One-loop Results Research Articles

Two-loop analysis of classically scale-invariant models with extended Higgs sectors

We present the first explicit calculation of leading two-loop corrections to the Higgs trilinear coupling λhhh in models with classical scale invariance (CSI), using the effective-potential approximation. Furthermore, we also study — for the first time at two loops — the relation that appears between the masses of all states in CSI theories, due to the requirement of reproducing correctly the 125-GeV Higgs-boson mass. In addition to obtaining analytic results for general CSI models, we consider two particular examples of Beyond-the-Standard-Model theories with extended Higgs sectors, namely an N-scalar model (endowed with a global O(N) symmetry) and a CSI version of the Two-Higgs-Doublet Model, and we perform detailed numerical studies of these scenarios. While at one loop the value of the Higgs trilinear coupling is identical in all CSI models, and deviates by approximately 82% from the (one-loop) SM prediction, we find that the inclusion of two- loop corrections lifts this universality and allows distinguishing different BSM scenarios with CSI. Taking into account constraints from perturbative unitarity and the relation among masses, we find for both types of scenarios we consider that at two loops λhhh deviates from its SM prediction by 100 ± 10% — i.e. a quite significant further deviation with respect to the one-loop result of ∼ 82%.

Quantum corrections to generic branes: DBI, NLSM, and more

We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

Ghost-antighost-gluon vertex from the Curci-Ferrari model: Two-loop corrections

The Curci-Ferrari model has been shown to provide a good grasp on pure Yang-Mills correlation functions in the Landau gauge, already at one-loop order. In a recent work, the robustness of these results has been tested by evaluating the two-loop corrections to the gluon and ghost propagators. We pursue this systematic investigation by computing the ghost-antighost-gluon vertex to the same accuracy in a particular kinematic configuration that makes the calculations simpler. Because both the parameters of the model and the normalizations of the fields have already been fixed in a previous work, the present calculation represents both a pure prediction and a stringent test of the approach. We find that the two-loop results systematically improve the comparison to Monte-Carlo simulations as compared to earlier one-loop results. The improvement is particularly significative in the SU($3$) case where the predicted ghost-antighost-gluon vertex is in very good agreement with the data. The same comparison in the SU($2$) case is not as good, however. This may be due to the presence of a larger coupling constant in the infrared in that case although we note that a similar mismatch has been quoted in non-perturbative continuum approaches. Despite these features of the SU($2$) case, it is possible to find sets of parameters fitting both the propagators and the ghost-antighost-gluon vertex to a reasonable accuracy.

Circular Wilson loops in defect mathcal{N} = 4 SYM: phase transitions, double-scaling limits and OPE expansions

We consider circular Wilson loops in a defect version of mathcal{N} = 4 super-Yang- Mills theory which is dual to the D3-D5 brane system with k units of flux. When the loops are parallel to the defect, we can construct both BPS and non-BPS operators, depending on the orientation of the scalar couplings in the R-symmetry directions. At strong ’t Hooft coupling we observe, in the non supersymmetric case, a Gross-Ooguri-like phase transition in the dual gravitational theory: the familiar disk solution dominates, as expected, when the operator is far from the defect while a cylindrical string worldsheet, connecting the boundary loop with the probe D5-brane, is favourite below a certain distance (or equivalently for large radii of the circles). In the BPS case, instead, the cylindrical solution does not exist for any choice of the physical parameters, suggesting that the exchange of light supergravity modes always saturate the expectation value at strong coupling. We study the double-scaling limit for large k and large ’t Hooft coupling, finding full consistency in the non-BPS case between the string solution and the one-loop perturbative result. Finally we discuss, in the BPS case, the failure of the double-scaling limit and the OPE expansion of the Wilson loop, finding consistency with the known results for the one-point functions of scalar composite operators.

One-loop amplitudes in AdS5\xd7S5 supergravity from mathcal{N} = 4 SYM at strong coupling

We explore the structure of maximally supersymmetric Yang-Mills correlators in the supergravity regime. We develop an algorithm to construct one-loop supergravity amplitudes of four arbitrary Kaluza-Klein supergravity states, properly dualised into single- particle operators. We illustrate this algorithm by constructing new explicit results for multi-channel correlation functions, and we show that correlators which are degenerate at tree level become distinguishable at one-loop. The algorithm contains a number of subtle features which have not appeared until now. In particular, we address the presence of non- trivial low twist protected operators in the OPE that are crucial for obtaining the correct one-loop results. Finally, we outline how the differential operators {hat{D}}_{pqrs} and ∆(8), which play a role in the context of the hidden 10d conformal symmetry at tree level, can be used to reorganise our one-loop correlators.

A tale of two exponentiations in mathcal{N} = 8 supergravity at subleading level

High-energy massless gravitational scattering in mathcal{N} = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ϵ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

Functional methods for false-vacuum decay in real time

We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest- descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering. While this amplitude may in principle be obtained by analytic continuation of its Euclidean counterpart, we work out in detail how it can be computed to one-loop order at the level of the path integral, i.e. evaluating the Gaußian integrals of fluctuations about the relevant complex saddle points. To that effect, we show how the eigenvalues and eigenfunctions on a thimble can be obtained by analytic continuation of the Euclidean eigensystem, and we determine the path-integral measure on thimbles. This way, using real-time methods, we recover the one-loop result by Callan and Coleman for the decay rate. We finally demonstrate our real-time methods explicitly, including the construction of the eigensystem of the complex saddle, on the archetypical example of tunneling in a quasi-degenerate quartic potential.

Electromagnetic angular momentum of the electron: One-loop studies

We study angular momentum of the electron stored in its electric and magnetic fields. We use for this purpose quantum electrodynamics in the covariant gauge. We show that a finite one-loop result for such angular momentum can be obtained without invoking any renormalization procedure. We compare it to the classical estimation relying on a short-distance cutoff.

Non-perturbative corrections to the quasiparticle velocity in graphene

Relativistic fermionic systems have physical quantities calculated by well established quantum electrodynamic prescriptions. In the last few years there has been an enormous interest in condensed matter systems in which the fermions exhibit relativistic dispersion, as Dirac fermions in graphene. We employ a non-perturbative method in order to obtain a non-perturbative correction to the quasiparticle velocity in graphene, and compare with the experimental data. We find a better agreement between the quasiparticle velocity corrected with non-perturbative corrections and measurements, when compared with the standard one-loop result. We also investigate the behavior of the beta function of the renormalization group theory, and find that the non-perturbative corrections do not alter the stability of the infrared fixed point found by the standard result.

Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity

We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function for a quartic self-interaction reproduces the well-known one-loop result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension D up to the first order in curvature. Furthermore, we present a sample of numerical simulations for D=3 in the first order in curvature. We consider the model with spontaneous symmetry breaking and obtain fully nonperturbative solutions for the vacuum expectation value of the scalar field and compare them with one- and two-loop solutions.

Scattering of spinning black holes from exponentiated soft factors

We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinor-helicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion.

Low-energy lepton physics in the MRSSM: (g \u2212 2)\u03bc, \u03bc\u2192e\u03b3 and \u03bc\u2192e conversion

Low-energy lepton observables are discussed in the Minimal R-symmetric Supersymmetric Standard Model. We present comprehensive numerical analyses and the analytic one-loop results for (g − 2)μ, μ → eγ, and μ → e conversion. The interplay between the three observables is investigated as well as the parameter regions with large g − 2. A striking difference to the MSSM is the absence of tanβ enhancements; however we find smaller enhancements governed by MRSSM-specific R-Higgsino couplings λd and Λd. As a result we find significant contributions to g − 2 only in a small parameter space with several SUSY masses below 200 GeV, compressed spectra and large λd, Λd. In this parameter space there is a correlation between all three considered observables. In the parameter region with small (g − 2)μ the SUSY masses can be larger and the correlation between μ → eγ and μ → e conversion is weak. Therefore already COMET Phase 1 has a promising sensitivity to the MRSSM.

Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid

We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $\text{U}(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum, and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading nonanalytic contributions to the energy-momentum tensor as well as the $\text{U}(1)$ current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydrokinetic equations reproduce the one-loop results derived from statistical field theory. We use these results to establish bounds on transport coefficients. We generalize the stochastic equation to a background flow undergoing Bjorken expansion. We compute the leading fractional power $\mathcal{O}({(\ensuremath{\tau}T)}^{\ensuremath{-}3/2})$ correction to the $\text{U}(1)$ current and compare with the first-order gradient term.

One-loop renormalization of staple-shaped operators in continuum and lattice regularizations

In this paper we present one-loop results for the renormalization of nonlocal quark bilinear operators, containing a staple-shaped Wilson line, in both continuum and lattice regularizations. The continuum calculations were performed in dimensional regularization, and the lattice calculations for the Wilson/clover fermion action and for a variety of Symanzik-improved gauge actions. We extract the strength of the one-loop linear and logarithmic divergences (including cusp divergences), which appear in such nonlocal operators; we identify the mixing pairs which occur among some of these operators on the lattice, and we calculate the corresponding mixing coefficients. We also provide the appropriate RI'-like scheme, which disentangles this mixing nonperturbatively from lattice simulation data, as well as the one-loop expressions of the conversion factors, which turn the lattice data to the MS-bar scheme. Our results can be immediately used for improving recent nonperturbative investigations of transverse momentum-dependent distribution functions (TMDs) on the lattice. Finally, extending our perturbative study to general Wilson-line lattice operators with n cusps, we present results for their renormalization factors, including identification of mixing and determination of the corresponding mixing coefficients, based on our results for the staple operators.

Pitfalls of iterative pole mass calculation in electroweak multiplets

.The radiatively induced mass splitting between components of an electroweak multiplet is typically of order 100 MeV. This is sufficient to endow the charged components with macroscopically observable lifetimes, and ensure an electrically neutral dark matter particle. We show that a commonly used iterative procedure to compute radiatively corrected pole masses can lead to very different mass splittings than a non-iterative calculation at the same loop order. By estimating the uncertainties of the two one-loop results, we show that the iterative procedure is significantly more sensitive to the choice of renormalisation scale and gauge parameter than the non-iterative method. This can cause the lifetime of the charged component to vary by up to 12 orders of magnitude if iteration is employed. We show that individual pole masses exhibit similar scale-dependence regardless of the procedure, but that the leading scale-dependent terms cancel when computing the mass splitting if and only if the non-iterative procedure is employed. We show that this behaviour persists at two-loop order: the precision of the mass splitting improves in the non-iterative approach, but our results suggest that higher-order corrections do not reduce the uncertainty in the iterative calculation enough to resolve the problem at two-loop order. We conclude that the iterative procedure should not be used for computing pole masses in situations where electroweak mass splittings are phenomenologically relevant.

Equation of state of the one- and three-dimensional Bose-Bose gases

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero-temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schr\"odinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic-droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the inter-species coupling constants.

The effective χ parameter in polarizable polymeric systems: One-loop perturbation theory and field-theoretic simulations.

We derive the effective Flory-Huggins parameter in polarizable polymeric systems, within a recently introduced polarizable field theory framework. The incorporation of bead polarizabilities in the model self-consistently embeds dielectric response, as well as van der Waals interactions. The latter generate a χ parameter (denoted χ̃) between any two species with polarizability contrast. Using one-loop perturbation theory, we compute corrections to the structure factor Sk and the dielectric function ϵ^(k) for a polarizable binary homopolymer blend in the one-phase region of the phase diagram. The electrostatic corrections to S(k) can be entirely accounted for by a renormalization of the excluded volume parameter B into three van der Waals-corrected parameters BAA, BAB, and BBB, which then determine χ̃. The one-loop theory not only enables the quantitative prediction of χ̃ but also provides useful insight into the dependence of χ̃ on the electrostatic environment (for example, its sensitivity to electrostatic screening). The unapproximated polarizable field theory is amenable to direct simulation via complex Langevin sampling, which we employ here to test the validity of the one-loop results. From simulations of S(k) and ϵ^(k) for a system of polarizable homopolymers, we find that the one-loop theory is best suited to high concentrations, where it performs very well. Finally, we measure χ̃N in simulations of a polarizable diblock copolymer melt and obtain excellent agreement with the one-loop theory. These constitute the first fully fluctuating simulations conducted within the polarizable field theory framework.

Fluctuation effects at the onset of the 2kF density wave order with one pair of hot spots in two-dimensional metals

We analyze quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate $2k_F$ wave vector connecting a single pair of hot spots on the Fermi surface. We compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a fluctuation expansion (one loop). Non-Fermi liquid behavior with anomalous frequency scaling and a vanishing quasi particle weight is obtained. The momentum dependence yields a divergent renormalization of the Fermi velocity and a flattening of the Fermi surface near the hot spots. Going beyond the leading order calculation we find that the one-loop result is not self-consistent. We show that any momentum-independent self-energy with a non-Fermi liquid frequency exponent wipes out the peak of the polarization function at the $2k_F$ wave vector, and thus destroys the mechanism favoring $2k_F$ density waves over those with generic wave vectors. However, a $2k_F$ density wave quantum critical point might survive in presence of a sufficiently flat renormalized Fermi surface.

Scale-invariant instantons and the complete lifetime of the standard model

In a classically scale-invariant quantum field theory, tunneling rates are infrared divergent due to the existence of instantons of any size. While one expects such divergences to be resolved by quantum effects, it has been unclear how higher-loop corrections can resolve a problem appearing already at one loop. With a careful power counting, we uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. We also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing and finite mass effects. In addition, we produce exact closed-form solutions for the functional determinants over scalars, fermions and vector bosons around the scale-invariant bounce, demonstrating manifest gauge invariance in the vector case. With these problems solved, we produce the first complete calculation of the lifetime of our universe: 10^139 years. With 95% confidence, we expect our universe to last more than 10^58 years. The uncertainty is part experimental uncertainty on the top quark mass and on ${\alpha}s$ and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the $mt/mh$ and the $mt/{\alpha}s$ planes, with uncertainty bands. To rule out absolute stability to $3{\sigma}$ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on ${\alpha}s(mZ)$ pushed below 0.00025.

Ultraviolet properties of the self-dual Yang-Mills theory

We compute the ultraviolet divergences in the self-dual Yang-Mills theory, both in the purely perturbative (zero instanton charge) and topologically non-trivial sectors. It is shown in particular that the instanton measure is precisely the same as the one-loop result in the standard Yang-Mills theory.