soft radiative corrections that can easily be extended to include an arbitrary number of Coulomb photons.
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor are obtained up to O(alpha^2). Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements.
We derive the integrated forms of specific initial-final tree-level four-parton antenna functions involving a massless initial-state parton and a massive final-state fermion as hard radiators. These antennae are needed in the subtraction terms required to evaluate the double real corrections to $t\bar{t}$ hadronic production at the NNLO level stemming from the partonic processes $q\bar{q}\to t\bar{t}q'\bar{q}'$ and $gg\to t\bar{t}q\bar{q}$.
We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four.
The dominant electroweak corrections to the production cross sections and partial decay widths of a light Standard-Model Higgs boson, with mass M_H << 2m_t, are due to top-quark loops. By means of a low-energy theorem, we study at the two-loop level the leading shifts in the Higgs-boson couplings to pairs of light fermions and gauge bosons induced by a sequential isodoublet of high-mass fermions. For tree-level and loop-induced Higgs-boson couplings, these corrections are of relative orders O(G_mu^2 m_F^4) and O(G_mu m_F^2), respectively, where m_F represents a generic heavy-fermion mass, with…
We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between MS and pole masses of the vector bosons Z and W. Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A …
The package aITALC has been developed for the automated calculation of radiative corrections to two-fermion production at $e^+ e^-$ colliders. The package uses Diana, Qgraf, Form, Fortran, FF, LoopTools, and further unix/linux tools. Numerical results are presented for $e^+e^- \to e^+e^-, mu^+mu^-, b \bar{s}, t \bar{c}$.
Effects of vacuum polarization by hadronic and heavy-fermion insertions were the last unknown two-loop QED corrections to high-energy Bhabha scattering and have been first announced in \cite{Actis:2007fs}. Here we describe the corrections in detail and explore their numerical influence. The hadronic contributions to the virtual O(alpha^2) QED corrections to the Bhabha-scattering cross-section are evaluated using dispersion relations and computing the convolution of hadronic data with perturbatively calculated kernel functions. The technique of dispersion integrals is also employed to derive th…
We have calculated the leading Yukawa corrections to the chargino, neutralino and gluino pole masses in the DR-bar scheme in the Minimal Supersymmetric Standard Model (MSSM) with the full set of complex parameters. We have performed a numerical analysis for a particular point in the parameter space and found typical corrections of a few tenths of a percent thus exceeding the experimental resolution as expected at the ILC. We provide a computer program which calculates two-loop pole masses for SUSY fermions with complex parameters up to the respective order in pertubation theory.
The implementation of QED initial-state radiative corrections in the process of four-fermion production at LEP200 and higher-energy e+e- colliders is discussed. Because of the presence of charged-current processes, this is a nontrivial problem, and we compare our approach with other existing treatments. We describe the Monte Carlo algorithm used for the generation of 4-fermion events with photon bremsstrahlung. Comparison between our event generator and semi-numerical calculations are presented, as well as predictions for W and Z pair related cross sections.
A new mechanism is proposed for generating neutrino masses radiatively through a non-minimal coupling to gravity of fermionic bilinears involving massive neutral fermions. Such coupling terms can arise in theories where the gravity sector is augmented by a scalar field. They necessarily violate the principle of equivalence, but such violations are not ruled out by present experiments. It is shown that the proposed mechanism is realised most convincingly in theories of the Randall- Sundrum type, where gravity couples strongly in the TeV range. The mechanism has the potential for solving both th…
Improved predictions for the Z-boson decay width and the hadronic Z-peak cross-section within the Standard Model are presented, based on a complete calculation of electroweak two-loop corrections with closed fermion loops. Compared to previous partial results, the predictions for the Z width and hadronic cross-section shift by about 0.6 MeV and 0.004 nb, respectively. Compact parametrization formulae are provided, which approximate the full results to better than 4 ppm.
Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to anomalous dipole moments of lepton from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual gauge bosons or Higgs fields. As the masses of virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly if the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. At the decoupling limit, we also present the leading corrections to lepton…
Higgs Yukawa couplings to down-type fermions receive, in the MSSM, supersymmetric quantum corrections that can be of order 1 for large values of tanβ, provided μ\sim MSUSY. Therefore, a sensitive prediction for observables driven by any of these couplings can only be obtained after an all-order resummation of the large corrections. We perform this necessary step and show, as an example, the effect of the resummation on the computation of the p\bar{p},pp \to t\bar{b}H^{-} + X cross-section and on the branching ratio BR(b\to sγ) at the next-to-leading order.
We evaluate the fermionic two-loop QCD corrections to the heavy-quark pair production process in the quark-antiquark channel. We obtain analytic results which are valid for any value of the Mandelstam invariants s and t, and of the heavy quark mass m. Our findings confirm previous results for the analytic evaluation in the small-mass limit and numerical results for the exact amplitude. We furthermore provide the expansion of the two-loop amplitude at the production threshold s ~ 4m^2.
Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to the rare decay $b\rightarrow s+γ$ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant coup…
In this paper we consider the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order in perturbation theory. We evaluate the fermionic corrections containing a closed massless fermion loop. The results are building blocks both for the bottom and top quark system at threshold. We explain in detail the methods used for the evaluation of the Feynman diagrams, classify the occurring master integrals and provide results for the latter. The numerical effects are significant. They have the tendency to improve the behaviour …
We present a study of the effective action approach to incorporate higher-order effects in e^+e^- -> n fermions. In its minimal version, the effective action approach is found to exhibit problems with unitarity and high-energy behaviour. We identify the origin of these problems by investigating the zero-mode solutions of the Ward Identities. A numerical analysis of the importance of the zero-mode solutions is presented for four-fermion production processes.
In a dense cloud of massive fermions interacting by exchange of a light scalar field, the effective mass of the fermion can become negligibly small. As the cloud expands, the effective mass and the total energy density eventually increase with decreasing density. In this regime, the pressure-density relation can approximate that required for dark energy. We apply this phenomenon to the expansion of the Universe with a very light scalar field and infer relations between the parameters available and cosmological observations. Majorana neutrinos at a mass that may have been recently determined, a…
We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter.
ZFITTER is a Fortran program for the calculation of fermion pair production and radiative corrections at high energy e+e- colliders; it is also suitable for other applications where electroweak radiative corrections appear. ZFITTER is based on a semi-analytical approach to the calculation of radiative corrections in the Standard Model. We present a summary of new features of the ZFITTER program version 6.42 compared to version 6.21. The most important additions are: (i) some higher-order QED corrections to fermion pair production, (ii) electroweak one-loop corrections to atomic parity violatio…
