One-loop Tadpole Research Articles

Causal diamonds, cluster polytopes and scattering amplitudes

The “amplituhedron” for tree-level scattering amplitudes in the bi-adjoint ϕ3 theory is given by the ABHY associahedron in kinematic space, which has been generalized to give a realization for all finite-type cluster algebra polytopes, labelled by Dynkin diagrams. In this letter we identify a simple physical origin for these polytopes, associated with an interesting (1 + 1)-dimensional causal structure in kinematic space, along with solutions to the wave equation in this kinematic “spacetime” with a natural positivity property. The notion of time evolution in this kinematic spacetime can be abstracted away to a certain “walk”, associated with any acyclic quiver, remarkably yielding a finite cluster polytope for the case of Dynkin quivers. The mathcal{A} n−3, mathcal{B} n−1/ mathcal{C} n−1 and mathcal{D} n polytopes are the amplituhedra for n-point tree amplitudes, one-loop tadpole diagrams, and full integrand of one-loop amplitudes. We also introduce a polytope overline{mathcal{D}} n, which chops the mathcal{D} n polytope in half along a symmetry plane, capturing one-loop amplitudes in a more efficient way.

Quasiclassical representation of the Volkov propagator and the tadpole diagram in a plane wave

The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED. In [Phys. Rev. A \textbf{103}, 076011 (2021)] a new "fully quasiclassical" representation of the Volkov states has been found, which is equivalent to the one known in the literature but which more transparently shows the quasiclassical nature of the quantum dynamics of an electron in a plane-wave field. Here, we derive the corresponding expression of the propagator by constructing it using the fully quasiclassical form of the Volkov states. The found expression allows one, together with the fully quasiclassical expression of the Volkov states, to compute probabilities in strong-field QED in an intense plane wave by manipulating only 2-by-2 rather than 4-by-4 Dirac matrices as in the usual approach. Moreover, apart from the exponential functions featuring the classical action of an electron in a plane wave, the fully quasiclassical Volkov propagator depends only on the electron kinetic four-momentum in the plane wave, which is a gauge-invariant quantity. Finally, we also compute the one-loop tadpole diagram in a plane wave starting from the Volkov propagator and we find that after renormalization it identically vanishes.

The one-loop tadpole in the geoSMEFT

Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

CHIRON: a package for ChPT numerical results at two loops

This document describes the package CHIRON which includes two libraries, chiron itself and jbnumlib. CHIRON is a set of routines useful for two-loop numerical results in Chiral Perturbation Theory (ChPT). It includes programs for the needed one- and two-loop integrals as well as routines to deal with the ChPT parameters. The present version includes everything needed for the masses, decay constants and quark-antiquark vacuum-expectation-values. An added routine calculates consistent values for the masses and decay constants when the pion and kaon masses are varied. In addition a number of finite volume results are included: one-loop tadpole integrals, two-loop sunset integrals and the results for masses and decay constants. The numerical routine library jbnumlib contains the numerical routines used in chiron. Many are to a large extent simple C++ versions of routines in the CERNLIB numerical library. Notable exceptions are the dilogarithm and the Jacobi theta function implementations. This paper describes what is included in CHIRON v0.50.

Effective action of β-deformed [formula omitted] SYM theory: Farewell to two-loop BPS diagrams

Within the background field approach, all two-loop sunset vacuum diagrams, which occur in the Coulomb branch of N = 2 superconformal theories (including N = 4 SYM), obey the BPS condition m 3 = m 1 + m 2 , where the masses are generated by the scalars belonging to a background N = 2 vector multiplet. These diagrams can be evaluated exactly, and prove to be homogeneous quadratic functions of the one-loop tadpoles J ( m 1 2 ) , J ( m 2 2 ) and J ( m 3 2 ) , with the coefficients being rational functions of the squared masses. We demonstrate that, if one switches on the β-deformation of the N = 4 SYM theory, the BPS condition no longer holds, and then generic two-loop sunset vacuum diagrams with three non-vanishing masses prove to be characterized by the following property: 2 ( m 1 2 m 2 2 + m 1 2 m 3 2 + m 2 2 m 3 2 ) > m 1 4 + m 2 4 + m 3 4 . In the literature, there exist several techniques to compute such diagrams. For the β-deformed N = 4 SYM theory, we carry out explicit two-loop calculations of the Kähler potential and F 4 term. Our considerations are restricted to the case of β real.

Anomaly-free nonsupersymmetric largeNgauge theories from orientifolds

We construct anomaly free non-supersymmetric large N gauge theories from orientifolds of Type IIB on C^3/G orbifolds. In particular, massless as well as tachyonic one-loop tadpoles are cancelled in these models. This is achieved by starting with ${\cal N}=1,2$ supersymmetric orientifolds with well defined world-sheet description and including discrete torsion (which breaks supersymmetry) in the orbifold action. In this way we obtain non-trivial non-chiral as well as anomaly free chiral large N gauge theories. We point out certain subtleties arising in the chiral cases. Subject to certain assumptions, these theories are shown to have the property that computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ oriented theory. This generalizes the analogous results recently obtained in supersymmetric large N gauge theories from orientifolds, as well as in (non)supersymmetric large N gauge theories without orientifold planes.

The Schrödinger functional and non-perturbative improvement

After describing the Schrödinger functional for standard and improved gluon and quark actions we present results for the non-perturbative clover coefficients of the SW quark action coupled to the Wilson plaquette action for β ≥ 5.7, as well as the Lüscher-Weisz one-loop tadpole improved gauge action, both in the quenched approximation.

Chargino Production in Different Supergravity Models and the Effect of the Tadpoles

If the lightest chargino is discovered at LEP2, the measurement of its mass and cross-section together with the mass of the lightest neutralino, enables the determination of the parameters that define the theory and the entire supersymmetric and Higgs spectrum. Within this context, we: (i) study the effect of the one-loop tadpoles in the minimization condition of the Higgs potential, by comparing the RGE-improved Higgs potential approximation with the calculation of the minimum including the effect of the one-loop tadpoles, and (ii) compare the prediction of two different supergravity models, namely, the model based on B=2m0 and motivated by the solution of the μ-problem, and the minimal supergravity model, based on A=B-m0.

Resummation methods at finite temperature: The tadpole way.

We examine several resummation methods for computing higher order corrections to the finite temperature effective potential, in the context of a scalar $\phi^4$ theory. We show by explicit calculation to four loops that dressing the propagator, not the vertex, of the one-loop tadpole correctly counts ``daisy'' and ``super-daisy'' diagrams.

ON CLOSED STRING COUNTERTERMS

A one-loop tadpole and a one-loop two-string counterterms are proposed, capable of restoring BRST invariance to the respective scattering amplitudes of polyhedral closed string field theory.

Tadpole graph in covariant closed string field theory

A one-loop tadpole graph in covariant closed string field theory must generate all inequivalent tori with one puncture. In order to determine the region of integration in moduli space we map the tadpole to a two-sheeted sphere and use the analyticity of the modular parameter with respect to the complex propagator parameter. It is shown that the naive closed string extension of the Witten open string vertex fails to give the correct modular region for this one-loop amplitude.