Theory Of Weak Interactions Research Articles

Testing effective field theory with the most general neutron decay correlations

Built on the seminal works by Jackson-Treiman-Wyld and Ebel-Feldman, we derive the most general free neutron differential decay rate where all massive particles (neutron, proton, and electron) are polarized. This introduces 33 new correlations in addition to the 18 existing ones, which overconstrain the coupling constants in the low-energy effective field theory of charged weak interactions, and thus provides stringent tests of the validity of the theory framework itself. We classify the correlation coefficients in terms of their Standard Model limit and discrete symmetries, and study their expansion with respect to the new physics coupling strengths, supplemented by the experiment-independent O(α) virtual electromagnetic radiative corrections. Published by the American Physical Society 2024

The Higgs Boson and its physics: an overview

The Higgs boson plays a central role in the Standard Model, as well as in theories which go beyond it. This article is therefore divided into two parts. The first takes s historical approach and shows how the mass problem entered weak interaction theory from the beginning and how it was solved by invoking the Higgs boson. This is followed by a construction of the Glashow–Salam–Weinberg model, again stressing the role played by the Higgs doublet. This part culminates in the Higgs boson discovery of 2012. The second part first discusses the shortcomings of the Standard Model and then touches upon the major theories which try to improve upon it, mostly with profound consequences on the Higgs sector. This is followed up by short descriptions of a number of popular extensions of the Higgs sector, and culminates in a brief introduction to effective field theory approaches to studying the Higgs sector.

ELECTROMAGNETIC CORRECTION IN THE MUON DECAY

The influence of electromagnetic interaction in one photon approximation was applied to study the muon decay in electroweak interaction. The divergences that ariose in this process were infrared ones in the low energy region. The divergent treatment was carried out with two methods: the minimum mass method and the dimensional regularization method. As a result, an electromagnetic correction was calculated for the muon electroweak decay rate. The results that we received confirm that the Fermi theory of weak interaction is a non-renormalizable theory.

The cradle of nonlinear asteroseismology: observations of oscillation mode variability in compact pulsating stars

We briefly review progress in developing a pathway to nonlinear astereoseismology, both from theoretical and observational aspects. As predicted by the theory of weak nonlinear interactions between resonant modes, their amplitude and frequency can be modulated according to various kinds of patterns. However, those subtle modulations could hardly be well characterized from ground-based photometric monitoring. The Kepler spacecraft offered a new window to find clear-cut evidence of well-determined amplitude and frequency modulations, leading to the first discoveries of such variations in pulsating white dwarf and hot B subdwarf stars. Fol-lowing that direction, a systematic survey of oscillation mode properties in compact pulsators monitored by Kepler suggests that mode variability is likely a common phenomenon, which remain unaccounted for by standard linear non-radial pulsation theory. To reach this conclusion firmly, the survey has now been extended to a larger context including compact stars observed by K2 and TESS. We expect that this extended survey will help to constrain key parameters governing weak nonlinear effects in stellar oscillations.

Impact of Clustering on the ^{8}Li β Decay and Recoil Form Factors.

We place unprecedented constraints on recoil corrections in the β decay of ^{8}Li, by identifying a strong correlation between them and the ^{8}Li ground state quadrupole moment in large-scale abinitio calculations. The results are essential for improving the sensitivity of high-precision experiments that probe the weak interaction theory and test physics beyond the standard model. In addition, our calculations predict a 2^{+} state of the α+α system that is energetically accessible to β decay but has not been observed in the experimental ^{8}Be energy spectrum, and has an important effect on the recoil corrections and β decay for the A=8 systems. This state and an associated 0^{+} state are notoriously difficult to model due to their cluster structure and collective correlations, but become feasible for calculations in the abinitio symmetry-adapted no-core shell-model framework.

Structure of the correlation coefficients S(Ee) and U(Ee) of the neutron β decay

In the standard effective V - A theory of low-energy weak interactions (i.e. in the Standard Model (SM)) we analyze the structure of the correlation coefficients S(E_e) and U(E_e), where E_e is the electron energy. These correlation coefficients were introduced to the electron-energy and angular distribution of the neutron beta decay by Ebel and Feldman ( Nucl. Phys. 4, 213 (1957)) in addition to the set of correlation coefficients proposed by Jackson et al. (Phys. Rev. 106, 517 (1957)). The correlation coefficients $S(E_e)$ and $U(E_e)$ are induced by simultaneous correlations of the neutron and electron spins and electron and antineutrino 3-momenta. These correlation structures do no violate discrete P, C and T symmetries. We analyze the contributions of the radiative corrections of order O(alpha/pi), taken to leading order in the large nucleon mass m_N expansion, and corrections of order O(E_e/m_N), caused by weak magnetism and proton recoil. In addition to the obtained SM corrections we calculate the contributions of interactions beyond the SM (BSM contributions) in terms of the phenomenological coupling constants of BSM interactions by Jackson et al. (Phys. Rev. 106, 517 (1957)) and the second class currents by Weinberg (Phys. Rev. 112, 1375 (1958)).

Weak and Strong Interaction of Excitation Kinks in Scalar Parabolic Equations

Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest PDE model of excitable media given by the scalar reaction diffusion-type theta -equations for excitable angular phase dynamics. On the one hand, we qualitatively study geometric kink positions using the comparison principle and the theory of terraces. This yields the minimal initial distance as a global lower bound, a well-defined sequence of collision data for kinks- and antikinks, and implies that periodic pure kink sequences are asymptotically equidistant. On the other hand, we study metastable dynamics of finitely many kinks using weak interaction theory for certain analytic kink positions, which admits a rigorous reduction to ODE. By blow-up type singular rescaling we show that distances become ordered in finite time, and eventually diverge. We conclude that diffusion implies a loss of information on kink distances so that the entropic complexity based on positions and collisions in the GHCA does not simply carry over to the PDE model.

Neutrino flavor oscillations without flavor states

We analyze the problem of neutrino oscillations via a fermionic particle detector model inspired by the physics of the Fermi theory of weak interactions. The model naturally leads to a description of emission and absorption of neutrinos in terms of localized two-level systems. By explicitly including source and detector as part of the dynamics, the formalism is shown to recover the standard results for neutrino oscillations without mention to "flavor states", which are ill defined in quantum field theory. This illustrates how particle detector models provide a powerful theoretical tool to approach the measurement issue in quantum field theory and emphasizes that the notion of flavor states, although sometimes useful, must not play any crucial role in neutrino phenomenology.

Investigations on the complex flows induced by dual-swept/dual-ramp wedges in supersonic flows

The caret inlet with a dual-swept/dual-ramp configuration has excellent stealth performance and aerodynamic capability. Most previous investigations on this configuration have focused on experiments and numerical simulations but there are relatively few theoretical investigations. In this study, the flow field characteristics of dual-swept/dual-ramp configuration are investigated analytically and numerically. An analytical approach that combines the shock dynamics with a “spatial dimension reduction” was used to analyze the characteristics of the wave structures and state parameters of the flow field. The effects of the sweep angles and inflow Mach number on the flow field characteristics are investigated. The results indicate that the problem of shock/shock interaction in two intersecting wedges of large back-swept angle is a problem of weak shock interaction. Therefore, the theory of weak shock interaction is used to investigate the flow field characteristics, including the uniformity of the flow field and the total pressure recovery performance.

Response functions and cross sections for inclusive neutrino scattering off $^2$H, $^3$H and $^3$He

For several decades there has been an interest in studying neutrino scattering on light nuclei, with the hope of increasing knowledge about the theory of weak interactions and electroweak unification. A study of several neutrino induced reactions on light nuclei (^22H, ^33H and ^33He) is presented here. The cross section for these reactions is evaluated using the nuclear response functions, which holds the information about the nuclear interactions and structure. This approach has been tested for break-up reactions on the deuteron before and is now extended to three-nucleon break-up reactions.

Socio-Cultural Aspects of the Standard Model in Elementary Particles Physics and the History of Its Creation

The article соnsiders the socio-cultural aspects of the standard model (SM) in elementary particle physics and history of its creation. SM is a quantum field gauge theory of electromagnetic, weak and strong interactions, which is the basis of the modern theory of elementary particles. The process of its elaboration covers a twenty-year period: from 1954 (the concept of gauge fields by C. Yang and R. Mills) to the early 1970s., when the construction of renormalized quantum chromodynamics and electroweak theory wеre completed. The socio-cultural aspects of SM are explored on the basis of a quasi-empirical approach, by studying the texts of its creators and participants in the relevant events. We note also the important role of such an “external” factor as large-scale state projects on the creation of nuclear and thermonuclear weapons, which provided personnel and financial support for fundamental research in the field of nuclear physics and elementary particle physics (the implementation of thermonuclear projects took place just in the 1950s, and most of the theorists associated with the creation of SM were simultaneously the main developers of thermonuclear weapons, especially in the USSR). The formation of SM is considered as a competition between two research programs (paradigms) – gauge-field and phenomenological, associated with the rejection of the field concept. The split of the scientific community of physicists associated with this competition is going on during this period. It’s accompanied by a kind of “negotiations”, which in the early 1970s lead to the triumph of the gauge field program and the restoration of the unity of the scientific community. The norms and rules of the scientific ethos played the regulatory role in this process. The scientific-realistic position of the metaphysical attitudes of the majority of theorists and their negative attitude to the concepts of philosophical relativism and social construction of scientific knowledge are emphasized. Some features of the history of SM creation are also noted, such as the positive role of aesthetic judgments; “scientific-school” form of research (in the USSR), its pros and cons; a connection to historical-scientific “drama of ideas” with “dramas of people” who made a wrong choice and (or) “missed their opportunities”.

“Comedy of mistakes” and “drama of humans”: on the domestic contribution to the creation of The Standard Model of elemantary particle in physics

The article explores domestic contribution to the creation of The Standard Model (SM). SM is a quantum field gauge theory of electromagnetic, weak and strong interactions, which is the basis of the modern theory of elementary particles. The process of its development covers a twenty-year period – from 1954 (the concept of non-Abelian Yang-Mills gauge fields) to the early 1970s, when the construction of renormalizable quantum chromodynamics and electroweak theory was completed. The reasons for the difficult perception of the Yang-Mills gauge field concept in the USSR are analyzed, associated primarily with the problem of “zero-charge” in quantum electrodynamics, and then in field theories of strong and weak interactions. This result, obtained by the leaders of the outstanding Russian scientific schools of theoretical physics, L. D. Landau, I. Ya. Pomeranchuk and their students, led to the rejection of the majority of Soviet physicists from field theory and to their transition to the position of a non-field phenomenological program (based on the S-matrix theory) in the construction of the theory of elementary particles.

Методологические проблемы синтеза теорий электромагнетизма и слабых взаимодействий

В статье представлен анализ методологических проблем создания теории электрослабых взаимодействий, связанных с оценкой ее онтологического статуса. Для этого рассмотрен процесс объединения теорий электромагнитных и слабых взаимодействий, имевший место в 60−70-х гг. XX в. Дан сравнительный анализ данного синтеза по отношению к классическим образцам объединения, отсылающим к работам И. Ньютона, Дж. Максвелла и А. Эйнштейна. Показано, что эпистемологическая специфика синтеза теорий электромагнитных и слабых взаимодействий в истории науки состоит в том, что он был осуществлен в рамках синтетической программы, ставившей своей целью построение последовательности теорий электрослабых взаимодействий в качестве последовательных приближений к калибровочной теории Янга − Миллса. Рассмотрены основные этапы реализации калибровочной синтетической программы, завершившейся разработкой так называемой модели Глэшоу − Вайнберга − Салама. Обосновывается, что во многом гибридный характер этой модели обусловливает ее незаконченный характер.

Model-independent bounds on the standard model effective theory from flavour physics

Meson-antimeson mixing provides the most stringent constraints on baryon- and lepton-number conserving New Physics, probing scales higher than 105 TeV. In the context of the effective theory of weak interactions, these constraints translate into severe bounds on the coefficients of ΔF=2 operators. Generalizing to the effective theory invariant under the Standard Model gauge group, valid above the electroweak scale, the bounds from ΔF=2 processes also affect ΔF=1 and even ΔF=0 operators, due to log-enhanced radiative corrections induced by Yukawa couplings. We systematically analyze the effect of the renormalization group evolution above the electroweak scale and provide for the first time the full set of constraints on all relevant dimension-six operators.

Hamiltonian models of interacting fermion fields in quantum field theory

We consider Hamiltonian models representing an arbitrary number of spin 1 / 2 fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction form factors are supposed to satisfy some regularity conditions in both position and momentum space. Without any restriction on the strength of the interaction, we prove that the Hamiltonian identifies to a self-adjoint operator on a tensor product of antisymmetric Fock spaces and we establish the existence of a ground state. Our results rely on new interpolated \(N_\tau \) estimates. They apply to models arising from the Fermi theory of weak interactions, with ultraviolet and spatial cutoffs.

Vacuum polarization of weak interaction theory in Krein space quantization

In this paper, one of the most important diagrams of weak interaction (vacuum polarization) is studied in Krein space quantization (KSQ). This diagram has divergent terms in Hilbert space which must be eliminated using a traditional regularization method like dimensional regularization whereas in KSQ the result is automatically finite and does not need renormalization.

Differences Between Two Weak Interaction Theories

This paper analyzes differences between theoretical elements of the Standard Model electroweak theory and corresponding properties of a dipole-dipole weak interaction theory. The analysis relies on a number of self-evident criteria that are valid for quantum theories. The results demonstrate the existence of fundamental errors in the electroweak theory and the advantage of the dipole-dipole weak interaction theory.

Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

Spectral Theory for the Weak Decay of Muons in a Uniform Magnetic Field

In this article we consider a mathematical model for the weak decay of muons in a uniform magnetic field according to the Fermi theory of weak interactions with V-A coupling. With this model we associate a Hamiltonian with cutoffs in an appropriate Fock space. No infrared regularization is assumed. The Hamiltonian is self-adjoint and has a unique ground state. We specify the essential spectrum and prove the existence of asymptotic fields from which we determine the absolutely continuous spectrum. The coupling constant is supposed sufficiently small.

Study the Acousto-Optic Spatial Filters Diffracted Light at Zeroth-Order Using MATLAB

This paper introduces the essentials of acousto-optics with the theory and applications using MATLAB. There are some software used to process acousto-optics filter and the implementation details of any acousto-optics algorithm are inaccessible. Our work is focused on software used to solving the coupled equations in Bragg diffraction by creating MATLAB function for use in Bragg regime and acoustic-optic spatial filtering and employing mainly the MATLAB program for solving this problem. We review the role of acousto-optic and spatial filtering for high-pass spatial filtering. Classically, acousto-optic interactions comprise scattering of photons by energetic phonons into higher and lower orders. Standard weak interaction theory describes diffraction in the Bragg regime as the propagation of a uniform plane wave of light through a uniform plane wave of sound, resulting in the well known first- and zeroth-order diffraction. We investigate Raman-Nath diffraction corresponding to near-Bragg diffraction. A result shows the dependence of various scattered orders on the incident angle/Bragg angle illustrating the Bessel function dependence.