One-loop Research Articles

Rovibrational spin-averaged transitions in the hydrogen molecular ions

We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $m\alpha^7$ and $m\alpha^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectroscopy experiments in HD$^+$. New values for the $m_p/m_e$ and $m_d/m_p$ mass ratios are determined.

A group theoretical approach to quantum gravity in (A)dS

This thesis is devoted to developing a group-theoretical approach towards quantum gravity in (Anti)-de Sitter spacetime. We start with a comprehensive review of the representation theory of de Sitter (dS) isometry group, focusing on the construction of unitary irreducible representations and the computation of characters. The three chapters that follow present the results of novel research conducted as a graduate student. Chapter 4 is based on [1]. We provide a general algebraic construction of higher spin quasinormal modes of de Sitter horizon and identify the boundary operator insertions that source the quasinormal modes from a local QFT point of view. Quasinormal modes of a single higher spin field in dSD furnish two nonunitary lowest-weight representations of the dS isometry group SO(1,D). We also show that quasinormal mode spectrums of higher spin fields are precisely encoded in the Harish-Chandra characters of the corresponding SO(1,D) unitary irreducible representations. Chapter 5 is based on work with D. Anninos, F. Denef and A. Law [2]. With potential application to constraining UV-complete microscopic models of de Sitter quantum gravity, we compute de Sitter entropy as the logarithm of the sphere path integral, for any possible low energy effective field theory containing a massless graviton, in arbitrary dimensions. The path integral is performed exactly at the one-loop level. The one-loop correction to the dS entropy is found to take a universal “bulk−edge” form, with the bulk part being an integral transformation of a Harish-Chandra character encoding quasinormal modes spectrum in a static patch of dS and the edge part being the same integral transformation of an edge character encoding degrees of freedom frozen on the dS horizon. In 3D de Sitter spacetime, the one-loop exact entropy is promoted to an all-loop exact result for truncated higher spin gravity, the latter admitting an SL(n,C) Chern-Simons formulation with n being the spin cut-off. Chapter 6 is based on [3]. Inspired by [2], we revisit the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime and show that it can be universally expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higherspin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters, leading to striking agreement with the predictions of higher spin holography. We also comment on the relation between our character integral formula and Rindler-AdS [4] thermal partition functions.

Stochastic Inflation at NNLO

Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.

Integrating out heavy fields in the path integral using the background-field method: general formalism

Building on an older method used to derive non-decoupling effects of a heavy Higgs boson in the Standard Model, we describe a general procedure to integrate out heavy fields in the path integral. The derivation of the corresponding effective Lagrangian including the one-loop contributions of the heavy particle(s) is particularly transparent, flexible, and algorithmic. The background-field formalism allows for a clear separation of tree-level and one-loop effects involving the heavy fields. Using expansion by regions the one-loop effects are further split into contributions from large and small momentum modes. The former are contained in Wilson coefficients of effective operators, the latter are reproduced by one-loop diagrams involving effective tree-level couplings. The method is illustrated by calculating potential non-decoupling effects of a heavy Higgs boson in a singlet Higgs extension of the Standard Model. In particular, we work in a field basis corresponding to mass eigenstates and properly take into account non-vanishing mixing between the two Higgs fields of the model. We also show that a proper choice of renormalization scheme for the non-standard sector of the underlying full theory is crucial for the construction of a consistent effective field theory.

Vacuum polarization energy of the kinks in the sinh-deformed models

We compute the one-loop quantum corrections to the kink energies of the sinh-deformed $\phi^{4}$ and $\varphi^{6}$ models in one space and one time dimensions. These models are constructed from the well-known polynomial $\phi^{4}$ and $\varphi^{6}$ models by a deformation procedure. We also compute the vacuum polarization energy to the non-polynomial function $U(\phi)=\frac{1}{4}(1-\sinh^{2}\phi)^{2}$. This potential approaches the $\phi^{4}$ model in the limit of small values of the scalar function. These energies are extracted from scattering data for fluctuations about the kink solutions. We show that for certain topological sectors with nonequivalent vacua the kink solutions of the sinh-deformed models are destabilized.

One-loop correction to the Casimir energy in Lifshitz-like theory

In this paper, Radiative Correction (RC) to the Casimir energy was computed for the self-interacting massive/massless Lifshitz-like scalar field, confined between a pair of plates with Dirichlet and Mixed boundary conditions in [Formula: see text] dimensions. Moreover, using the results obtained for the Dirichlet Casimir energy, the RC to the Casimir energy for Periodic and Neumann boundary conditions were also draw outed. To renormalize the bare parameters of the Lagrangian, a systematic perturbation expansion was used in which the counterterms were automatically obtained in a position-dependent manner. In our view, the position dependency of the counterterm was allowed, since it reflected the effects of the boundary condition imposed or the background space in the problem. All the answers obtained for the Casimir energy were consistent with well-known physical expects. In a language of graphs, the Casimir energy for the massive Lifshitz-like scalar field confined with four boundary conditions (Dirichlet, Neumann, Mixed, and Periodic) was also compared to each other, and as a concluding remark, the sign and magnitude of their values were discussed.

The gravitational field of a star in quadratic gravity

The characterization of the gravitational field of isolated objects is still an open question in quadratic theories of gravity.We study static equilibrium solutions for a self-gravitating fluid in extensions of General Relativity includingterms quadratic in the Weyl tensor C μνρσ and in the Ricci scalar R, as suggested by one-loop corrections to classical gravity. By the means of a shooting method procedure we link the total gravitational mass and the strength of the Yukawa corrections associated with the quadratic terms with the fluid properties at the center.It is shown that the inclusion of the C μνρσ μνρσ coupling in the lagrangian has a much strongerimpact than the R 2 correction in the determination of the radius and of the maximum mass of a compact object.We also suggest that the ambiguity in the definition of mass in quadratic gravity theories can convenientlybe exploited to detect deviations from standard General Relativity.

Higgs boson decay to paired Bc: Relativistic and one-loop corrections

The exclusive decays of the Higgs boson to BcBc and Bc⁎Bc⁎ pairs are studied. The hard parts of the decay amplitudes are estimated within the perturbative Standard Model up to one-loop corrections. The soft fusion of heavy quarks to the quarkonium is described in framework of the relativistic quark model.

Optical conductivity of a Dirac-Fermi liquid

A Dirac-Fermi liquid (DFL)--a doped system with Dirac spectrum--is an important example of a non-Galilean-invariant Fermi liquid (FL). Real-life realizations of a DFL include, e.g., doped graphene, surface states of three-dimensional (3D) topological insulators, and 3D Dirac/Weyl metals. We study the optical conductivity of a DFL arising from intraband electron-electron scattering. It is shown that the effective current relaxation rate behaves as $1/\tau_{J}\propto \left(\omega^2+4\pi^2 T^2\right)\left(3\omega^2+8\pi^2 T^2\right)$ for $\max\{\omega, T\}\ll \mu$, where $\mu$ is the chemical potential, with an additional logarithmic factor in two dimensions. In graphene, the quartic form of $1/\tau_{J}$ competes with a small FL-like term, $\propto\omega^2+4\pi^2 T^2$, due to trigonal warping of the Fermi surface. We also calculated the dynamical charge susceptibility, $\chi_\mathrm{c}({\bf q},\omega)$, outside the particle-hole continua and to one-loop order in the dynamically screened Coulomb interaction. For a 2D DFL, the imaginary part of $\chi_\mathrm{c}({\bf q},\omega)$ scales as $q^2\omega\ln|\omega|$ and $q^4/\omega^3$ for frequencies larger and smaller than the plasmon frequency at given $q$, respectively. The small-$q$ limit of $\mathrm{Im} \chi_\mathrm{c}({\bf q},\omega)$ reproduces our result for the conductivity via the Einstein relation.

Weak deflection angle by electrically and magnetically charged black holes from nonlinear electrodynamics

Nonlinear electrodynamic (NLED) theories are well motivated for their extensions to classical electrodynamics in the strong field regime, and have been extensively investigated in the search for regular black hole solutions. In this paper, we focus on two spherically symmetric and static black hole solutions based on two types of NLED---the Euler-Heisenberg NLED model and the Bronnikov NLED model---and calculate the weak deflection angle of light and charged particles by these two black holes with the help of the Gauss-Bonnet theorem. We investigate the effects of the one-loop corrections to quantum electrodynamics on the deflection angle and analyze the behavior of the deflection angle by a regular magnetically charged black hole. It is found that both the electric and magnetic charges of the black hole reduce the weak deflection angle, and the one-loop corrections make a positive contribution to the deflection angle, but their influence is deeply suppressed by the impact parameter. For the charged particles, due to electrostatic interaction, the weak deflection angle changes noticeably and the influence of the one-loop corrections is enhanced. We find that the regular magnetically charged black hole based on the Bronnikov NLED model has a smaller deflection angle than the singular one. We also calculate the deflection angle of light by the geodesic method for verification. In addition, we discuss the effects of a cold nonmagnetized plasma on the deflection angle and find that the deflection angle increases with the plasma parameter.

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.

Erratum: Universality hypothesis breakdown at one-loop order [Phys. Rev. D 97 , 105006 (2018)

Received 18 May 2021DOI:https://doi.org/10.1103/PhysRevD.104.029901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum field theoryPropertiesSymmetries in condensed matterParticles & Fields

Radiative neutrino masses, lepton flavor mixing and muon g \u2212 2 in a leptoquark model

We propose a leptoquark model with two scalar leptoquarks {S}_1left(overline{3},1,frac{1}{3}right) and {tilde{R}}_2left(3,2,frac{1}{6}right) to give a combined explanation of neutrino masses, lepton flavor mixing and the anomaly of muon g − 2, satisfying the constraints from the radiative decays of charged leptons. The neutrino masses are generated via one-loop corrections resulting from a mixing between S1 and {tilde{R}}_2 . With a set of specific textures for the leptoquark Yukawa coupling matrices, the neutrino mass matrix possesses an approximate μ-τ reflection symmetry with (Mν)ee = 0 only in favor of the normal neutrino mass ordering. We show that this model can successfully explain the anomaly of muon g − 2 and current experimental neutrino oscillation data under the constraints from the radiative decays of charged leptons.

Electromagnetic albedo of Quantum Black Holes

We compute the albedo (or reflectivity) of electromagnetic waves off the electron-positron Hawking plasma that surrounds the horizon of a Quantum Black Hole. We adopt the “modified firewall conjecture” for fuzzballs [1, 2], where we consider significant electromagnetic interaction around the horizon. While prior work has treated this problem as an electron-photon scattering process, we find that the incoming quanta interact collectively with the fermionic excitations of the Hawking plasma at low energies. We derive this via two different methods: one using relativistic plasma dispersion relation, and another using the one-loop correction to photon propagator. Both methods find that the reflectivity of long wavelength photons off the Hawking plasma is significant, contrary to previous claims. This leads to the enhancement of the electromagnetic albedo for frequencies comparable to the Hawking temperature of black hole horizons in vacuum. We comment on possible observable consequences of this effect.

Testing one-loop galaxy bias: Joint analysis of power spectrum and bispectrum

We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order ("one-loop") description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness-of-fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order ("tree-level") bispectrum. Using measurement uncertainties that correspond to an effective survey volume of $6\,(\mathrm{Gpc}/h)^3$, we determine that the one-loop corrections roughly double the applicable range of scales, from $\sim 0.17\,h/\mathrm{Mpc}$ (tree-level) to $\sim 0.3\,h/\mathrm{Mpc}$. This converts into a $1.5 - 2$x improvement on constraints of the linear bias parameter at fixed cosmology, and a $1.5 - 2.4$x shrinkage of uncertainties on the amplitude of fluctuations $A_s$, which clearly demonstrates the benefit of extracting information from nonlinear scales despite having to marginalize over a larger number of bias parameters. Besides, our precise measurements of galaxy bias parameters up to fourth order allow for thorough comparisons to coevolution relations, showing excellent agreement for all contributions generated by the nonlocal action of gravity. Using these relations in the likelihood analysis does not compromise the model validity and is crucial for obtaining the quoted improvements on $A_s$. We also analyzed the impact of higher-derivative and scale-dependent stochastic terms, finding that for a subset of our tracers the former can boost the performance of the tree-level model with constraints on $A_s$ that are only slightly degraded compared to the one-loop model.

Contribution of heavy neutrinos to decay of standard-model-like Higgs boson →μτ in a 3-3-1 model with additional gauge singlets

Abstract In the framework of the improved version of the 3-3-1 models with right-handed neutrinos, which are added to the Majorana neutrinos as new gauge singlets, the recent experimental neutrino oscillation data is completely explained through the inverse seesaw mechanism. We show that the major contributions to $Br(\mu\rightarrow e\gamma)$ are derived from corrections at one-loop order of heavy neutrinos and bosons. But, these contributions are sometimes mutually destructive, creating regions of parametric spaces where the experimental limits of $Br(\mu\rightarrow e\gamma)$ are satisfied. In these regions, we find that $Br(\tau\rightarrow \mu\gamma)$ can achieve values of $10 ^{- 10}$ and $Br(\tau\rightarrow e\gamma)$ may even reach values of $10 ^{- 9}$, very close to the upper bound of the current experimental limits. Those are ideal areas to study lepton-flavor-violating decays of the standard-model-like Higgs boson ($h_1^0$). We also point out that the contributions of heavy neutrinos play an important role in changing $Br(h_1^0\rightarrow \mu\tau)$; this is presented through different forms of mass mixing matrices ($M_R$) of heavy neutrinos. When $M_R \sim \mathrm{diag}(1,1,1)$, $Br(h_1^0\rightarrow \mu\tau)$ can attain a greater value than in the cases $M_R \sim \mathrm{diag}(1,2,3)$ and $M_R \sim \mathrm{diag}(3,2,1)$; the largest that $Br(h_1^0\rightarrow \mu\tau)$ can reach is very close $10 ^{-3}$.

W+W−H production through bottom quarks fusion at hadron colliders

With the standard model working well in describing the collider data, the focus is now on determining the standard model parameters as well as for any hint of deviation. In particular, the determination of the couplings of the Higgs boson with itself and with other particles of the model is important to better understand the electroweak symmetry breaking sector of the model. In this letter, we look at the process pp→WWH, in particular through the fusion of bottom quarks. Due to the non-negligible coupling of the Higgs boson with the bottom quarks, there is a dependence on the WWHH coupling in this process. This sub-process receives the largest contribution when the W bosons are longitudinally polarized. We compute one-loop QCD corrections to various final states with polarized W bosons. We find that the corrections to the final state with the longitudinally polarized W bosons are large. It is shown that the measurement of the polarization of the W bosons can be used as a tool to probe the WWHH coupling in this process. We also examine the effect of varying WWHH coupling in the κ-framework.

Radiative seesaw mechanism for charged leptons

We discuss a mechanism where charged lepton masses are derived from one-loop diagrams mediated by particles in a dark sector including a dark matter candidate. We focus on a scenario where the muon and electron masses are generated at one loop with new $\mathcal{O}(1)$ Yukawa couplings. The measured muon anomalous magnetic dipole moment, $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$, can be explained in this framework. As an important prediction, the muon and electron Yukawa couplings can deviate significantly from their standard model predictions, and such deviations can be tested at High-Luminosity LHC and future ${e}^{+}{e}^{\ensuremath{-}}$ colliders.

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.

Graviton backreaction on the local cosmological expansion in slow-roll inflation

We compute the graviton one-loop correction to the expectation value of the local expansion rate in slow-roll inflation, with both slow-roll parameters finite. The calculation is based on a recent method to explicitly construct gauge-invariant observables in perturbative quantum gravity at all orders in perturbation theory, and it is particularly suited in cases of highly-symmetrical space-time backgrounds. Our analysis adds to recent calculations of that correction in de Sitter space-time and in single-field inflation with constant deceleration. In the former case a vanishing one-loop correction was found, while in the latter the quantum backreaction produces a secular effect that accelerates the expansion. The quantum correction we describe here produces a finite secular effect that can either accelerated or decelerate the background expansion, depending on the value of the slow-roll parameters.