Loop Feynman Diagrams Research Articles

The form factors for hadronic tau decay using background field method

In the two body hadronic tau decays, such as τ→Kπ(η)ν, vector mesons play important role. Belle and Babar measured hadronic invariant mass spectrum of τ→Kπν decay. To compare the spectrum with theoretical prediction, we develop the chiral Lagrangian with vector mesons in [D. Kimura, K. Y. Lee and T. Morozumi, arXiv:1201.1794 [hep-ph]]. We compute the form factors of the hadronic τ decay taking account of the quantum corrections of Nambu Goldstone bosons. We also show how to renormalize the divergence of the Feynman diagrams with arbitrary number of loops and determine the counterterms within one loop using background field method. In this report, we discuss the renormalization of [D. Kimura, K. Y. Lee and T. Morozumi, arXiv:1201.1794 [hep-ph]] by considering the one loop Feynman diagrams.

PARITY ANOMALY IN DIRAC EQUATION IN (1+2) DIMENSIONS, QUANTUM ELECTRODYNAMICS AND PAIR PRODUCTION

We show that parity operator plays an interesting role in Dirac equation in (1+2) dimensions and can be used for defining chiral charges. Further the "anomalous" current induced by an external gauge field can be related to the anomalous divergence of an axial vector current which arises due to quantum radiative corrections provided by triangular loop Feynman diagrams in analogy with the corresponding axial anomaly in (1+3) dimensions. It is shown that the nonconservation of "chiral charge" due to anomaly is related with the topological Chern–Simons charge. As an application pair creation of massless fermions in electric field is discussed.

Do we need Feynman diagrams for higher order perturbation theory?

We compute the two loop and three loop corrections to the beta function for Yang–Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.

Loop lessons from Wilson loops in $ \mathcal{N} = 4 $ supersymmetric Yang-Mills theory

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one- and two- parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynman diagrams, we derive Feynman parameterizations of complicated planar and non-planar Feynman diagrams which simplify their evaluation. For illustration, we compute numerically a four-loop hexagon scalar Feynman diagram.

Problems of automatic calculation for collider physics

A review of various systems for automated calculation of tree-level and loop Feynman diagrams, Monte Carlo integration over multidimensional phase space, and event generation for modern and future colliders (LHC and ILC) is presented. The CompHEP system possibilities are considered in greater detail.

FERMION-BOSON LOOPS WITH BILINEAR R-PARITY VIOLATION LEADING TO MAJORANA NEUTRINO MASS AND MAGNETIC MOMENTS

We present analytic expressions corresponding to a set of one loop Feynman diagrams, built within R-parity violating (RpV) minimal supersymmetric standard model (MSSM). Diagrams involve both bilinear and trilinear RpV couplings and represent Majorana neutrino masses and magnetic moments.

Operator representation for Matsubara sums

In the context of the imaginary-time formalism for a scalar thermal field theory, it is shown that the result of performing the sums over Matsubara frequencies associated with loop Feynman diagrams can be written, for some classes of diagrams, in terms of the action of a simple linear operator on the corresponding energy integrals of the Euclidean theory at T=0. In its simplest form the referred operator depends only on the number of internal propagators of the graph. More precisely, it is shown explicitly that this \emph{thermal operator representation} holds for two generic classes of diagrams, namely, the two-vertex diagram with an arbitrary number of internal propagators, and the one-loop diagram with an arbitrary number of vertices. The validity of the thermal operator representation for diagrams of more complicated topologies remains an open problem. Its correctness is shown to be equivalent to the correctness of some diagrammatic rules proposed a few years ago.

Coproduct and star product in field theories on Lie-algebra noncommutative space-times

We propose a new approach to field theory on \ensuremath{\kappa}-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the \ensuremath{\kappa}-Poincar\'e coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in \ensuremath{\kappa}-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in \ensuremath{\kappa}-Minkowski field theories it is convenient to introduce the concepts of ``planar'' and ``nonplanar'' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times.

Lattice regularization for chiral perturbation theory

The SU(3) chiral lagrangian for the lightest octets of mesons and baryons is constructed on a spacetime lattice. The lattice spacing acts as an ultraviolet momentum cutoff which appears directly in the Lagrangian so chiral symmetry remains explicit. As the lattice spacing vanishes, Feynman loop diagrams typically become divergent due to inverse powers of the lattice spacing, and these divergences get absorbed into counterterms such that the standard results of dimensional regularization are obtained. One advantage of lattice regularization is that power divergences are seen explicitly. In the present work, the octet meson masses, the octet baryon masses and the pion-nucleon sigma term are all computed explicitly to one loop order.

Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, eta, and mass renormalization critical exponents at O(1/N_f^2) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MSbar results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N_f^2). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for eta in arbitrary covariant gauge is given.

Radiative corrections to the Higgs-boson decay rate Gamma (H-->ZZ) in the minimal supersymmetric model.

We consider radiative corrections to the decay rate $\Gamma(H\rightarrow ZZ)$ of the heavy {\it CP}-even Higgs boson of the minimal supersymmetric model to two $Z$ bosons. We perform a one loop Feynman diagram calculation in the on-mass-shell renormalization scheme, and include the third generation of quarks and squarks. The tree level rate is suppressed by a mixing angle factor and decreases as $1/M_H$ for large $M_H$. The corrected rate overcomes this suppression and increases with $M_H$ for $M_H > 500$~GeV. The corrections can be very large and depend in detail on the top squark masses and $A$-term, as well as the supersymmetric Higgs mass parameter $\mu$.

Use of helicity methods in evaluating loop integrals: A QCD example

We discuss the use of helicity methods in evaluating loop diagrams by analyzing a specific example: the one-loop contribution to e +e - → qq̄g in massless QCD. By using covariant helicity representations for the spinor and vector wave functions we obtain the helicity amplitudes directly from the Feynman loop diagrams by covariant contraction. The necessary loop integrations are considerably simplified since one encounters only scalar loop integrals after contraction. We discuss crossing relations that allow one to obtain the corresponding one-loop helicity amplitudes for the crossed processes as e.g. qq̄ → (W, Z, γ∗) + g including the real photon cases. As we treat the spin degrees of freedom in four dimensions and only continue momenta to n dimensions (dimensional reduction scheme) we explicate how our results are related to the usual dimensional regularization results.

Description of Non-Polynomial Quantum Field Theories by Superpropagator Method

The description of superpropagator method and its applications to the mesodynamics, weak interaction, electrodynamics involving gravity and the chiral invariant field theory is given. The low-energy behaviour of particles is described, taking into account the loop Feynman diagrams. The renormalizations of physical quantities are finite and are expressed in terms of coupling constants. Partly this work was reported at the Third International Conference on Non-Local Quantum Field Theory in 1973 at Alushta, USSR.