Higher-order Corrections Research Articles

One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes

As one of the promising candidates of cold dark matter (DM), primordial black holes (PBHs) were formed due to the collapse of over-densed regions generated by the enhanced curvature perturbations during the radiation-dominated era. The enhanced curvature perturbations are expected to be non-Gaussian in some relevant inflation models and hence the higher-order loop corrections to the curvature power spectrum might be non-negligible as well as altering the abundance of PBHs. In this paper, we calculate the one-loop correction to the curvature power spectrum with local-type non-Gaussianities characterizing by $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ denotes the variance of Gaussian part of enhanced curvature perturbation, and such a perturbativity condition can provide a stringent constraint on the relevant inflation models for the formation of PBHs.

High-order QED correction impacts on phase transition of the Euler-Heisenberg AdS black hole

Two-phase transition branches of the Euler-Heisenberg (EH) anti-de Sitter (AdS) black hole (BH) were derived from its phase transition critical behavior by Magos et al. [Phys. Rev. D. 102, 084011 (2020)]. We found that the phase transition is unstable. Considering the high-order quantum electrodynamics (QED) correction, we re-derive the EHAdS BH solution and investigate its critical thermodynamic quantities. It is found that the corrected EHAdS BH has only one stable phase transition branch, and its critical exponents are equivalent to that of the vdW system. From the microscopic point of view, we also derive its normalized scalar curvature based on the Ruppeiner geometry. Different from two concave surfaces of the scalar curvature without considering the high-order QED correction, we show that the corrected Ruppeiner geometry has only one concave surface. Our results indicate that the phase transition instability derived by Magos $et~al.$ is due to without considering the high-order QED correction.

Variational vs perturbative relativistic energies for small and light atomic and molecular systems.

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit-Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α4Eh) non-radiative QED correction is 5% of the leading-order (α3Eh) non-radiative QED correction for Z = 2 (He), but it is 40% already for Z = 4 (Be2+), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

Mass Generation and Gravity

Despite the success of the Higgs mechanism to account for the generation of masses of the Standard Model (SM) elementary particles, the ultimate nature and origin of “mass” remain open questions in contemporary physics. From a foundational perspective, mass should be fundamentally related to the gravitational interaction and, according to Mach, with the structure of the Universe. In the present letter, a fully dynamical mass generation mechanism induced by higher-order corrections in the GR Lagrangian is discussed. Notably, the vacuum energy plays a key role in this process, which applies to both vector bosons and fermions. We show that, at the classical level, the Higgs mechanism can be though of as a particular case of the present mechanism.

Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to H2+

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m\alpha^7 \ln(\alpha)$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $m\alpha^6$-order relativistic correction, for the case of H$_2^+$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.

QED calculations of energy levels of heliumlike ions with 5≤Z≤30

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$ is presented for the ground and $n=2$ excited states of heliumlike ions. After subtracting the first terms of the $Z\ensuremath{\alpha}$ expansion from the all-order results, we identify the higher-order QED effects of order $m{\ensuremath{\alpha}}^{7}$ and higher. Combining the higher-order remainder with the results complete through order $m{\ensuremath{\alpha}}^{6}$ from Yerokhin and Pachucki [Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and nonmixing $n=2$ states of heliumlike ions with $Z=5\text{--}30$. For the mixing $2\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ and $2\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z>10$.

Revisiting inclusive decay widths of charmed mesons

Determining for the first time the Darwin operator contribution for the non-leptonic charm-quark decays and using new non-perturbative results for the matrix elements of ∆C = 0 four-quark operators, including eye-contractions, we present a comprehensive study of the lifetimes of charmed mesons and inclusive semileptonic decay rates as well as the ratios, within the framework of the Heavy Quark Expansion (HQE). We find good agreement with experiment for the ratio τ(D+)/τ(D0), for the total {D}_s^{+} -meson decay rate, for the semileptonic rates of all three mesons D0, D+ and {D}_s^{+} , and for the semileptonic ratio {Gamma}_{sl}^{D^{+}}/{Gamma}_{sl}^{D^0} . The total decay rates of the D0 and D+ mesons are underestimated in our HQE approach and we suspect that this is due to missing higher-order QCD corrections to the free charm quark decay and the Pauli interference contribution. For the SU(3)F breaking ratios tau left({D}_s^{+}right)/tau left({D}^0right) and {Gamma}_{sl}^{D_s^{+}}/{Gamma}_{sl}^{D^0} our predictions lie closer to one than experiment. This might originate from the poor knowledge of the non-perturbative parameters {mu}_G^2 , {mu}_{uppi}^2 and {rho}_D^3 in the D0 and {D}_s^{+} systems. These parameters could be determined by experimental studies of the moments of inclusive semileptonic D meson decays.

Lepton pair photoproduction in peripheral relativistic heavy-ion collisions

We study the lepton pair photoproduction in peripheral heavy-ion collisions based on the formalism in our previous work [R.-j. Wang, S. Pu, and Q. Wang, Phys. Rev. D 104, 056011 (2021)]. We present the numerical results for the distributions of the transverse momentum, azimuthal angle and invariant mass for ${e}^{+}{e}^{\ensuremath{-}}$ and ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pairs as functions of the impact parameter and other kinematic variables in $\mathrm{Au}+\mathrm{Au}$ collisions. Our calculation incorporates the information on the transverse momentum and polarization of photons which is essential to describe the experimental data. We observe a broadening effect in the transverse momentum for lepton pairs with and without smear effects. We also observe a significant enhancement in the distribution of $\mathrm{cos}(2\ensuremath{\varphi})$ for ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pairs. Our results provide a baseline for future studies of other higher order corrections beyond Born approximation and medium effects in the lepton pair production.

Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in four dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries that contribute dominantly to the large-$j$ Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to ${e}^{i\mathcal{I}}$, where $\mathcal{I}$ is the Regge action of the geometry plus corrections of higher order in curvature. As a result, in the semiclassical regime, the spinfoam amplitude reduces to an integral over Regge geometries weighted by ${e}^{i\mathcal{I}}$, where $\mathcal{I}$ is the Regge action plus corrections of higher order in curvature. As a by-product, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity.

Logarithmic corrections for jet production at the LHC

Several important processes and analyses at the LHC are sensitive to higher-order perturbative corrections beyond what can currently be calculated at fixed order. One important class of logarithmic corrections are those which appear when the centre-of-mass energy of a QCD collision is much larger than the transverse momenta of the observed jets. We describe the High Energy Jets (HEJ) framework, which includes the dominant high-energy logarithms to provide all-order predictions for several LHC processes including Higgs, W, or Z boson production in association with jets. We will summarise some recent developments, in particular the first matching of HEJ to a NLO calculation.

Bubble nucleation to all orders

This paper extends classical results by Langer and Kramers [1–3] and combines them with modern methods from high-temperature field theory [4–8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders — the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9–11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4–7, 12–14], all results only hold within this framework.

Existence and regularity of source-type self-similar solutions for stable thin-film equations

We investigate the existence and the boundary regularity of source-type self-similar solutions to the thin-film equation $h\_t=-(h^nh\_{zzz})z+(h^{n+3}){zz},$ $t>0,; z\in \mathbb{R};; h(0,z)= \omega \delta(z)$ where $n\in (3/2,3),; \omega > 0$ and $\delta$ is the Dirac mass at the origin. It is known that the leading order expansion near the edge of the support coincides with that of a traveling-wave solution for the standard thin-film equation: $h\_t=-(h^nh\_{zzz})\_z$. In this paper we sharpen this result, proving that the higher-order corrections are analytic with respect to three variables: the first one is just the {spatial} variable, whereas the second and the third (except for $n = 2$) are irrational powers of it. It is known that this third variable does not appear for the thin-film equation without gravity.

NLO QCD corrections to full off-shell production of toverline{t}Z including leptonic decays

Motivated by ongoing new physics searches in the top-quark sector at the Large Hadron Collider we report on the calculation of NLO QCD corrections to the Standard Model pp → toverline{t}Z + X process in the tetra-lepton decay channel. This calculation is based on the matrix elements for the {e}^{+}{nu}_e{mu}^{-}{overline{nu}}_{mu }boverline{b}{tau}^{+}{tau}^{-} final state and includes all resonant and non-resonant Feynman diagrams, interferences and off-shell effects of the top quark as well as the W and Z gauge bosons. Also incorporated are photon-induced contributions. As it is customary for such studies, we show theoretical predictions for both fixed and dynamical factorisation and renormalisation scale choices and different PDF sets. Furthermore, we study the main theoretical uncertainties that are associated with neglected higher-order terms in the perturbative expansion and with the parameterisation of the PDF sets. In order to investigate the size of off-shell effects and higher-order corrections in top-quark decays, we perform a second computation for this process, which is based on the narrow-width-approximation where the top quarks, W and Z gauge bosons are kept on-shell. Results are given for the integrated and differential fiducial cross sections for the LHC Run II center-of-mass energy of 13 TeV.

QCD corrections in tqgamma production at hadron colliders

We study QCD corrections for the associated production of a single top quark and a photon (tqgamma production) at hadron colliders. We calculate the NLO cross section at LHC and future collider energies for a variety of kinematical cuts, and we estimate uncertainties from scale dependence and from parton distributions. We also calculate differential distributions in top-quark transverse-momentum and rapidity as well as photon energy. Finally, we study higher-order corrections from soft-gluon emission for this process, and we provide approximate NNLO (aNNLO) results for the cross section and top-quark differential distributions. We also compare our calculations with recent measurements from CMS and ATLAS at the LHC and find that the aNNLO corrections improve the comparison between the data and the Standard Model predictions.

Single-channel or multichannel thermal transport: Effect of higher-order anharmonic corrections on the predicted phonon thermal transport properties of semiconductors

The phonon thermal transport properties of eight ternary intermetallic semiconductors are investigated by accounting for higher-order four-phonon scattering, phonon renormalization, and multichannel thermal transport. The commonly used lowest-order theory, which accounts only for three-phonon scattering and without phonon renormalization, fails drastically for the considered materials and underpredicts the thermal conductivity by up to a factor of two. The thermal conductivity decreases for three compounds and increases for five compounds with the application of higher-order corrections owing to a contrasting role of four-phonon scattering and phonon stiffening on the predicted thermal conductivity. Using the higher-order theory, at a temperature of 300 K, the lowest obtained thermal conductivity is 0.31 W/m K for ${\text{BiCsK}}_{2}$ and three other compounds (${\text{SbCsK}}_{2}$, ${\text{SbRbNa}}_{2}$, and ${\text{SbRbK}}_{2}$) have thermal conductivities lower than $0.5\phantom{\rule{0.28em}{0ex}}\text{W/m}\phantom{\rule{0.16em}{0ex}}\text{K}$ via the particlelike phonon transport channel. The contribution from the wavelike coherent transport channel is lower than 0.05 W/m K in all of these ultralow thermal conductivity compounds. The higher-order theory is crucial for the correct description of thermal transport physics, failing which the thermal transport is wrongly characterized as multichannel transport by the lowest-order theory.

Growth of power spectrum due to decrease of sound speed during inflation

We study the amplification of the curvature perturbations due to a small sound speed and find that its origin is different completely from that due to the ultraslow-roll inflation. This is because when the sound speed is very small the enhancement of the power spectrum comes from the fact that the curvature perturbations at the scales smaller than the cosmic microwave background (CMB) scale become scale variant, rather than growing that leads to the amplification of the curvature perturbations during the ultraslow-roll inflation. At large scales, the power spectrum of the curvature perturbations remains to be scale invariant, which is consistent with the CMB observations, and then it will have a transient ${k}^{2}$ growth and finally approach a ${k}^{4}$ growth as the scale becomes smaller and smaller. Thus, the power spectrum can be enhanced to generate a sizable amount of primordial black holes. Furthermore, when the high order correction in the dispersion relation of the curvature perturbations is considered, the growth of the power spectrum of the curvature perturbations has the same origin as that in the case without this correction.

Higher-order corrections to exclusive heavy vector meson production

We present results for higher-order corrections to exclusive production. This includes the first relativistic correction of order v^2v2 in quark velocity, and next-to-leading order corrections in \alpha_sαs for longitudinally polarized production. The relativistic corrections are found to be important for a good description of the HERA data, especially at small values of the photon virtuality. The next-to-leading order results for longitudinal production are evaluated numerically. We also demonstrate how the vector meson production provides complementary information to the structure functions for extracting the initial condition for the small-xx evolution of the dipole-proton scattering amplitude.

PineAPPL: NLO EW corrections for PDF processes

Modern parton distribution function (PDF) determinations either neglect higher-order corrections in the electroweak (EW) coupling or implement them approximately for a subset of PDF processes. We present a new tool, PineAPPL, which supports perturbative correction in arbitrary powers of the EW and strong coupling constant, and stores theoretical predictions independently of the used PDFs in so-called interpolation grids. These are the foundation of any PDF determination, and will allow us to perform a PDF fit taking into account EW corrections for all processes consistently. Apart from PDF determinations PineAPPL can also be used in precision phenomenology to study the impact of different choices of PDF sets, without rerunning the time-consuming computation. As an application of this tool we show Drell-Yan (DY) lepton-pair production were larger effects of NLO EW corrections can be seen that will potentially influence the PDF fit and comment about which observables are particularly suited and NLO EW PDF fit and which are not.

$tW$ and $tZ'$ production at hadron colliders

We present theoretical results with soft-gluon corrections for two separate processes: (1) the production of a single top quark in association with a W boson in the Standard Model; and (2) the production of a single top quark in association with a heavy Z' boson in new physics models with or without anomalous couplings. We show that the higher-order corrections from soft-gluon emission are dominant for a wide range of collider energies. Results are shown for the total cross sections and top-quark transverse-momentum and rapidity distributions for tW and tZ' production at LHC and future collider energies up to 100 TeV. The uncertainties from scale dependence and parton distribution functions are also analyzed.

Hybrid high-energy/collinear factorization in a heavy-light dijets system reaction

We propose the inclusive hadroproduction of a heavy-light dijet system, as a new channel for the investigation of high-energy QCD. We build up a hybrid factorization that incorporates a partial next-to-leading BFKL resummation inside the standard collinear description of observables. We present a detailed analysis of different distributions: cross-section summed over azimuthal angles and differential in rapidity and azimuthal distribution. The stability that these distributions show under higher-order corrections motivates our interest in future studies, doable at new generation colliding machines.