Direct verification of warped hierarchy-and-flavor models

We consider direct experimental verification of warped models, based on the Randall-Sundrum (RS) scenario, that explain gauge and flavor hierarchies, assuming that the gauge fields and fermions of the standard model (SM) propagate in the 5D bulk. Most studies have focused on the bosonic Kaluza-Klein (KK) signatures and indicate that discovering gauge KK modes is likely possible, yet challenging, while graviton KK modes are unlikely to be accessible at the CERN LHC, even with a luminosity upgrade. We show that direct evidence for bulk SM fermions, i.e. their KK modes, is likely also beyond the reach of a luminosity-upgraded LHC. Thus, neither the spin-2 KK graviton, the most distinct RS signal, nor the KK SM fermions, direct evidence for bulk flavor, seem to be within the reach of the LHC. We then consider hadron colliders with $\sqrt{s}=21$, 28, and 60 TeV. We find that discovering the first KK modes of SM fermions and the graviton typically requires the Next Hadron Collider (NHC) with $\sqrt{s}\approx 60\mathrm{TeV}$ and $\mathcal{O}(1){\mathrm{ab}}^{-1}$ of integrated luminosity. If the LHC yields hints of these warped models, establishing that nature is described by them, or their 4D conformal field theory duals, requires an NHC-class machine in the post-LHC experimental program.

Figure 1

Rates for the associated production of first $t_L$ and $b_L$ KK excitations together with their corresponding zero modes at the LHC; the results for $t(b{)}_L$ correspond to the higher (lower) member of each histogram pair, respectively. Here the first gluon KK mass is fixed at 3 TeV, and we show the results as a function of the fermion pair mass. The three sets of histograms assume that the $b_L$ KK mass is 100 (200, 300) GeV heavier than the gauge KK, whereas the threshold for $t_L$ is somewhat higher due to the larger zero-mode top mass.

Figure 2

Same as the last figure but now for different values of $\sqrt{s}$ and taking the first gluon KK and fermion KK masses to be degenerate at 3 TeV. From bottom to top the histograms correspond to $\sqrt{s}=14$, 21, 28, and 60 TeV, respectively.

Figure 3

Fermion KK pair-production rate at various collider energies as a function of the fermion pair invariant mass, assuming that the first gluon and fermion KK states are degenerate with a mass of 3 TeV. From bottom to top the histograms correspond to $\sqrt{s}=14$, 21, 28, and 60 TeV, respectively. No cuts have been applied. The dotted histogram shows the result of only including zero-mode gluon exchange.

Figure 4

Same as the previous figure but now assuming that the KK fermion is 10% more massive than the first gauge KK state.

Figure 5

Production rate for the first graviton KK excitation decaying into two $Z$ bosons, assuming a rapidity cut $|y|<2(1)$ on the $Z$’s corresponding to the dotted (solid) histograms. The histograms correspond, from bottom to top, to collider energies of $\sqrt{s}=14$, 21, 28, and 60 TeV, respectively; $Z$ branching fractions are not included, and $k/{\overline{M}}_P=0.5$ has been assumed.

Figure 6

Same as the previous figure but now with $k/{\overline{M}}_P=1.0$.

Figure 7

Same as the previous figure but now with $k/{\overline{M}}_P=0.1$.

Figure 8

Same as Fig. 3 except now for the pair production of the lightest gluon KK state.

Figure 9

The resonant production rate for the first gluon KK state in the $t\overline{t}$ channel assuming $|y|<2.5$ for the dotted case and $|y|<1$ for the solid one. From bottom to top, the histograms correspond to $\sqrt{s}=14$, 21, 28, and 60 TeV, respectively. No efficiencies or branching fractions are included.

Figure 10

Signal rate for a possible gluon KK resonance as a function of the collider energy employing the cuts described in the text. Branching fractions and efficiencies have been neglected. From top to bottom, the results are shown for gluon KK masses in the range from 3 to 12 TeV in steps of 1 TeV.

Figure 11

Same as the previous figure but now showing the signal significance. Again, branching fractions and efficiencies have been neglected.