Catching a New Force by the Tail

The Large Hadron Collider (LHC) is sensitive to new heavy gauge bosons that produce narrow peaks in the dilepton invariant mass spectrum up to about $m_{Z^{\prime }}\sim 5\mathrm{TeV}$ $Z^{\prime }\mathrm{s}$ that are too heavy to produce directly can reveal their presence through interference with standard model dilepton production. We show that the LHC can significantly extend the mass reach for such $Z^{\prime }\mathrm{s}$ by performing precision measurements of the shape of the dilepton invariant mass spectrum. The high-luminosity LHC can exclude, with 95% confidence, new gauge bosons as heavy as $m_{Z^{\prime }}\sim 10–20\mathrm{TeV}$ that couple with gauge coupling strength of $g_{Z^{\prime }}\sim 1–2$.

Figure 1

At energies $E$ much smaller than the mass $M$ of the heavy gauge boson $Z^{\prime }$, the effect of the new physics on the Drell-Yan process, $pp\to {\ell }^{+}{\ell }^{-}$, is encoded by a finite set of four-fermion contact operators.

Figure 2

Left panel: Ratio of the dilepton invariant mass distribution in the $Z^{\prime }$ model to the SM. The solid lines are calculated using the full model of Eq. (1), while the dashed lines are calculated using the effective field theory (EFT) of Eq. (5). In the gray region, there are three expected SM events with a luminosity of $3{\mathrm{ab}}^{-1}$. Right panel: Systematic theoretical uncertainties used in our analysis. We also show the size of the statistical uncertainty associated with the SM prediction.

Figure 3

95% C.L. lower bound on $M/R$ as a function of $\theta$. The constraint coming from low-energy experiments is shown in gray, while the reach of the LHC is shown in orange. Specific models are identified: pure $B-L$ ($\tan \theta =0$), hypercharge ($\tan \theta =+\infty$), $T_{3R}$ ($\tan \theta =-2$), and $U(1{)}_{\chi }$ ($\tan \theta =-4/5$) [23, 24]. Notice that these relations are defined at tree level.

Figure 4

Left panel: 95% C.L. lower bound on $M/R$ as a function of $m_{\ell \ell \mathrm{cut}}$, for three example models, defined by specific choices of $\theta$ (see Fig. 3). Right panel: 95% C.L. lower bound on $M/R$ for the hypercharge model ($\theta =\pi /2$) as a function of $m_{\ell \ell \mathrm{cut}}$. We show how the bound differs using two different choices for the total integrated luminosity ($300{\mathrm{fb}}^{-1}$ and $3{\mathrm{ab}}^{-1}$) and switching off the theoretical uncertainty on higher-order EW corrections.

Figure 5

Comparison between the 95% C.L. upper bound on $g_Y$ extracted using the EFT of Eq. (5) (orange lines), with $m_{\ell \ell \mathrm{cut}}=M-2.5\times {\mathrm{\Gamma }}_{Z^{\prime }}$ (orange shaded), and the full model of Eq. (5) (blue lines). The two bounds agree for masses $5.5\mathrm{TeV}\lesssim M\lesssim 25\mathrm{TeV}$. For smaller $M$, the EFT does not capture on-shell $Z^{\prime }$ production, and the bound extracted from the full model is much stronger. At larger masses and couplings, finite $Z^{\prime }$ width effects, which are not included in the EFT calculation, become important and lead to a weakening of the bound in the full model. The gray region shows the region which is excluded by low energy measurements.