Distinguishing flavor nonuniversal colorons from $Z^{\prime }$ bosons at the LHC

Electrically neutral massive color-singlet and color-octet vector bosons, which are often predicted in theories beyond the Standard Model, have the potential to be discovered as dijet resonances at the LHC. A color-singlet resonance that has leptophobic couplings needs further investigation to be distinguished from a color-octet one. In previous work, we introduced a method for discriminating between the two kinds of resonances when their couplings are flavor universal, using measurements of the dijet resonance mass, total decay width, and production cross section. Here, we describe an extension of that method to cover a more general scenario, in which the vector resonances could have flavor-nonuniversal couplings; essentially, we incorporate measurements of the heavy-flavor decays of the resonance into the method. We present our analysis in a model-independent manner for a dijet resonance with mass 2.5–6.0 TeV at the LHC with $\sqrt{s}=14\mathrm{TeV}$ and integrated luminosities of 30, 100, 300, and $1000{\mathrm{fb}}^{-1}$ and show that the measurements of the heavy-flavor decays should allow conclusive identification of the vector boson. Note that our method is generally applicable even for a $Z^{\prime }$ boson with non-Standard invisible decays. We include an Appendix of results for various resonance couplings and masses to illustrate how well each observable must be measured to distinguish colorons from $Z^{\prime }\mathrm{s}$.

Figure 1

Ratios of parton density functions as a function of the mass of the produced vector resonance. This figures shows two such ratios: the relative contribution of parton density functions, defined in Eq. (15), for the down-type quarks of the first two generations $(\frac{W_d+W_s}{W_u+W_c})$ (top curve, in red) and for bottom quarks $(\frac{W_b}{W_u+W_c})$ (bottom curve, in blue) relative to the up-type quarks for the first two generations. The values have been calculated using CT09MCS parton distribution functions with factorization scale varied by a factor of 2 away from the mass of the resonance in the range 2.5–6.0 TeV. The results of this variation are illustrated as a band for each function. Note that the upper curve depends only weakly on the resonance mass and that the lower curve’s values are $\mathcal{O}({10}^{-3})$ or less over the entire mass range.

Figure 2

Region of parameter space where the color discriminant variable analysis applies at the LHC with $\sqrt{s}=14\mathrm{TeV}$, for different sets of coupling ratios, ${\rho }_q\equiv \frac{g_q^2}{g_u^2+g_d^2}$. The $5\sigma$ discovery reach, with statistical and systematic uncertainties included, is shown in varying shades of blue for luminosities ranging from $30{\mathrm{fb}}^{-1}$ to $1000{\mathrm{fb}}^{-1}$. The red area marked “no reach” lies beyond the discovery reach at $1000{\mathrm{fb}}^{-1}$ The gray area on the left of each plot marked “excluded” has been excluded by the 8 TeV LHC [43]. In the region above the dashed line marked $\mathrm{\Gamma }\ge 0.15M$, the narrow-width approximation used in dijet resonance searches is not valid [60, 61, 62]. In the region below the horizontal dashed line marked $\mathrm{\Gamma }\le M_{\text{res}}$, the experimental mass resolution is larger than the intrinsic width [43], so that one cannot determine $D_{\text{col}}$. In each figure, for fixed ${\rho }_q$, $D_{\text{col}}$ is a function of resonance mass only, with values shown along the upper horizontal axis. The contours marked 20% and 50% indicate the region above which the uncertainty in measuring $D_{\text{col}}$, as estimated in Sec. 4a, is lower than 20% and 50%, respectively.

Figure 3

Same as Fig. 2 but for a flavor-nonuniversal $Z^{\prime }$. Notice that while a leptophobic $Z^{\prime }$ having relatively large couplings to quarks in the third generation is still within the reach of the future LHC, its total width would typically be too large to be included in analyses for narrow resonances.

Figure 4

Illustration that the proposed measurements suffice to identify the color structure of a new dijet resonance. These plots show regions of the three-dimensional parameter space $\frac{g_u^2}{g_u^2+g_d^2}$ vs $\frac{{\sigma }_{t\overline{t}}}{{\sigma }_{jj}}$ vs $\frac{{\sigma }_{b\overline{b}}}{{\sigma }_{jj}}$, at fixed values of mass (3 TeV on the top panels and 4 TeV on the bottom panels) where dijet cross section and $D_{\text{col}}$ fall within a certain range. The cross section lies within about 35% of the value required for a $5\sigma$ discovery at the LHC with $\sqrt{s}=14\mathrm{TeV}$ at $\mathcal{L}=1000{\mathrm{fb}}^{-1}$. Similarly, $D_{\text{col}}$ is chosen to lie within $\pm 50\%$ of $3\times {10}^{-3}$ for illustration. Points in parameter space that are accessible to the LHC are circles highlighted in blue for $C$ and triangles highlighted in green for $Z^{\prime }$. Each plot on the left panel is shown again, as viewed from above, on the right. The two views make clear that colorons and Z’ bosons lie in distinguishably separate regions of parameter space; in particular, our inability to measure the ratio $\frac{g_u^2}{g_u^2+g_d^2}$ will not prevent us from determining the color structure of a new vector resonance at the 14 TeV LHC.

Figure 5

Further illustration that measuring ${\sigma }_{t\overline{t}}$ and ${\sigma }_{b\overline{b}}$ will show whether a resonance of a given mass, dijet cross section, and $D_{\text{col}}$ is a coloron or $Z^{\prime }$. We display regions of parameter space that correspond to a dijet cross section within $1\sigma$ uncertainty of the value required for a discovery at the LHC with $\sqrt{s}=14\mathrm{TeV}$ at $\mathcal{L}=1000{\mathrm{fb}}^{-1}$ (the same values used in Fig. 4), and that also have the illustrative color discriminant variable within a range of 50% around value of $D_{\text{col}}=3\times {10}^{-3}$, for resonances with masses 3 TeV (top panel) and 4 TeV (bottom panel). Coloron and $Z^{\prime }$ models that are within reach are displayed in a blue region and a diagonally hatched green region, respectively. Note that in nearly all of the displayed areas, the colorons and $Z^{\prime }$ bosons lie in different regions of parameter space. However, at the bottom left panel for a 4 TeV resonance, the bands for a $C$ coupling only to down-type light quarks and a $Z^{\prime }$ coupling only to up-type light quarks approach closely; see also Fig. 8.

Figure 6

(a) Left panel: central values for $W_u+W_c$ (the red band on top) and $W_d+W_s$ (the blue band at the bottom) with uncertainty bands evaluated using CT10NLO PDF set. (b) Right panel: fractional errors for $W_u+W_c$ (red line on top) and $W_d+W_s$ (blue line at the bottom) evaluated using CT10NLO PDF set.

Figure 7

The region of parameter space corresponding to viable models of colorons (in blue) and $Z^{\prime }$ bosons (in green, with diagonal hatches) that is consistent with measurements, at the LHC with $\sqrt{s}=14\mathrm{TeV}$, of the ratios ${\sigma }_{t\overline{t}}$ and ${\sigma }_{b\overline{b}}$ for values of $D_{\text{col}}$ within a 20% (region between dashed lines) and 50% (region between solid lines) range, for a fixed value of dijet cross section. The dijet cross section for each mass is the value allowing a $5\sigma$ discovery at the 14 TeV LHC. These plots illustrate the measurement precision in ${\sigma }_{t\overline{t}}$ and ${\sigma }_{b\overline{b}}$ that is required to distinguish between the coloron and the leptophobic $Z^{\prime }$. The set of plots for resonances with a mass of 3.0 TeV (3.5 TeV) is in the top (bottom) panel.

Figure 8

Same as Fig. 7, but for 4.0 (top panel) and 4.5 TeV (bottom panel) resonances.