Magnetic dipole transitions in atomic and particle physics: ions and psions

Abstract

Magnetic dipole (Ml) transitions in atomic systems can be classified into two types. If in a non-relativistic description of the atomic states the spatial parts of the initial and final wavefunctions are the same, as in the hydrogenic transition 22P312-+ PPpl/~+y, one has an 'ordinary' or 'unhindered' transition. If the spatial parts are Joseph Sucher interaction between the quark and the antiquark is illustrated. A brief survey is given of recent attempts to overcome the deficiencies of the model. The review concludes with a discussion of other problems of current interest in which relativistic M1 transitions may play an important role. This review was received in March 1978. Magnetic dipole transitions in atomic and particle physics: ions and psions 1783 Contents 1. Introduction. 2. Theory of M1 transitions in H and H-like ions , 2.1. Non-relativistic theory. 2.2. Relativistic theory. 2.3. How do metastable S states decay? A brief history 3.1. Experimental developments in the 1970s 3.2. Theory of the 23S1-+ 11So+y decay. 3.3. Comparison of theory with experiment. 4.1. The discovery of the psions. 4.2. T h e three c's: charm, colour and confinement 4.3. Width of (E , c) bound states and the 021 rule 5.1. Description of the model 5.2. Qualitative predictions and comparison with experiment. 5.3. Quantitative aspects of the extreme non-relativistic model 6. Radiative transitions of two-body bound states of spin-& particles 6.1. Relativistic wave equation. 6.2. Transformation to Pauli-type wavefunctions , 6.3. Effective potential. 6.4. Theory of radiative decay 6.5. Partial summary and cases of special interest , 6.6. Decay rate formulae. 7. Application to the narrow resonances. 7.1. Computation of M1 decay rates , 7.2. Comparison with experiment. 7.3. Survey of present status 8. Concluding remarks .

Lattice QCD estimate of the η c (2S) → J/ψγ decay rate

“…We checked that in the continuum limit our result for m ηc(2S) /m ηc = 1.23 (2), is fully consistent with the measured (m ηc(2S) /m ηc ) exp. = 1.22.…”

“…It was first observed in ref. [2] that a substantial part of relativistic corrections cancel in ψ(2S) → η c γ, whereas they add up in the case of η c (2S) → J/ψγ to further enhance its decay rate. In the effective field theory approach [12], that point has been recently emphasized in ref.…”

“…In this paper we again work with the charmonium states that are all below the D ( * )D( * ) production threshold and therefore the dependence on the light (sea) quark should remain negligible. 2 For that reason, in this study, we focus on a subset of gauge field configurations considered in ref. [10] and study one value of the light sea quark mass per lattice spacing but we increase the statistics in order to be able to isolate the radially excited state from our correlation functions.…”

“…where P (2) is the operator optimally interpolating the η c (2S) state obtained in the previous section, V i =cγ i c is the smeared operator interpolating the J/ψ, and J em j =cγ j c is the local vector current, renormalized by using Z V (g 2 0 ) given in table 1. We benefit from the time reversal symmetry that relates the photon emission and the photon absorption…”

“…The matrix element is then obtained after dividing the source operators from the three-point function (4.1), namely, 8) where the values of Z V,P (2) , E J/ψ and m ηc are obtained from the study of two-point correlation functions. In figure 3 we illustrate the plateau of R 3 (t) which is then fit to a constant (shaded area in figure 3) that corresponds to the matrix element, J/ψ|J em µ |η c (2S) , from which we then get the form factor V 12 (0), cf.…”