Sensitivity to light weakly-coupled new physics at the precision frontier

Precision measurements of rare particle physics phenomena (flavor oscillations and decays, electric dipole moments, etc.) are often sensitive to the effects of new physics encoded in higher-dimensional operators with Wilson coefficients given by $\mathrm{C}/({\mathrm{\Lambda }}_{\mathrm{NP}}{)}^n$, where C is dimensionless, $n\ge 1$, and ${\mathrm{\Lambda }}_{\mathrm{NP}}$ is an energy scale. Many extensions of the Standard Model predict that ${\mathrm{\Lambda }}_{\mathrm{NP}}$ should be at the electroweak scale or above, and the search for new short-distance physics is often stated as the primary goal of experiments at the precision frontier. In rather general terms, we investigate the alternative possibility—$\mathrm{C}\ll 1$, and ${\mathrm{\Lambda }}_{\mathrm{NP}}\ll m_W$—to identify classes of precision measurements sensitive to light new physics (hidden sectors) that do not require an ultraviolet completion with additional states at or above the electroweak scale. We find that hadronic electric dipole moments, lepton number and flavor violation, nonuniversality, as well as lepton $g-2$ can be induced at interesting levels by hidden sectors with light degrees of freedom. In contrast, many hadronic flavor- and baryon number-violating observables, and precision probes of charged currents, typically require new physics with ${\mathrm{\Lambda }}_{\mathrm{NP}}\gtrsim m_W$. Among the leptonic observables, we find that a nonzero electron electric dipole moment near the current level of sensitivity would point to the existence of new physics at or above the electroweak scale.

Figure 1

A schematic view of the parameter space of mass scale vs coupling for physics beyond the SM. The horizontal axis represents the mass (or energy) scale, whereas the vertical scale shows the visibility of the model, in terms of the coupling to the SM. The blue visible area is accessible through direct searches. While new high energy physics can contribute to all precision observables, as discussed in this paper there are interesting classes of observables that are also sensitive to low-mass new physics. These are shown in green, and test lepton universality (LU), lepton flavor violation (LFV), lepton $g-2$ (MDM), and lepton number violation (LNV). However, observables in the hadronic sector in red, e.g. hadronic flavor violation (HFV) and baryon number violation (BNV), and also lepton electric dipole moments (LEDMs) generally require some new high scale physics. The arrows indicate the pressure imposed on models through increasing experimental sensitivity.

Figure 2

A plot of the angles ${\mathrm{\Theta }}_{\mu ,\tau }$ given by Eqs. (10), with $M_D=3\mathrm{GeV}$. The gray band is inconsistent with the assumption that $\epsilon \ll m_D$.

Figure 3

Example of a $\mu \to e\gamma$ diagram.

Figure 4

Phase space factors $I_{0,1,2}$ for the $\tau \to l\nu \nu$ decay.

Figure 5

Plots showing the allowed regions in (a) $\{\epsilon ,{\mathrm{\Theta }}_e\}$ and (b) $\{M_D,{\mathrm{\Theta }}_e\}$ respectively, with $N_h=2$. The lines correspond to saturation of the respective bounds. $M_D$ is bounded above by the requirement $M_D<m_W$, and from below by the $0\nu \beta \beta$ constraint $M_D\gg 0.1\mathrm{GeV}$. We note that at large $\epsilon$, the $\mu -e$ conversion constraint is by far the strongest, though universality becomes stronger at low $\epsilon$. The darker gray area represents the regime where $\epsilon /m_e>{10}^{-1}$, with $\epsilon$ no longer ‘small’. For completeness, we also show a constraint from on-shell production of sterile states at the CHARM fixed target experiment [59], which applies for $M_D\lesssim 2\mathrm{GeV}$.

Figure 6

An example of a W-loop diagram contributing to the lepton EDM. The crosses indicate neutrino mass insertions.

Figure 7

The $CP$-odd $hF\tilde{F}$ vertex.