Self-consistent bounds on Beyond the Standard Model bosons from spectroscopy of muonic atoms with magic nuclei

Abstract

Spectroscopy of muonic atoms is, to date, the most accurate technique to extract parameters of the nuclear charge density. The same reasons for their heightened sensitivity to nuclear parameters, a large overlap of the muonic wavefunction with the nucleus, makes them attractive systems to test Beyond the Standard Model (BSM) Physics. This raises concerns of self-consistency as the same data are used to, first, extract nuclear parameters, and second, check the consistency with BSM models. We combine the two steps and self-consistently extract the nuclear and BSM parameters. We show that the data are consistent with vanishing BSM coupling and extract robust exclusion bounds. We further note that the nuclear parameters change under the influence of those BSM couplings on the parameter fits and compare with the fit solely based on quantum electrodynamics (QED).

Figures (3)

• Figure 1: A plot of the $\mu-^{90}$Zr fit described in the text. Here we show results for a massless scalar boson $X$. a) The figure shows the resulting energy residuals $\Delta E_a^\mathrm{Pb}$ after the fit in orange. In green we show the previous fit for $\alpha_X = 0$. b), c), and d) show the likelihood contours for the three free parameters and the dotted lines indicate the best-fit parameters for the ´QED only' fit. The orange contours correspond to cuts through the best-fit parameters of the ´QED+BSM' fit. For convenience we show the same cuts through the BSM fit likelihood surface at the best-fit QED only parameters in light blue. This highlights the consistency of those parameters with the fit despite the deceptively far orange region. The dotted lines indicate those best-fit QED only parameters. In figure d) the black solid lines highlight the constant rms charge radius curves and the green ellipse shows the likelihood contour for the QED only case.
• Figure 2: The plot shows the parameter space for a new scalar particle. The gray region shows previous exclusions coming from Lamb shift measurements of light muonic atoms and the transition $3d_{5/2}-2p_{3/2}$ in $\mu-^{24}$Mg and $\mu-^{28}$Si Beltrami:1985dc. In orange we depict the self-consistent bounds coming from $\mu-^{90}$Zr spectroscopy, those from $\mu-^{120}$Sn in green, and $\mu-^{208}$Pb in blue. The dashed lines indicate the best-fit BSM coupling in the same colours as the corresponding exclusion regions.
• Figure 3: This plot shows the energy difference \ref{['Eq:Erg_diff']} resulting from a change in nuclear charge density distribution. The first $N$ moments are fixed to coincide. As can be seen, the more moments are fixed, the smaller the energy difference will be. Further, the orange shaded areas indicate the uncertainties utilised in the fit. In the lowest plot the fit for Pb is depicted where the level of uncertainty, depicted in gray, is too small for a nuclear charge distribution with only 2 free parameters. Therefore the energy difference for $N=2$ is taken as a proxy for the shape uncertainty and added to the Pb-fit. The result of this procedure is the orange region. Note that this does affect the best-fit values, however they agree within their error bars.