Sub-GeV $U(1{)}_R$ gauge boson to address the proton radius discrepancy

We propose a Standard Model extension by a $U(1{)}_R$ gauge symmetry where only right-handed chiral fermions can carry a nontrivial charge. Here, we show that the simplest anomaly-free solution to accommodate the proton charge radius discrepancy takes right-handed muons, ${\mu }_R$, and first generation quarks, $u_R$ and $d_R$. Consistency with the latest muon’s ($g-2$) measurements is achieved through an extra light scalar, which itself must lie in the tens of MeV mass range to be viable.

Figure 1

Set of right-handed fermion combinations free of gauge anomalies. The solid red line connecting the three blobs illustrates the link between nucleons and muons as demanded by the proton radius puzzle.

Figure 2

$Z^{\prime }$ mass-coupling curve fitting the $\mathrm{\Delta }{r}_p^2$ discrepancy (solid black) obtained from equating the rhs of Eq. (6) to $306.4\mu \mathrm{eV}$ and the corresponding $U(1{)}_R$-breaking singlet vev (magenta dashed).

Figure 3

Contours of $s$-like (green) and ${\phi }_2$-like (orange) scalar masses at two $v_{{\mathrm{\Phi }}_2}$ choices (i.e., at two $y$ muon Yukawa choices). The LHC limit on muonphuilic $H^{+}$ scalars is shown, which pushes $y$ to large values near the perturbative $4\pi$ value.

Figure 4

Zooms of Fig. 3 right panel, one around the LHC limit on $H^{+}$ scalars (left) and the other around the $m_{H^{+}}=1\mathrm{TeV}$ mass contour. Red crosses mark the benchmarks in Table 2.

Figure 5

$(g-2{)}_{\mu }$ contribution by a $Z^{\prime }$ coupled to RH fermions (cyan contours). The $\mathrm{\Delta }{r}_p^2$ fitting curve is depicted in dashed black. The $(g-2{)}_{\mu }$ lattice bound exclusion from Eq. (17) is shaded red.

Figure 6

Left: $Z^{\prime }$-only (blue curve) and joint $Z^{\prime }+s$ contribution to $(g-2{)}_{\mu }$ (black curves). The vertical $g^{\prime }$ ticks indicate corresponding gauge coupling values fitting $\mathrm{\Delta }{r}_p^2$ at each $m_{Z^{\prime }}$. Right: zoomed region for the $(g-2{)}_{\mu }$ lattice bound (dashed red) and $2\sigma$ band of the new physics hint (green).