Is the $\overline{\theta }$ Parameter of QCD Constant?

Testing the cosmological variation of fundamental constants of nature can provide valuable insights into new physics scenarios. While many such constraints have been derived for standard model coupling constants and masses, the $\overline{\theta }$ parameter of QCD has not been as extensively examined. In this Letter, we discuss potentially promising paths to investigate the time dependence of the $\overline{\theta }$ parameter. While laboratory searches for $CP$-violating signals of $\overline{\theta }$ yield the most robust bounds on today’s value of $\overline{\theta }$, we show that $CP$-conserving effects provide constraints on the variation of $\overline{\theta }$ over cosmological timescales. We find no evidence for a variation of $\overline{\theta }$ that could have implied an “iron-deficient” Universe at higher redshifts. By converting recent atomic clock constraints on a variation of constants, we infer $d({\overline{\theta }}^2)/dt\le 6\times {10}^{-15}{\mathrm{yr}}^{-1}$, at $1\sigma$. Finally, we also sketch an axion model that results in a varying $\overline{\theta }$ and could lead to excess diffuse gamma ray background, from decays of axions produced in high redshift supernova explosions.

Figure 1

Constraints on $\mathrm{\Delta }({\overline{\theta }}^2)$ derived from bounds on $\mathrm{\Delta }\mu /\mu$ in Table 1 across a range of redshifts $z$. The two data points at $z=2.659$ and 2.66 have been combined and averaged. The best fit points are shown as black circles and the $1\sigma$ uncertainties are shown in blue. Some data points from Table 1 lead to negative $\mathrm{\Delta }({\overline{\theta }}^2)$ and therefore to unphysical values of $\overline{\theta }$, which we show in the gray region.