Model of electromagnetic interactions with spin-1/2 neutral particles

We address the bound-state dynamics of relativistic spin-1/2 neutral particles (in this paper, Dirac neutrinos) with anomalous magnetic dipole moment in the presence of an electromagnetic (EM) field described by a generalized Dirac–Pauli equation. This equation of motion is derived including appropriate couplings between Lorentz scalar and pseudoscalar fields with the EM field in the Lagrangian of the system. Specifically, we exactly solve the bound-state problem of neutrinos in the presence of a homogeneous magnetic field in cylindrical coordinates. We comment on the relevance of this approach to study Dirac neutrino self-interactions.

Neutron interactions with electromagnetic fields and single-neutron solitons

We address the bound-state dynamics of a neutron with anomalous magnetic dipole moment in the presence of electromagnetic (EM) fields described by a generalized Dirac–Pauli equation. This generalization consists of including appropriate couplings between Lorentz scalar and pseudoscalar fields with EM fields in the Lagrangian of the system. We exactly solve two single-particle problems: first, a Hydrogen-like system; second, a relativistic Schrödinger-like equation for a linear confining potential. We comment on the relevance of this approach to explore fermion (e.g. neutron) self-interactions as solitonic models of the neutron.

Мeson resonances in the relativistic quark model

In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by comparison of the calculation results with the data for the masses of ρ and D mesons.

Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear also in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process. We first discuss the classification of operators and how to construct a good set of basis using both off-shell field theory method and on-shell form factor formalism. To study loop corrections, we apply efficient unitarity-IBP strategy and compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the UV divergences of form factor results, we extract the renormalization matrices and analyze the operator mixing behavior in detail. The form factors we compute are also equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs EFT. We obtain the analytic finite remainder functions which exhibit several universal transcendentality structures.

Drell-Yan qT resummation of fiducial power corrections at N3LL

We consider Drell-Yan production pp → V*X → LX at small qT ≪ Q, where qT and Q are the total transverse momentum and invariant mass of the leptonic final state L. Experimental measurements require fiducial cuts on L, which in general introduce enhanced, linear power corrections in qT/Q. We show that they can be unambiguously predicted from factorization, and resummed to the same order as the leading-power contribution. For the fiducial qT spectrum, they constitute the complete linear power corrections. We thus obtain predictions for the fiducial qT spectrum to N3LL and next-to-leading-power in qT/Q. Matching to full NNLO ($$ {\alpha}_s^2 $$ α s 2 ), we find that the linear power corrections are indeed the dominant ones, and once included by factorization, the remaining fixed-order corrections become almost negligible below qT ≲ 40 GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial ϕ* spectrum at N3LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of qT and ϕ*. We also consider the $$ {p}_T^{\mathrm{\ell}} $$ p T ℓ spectrum. We show that it develops leptonic power corrections in qT/(Q − 2$$ {p}_T^{\mathrm{\ell}} $$ p T ℓ ), which diverge near the Jacobian peak $$ {p}_T^{\mathrm{\ell}} $$ p T ℓ ∼ Q/2 and must be kept to all powers to obtain a meaningful result there. Doing so, we obtain for the first time an analytically resummed result for the $$ {p}_T^{\mathrm{\ell}} $$ p T ℓ spectrum around the Jacobian peak at N3LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. We show that in practice this is equivalent to often-used recoil prescriptions, for which our results now provide rigorous, formal justification. Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, which for Z/γ* → ℓℓ or W → ℓν directly map onto the commonly used angular coefficients, but also holds for arbitrary leptonic final states. In particular, for suitably defined Born-projected leptons it still yields a LO-like angular decomposition even when including QED final-state radiation. Finally, we also discuss the application to qT subtractions. Including the unambiguously predicted fiducial power corrections significantly improves their performance, and in particular makes them applicable near kinematic edges where they otherwise break down due to large leptonic power corrections.

On the Synergic Relationships between Special Relativity and Quantum Theories

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

Relativistic Properties of a Lagrangian and a Hamiltonian in Quantum Theories

Relativistic properties of a Dirac Lagrangian density are compared with those of a Dirac Hamiltonian density. Differences stem from the fact that a Lagrangian density is a Lorentz scalar, whereas a Hamiltonian density is a 00-component of a second rank tensor, called the energy-momentum tensor. This distinction affects the form of an interaction term of a Dirac particle. In particular, a tensor interaction term of a Dirac Lagrangian density transforms to a difference between a vector and an axial vector of the corresponding Hamiltonian density. This outcome shows that fundamental principles can prove the V-A attribute of weak interactions. A further analysis supports these results. Inherent problems of the electroweak theory are discussed.

Electrostatic simulation of the Jackiw-Rebbi zero energy state

We present an analogy between the one dimensional Poisson equation in inhomogeneous media and the Dirac equation in one space dimension with a Lorentz scalar potential for zero energy. We illustrate how the zero energy state in the Jackiw-Rebbi model can be implemented in a simple one dimensional electrostatic setting by using an inhomogeneous electric permittivity and an infinite charged sheet. Our approach provides a novel insight into the Jackiw-Rebbi zero energy state and provides a helpful way to visualize and teach this important quantum field theory model using basic electrostatics.