Calcium anomaly as evidence for a new boson with mass in the range 10 eV to 10 MeV

I learned about findings giving support for the view about a new interaction implying that the energies of electrons depend on the neutron number of the atom in a way, which is not explainable in the standard model (see this). A new interaction mediated by a scalar boson with mass in the range 10 eV-10 MeV is proposed as an explanation for the findings. There are many other anomalies, which a boson with a mass ∼ 17 MeV could explain.

The following gives the abstract of the article published in Phys Rev Letters.

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-standard-model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order standard model (SM) effects from BSM physics. We measure the IS of the transitions ³P₀→ ³P₁ in Ca¹⁴⁺ and ²S_1/2 → ²D_5/2 in Ca⁺ with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below 4× 10^-11 for the five stable, even isotopes of calcium (^{40,42,44,46,48}Ca).
Combined, these measurements yield a calcium KP nonlinearity with a significance of ∼ 10³σ. Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between 10 eV/c² and 10⁷ eV/c².

My understanding of what has been done is as follows.

1. Nonlinear isotope shift (IS) in KP for Ca isotopes A=42,44,46,48 relative to the isotope A=40 observed. Note that or ³P₀→ ³P₁ in Ca¹⁴⁺ 14-fold electronic ionization so that the electronic configuration is [He]2s² 2p².
2. What is measured are the differences δ ν^A₅₇₀ and δ ν^A₇₂₉ of the frequencies (equivalently energies) of the initial and final electronic configuration for these two transitions as function of A ∈ {10,42,44,46,48}. From these shifts the differences δ ν^A,40₅₇₀=δ ν^A₅₇₀-δ ν⁴⁰₅₇₀ and δ ν^A,40₇₂₉ = δ ν^A₇₂₉- δ ν⁴⁰₇₂₉ of these shifts for δ ν^A,40₅₇₀=δ ν^A₅₇₀-δ ν⁴⁰₅₇₀ with A ∈{42,44,46,48} are deduced.
3. If the effects of the neutron number on the electron energies equals to that predicted by standard model, δ ν^A,40₇₂₉ should be a linear function of δ ν^A,40₅₇₀. In the graphical representation the linearity allows to replaced the shifts with δ ν^A,40₅₇₀ → δ ν^A,40₅₇₀ -452 [GHz amu]==X and δ ν^A,40₇₂₉ → δ ν^A,40₇₂₉- 2327 [GHz amu]==Y are performed. This gives the King plot representing Y as function of X.
4. Fig 1. of the article gives the shifts for Ca isotopes for A∈{42,44,46,48} and from the 4 boxes magnifying the graph for the isotope shifts for these values of A show a small non-linearity: the red ellipses are not located at the blue vertical lines. For A= 42,44,48 the red ellipse is shifted to the right but for A=46 it is shifted to the left.

A Yukava scalar with mass in range 10 eV to 10⁷ eV proposed as an explanation. I am not able to conclude whether the scalar property is essential or whether also pseudoscalar is possible. The coupling to the boson affects the binding energies of electrons so that they have additional dependence on the neutron number. If the King plot were linear, the difference would be proportional to the neutron number implying proportional to A-40. The slope of the curve would be 45 degrees. Note that from the table I the differences are in the range .1 meV to 1 meV about δ E/E ∼ 10^-4. One neutron pair corresponds to an energy difference of order .1 meV.

One can consider two options in the TGD framework.

1. The upper bound for the boson mass is about 10 MeV and this suggests 17 MeV pseudoscalar which could explain several earlier nuclear physics anomalies (see this and this) and for which I have proposed a TGD inspired model (see this). In particular, X boson explains Yb anomaly for which also non-linearity of the King plot was observed. This anomaly to the deformations of nuclei caused by adding neutrons.
2. In the TGD framework one can consider also a second option, which is M⁴ Kähler force as a new interaction. M⁴ Kähler potential contributes to electroweak U(1) force if total Kähler potential replaces CP₂ Kähler potential in classical U(1) gauge potential. Could M⁴ Kähler potential give a contribution of the required size to the neutron-electron interaction? I have discussed this contribution in (see this). A simple model shows that the effects are extremely small. This implies that the new interaction does not imply any obvious anomalies. At the level of the embedding space Dirac equation, the effects are dramatic. The basic implication is that colored states of fermions have mass of order CP₂ mass and only color singlets can be light. One implication is that the g-2 anomaly is real since the calculation using hadronic data as input rather than lattice QCD gives the anomaly (see this).

See the article X boson as evidence for nuclear string model or the chapter Nuclear String Hypothesis.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.