Leading-order relativistic corrections to the Zeeman splitting of hyperfine structure levels in two-fermion bound-state systems

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

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Leading-order relativistic corrections to the g factor of H2+

Physical Review A ◽

10.1103/physreva.104.032822 ◽

2021 ◽

Vol 104 (3) ◽

Author(s):

Jean-Philippe Karr

Keyword(s):

Leading Order ◽

G Factor ◽

Relativistic Corrections

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Energy levels in muonic helium

EPJ Web of Conferences ◽

10.1051/epjconf/201922203009 ◽

2019 ◽

Vol 222 ◽

pp. 03009

Author(s):

A.V. Eskin ◽

V.I. Korobov ◽

A.P. Martynenko ◽

V.V. Sorokin

Keyword(s):

Hyperfine Structure ◽

Bound States ◽

Energy Levels ◽

Computer Code ◽

Bound State ◽

Relativistic Correction ◽

Matrix Elements ◽

Gaussian Form ◽

Stochastic Variational Method ◽

The Matrix

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.

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BOUND-STATE/ELEMENTARY-PARTICLE DUALITY IN THE HIGGS SECTOR AND THE CASE FOR AN EXCITED "HIGGS" WITHIN THE STANDARD MODEL

Modern Physics Letters A ◽

10.1142/s0217732313501034 ◽

2013 ◽

Vol 28 (28) ◽

pp. 1350103 ◽

Cited By ~ 27

Author(s):

AXEL MAAS

Keyword(s):

Elementary Particle ◽

Standard Model ◽

Cross Sections ◽

Bound States ◽

Weak Interactions ◽

Higgs Sector ◽

Bound State ◽

Leading Order ◽

Expectation Value ◽

The Standard Model

Though being weakly interacting, QED can support bound states. In principle, this can be expected for the weak interactions in the Higgs sector as well. In fact, it has been argued long ago that there should be a duality between bound states and the elementary particles in this sector, at least in leading order in an expansion in the Higgs quantum fluctuations around its expectation value. Whether this remains true beyond the leading order is being investigated using lattice simulations, and support is found. This provides a natural interpretation of peaks in cross-sections as bound states. This would imply that (possibly very broad) resonances of Higgs and W and Z bound states could exist within the Standard Model.

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