One-loop Radiative Corrections Research Articles

Bosonic multi-Higgs correlations beyond leading order

The production of multiple Higgs bosons at the LHC and beyond is a strong test of the mechanism of electroweak symmetry breaking. Taking inspiration from recent experimental efforts to move toward limits on triple-Higgs production at the Large Hadron Collider, we consider generic bosonic deviations of HH and HHH production from the Standard Model in the guise of Higgs effective field theory (HEFT). Including one-loop radiative corrections within the HEFT and going up to O(p4) in the momentum expansion, we provide a detailed motivation of the parameter range that the LHC (and future hadron colliders) can explore, through accessing nonstandard coupling modifications and momentum dependencies that probe Higgs boson nonlinearities. In particular, we find that radiative corrections can enhance the sensitivity to Higgs self-coupling modifiers and HEFT-specific momentum dependencies can vastly increase triple-Higgs production, thus providing further motivation to consider these processes during the LHC’s high-luminosity phase. Published by the American Physical Society 2024

The Sommerfeld theory with the Uehling potential

The Uehling potential is the one-loop radiative correction to the photon propagator. The correction can be graphically represented by the Feynman diagram of the second order. The physical meaning of this diagram is the process Y-> (e- + e+) -> Y , where Y is denotation for photon, and e-, e+ is the electron-positron pair. It means that photon can exist in the intermediate state with e+, e- being virtual particles. Then, the Coulomb potential with radiative corrections can be inserted in the Sommerfeld quantum equation in order to find the Sommerfeld energy.

Precise calculation of one-loop radiative corrections in møller scattering

Precise calculation of one-loop radiative corrections in møller scattering

Primordial black holes and scalar-induced gravitational waves in radiative hybrid inflation

We study the possibility that primordial black holes (PBHs) can be formed from large curvature perturbations generated during the waterfall phase transition due to the effects of one-loop radiative corrections of Yukawa couplings between the inflaton and a dark fermion in a non-supersymmetric hybrid inflationary model. We obtain a spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, and a tensor-to-scalar ratio r, consistent with the current Planck data. Our findings show that the abundance of PBHs is correlated to the dark fermion mass mN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_N$$\\end{document} and peak in the GW spectrum. We identify parameter space where PBHs can be the entire dark matter (DM) candidate of the universe or a fraction of it. Our predictions are consistent with any existing constraints of PBH from microlensing, BBN, CMB, etc. Moreover, the scenario is also testable via induced gravitational waves (GWs) from first-order scalar perturbations detectable in future observatories such as LISA and ET. For instance, with inflaton mass m∼2×1012\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m \\sim 2\ imes 10^{12}$$\\end{document} GeV, mN∼5.4×1015\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_N \\sim 5.4\ imes 10^{15}$$\\end{document} GeV, we obtain PBHs of around 10-13M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-13}\\, M_\\odot $$\\end{document} mass that can explain the entire abundance of DM and predict GWs with amplitude ΩGWh2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _\ extrm{GW}h^2$$\\end{document}∼10-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 10^{-9}$$\\end{document} with peak frequency f∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document} 0.1 Hz in LISA. By explicitly estimating fine-tuning we show that the model has very mild tuning. We discuss successful reheating at the end of the inflationary phase via the conversion of the waterfall field into standard model (SM) particles. We also briefly speculate a scenario where the dark fermion can be a possible heavy right-handed neutrino (RHN) which is responsible for generating the SM neutrino masses via the seesaw mechanism. The RHN can be produced due to waterfall field decay and its subsequent decay may also explain the observed baryon asymmetry in the universe via leptogenesis. We find the reheat temperature TR≲5×109\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_R\\lesssim 5\ imes 10^9$$\\end{document} GeV that explains the matter-anti-matter asymmetry of the universe.

Precise Calculations of One-Loop Radiative Corrections in Møller Scattering

Precise Calculations of One-Loop Radiative Corrections in Møller Scattering

Full one-loop radiative corrections to e+e−→H+H− in the inert doublet model

We compute the full one-loop radiative corrections for charged scalar pair production e+e−→H+H− in the inert doublet model. The on-shell renormalization scheme has been used. We take into account both the weak contributions as well as the soft and hard QED corrections. We compute both the real emission and the one-loop virtual corrections using the Feynman diagrammatic method. The resummed cross section is introduced to cure the Coulomb singularity which occurs in the QED corrections. We have analyzed the parameter space of the inert doublet model in three scenarios after taking into account theoretical constraints, the collider experimental bounds, and dark matter search bounds as well. It is found that the weak interaction dominates the radiative corrections, and its size is determined by the triple Higgs coupling λh0H+H−, which is further connected to the mass of the charged scalar. In the scenario where all the constraints are taken into account, we find that for s=250 GeV and s=500 GeV, the weak corrections are around −6%∼−5% and −10%∼−3%, respectively. While for s=1000 GeV, the weak corrections can reach −15%∼+25%. The new feature is that the weak corrections can be positive near the threshold when the charged scalar is heavier than 470 GeV. Six benchmark points for future collider searches have been proposed. Published by the American Physical Society 2024

One-loop radiative corrections in bumblebee-Stueckelberg model

This work aims to study the radiative corrections in a vector model with spontaneous Lorentz symmetry violation, known in the literature as the bumblebee model. We consider such a model with self-interaction quadratic smooth potential responsible for spontaneous Lorentz symmetry breaking. The spectrum of this model displays a transversal nonmassive mode, identified as Nambu-Goldstone, and a massive longitudinal mode. Besides the Lorentz symmetry, this model also exhibits gauge symmetry violation. To restore the gauge symmetry, we introduce the Stueckelberg field and calculate the two-point function by employing the principal-value (PV) prescription. The result is nontransversal, leading to a massive excited mode.

Lorentz-violating extension of scalar QED at finite temperature

In this work, we calculate the one-loop self-energy corrections to the gauge field in scalar electrodynamics modified by Lorentz-violating terms within the framework of the standard model extension (SME). We focus on both CPT-even and CPT-odd contributions. The kinetic part of the scalar sector contains a CPT-even symmetric Lorentz-breaking tensor, and the interaction terms include a vector contracted with the usual covariant derivative in a gauge-invariant manner. We computed the one-loop radiative corrections using dimensional regularization for both the CPT-even and CPT-odd cases. Additionally, we employed the Matsubara formalism to account for finite temperature effects.

One-loop formulas for off-shell decay \(H^* \rightarrow W^+W^-\) in 't Hooft-Veltman gauge and its applications

We present analytic results for one-loop radiative corrections to off-shell decay \(H^* \rightarrow W^+W^-\) in 't Hooft-Veltman gauge within the Standard Model framework. In numerical results, we show off-shell decay rate and its corrections with varying off-shell Higgs mass. The results show that the corrections are of 10% contributions to the total decay rates. Furthermore, we study the impacts of one-loop radiative corrections to the off-shell decay \(H^* \rightarrow W^+W^-\) in Higgs processes at future colliders. The signal processes such as \(e^-e^+\rightarrow ZH^*\rightarrow Z(WW)\) with including the initial beam polarizations and \(e^-e^+\rightarrow \nu_e\bar{\nu}_e H^* \rightarrow \nu_e\bar{\nu}_e (WW)\) and \(e^-\gamma \rightarrow e^-H^* \rightarrow e^-WW\) are examined. We find that the effects are visible impacts and these should be taken into account at future colliders.

Strong signature of one-loop self-energy in polarization resolved nonlinear Compton scattering

The polarization dynamics of electrons including multiple nonlinear Compton scattering during the interaction of a circularly polarized ultraintense laser pulse with a counterpropagating ultrarelativistic electron beam is investigated. While electron polarization emerges mostly due to spin-flips at photon emissions, there is a nonradiative contribution to the polarization which stems from the one-loop QED radiative corrections to the self-energy, which admits of a simple physical model. We put forward a method to single out the nonradiative contribution to the polarization, employing the reflection regime of the interaction when the radiation reaction is significant. The polarization of electrons that penetrate in the forward direction through a colliding laser is shown to be dominated by the loop effect, while the reflected electrons are mostly polarized by spin-flips at photon emissions. We confirm this effect by quantum Monte Carlo simulations considering the helicity transfer from the laser field to the electrons, taking into account the opposite sign of the polarizations induced by the nonradiative loop effect and radiative spin-flip. Our Monte Carlo simulations show a polarization signal as high as $\ensuremath{\gtrsim}10%$ from the nonradiative effect, amenable for experimental detection with current technology.

The Radiative Corrections to the Maxwell Equations

The one-loop radiative correction to the photon propagator can be graphically represented by the Feynman diagram of the second order. The physical meaning of this diagram is the process Y-> (e- + e+) -> Y , where Y is denotation for photon, and e-, e+ is the electron-positron pair. It means that photon can exist in the intermediate state with the electron and positron as virtual particles. The photon propagation function based on such process with electron-positron pair e-, e+ is derived. The modified Lagrangian of electromagnetic field is derived supposing the modified Green function of photon. The Schwinger source methods of quantum field theory was applied. Then, the modified Maxwell equations are derived from the new Lagrangian.

One-loop radiative corrections to photon-pair production in polarized positron-electron annihilation

A theoretical description of photon-pair production in polarized positron-electron annihilation is presented. Complete one-loop electroweak radiative corrections are calculated taking into account the exact dependence on the electron mass. Analytical results are derived with the help of the SANC system. The relevant contributions to the cross section are calculated analytically using the helicity amplitude approach. The cases of unpolarized and longitudinally polarized fermions in the initial state are investigated. Calculations are realized in the Monte Carlo integrator MCSANCee and generator ReneSANCe which allow one the implementation of any experimental cuts used in the analysis of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data of both low and high energies.

Three- and four-point functions in CPT -even Lorentz-violating scalar QED

The renormalization of quantum field theories usually assumes Lorentz and gauge symmetries, besides the general restrictions imposed by unitarity and causality. However, the set of renormalizable theories can be enlarged by relaxing some of these assumptions. In this work, we consider the particular case of a CPT-preserving but Lorentz-breaking extension of scalar QED. For this theory, we calculate the one-loop radiative corrections to the three- and four-point scalar-vector vertex functions, at the lowest order in the Lorentz violation parameters; and we explicitly verify that the resulting low-energy effective action is compatible with the usual gauge invariance requirements. With these results, we complete the one-loop renormalization of the model at the leading order in the Lorentz-violating parameters.

One-loop corrections for WW to HH in Higgs EFT with the electroweak chiral Lagrangian

In this work we present the computation of the one-loop electroweak radiative corrections to the scattering process $WW\to HH$ within the context of the Higgs Effective Field Theory (HEFT). We assume that the fermionic interactions are like in the Standard Model, whereas the Beyond Standard Model interactions in the bosonic sector are given by the Electroweak Chiral Lagrangian. The computation of the one-loop amplitude and the renormalization program is performed in terms of the involved one-particle-irreducible functions (1PI) and using $R_\xi$ covariant gauges. The renormalization of 1PI functions at arbitrary external momenta is a more ambitious program than just renormalizing the amplitude with on-shell external legs and it has the advantage that they can be used in several scattering amplitudes. In fact, we use here some of the 1PI functions already computed in our previous work (devoted to $WZ \to WZ$). We will complement them here with the computation of the new 1PI functions required for $WW \to HH$. From this renormalization procedure we will also derive the full set of renormalized coefficients of the EChL that are relevant for this scattering process. In the last part, we will present the numerical results for the EChL predictions of the one-loop level cross section, $\sigma(WW \to HH)|_{\rm 1-loop}$, as a function of the center of mass energy, showing the relative size of the one-loop radiative corrections respect to the tree level prediction in terms of the EChL coefficients. The results of the one-loop corrections to $WW \to HH$ for the SM case will be also presented, for comparison with the EChL case, following the same computational method, i.e., by means of the renormalization of 1PI functions.

Primordial black holes and gravitational waves in hybrid inflation with chaotic potentials

We study the formation of primordial black hole (PBH) dark matter and the generation of scalar induced secondary gravitational waves (SIGWs) in a non-supersymmetric model of hybrid inflation with chaotic (polynomial-like) potential, including one-loop radiative corrections. A radiatively corrected version of these models is entirely consistent with Planck's data. By adding non-canonical kinetic energy term in the lagrangian, the inflation experiences a period of ultra-slow-roll, and the amplitude of primordial power spectrum is enhanced to O(10−2). The enhanced power spectra of primordial curvature perturbations can have both sharp and broad peaks. A wide mass range of PBHs is realized in our model with the frequencies of scalar induced gravitational waves ranged from nHz to kHz. We present several benchmark points where the PBH mass generated during inflation is around (1−100)M⊙, (10−9−10−7)M⊙ and (10−16−10−11)M⊙. The PBHs can make up most of the dark matter with masses around (10−16−10−11)M⊙ and (1−100)M⊙, and their associated SIGWs can be probed by the upcoming ground and space-based gravitational wave (GW) observatories. The evidence of stochastic process recently reported by NANOGrav may be interpreted as SIGWs associated with the formation of PBHs. These SIGWs may also be tested by future interferometer-type GW observations of SKA, DECIGO, LISA, BBO, TaiJi, TianQin, CE and ET.

Computing one-loop radiative corrections in τ → π(K)ν[γ] and testing new physics

Without a doubt the ratios Rτ/p = Γ(τ → Pντ[γ])/Γ(P → μνμ[γ]) (P = π, K) give a convenient scenario to test the lepton universality, the CKM unitarity and to search for non-standard interactions in τ decays. Moreover, the previous theoretical estimation of these observables is more than twenty-five years old and some assumptions of that estimation are unrealistic. Therefore, an update of Rτ/P was timely. The one-loop radiative corrections have been computed by considering an expansion of Chiral Perturbation Theory including the lightest spin-one resonances and respecting the short-distance behavior dictated by QCD. We have reported δRτ/π = (0.18±0.57)% and δRτ/K = (0.97±0.58)%, where the uncertainties have been induced fundamentally by the estimation of the counterterms. We have tested the lepton universality, the CKM unitarity and have searched for new physics in τ decays. As a by-product, we have also determined the theoretical radiative corrections to the τ → Pντ[γ] decay rates, δτπ = —(0.24 ± 0.56)% and δτK = —(0.15 ± 0.57)%.

Restricting loop expansions in gauge theories coupled to matter

Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with both the Yang–Mills (YM) and Einstein–Hilbert (EH) action; the resulting theory is both renormalizable and unitary, has a positive energy spectrum and has no negative norm states contributing to physical processes. Although this approach cannot be consistently used with scalar fields alone, scalar fields can be coupled to gauge fields so that loop effects in the gauge sector are restricted to one-loop order in a way that satisfies the usual criterion for a consistent quantum field theory. The tree-level diagrams are those of the classical theory in which the metric couples to the energy–momentum tensor.

Electroweak Effects in e+e−→ZH Process

Electroweak radiative corrections to the cross-section of the process e+e−→ZH are considered. The complete one-loop electroweak radiative corrections are evaluated with the help of the SANC system. Higher-order contributions of the initial-state radiation are computed in the QED structure function formalism. Numerical results are produced by a new version of the ReneSANCe event generator and MCSANCee integrator for the conditions of future electron-positron colliders. The resulting theoretical uncertainty in the description of this process is estimated.

One-loop electroweak radiative corrections to charged lepton pair production in photon-photon collisions

We provide high-precision predictions for muon-pair and tau-pair productions in a photon-photon collision by considering a complete set of one-loop-level scattering amplitudes, i.e., electroweak (EW) corrections together with soft and hard QED radiation. Accordingly, we present a detailed numerical discussion with particular emphasis on the pure QED corrections as well as genuinely weak corrections. The effects of angular and initial beam polarization distributions on production rates are also discussed. An improvement is observed by a factor of two with oppositely polarized photons. Our results indicate that the one-loop EW radiative corrections enhance the Born cross section and the total relative correction is typically about 10% for both production channels. It appears that the full EW corrections to $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}$ are required to match a percent level accuracy.

One-loop radiative corrections to e+e\u2212 \u2192 Zh0/H0A0 in the Inert Higgs Doublet Model

We compute the full one-loop radiative corrections (including both weak and QED corrections) for two processes e+e− → Zh0, H0A0 in the Inert Higgs Doublet model (IHDM). Up to O(αw) and O(αem) order, we use FeynArts/FormCalc to compute the one-loop virtual corrections and Feynman Diagram Calculation (FDC) to evaluate the real emission, respectively. Being equipped with these computing tools, we investigate radiative corrections of new physics for five scenarios with three typical collision energies of future electron-positron colliders: 250 GeV, 500 GeV, and 1000 GeV. By scanning the parameter space of IHDM, we identify the allowed regions which are consistent with constraints and bounds, from both theoretical and experimental sides. We find that the radiative corrections of the IHDM to e+e− → Zh0 can be sizeable and are within the detection potentials of future Higgs factories. We also find that the new physics of IHDM could also be directly detected by observing the process e+e− → H0A0 which could have large enough production rate. We propose six benchmark points and examine their salient features which can serve as physics targets for future electron-positron colliders, such as CEPC/CLIC/FCC-ee/ILC as well as for LHC.