Order Feynman Research Articles

Double scaling limit of the prismatic tensor model

In Giombi et al (2018 Phys. Rev. D 98 105005), a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using the intermediate field method. We explicitly exhibit the next-to-leading order Feynman graphs in the expansion. Using appropriate combinatorial tools, we further study the general term of the expansion and we compute the two-point function in the double scaling limit. We find that the double scaling limit mechanism implemented here is similar to the one implemented for various quartic tensor models.

Double Electron–Positron Pair Production with Two-electron Capture in Relativistic Heavy-ion Collisions

We calculated the cross section of double electron-positron pair production with two-electron capture for the collisions of Pb+Pb ions and we did our calculations at LHC energies. We applied a similar methodology for the calculation of bound-free electron-positron pair production. We used perturbation theory and implemented Monte Carlo integration techniques to calculate the lowest order Feynman diagrams. We also compared our double electron-positron pair production with two-electron capture cross section results obtained in the literature. These calculations may help us to learn more about strong QED.

Wilson-Fisher fixed points for any dimension

The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -\beta of the Laplacian. The parameter \beta can be tuned so as to make that interaction marginal for any dimension. The lowest order Feynman diagrams corresponding to coupling constant renormalization, mass renormalization, and field renormalization are computed. In all cases a non-trivial IR fixed point is obtained. Remarkably, for dimensions different from 4, field renormalization is required at the one-loop level. For d=4, the theory reduces to the usual local \phi^{4} field theory and field renormalization is required starting at the the two-loop level. The critical exponents \nu and \eta are computed for dimensions 2,3,4 and 5. For dimensions greater than four, the critical exponent \eta turns out to be negative for \epsilon>0, which indicates a violation of the unitarity bounds.

Critical behavior of a nonlocalϕ4field theory and asymptotic freedom

The critical behavior of a nonlocal scalar field theory is studied. This theory has a nonlocal kinetic term which involves a real power $1\ensuremath{-}2\ensuremath{\alpha}$ of the Laplacian. The interaction term is the usual local ${\ensuremath{\phi}}^{4}$ interaction. The lowest order Feynman diagrams corresponding to coupling constant renormalization, mass renormalization, and field renormalization are computed. Particular features appearing in the renormalization of this nonlocal theory that differ from the case of local theories are studied. The previous calculations lead to the perturbative computation of the coupling constant beta function and critical exponents $\ensuremath{\nu}$ and $\ensuremath{\eta}$. In four dimensions for $\ensuremath{\alpha}<0$ this beta function presents asymptotic freedom in the UV. This is remarkable since no non-Abelian vector fields are included. However, this comes at the expense of losing reflection positivity.

Gravity and Spin Forces in Gravitational Quantum Field Theory**Supported in part by the National Science Foundation of China (NSFC) under Grant Nos. 11690022 and 11475237, Strategic Priority Research Program of the Chinese Academy of Sciences (CAS), under Grant No. XDB23030100, Key Research Program QYZDYSSW-SYS007, and the CAS Center for Excellence in Particle Physics (CCEPP)

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newtonʼs gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.

First order Feynman–Kac formula

We study the parabolic integral kernel for the weighted Laplacian with a potential. For manifolds with a pole we deduce formulas and estimates for the derivatives of the Feynman–Kac kernels and their logarithms, these are in terms of a ‘Gaussian’ term and the semi-classical bridge.

Renormalization of an Abelian tensor group field theory: solution at leading order

We study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.

Computations and generation of elements on the Hopf algebra of Feynman graphs

Two programs, feyngen and feyncop, were developed. feyngen is designed to generate high loop order Feynman graphs for Yang-Mills, QED and ϕk theories. feyncop can compute the coproduct of these graphs on the underlying Hopf algebra of Feynman graphs. The programs can be validated by exploiting zero dimensional field theory combinatorics and identities on the Hopf algebra which follow from the renormalizability of the theories. A benchmark for both programs was made.

Feynman graph generation and calculations in the Hopf algebra of Feynman graphs

Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang–Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs. Program summaryProgram title:feyngen, feyncopCatalogue identifier: AEUB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2657No. of bytes in distributed program, including test data, etc.: 22606Distribution format: tar.gzProgramming language: Python.Computer: PC.Operating system: Unix, GNU/Linux.RAM: 64 m bytesClassification: 4.4.External routines: nauty [1], geng, multig (part of the nauty package)Nature of problem:Performing explicit calculations in quantum field theory Feynman graphs are indispensable. Infinities arising in the perturbative calculations make renormalization necessary. On a combinatorial level renormalization can be encoded using a Hopf algebra [2] whose coproduct incorporates the BPHZ procedure. Upcoming techniques initiated an interest in relatively large loop order Feynman diagrams which are not accessible by traditional tools.Solution method:Both programs use the established nauty package to ensure high performance graph generation at high loop orders. feyngen is capable of generating φk-theory, QED and Yang–Mills Feynman graphs and of filtering these graphs for the properties of connectedness, one-particle-irreducibleness, 2-vertex-connectivity and tadpole-freeness. It can handle graphs with fixed external legs as well as those without fixed external legs.feyncop uses basic graph theoretical algorithms to compute the coproduct of graphs encoding their Hopf algebra structure.Running time:All 130516 1PI, φ4, 8-loop diagrams with four external legs can be generated, together with their symmetry factor, by feyngen within eight hours and all 342430 1PI, QED, vertex residue type, 6-loop diagrams can be generated in three days both on a standard end-user PC. feyncop can calculate the coproduct of all 2346 1PI, φ4, 8-loop diagrams with four external legs within ten minutes.

Electron g‐factor determinations in Penning traps

AbstractThe magnetic moment of the electron, expressed by the g‐factor in units of the Bohr magneton, is a key quantity in the theory of quantum electrodynamics (QED). Experiments using single particles confined in Penning traps have provided very precise values of the g‐factor for the free electron as well as the electron bound in hydrogen‐like ions. In this paper the status of these experiments is reviewed. The results allow testing calculations of higher order Feynman diagrams. Comparison of experimental and theoretical results for free and bound particles show no discrepancy within the limits of error, thus representing to date the most sensitive test of QED. Moreover, the g‐factor provides a unique access to fundamental constants, as e.g. the electron mass or the fine structure constant.

Anomalous <span class="cmmi-10">Wtb </span>Coupling at the LHC

Some distributions of the mu- in the top quark pair production reaction pp -> b u anti-d anti-b mu- anti-nu_mu at the LHC are calculated to leading order in the presence of the anomalous Wtb coupling with operators of dimension up to five. The distributions in the transverse momentum, rapidity and cosine of the mu- angle with respect to the beam in the laboratory frame and with respect to the reversed momentum of the b-quark in the rest frame of W-boson are changed rather moderately by the anomalous Wtb coupling. The distributions computed with the full set of leading order Feynman diagrams practically do not differ from those computed with the t anti-t production diagrams, with typical acceptance cuts. This demonstrates very little effect of the off resonance background contributions.

Remarks on gaugino screening

Gauge mediated models of supersymmetry breaking often exhibit "gaugino screening," where to leading order in F, gaugino masses are unaffected by higher dimensional Kahler potential interactions between the supersymmetry breaking spurion and the messengers. We provide a derivation of this phenomenon which utilizes the gaugino counterterm originally proposed in the context of anomaly mediation by Dine and Seiberg. We argue that this counterterm is present when there are non-zero messenger F-terms, and can cancel the leading order Feynman diagram contribution to the gaugino mass. We provide a nontrivial check of the regulator independence of our results by performing the computation using both dimensional reduction and Pauli-Villars. This analysis reconciles an apparent contradiction between diagrammatics and analytic continuation into superspace.

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2*epsilon dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop epsilon-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available.

Scaling behavior of three-dimensional group field theory

Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel–Louapre positive regularization (hereafter the BFL model) with an ‘ultraviolet’ cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, in a self-contained way, the modern tools of constructive field theory: we construct the Borel sum of the BFL perturbative series via a convergent ‘cactus’ expansion, and establish the ‘ultraviolet’ scaling of its Borel radius. Our method shows how the ‘sum over triangulations’ in quantum gravity can be tamed rigorously, and paves the way for the renormalization program in group field theory.

Renormalizability and nonrenormalizable interactions

Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, higher order Feynman diagrams become self-convergent and nonrenormalizable interactions become renormalizable. As an example, the vacuum fluctuation effects on ρ meson mass for the vector-tensor coupling model is discussed. It is found that the result can agree with the experimental value when coupling constant is adjusted.

Off resonance background effects in [formula omitted

The top quark Yukawa coupling to the intermediate mass Higgs boson can be determined in the reaction e + e − → t t ¯ H that, after taking into account decays, will be detected at the International Linear Collider through reactions with 8 particles in the final state. Such 2 → 8 reactions receive contributions from tens thousands of Feynman diagrams, already in the lowest order of Standard Model, most of which comprise background to resonant associated production and decay of the top quark pair and Higgs boson. We illustrate the background effects by comparing cross sections of three reactions, which represent different detection channels of e + e − → t t ¯ H , calculated with the complete sets of the lowest order Feynman diagrams with the corresponding signal cross sections calculated with the diagrams of associated production and decay of off mass shell top quark pair and Higgs boson only. The comparison that is performed with different selections of cuts shows that the background effects are sizeable, but they can be reduced by appropriate choice of cuts.

One-loop electroweak factorizable correctionsfor the Higgsstrahlung at a linear collider

We present standard model predictions for a four fermion reaction e+ e- -> mu+ mu- bar_b b being one of the best detection channels of a low mass Higgs boson produced through the Higgsstrahlung mechanism at a linear collider. We include leading virtual and real QED corrections to all the lowest order Feynman diagrams of e+ e- -> mu+ mu- bar_b b and the complete O(alpha) electroweak corrections to the Z-Higgs production and to the Z and Higgs boson decay widths in the double pole approximation.

Fifth-order contributions to ultrafast spectrally resolved vibrational echoes: heme-CO proteins.

The fifth order contributions to the signals of ultrafast infrared spectrally resolved stimulated vibrational echoes at high intensities have been investigated in carbonmonoxy heme proteins. High intensities are often required to obtain good data. Intensity dependent measurements are presented on hemoglobin-CO (Hb-CO) and a mutant of myoglobin, H64V-CO. The spectrally resolved vibrational echoes demonstrate that fifth order effects arise at both the 1-0 and the 2-1 emission frequencies of the stretching mode of the CO chromophore bound at the active site of heme proteins. Unlike one-dimensional experiments, in which the signal is integrated over all emission frequencies, spectrally resolving the signal shows that the fifth order contributions have a much more pronounced influence on the 2-1 transition than on the 1-0 transition. By spectrally isolating the 1-0 transition, the influence of fifth order contributions to vibrational echo data can be substantially reduced. Analysis of fifth order Feynman diagrams that contribute in the vibrational echo phase-matched direction demonstrates the reason for the greater influence of fifth order processes on the 1-2 transition, and that the fifth order contributions are heterodyne amplified by the third order signal. Finally, it is shown that the anharmonic oscillations in vibrational echo data of Hb-CO that previous work had attributed strictly to fifth order effects arise even without fifth order contributions.

Long-distance contributions to the QCD pressure

The QCD pressure is a most fundamental quantity, for which lattice data is available up to a few times the critical temperature $T_c$. Perturbation theory, even at very high temperatures, has serious convergence problems. Combining analytical and 3d numerical methods, we show that it is possible to compute the QCD pressure from about $2 T_c$ to infinity. We also describe an algorithm to generate and classify high order Feynman diagrams which is tailored to minimize computational effort.

CASIMIR EFFECTS IN RENORMALIZABLE QUANTUM FIELD THEORIES

We present a framework for the study of one–loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.