Minimal anomalous $U(1{)}^{\prime }$ extension of the MSSM

We study an extension of the minimal supersymmetric standard model by an anomalous Abelian vector multiplet and a Stückelberg multiplet. The anomalies are cancelled by the Green-Schwarz mechanism and the addition of Chern-Simons terms. The advantage of this choice over the standard one is that it allows for arbitrary values of the quantum numbers of the extra $U(1)$. As a first step toward the study of hadron annihilations producing four leptons in the final state (a clean signal which might be studied at LHC), we then compute the decays $Z^{\prime }\to Z_0\gamma$ and $Z^{\prime }\to Z_0{Z}_0$. We find that the largest values of the decay rate are $\sim {10}^{-4}\mathrm{GeV}$, while the expected number of events per year at LHC is at most of the order of 10.

Figure 1

The Ward identities for the amplitude $V_{\rho }^{(0)}(p+q)\to V_{\mu }^{(1)}(p)V_{\nu }^{(1)}(q)$ in the unbroken phase include the GCS as well as the axionic couplings. The solid lines represent fermions and the wiggle lines are gauge fields. Dashed lines are scalars. Each depicted diagram also contains the exchange $(\mu ,p)\leftrightarrow (\nu ,q)$.

Figure 2

The Ward identities for the amplitude $V_{\rho }^{(0)}(p+q)\to V_{\mu }^{(1)}(p)V_{\nu }^{(1)}(q)$ in the broken phase.

Figure 3

Diagrams for $Z^{\prime }\to Z_0\gamma$.

Figure 4

$M_{Z^{\prime }}=1\mathrm{TeV}$.

Figure 5

$M_{Z^{\prime }}=2\mathrm{TeV}$.

Figure 6

$M_{Z^{\prime }}=4\mathrm{TeV}$.

Figure 7

Number of $Z^{\prime }$ produced at LHC in 1 yr for $\mathcal{L}={10}^{34}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ and $\sqrt{s}=14\mathrm{TeV}$, in units of $Q_Q^2$, in function of the mass of the $Z^{\prime }$.

Figure 8

Number of $Z^{\prime }\to Z_0{Z}_0$ at LHC in 1 yr for $\mathcal{L}={10}^{34}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, $\sqrt{s}=14\mathrm{TeV}$, and $M_{Z^{\prime }}=1\mathrm{TeV}$.

Figure 9

The anomalous triangle diagram.

Figure 10

Nonanomalous diagrams for trilinear neutral gauge boson amplitudes.