Signatures of Gravitational Fixed Points at the Large Hadron Collider

We study quantum-gravitational signatures at the CERN Large Hadron Collider (LHC) in the context of theories with extra spatial dimensions and a low fundamental Planck scale in the TeV range. Implications of a gravitational fixed point at high energies are worked out using Wilson’s renormalization group. We find that relevant cross sections involving virtual gravitons become finite. Based on gravitational lepton pair production we conclude that the LHC is sensitive to a fundamental Planck scale of up to 6 TeV.

Figure 1

Running anomalous dimensions (upper panel) and gravitational couplings (lower panel) from (5, 6) for $D=4+n$ dimensions with $n=1,\dots ,7$ (from right to left). The crossover takes place at the respective Planck scale.

Figure 2

The $5\sigma$ discovery contours in $M_D$ at the LHC, shown as a function of a cutoff $\Lambda$ on $E_{\mathrm{parton}}$ for an assumed integrated luminosity of $10{\mathrm{fb}}^{-1}$. Thin lines show a $\pm 10\%$ variation of $k_{\mathrm{tr}}$ about $M_D$, the straight line is $M_D^{\max }=\Lambda$. The leveling off at $M_D^{\max }\approx \Lambda$ reflects the gravitational UV fixed point. To enhance the reach we require $m_{\ell \ell }^{\min }=\min (M_D/3,2\mathrm{TeV})$.

Figure 3

Comparison of normalized distributions of the partonic energy $E_{\mathrm{parton}}$ for the dimension-8 operator correction to Drell-Yan production at the LHC ($n=3$). Full line: present work, dashed line: approximation (9) with $\Lambda =M_D$.