Unparticle self-interactions at the Large Hadron Collider

We investigate the effect of unparticle self-interactions at the Large Hadron Collider (LHC). Especially, we discuss the three-point correlation function, which is determined by conformal symmetry up to a constant, and study its relation to processes with four-particle final states. These processes could be used as a favorable way to look for unparticle physics, and for weak enough couplings to the standard model, even the only way. We find updated upper bounds on the cross sections for unparticle-mediated $4\gamma$ final states at the LHC and novel upper bounds for the corresponding $2\gamma 2\ell$ and $4\ell$ final states. The size of the allowed cross sections obtained are comparably large for large values of the scaling dimension of the unparticle sector, but they decrease with decreasing values of this parameter. In addition, we present relevant distributions for the different final states, enabling the possible identification of the unparticle scaling dimension if there was to be a large number of events of such final states at the LHC.

Figure 1

The function $T_I(p_1^2/s,p_2^2/s)$ for $d=1.1$ (top panel), $d=1.5$ (middle panel), and $d=1.9$ (bottom panel). The graphs are shown as a function of $p_1^2/s$ for the following six discrete values: $p_2^2/s={10}^{-5}$ (thick, dash-dotted), ${10}^{-4}$ (thick, dashed), ${10}^{-3}$ (thick, solid), ${10}^{-2}$ (thin, dash-dotted), ${10}^{-1}$ (thin, dashed), and 1 (thin, solid).

Figure 2

The Feynman diagram for the subprocesses $gg/q\overline{q}\to \mathcal{U}\to \mathcal{U}\mathcal{U}\to f_1{\overline{f}}_1{f}_2{\overline{f}}_2$.

Figure 3

The distributions of photon two-body invariant masses in unparticle-mediated $4\gamma$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV. Note that each event contributes six counts.

Figure 4

The distributions of photon four-body invariant masses in unparticle-mediated $4\gamma$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 75 GeV.

Figure 5

The $p_T$-distributions of the highest-$p_T$ photon in unparticle-mediated $2\gamma 2\ell$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV.

Figure 6

The distributions of the charged lepton invariant masses in unparticle-mediated $2\gamma 2\ell$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV.

Figure 7

The $p_T$ distributions of the highest-$p_T$ lepton in unparticle-mediated $4\ell$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV.

Figure 8

The distributions of the three-body invariant lepton masses in unparticle-mediated $4\ell$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV. Note that each event contributes two counts.

Figure 9

The missing transverse momentum in unparticle-mediated $2\gamma \nu \overline{\nu }$ events at the LHC for three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV.

Figure 10

The missing transverse momentum in unparticle-mediated $2\ell \nu \overline{\nu }$ events at the LHC or three different values of the scaling dimension $d=1.9$ (red solid curve), $d=1.5$ (black dashed curve), and $d=1.1$ (blue dashed-dotted curve). The bin width used is 25 GeV. Note the different scale on the ${\mathrm{p̸}}_T$ axis as compared to Fig. 9.