Possible small-$x$ effects in the Kaluza-Klein graviton and radion production at high energies

We study the single graviton production at the CERN LHC using the $k_T$-factorization approach of QCD. We consider the Arkani-Hamed-Dimopoulos-Dvali scenario and Randall-Sundrum model with one warped extra dimension and derive the production amplitudes for spin-2 (Kaluza-Klein excitation of the graviton) and spin-0 (radion) states, including subsequent graviton decay into the dilepton or diphoton pairs. We use the transverse momentum dependent (unintegrated) parton densities in a proton obtained from the Ciafaloni-Catani-Fiorani-Marchesini evolution equation, which resums the leading logarithmic small-$x$ corrections to the production cross sections, and estimate the uncertainties of our predictions. We demonstrate that the small-$x$ effects can manifest themselves in the different angular distributions of graviton decay products and give some examples of what these distributions can look like at the LHC energies.

Figure 1

The cross sections of KK graviton production with its subsequent dilepton decay calculated as a function of the total center-of-mass energy in the RS model with $c_0=0.01$ (left panel) and the ADD model with $n=3$ (right panel). The solid and dashed curves correspond to the $k_T$-factorization and LO pQCD predictions, respectively. The ratios of these predictions at $m_1=500$, 700, and 900 GeV for the RS model and $M_s=500$, 750, and 1000 GeV for the ADD model are shown below by the solid, dashed, and dash-dotted curves.

Figure 2

The cross sections of KK graviton production with its subsequent diphoton decay calculated as a function of the total center-of-mass energy in the RS model with $c_0=0.01$ (left panel) and the ADD model with $n=3$ (right panel). Notation of all curves is the same as in Fig. 1.

Figure 3

The cross sections of KK graviton production with its subsequent dilepton (left panel) and diphoton (right panel) decays calculated as a function of the total center-of-mass energy in the RS model with $c_0=0.01$ and $m_1=500\mathrm{GeV}$. The solid curves represent the predictions obtained with the A0 TMD parton densities at the default scale, whereas the shaded band represents the scale uncertainties of these calculations, as is described in the text. The dashed lines correspond to the predictions obtained with the B0 TMD parton distributions.

Figure 4

The distributions on the KK decay dilepton transverse momentum $p_T^{ll}$ (left panel) and azimuthal angle difference $\mathrm{\Delta }{\varphi }^{ll}$ (right panel) between the 4-momenta of these leptons calculated at $\sqrt{s}=14\mathrm{TeV}$ in the RS model with $c_0=0.01$. The solid, dashed, and dash-dotted curves correspond to $m_1=500$, 700, and 900 GeV, respectively.

Figure 5

The angular distributions $d\sigma /d\cos {\theta }^{*}$ of the KK graviton decay lepton pair calculated in the RS model with $c_0=0.01$ (left panel) and the ADD model with $n=3$ (right panel) at $\sqrt{s}=14\mathrm{TeV}$. Notation of all curves is the same as in Fig. 1.

Figure 6

The angular distributions $d\sigma /d\cos {\theta }^{*}$ of the KK graviton decay photon pair calculated in the RS model with $c_0=0.01$ (left panel) and the ADD model with $n=3$ (right panel) at $\sqrt{s}=14\mathrm{TeV}$. Notation of all curves is the same as in Fig. 1.

Figure 7

The contributions from transversal and longitudinal off-shell gluon polarizations to the $d\sigma /d\cos {\theta }^{*}$ distributions for dilepton (left panel) and diphoton (right panel) KK graviton decay modes calculated in the ADD model with $n=3$, $M_s=500\mathrm{GeV}$ and $\sqrt{s}=14\mathrm{TeV}$. The dashed and dash-dotted curves correspond to the transversal and longitudinal components, respectively. The solid curves represent their sum.

Figure 8

The total cross sections (left panel) and transverse momentum distributions (right panel) of radion production calculated for several values of radion mass $m_r$ at ${\mathrm{\Lambda }}_r=3\mathrm{TeV}$. Notation of all curves in the left panel is the same as in Fig. 1. The transverse momentum distributions are calculated at $\sqrt{s}=14\mathrm{TeV}$.