Simple non-Abelian extensions of the standard model gauge group and the diboson excesses at the LHC

The ATLAS collaboration reported excesses at around 2 TeV in the diboson production decaying into hadronic final states. We consider the possibility of explaining the excesses with extra gauge bosons in two simple non-Abelian extensions of the standard model. One is the so-called $G(221)$ models with a symmetry structure of $SU(2{)}_1\otimes SU(2{)}_2\otimes U(1{)}_X$ and the other is the $G(331)$ models with an extended symmetry of $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$. The $W^{\prime }$ and $Z^{\prime }$ bosons emerge after the electroweak symmetry is spontaneously broken. Two patterns of symmetry breaking in the $G(221)$ models are considered in this work: one is $SU(2{)}_L\otimes SU(2{)}_2\otimes U(1{)}_X\to SU(2{)}_L\otimes U(1{)}_Y$, the other is $SU(2{)}_1\otimes SU(2{)}_2\otimes U(1{)}_Y\to SU(2{)}_L\otimes U(1{)}_Y$. The symmetry breaking of the $G(331)$ model is $SU(3{)}_L\otimes U(1{)}_X\to SU(2{)}_L\otimes U(1{)}_Y$. We perform a global analysis of $W^{\prime }$ and $Z^{\prime }$ phenomenology in ten new physics models, including all the channels of $W^{\prime }/Z^{\prime }$ decay. Our study shows that the leptonic mode and the dijet mode of $W^{\prime }/Z^{\prime }$ decays impose a very stringent bound on the parameter space in several new physics models. Such tight bounds provide a useful guide for building new physics models to address on the diboson anomalies. We also note that the left-right and leptophobic models can explain the $3.4\sigma WZ$ excess if the $2.6\sigma$ deviation in the $W^{+}{W}^{-}$ pair around 2 TeV were confirmed to be a fluctuation of the SM backgrounds.

Figure 1

The NLO cross section of $pp\to W^{\prime }/Z^{\prime }$ with a sequential coupling as a function of $M_{W^{\prime }/Z^{\prime }}$ calculated with the CT14 NNLO PDFs at LHC Run-1. (a) The PDF uncertainty bands and (b) the relative PDF uncertainties $\mathrm{\Delta }\sigma /\sigma$ of ${\sigma }_{W^{\prime }}$ and ${\sigma }_{Z^{\prime }}^u$ and ${\sigma }_{Z^{\prime }}^d$, where ${\sigma }_{Z^{\prime }}^u$ and ${\sigma }_{Z^{\prime }}^d$ represent the cross sections induced by up-type and down-type quark initial states, respectively.

Figure 2

${\sigma }_{W^{\prime }}$ versus ${\sigma }_{Z_u^{\prime }}$ (a), ${\sigma }_{Z_d^{\prime }}$ (b) and ${\sigma }_{Z^{\prime }}$ (c) for $M_{W^{\prime }}=M_{Z^{\prime }}=2\mathrm{TeV}$. The blue point represents the cross sections calculated with 56 sets of PDFs while the red spot label the cross section evaluated with the central PDF.

Figure 3

The contours of the total width of $W^{\prime }$ (a) and the ratio of total width and mass of $W^{\prime }$ (b) in the plane of $c_{\varphi }$ and $s_{2\beta }$ in the left-right model.

Figure 4

The contours of the cross section (a) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WZ)$, (b) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WH)$, (c) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to e\nu )$ and (d) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to tb)$ in the plane of $c_{\varphi }$ and $s_{2\beta }$. The vertical line ($jj$) denotes the constraint from the di-jet measurements. The yellow band represents the degenerated mass region of $W^{\prime }$ and $Z^{\prime }$.

Figure 5

The cross section of $pp\to W^{\prime }\to WZ/WH$ (red curves) and $pp\to W^{\prime }\to jj$ (blue curves) as a function of $c_{\varphi }$ with $s_{2\beta }=1$. The dashed curves represent the PDF uncertainties. The green shaded region represents the parameter space compatible with the $WZ$ excess. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$. The current experimental limits of $\sigma (pp\to W^{\prime }\to jj)<102\mathrm{fb}$ and $\sigma (pp\to W^{\prime }\to WH)<7.1\mathrm{fb}$ are also plotted.

Figure 6

The total width (a) and the branching ratios of all the decay modes (b) of $Z^{\prime }$ as a function of $c_{\varphi }$. The $jj$ mode includes all the light quark flavors ($u$, $d$, $c$, $s$, $b$), the $tt$ mode denotes the top-quark pair final state, the $\ell \ell$ mode sums over the charged leptons while the $\nu \nu$ mode sums over all the three neutrino final states.

Figure 7

The contours of the cross section $\sigma (Z^{\prime })\times \mathrm{BR}(Z^{\prime }\to XY)$, where $X$ and $Y$ denote the SM particles in the $Z^{\prime }$ decay as a function of $c_{\varphi }$. The shaded bands along each curve represent the region compatible with the current experimental data. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$.

Figure 8

The total width ${\mathrm{\Gamma }}_{W^{\prime }}$ (a) and ${\mathrm{\Gamma }}_{W^{\prime }}/M_{W^{\prime }}$ (b) in the plane of $c_{\varphi }$ and $s_{2\beta }$ in the leptophobic doublet model.

Figure 9

The contours of the cross section (a) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WZ)$, (b) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WH)$, (c) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to e\nu )$, and (d) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to tb)$ in the plane of $c_{\varphi }$ and $s_{2\beta }$. The vertical line ($jj$) denotes the constraint from the dijet measurements. The yellow band represents the degenerated mass region of $W^{\prime }$ and $Z^{\prime }$.

Figure 10

The cross section of $pp\to W^{\prime }\to WZ/WH$ (red curves) and $pp\to W^{\prime }\to jj$ (blue curves) as a function of $c_{\varphi }$ with $s_{2\beta }=1$. The dashed curves represent the PDF uncertainties. The green shaded region represents the parameter space compatible with the $WZ$ excess. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$. The current experimental limits of $\sigma (pp\to W^{\prime }\to jj)<102\mathrm{fb}$ and $\sigma (pp\to W^{\prime }\to WH)<7.1\mathrm{fb}$ are also plotted.

Figure 11

The total width (a) and the branching ratios of all the decay modes (b) of $Z^{\prime }$ as a function of $c_{\varphi }$ in leptophobic model.

Figure 12

The contours of the cross section $\sigma (Z^{\prime })\times \mathrm{BR}(Z^{\prime }\to XY)$, where $X$ and $Y$ denote the SM particles in the $Z^{\prime }$ decay as a function of $c_{\varphi }$ in the leptophobic model.

Figure 13

The total width ${\mathrm{\Gamma }}_{W^{\prime }}$ (a) and ${\mathrm{\Gamma }}_{W^{\prime }}/M_{W^{\prime }}$ (b) in the plane of $c_{\varphi }$ and $s_{2\beta }$ in the hadrophobic doublet model.

Figure 14

The contours of the cross section (a) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WZ)$, (b) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WH)$, (c) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to e\nu )$ and (d) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to tb)$ in the plane of $c_{\varphi }$ and $s_{2\beta }$ in the hadrophobic doublet model. All the cross sections are in the unit of fb. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$.

Figure 15

The total width ${\mathrm{\Gamma }}_{Z^{\prime }}$ (a) and the branching ratios of the $Z^{\prime }$ decay (b) as a function of $c_{\varphi }$ in hadrophobic model.

Figure 16

The contours of the cross section of $\sigma (Z^{\prime })\times \mathrm{BR}(Z^{\prime }\to XY)$, where $X$ and $Y$ denote the SM particles in the $Z^{\prime }$ decay as a function of $c_{\varphi }$ in the hadrophobic model. The shaded bands are corresponding to the allowed regions by the current experimental data. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$.

Figure 17

The total width ${\mathrm{\Gamma }}_{W^{\prime }}$ (a) and ${\mathrm{\Gamma }}_{W^{\prime }}/M_{W^{\prime }}$ (b) in the plane of $c_{\varphi }$ and $s_{2\beta }$ in the fermiophobic doublet model.

Figure 18

The contours of the cross section (a) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WZ)$, (b) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to WH)$, (c) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to e\nu )$ and (d) $\sigma (W^{\prime })\times \mathrm{BR}(W^{\prime }\to tb)$ in the plane of $c_{\varphi }$ and $s_{2\beta }$ in the fermiophobic doublet model. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$.

Figure 19

The total width (a) and the branching ratios of $Z^{\prime }$ decays (b) as a function of $c_{\varphi }$ in fermiophobic model.

Figure 20

The cross section contours of $\sigma (Z^{\prime })\times \mathrm{BR}(Z^{\prime }\to XY)$, where $X$ and $Y$ denote the SM particles in the $Z^{\prime }$ decay as a function of $c_{\varphi }$ in the fermiophobic model. The yellow shaded region is required for $M_{W^{\prime }}\simeq M_{Z^{\prime }}$.

Figure 21

(a) The total width ${\mathrm{\Gamma }}_{W^{\prime }}$ as a function of $c_{\varphi }$ in the un-unified (UU) model of BP-II. (b) The decay branching ratio $BR(W^{\prime }\to XY)$ as a function of $c_{\varphi }$. (c) The cross section $\sigma (pp\to W^{\prime }\to XY)$ as a function of $c_{\varphi }$ at the LHC Run-1. The shaded band of each curve satisfies the current experiment data.

Figure 22

(a) The total width ${\mathrm{\Gamma }}_{Z^{\prime }}$ as a function of $c_{\varphi }$ in the un-unified (UU) model of BP-II. (b) The decay branching ratio $\mathrm{BR}(Z^{\prime }\to XY)$ as a function of $c_{\varphi }$ in the un-unified (UU) model of BP-II. (c) The cross section $\sigma (pp\to Z^{\prime }\to XY)$ at LHC Run-1 as a function of $c_{\varphi }$ in the un-unified (UU) model of BP-II. The shaded band of each curve satisfies the current experiment.

Figure 23

(a) The total width ${\mathrm{\Gamma }}_{W^{\prime }}$ as a function of $c_{\varphi }$ in the nonuniversal (NU) model of BP-II. (b) The decay branching ratio $\mathrm{BR}(W^{\prime }\to XY)$ as a function of $c_{\varphi }$. (c) The cross section $\sigma (pp\to W^{\prime }\to XY)$ versus $c_{\varphi }$ at the LHC Run-1 in the NU model. The shaded band along each curve satisfies the current experimental data.

Figure 24

(a) The total width ${\mathrm{\Gamma }}_{Z^{\prime }}$ versus $c_{\varphi }$ in the nonuniversal (NU) model of BP-II. (b) The decay branching ratio $\mathrm{BR}(Z^{\prime }\to XY)$ as a function of $c_{\varphi }$. (c) The cross section $\sigma (pp\to Z^{\prime }\to XY)$ versus $c_{\varphi }$ at the LHC Run-1. The shaded band along each curve satisfies the current experimental data.

Figure 25

The cross section of $Z^{\prime }$ production versus $M_{Z^{\prime }}$ for different choices of $\beta$ in the $G(331)$ model at the LHC Run-1. For comparison the production cross section of a sequential $Z^{\prime }$ boson is also plotted (black-dotted curve).

Figure 26

(a) The branching ratio $\mathrm{BR}(Z^{\prime }\to WW/ZH)$ as a function of $\alpha$ for different choices of $\beta$. (b) The cross section $\sigma (Z^{\prime })\times \mathrm{BR}(Z^{\prime }\to WW/ZH)$ as a function of $\alpha$ for different choices of $\beta$ at the LHC Run-1. The shaded bands along the curves represent the parameter space that could explain the $WW$ excess. The black-dashed horizontal line shows the upper limit of $ZH$.

Figure 27

The cross section of $\sigma (pp\to Z^{\prime }\to t\overline{t})$ (a), $\sigma (pp\to Z^{\prime }\to jj)$ (b) and $\sigma (pp\to Z^{\prime }\to e\overline{e})$ (c) as a function of $\alpha$ in the $G(331)$ model. The current experimental limits are also displayed.