FCNC decays of standard model fermions into a dark photon

We analyze a new class of FCNC processes, the $f\to f^{\prime }\overline{\gamma }$ decays of a fermion $f$ into a lighter (same-charge) fermion $f^{\prime }$ plus a massless neutral vector boson, a dark photon $\overline{\gamma }$. A massless dark photon does not interact at tree level with observable fields, and the $f\to f^{\prime }\overline{\gamma }$ decay presents a characteristic signature where the final fermion $f^{\prime }$ is balanced by a massless invisible system. Models recently proposed to explain the exponential spread in the standard-model Yukawa couplings can indeed foresee an extra unbroken dark $U(1)$ gauge group, and the possibility to couple on-shell dark photons to standard-model fermions via one-loop magnetic-dipole kind of FCNC interactions. The latter are suppressed by the characteristic scale related to the mass of heavy messengers, connecting the standard model particles to the dark sector. We compute the corresponding decay rates for the top, bottom, and charm decays ($t\to c\overline{\gamma }$, $u\overline{\gamma }$, $b\to s\overline{\gamma }$, $d\overline{\gamma }$, and $c\to u\overline{\gamma }$), and for the charged-lepton decays ($\tau \to \mu \overline{\gamma }$, $e\overline{\gamma }$, and $\mu \to e\overline{\gamma }$) in terms of model parameters. We find that large branching ratios for both quark and lepton decays are allowed in case the messenger masses are in the discovery range of the LHC. Implications of these new decay channels at present and future collider experiments are briefly discussed.

Figure 1

Feynman rules for interaction vertices and propagators entering the computation of the one-loop $q\to q^{\prime }\overline{\gamma }$ decay amplitude. The symbols $q_{L/R}^i$ and $Q_{L/R}^{U_i,D_i}$ stand for the quark and dark-quark fields, respectively, with $L/R$ denoting the left-/right-handed chirality projections. $S_n^{U_j}$ and $S_n^{D_j}$ stand for the mass eigenstates ($n=1$, 2) in the up and down messenger sectors, respectively, while $\overline{\gamma }$ is the dark-photon field.

Figure 2

Feynman diagrams (a)–(d) contributing to the FCNC decay $q^i\to q^j\overline{\gamma }$ with $q=U$, $D$ and $i>j$, where $q_{L,R}^{i,j}$ are the initial ($i$), final ($j$) quarks, with $L/R$ indicating the left/right chirality projections, $Q^{q_i}$ and $S_n^{q_i}$ the corresponding dark quarks and messenger fields, respectively, with the latter in the basis of mass eigenstates ($n=1$, 2), while $\overline{\gamma }$ stands for the dark-photon line.

Figure 3

Allowed regions (colored areas) by DM and vacuum stability (VS) constraints for $\mathrm{BR}(t\to q\overline{\gamma })$ and for the average messenger mass scales $\overline{m}$ and ${\overline{m}}_D$ versus the corresponding mixing $\xi$ and ${\xi }_D$, in the UF (left) and NUF (right) scenarios, respectively.

Figure 4

Regions allowed by $b\to s\gamma$ data at 95% C.L. (represented by superimposed colored areas), for the effective messenger mass scale ${\overline{m}}_D^{32}$ defined in Eq. (71), as a function of $x_3^D$ and for different values of the mixing parameter ${\xi }_D$. Regions $x_3^D>1-{\xi }_D$ are excluded by DM constraints.

Figure 5

Allowed regions (dark blue colored areas) by DM and vacuum stability (VS) constraints for $\mathrm{BR}(b\to q\overline{\gamma })$ and for the average messenger mass scales $\overline{m}$ and ${\overline{m}}_D$ versus the corresponding mixing $\xi$ and ${\xi }_D$, in the UF (left) and NUF (right) scenarios, respectively. In the UF (NUF) scenario, we assume $\overline{e}{\overline{e}}_3^D=1$,  ${\eta }_L^{j3}/{\eta }_L^{33}=1(0.1)$, with $j=1$, 2. Red regions are excluded by the $b\to s\gamma$ constraints, and light-blue regions are excluded by both $b\to s\gamma$ and $B_d{\overline{B}}_d$ mixing constraints.

Figure 6

Allowed regions (colored areas) by DM and vacuum-stability (VS) constraints for $\mathrm{BR}(c\to u\overline{\gamma })$ and for the average messenger mass scales $\overline{m}$ and ${\overline{m}}_D$ versus the corresponding mixing $\xi$ and ${\xi }_D$, in the UF (left) and NUF (right) scenarios, respectively. In the left (right) plots we assume $\overline{e}{\overline{e}}_2^U=1$, ${\rho }_L^{12}/{\rho }_L^{22}\simeq 1$ ($\overline{e}{\overline{e}}_2^D=1$, ${\eta }_L^{12}/{\eta }_L^{22}\simeq 1$) with all other matrix elements of flavor matrices set to zero.

Figure 7

Regions allowed by constraints on $\mathrm{BR}(\tau \to \mu \gamma )$ at 90% C.L. (represented by superimposed colored areas), for the effective messenger mass scale ${\overline{m}}_L^{32}$ defined in Eq. (97), as a function of $x_3^L$ and for several values of the mixing ${\xi }_L$ parameter. Regions $x_3^L>1-{\xi }_L$ are excluded by DM constraints.

Figure 8

Regions allowed by DM and vacuum stability (VS) constraints for $\mathrm{BR}(\tau \to \ell \overline{\gamma })$ (left) and $\mathrm{BR}(\mu \to e\overline{\gamma })$ (right), and for the average messenger mass scale ${\overline{m}}_L$ versus the mixing ${\xi }_L$, in the UF scenario (blue areas). Superimposed red areas are the subregions excluded by direct constraints on $\mathrm{BR}(\ell \to {\ell }^{\prime }\gamma )$. In the left (right) plot, we assume $\overline{e}{\overline{e}}_3^L=1$,  ${\tilde{\eta }}_L^{j3}/{\tilde{\eta }}_L^{33}={10}^{-2}$ ($\overline{e}{\overline{e}}_3^L=1$, ${\tilde{\eta }}_L^{12}/{\tilde{\eta }}_L^{22}={10}^{-4}$), with $j=1$, 2.

Figure 9

Regions allowed by $\mu \to e\gamma$ constraints at 90% C.L. (represented by superimposed colored areas), for the effective messenger mass scale ${\overline{m}}_L^{21}$ defined in Eq. (106), as a function of $x_3^L$ and for different values of the mixing ${\xi }_L$. Regions $x_3^L>1-{\xi }_L$ are excluded by DM constraints.