Acetaldehyde as a molecule for testing variations of electron-to-proton mass ratio

TL;DR

This work addresses potential spatial variations of the electron-to-proton mass ratio $\mu$ by computing sensitivity coefficients $Q$ for CH$_3$CHO torsion–rotation transitions in the microwave range. It introduces a seven-parameter effective Hamiltonian to model torsion–rotation coupling and derives $Q$ by perturbing $\mu$ to $\mu_0(1\pm\varepsilon)$, with $\varepsilon$ values of $10^{-3}$ and $10^{-4}$. The results show most CH$_3$CHO transitions have $Q$ near unity ($0.62 \le Q \le 1.4$), with a notable high-$Q$ line $Q=3.61$, and demonstrate that acetaldehyde can be used with methanol lines for stringent $\Delta\mu/\mu$ tests. Using line data from three molecular clouds at $D_{\rm GC}\sim 8$ kpc, the study finds $\Delta\mu/\mu = (0.1\pm0.4)\times10^{-7}$, implying $\Delta\mu/\mu < 4\times10^{-8}$ and supporting the local position invariance in the Galactic disk.

Abstract

We present the quantum-mechanical calculations of the dimensionless sensitivity coefficients Q to small changes in the fundamental physical constant mu = m_e/m_p - the electron-to-proton mass ratio - for a number of low-frequency (1-50 GHz) transitions of the acetaldehyde (CH3CHO) molecule. The calculations show that Q varies in the range from 0.62 to 3.61. An example of the practical use of the CH3CHO and CH3OH lines tracing the same regions in three molecular clouds, located at large galactocentric distances (D_GC ~ 8 kpc) is considered. This results in a limit on the mu variations of Delta mu/mu = (0.1 +/- 0.4)*10^(-7) which is in line with previously obtained most stringent upper limits on changes in mu based on other molecules and methods. The limit obtained restricts hypothetical violations of the Einstein principle of the local position invariance at the level of 4*10^(-8) in the Galactic disk at large galactocentric distances.

Figures (1)

• Figure 1: Partial rotational level diagrams of $A$- and $E$- levels of acetaldehyde CH$_3$CHO in the torsional ground state ($v_t=0$). The energy of the ground torsion state of the $E$-type acetaldehyde is 0.097 K.