Loop Feynman Diagrams Research Articles

Holographic RG flows from four-dimensional N = 2 gauged supergravities

In quantum field theories, the examination of particle interactions is facilitated through the application of Feynman diagrams. The computation of loop Feynman diagrams often yields divergent or infinite values. To tackle this issue, a method known as renormalization is employed, which entails the removal of these infinities. The phenomenon of a physical system undergoing changes under different scales gives rise to a concept referred to as the renormalization group. Certain renormalization group trajectories, denoted as RG flows, describe transformations of a conformal field theory (CFT) into other conformal or non-conformal theories. These transformations result in deformations of a UV conformal fixed point into another fixed point or into a non-conformal phase within the infrared (IR) regime. In this study, we investigate holographic RG flows originating from N = 2 gauged supergravity with an SO(2) × SO(6) gauge group. These solutions delineate RG flows from the N = 2 CFT to a three-dimensional non-conformal field theory driven by mass deformations. This transformation is elucidated through the AdS/CFT correspondence, also known as AdS/CFT holography.

Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs

Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs

Laplace’s method for elastic scattering diagrams within multiparticle fields model

We apply the multiparticle fields model to calculate the differential cross section $d\ensuremath{\sigma}/dt$ of elastic proton-proton scattering. This problem includes the calculation of multidimensional integrals arising from the loop Feynman diagrams. We demonstrated how these integrals can be reduced with Laplace's method to one- and two-dimensional integrals which can be calculated numerically. The obtained result qualitatively describes the minimum in differential cross section dependency $d\ensuremath{\sigma}/dt(t)$.

General one-loop formulas for Hrightarrow fbar{f}gamma and its applications

General one-loop contributions to the decay processes Hrightarrow fbar{f}gamma and its applications are presented in this paper. We consider all possible contributions of the additional heavy vector gauge bosons, heavy fermions, and charged (also neutral) scalar particles propagating in Feynman loop diagrams. Therefore, analytic results are valid in a wide class of models beyond the Standard Model. Analytic formulas for the form factors are expressed in terms of Passarino-Veltman functions in the standard notations of LoopTools. Hence, the decay rates can be evaluated numerically by using this package. The computations are then applied to the cases of the Standard Model, U(1)_{B-L} extension of the Standard Model as well as Two Higgs Doublet Model. Phenomenological results for all the above models are studied. We observe that the effects of new physics are sizable contributions and these can be probed at future colliders.

Equivalence of light-front and covariant quantum electrodynamics at one-loop level and the form of the gauge boson propagator

We consider the three fundamental one loop Feynman diagrams of QED viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge and discuss the equivalence of their standard covariant expressions with the light-front expressions obtained using light-cone time-ordered Hamiltonian perturbation theory. Although this issue has been considered by us and others previously, our emphasis in this article is on addressing the ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We generalize our earlier results and show, using an alternative method called the Asymptotic Method, how integrating over the light-front energy consistently in the covariant expression of each of the three one loop corrections leads to the propagating as well as the instantaneous diagrams of the light-front theory. In doing so, we re-establish the necessity of using the correct form of gauge boson propagator.

Study of the Rare B-meson Decays with the ATLAS Experiment

The searching for New Physics beyond the Standard Model of particles is one of the main aims of the current particle experiments. Rare b-hadron decays, occurring at the first level through loop Feynman diagrams, are strongly sensitive to the possible existence of new particles. Recent analyses from the LHCb experiment, measuring decay angles distributions in rare B-meson decay into a kaon K0* and two muons, hints a deviation from the Standard Model prediction. The ATLAS experiment works on a similar analysis of the decay Bd0 → K*μ−μ+ in order to confirm this deviation. The new particles’ existence could be observed in the deviations from the predicted decay’s angular distribution. This work provides input for the future analysis of this rare decay in the data-taking period of Run 2. To be more specific, observing of the fine deviations requires the precise description of the measured data and the Standard Model’s predictions. The improvement to the Run 1 analysis was achieved by an expansion of the fit function in a series of spherical harmonic functions. Next, the effect of the remaining background events in the signal dataset was repressed by adding masses mB and mK* to the final fit. That required to know functions’ prescriptions of the mB and mK* distributions for the signal decay and the expected background hence looking for their prescriptions was a part of this work too. The invariant B mass was described by the Gauss distribution with a per-event error. The per-event fit has to take into account the so-called Punzi effect in some cases which was also discussed here.

Chiral anomaly calculation in the extended coupled Rarita-Schwinger model

We recalculate the chiral anomaly in the Abelian gauge model in which a spin-$\frac{1}{2}$ field is directly coupled to a Rarita-Schwinger spin-$\frac{3}{2}$ field, using the extended theory in which there is an exact fermionic gauge invariance. Since the standard gauge fixing and ghost analysis applies to this theory, the ghost contribution to the chiral anomaly is $-1$ times the standard chiral anomaly for spin-$\frac{1}{2}$. Calculation of the fermion loop Feynman diagrams contributing to the coupled model anomaly gives a result of $6$ times the standard anomaly, so the total anomaly is $5$ times the standard anomaly. This agrees with the result obtained from the unextended model taking the ghost contribution there as $0$, corresponding to a non-propagating ghost arising from exponentiating the second class constraint determinant, together with the fermion loop anomaly contribution in the unextended model of $5$ times the standard anomaly.

Enumeration of N-rooted maps using quantum field theory

A one-to-one correspondence is proved between the N-rooted ribbon graphs, or maps, with e edges and the (e−N+1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N-rooted maps and for the numbers of N-rooted maps with a given number of edges using the path integral approach applied to the corresponding quantum field theory.

The twistor Wilson loop and the amplituhedron

The amplituhedron provides a beautiful description of perturbative superamplitude integrands in mathcal{N}=4 SYM in terms of purely geometric objects, generalisations of polytopes. On the other hand the Wilson loop in supertwistor space also gives an explicit description of these superamplitudes as a sum of planar Feynman diagrams. Each Feynman diagram can be naturally associated with a geometrical object in the same space as the amplituhedron (although not uniquely). This suggests that these geometric images of the Feynman diagrams give a tessellation of the amplituhedron. This turns out to be the case for NMHV amplitudes. We argue however that beyond NMHV this is not true. Specifically, each Feynman diagram leads to an image with a physical boundary and spurious boundaries. The spurious ones should be “internal”, matching with neighbouring diagrams. We however show that there is no choice of geometric image of the Wilson loop Feynman diagrams which yields a geometric object without leaving unmatched spurious boundaries.

Effective Euler–Heisenberg Lagrangians in models of QED

The main goal of this paper is a direct diagrammatic evaluation of the effective four-photon Lagrangian of the Euler–Heisenberg type for the quantum electrodynamics of massive charged vector bosons. This QED model is naturally embedded in the standard electroweak theory, and we have carried out the corresponding one-loop calculation in the unitary gauge. As far as we know, such a work has not been published before since usually the R-gauge techniques are preferred for the computation of loop Feynman diagrams. We have recovered the result obtained many years ago by Vanyashin and Terent’ev, who used a specific functional method. For completeness and for validation of our techniques, we have also redone the analogous calculations for scalar and spinor QED.

Divergence Free QED Lagrangian in (2 + 1)-Dimensional Space-Time with Three Different Regularization Prescriptions

Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.

Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals

We give numerical integration results for Feynman loop diagrams such as those covered by Laporta (2000) and by Baikov and Chetyrkin (2010), and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration using multivariate techniques from the ParInt package for multivariate integration, as well as iterated integration with programs from the Quadpack package, and a trapezoidal method based on a double exponential transformation. ParInt is layered over MPI (Message Passing Interface), and incorporates advanced parallel/distributed techniques including load balancing among processes that may be distributed over a cluster or a network/grid of nodes. Results are included for 2-loop vertex and box diagrams and for sets of 2-, 3- and 4-loop self-energy diagrams with or without UV terms. Numerical regularization of integrals with singular terms is achieved by linear and non-linear extrapolation methods.

A string theory which isn\u2019t about strings

Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct ab initio quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in D = 26 factorizes into contributions of massless spin-two and a pair of massive spin-two fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.

Inflationary preheating dynamics with two-species condensates

We discuss the amplification of loop corrections in quantum many-body systems through dynamical instabilities. As an example, we investigate both analytically and numerically a two-component ultracold atom system in one spatial dimension. The model features a tachyonic instability, which incorporates characteristic aspects of the mechanisms for particle production in early-universe inflaton models. We establish a direct correspondence between measureable macroscopic growth rates for occupation numbers of the ultracold Bose gas and the underlying microscopic processes in terms of Feynman loop diagrams. We analyze several existing ultracold atom setups featuring dynamical instabilities and propose optimized protocols for their experimental realization. We demonstrate that relevant dynamical processes can be enhanced using a seeding procedure for unstable modes and clarify the role of initial quantum fluctuations and the generation of a non-linear secondary stage for the amplification of modes.

Ultrafast exciton–polariton scattering towards the Dirac points

Using the Feynman–Dyson diagram technique, we study nonlinear polariton–polariton scattering in a two-dimensional micropillar-based optical superlattice with hexagonal symmetry. We demonstrate that both the emerging polariton chirality and the loop Feynman diagrams up to infinite order should be strictly accounted for in the evaluation of the self-energy of the system. Further, we explicitly show that in such a design the time of polariton scattering towards the Dirac points can be drastically decreased which can be used, for instance, in engineering novel classes of polariton lasers with substantially reduced thresholds.

Adaptive Integration and Singular Boundary Transformations

We apply and compare results of transformations used to annihilate boundary singularities for multivariate integration over hyper-rectangular and simplicial domains. While classically these transformations are applied with a product trapezoidal rule, we use adaptive methods in the PARINT software package, based on rules of higher polynomial degree for the integration over subdomains. PARINT is layered over the MPI environment (Message Passing Interface) and deploys advanced parallel computation techniques such as load balancing among processes that are distributed over a network of nodes. The message passing is performed in a non-blocking and asynchronous manner, and permits overlapping of computation and communication. Comparisons of computation times using long double vs. double precision confirm that the extended format does not considerably increase the time for long doubles. We further apply the proposed methods to problems arising from self-energy Feynman loop diagrams with massless internal lines, in particular where the corresponding integrand has singularities on the boundaries of the integration domain.

Quantum electroweak symmetry breaking through loop quadratic contributions

Based on two postulations that (i) the Higgs boson has a large bare mass mH≫mh≃125 GeV at the characteristic energy scale Mc which defines the Standard Model (SM) in the ultraviolet region, and (ii) quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale μ moves from Mc down to a transition scale μ=ΛEW at which the additive renormalized Higgs mass parameter mH2(Mc/μ) gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be ΛEW≃760 GeV, which provides another basic energy scale for the SM besides Mc. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as ΛEW lies within the probing reach of the LHC and the future Great Collider.

Automatic numerical integration methods for Feynman integrals through 3-loop

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.

A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagrams with multi-loop integrals which may require multi-precision calculation. We developed a dedicated accelerator system for multiprecision calculations (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.

Adaptive Integration for 3-loop Feynman Diagrams with Massless Propagators

Abstract We apply multivariate adaptive integration to problems arising from self-energy Feynman loop diagrams with massless internal lines. Results are obtained with the PARINT software package, which is layered over MPI (Message Passing Interface) and incorporates advanced parallel computation techniques such as load balancing among processes that may be distributed over a network of nodes. To solve theproblems numerically we introduce a parameter l in a factor of the integrand function. Some problem categories allow setting l = 0; other cases require an extrapolation as l → 0 . Furthermore we apply extrapolation with respect to the dimensional regularization parameter by setting the dimension n = 4–2 ɛ and extrapolating as ɛ →0 . Timing results with ParInt show near optimal parallel speedups for the problems at hand.