New measurements with stopped particles at the LHC

Metastable particles are common in many models of new physics at the TeV scale. If charged or colored, a reasonable fraction of all such particles produced at the LHC will stop in the detectors and give observable out-of-time decays. We discuss strategies for measuring the type of decay (two- vs three-body), the types of particles produced, and the angular distribution of the produced particles using the LHC detectors. We demonstrate that with a plausible level of control over experimental uncertainties and $\mathcal{O}(10–100)$ observed decay events, the gauge properties and some couplings of the new particles can be measured. If the new particle has a dominant three-body decay, then the spin properties of the particles and Lorentz structure of the decay operator can also be distinguished or constrained. These measurements can not only reveal the correct model of new physics at the TeV scale, but also give information on physics giving rise to the decay at energy scales far above those the LHC can probe directly.

Figure 1

A schematic view of the event geometry we are considering. This is a cross-sectional $x\mathrm{\text{−}}y$ view of a detector taken from Ref. 72. The inner shaded circles comprise the tracking chamber. Moving outwards, the segmented shaded annuli are first the electromagnetic calorimeter followed by the hadronic calorimeter. The outermost layers are the muon chambers. An MMCP $X$ that had stopped in the ECAL decays into two jets and an invisible $Y$ which escapes the detector without interacting. The ECAL cell where the decay took place shows energy deposition. One of the jets exits the ECAL and deposits its energy into the HCAL. The second jet exits the ECAL in another direction, leaving tracks which do not point back to the interaction region, and then depositing energy in a different region of both the ECAL and HCAL. This is a schematic representation; the $\varphi$ resolution of the actual detector is much finer in both the ECAL and HCAL, so that the cells that lit up in the calorimeter should give enough information to approximately determine ${\theta }_{12}$, the angle between the jets.

Figure 2

Feynman diagrams for the decays of a long-lived gluino in split SUSY. The blob represents the four-point vertex generated after integrating out the heavy squark. The diagram on the left is a tree-level three-body decay to two quarks and a neutralino, while the diagram on the right is the loop-level two-body decay to a neutralino and a gluon. In certain regions of parameter space, the loop-induced decay can become dominant over the three-body decay [82].

Figure 3

Feynman diagrams for decays of a chargino LSP in the RPV scenario. The blob represents a tiny RPV coupling $\lambda$, which mediates the decay of the chargino to three charged leptons, or to one charged lepton and two neutrinos. We have suppressed lepton flavor indices, but in the text we only consider ${\lambda }_{323}$ to be non-zero.

Figure 4

Selected angular distributions $dN/d\theta$ for angular resolutions of $\Delta \theta =10°$, 30°, and 60° from left to right for highly relativistic WIMP ($m_X/m_Y=10$). Solid (green): Reference split SUSY three-body distribution $O_{S2}^{ff}$. Dashed (red): other representative allowed operators with same MMCP and WIMP spin and gauge representation ($O_{T1}^{ff}$, $O_{T2}^{ff}$, $O_{S1}^{ff}$ from top to bottom on LHS). Dot-dashed (blue): operators allowed for same gauge representation but different spins ($O_T^{vv}$, $O_S^{vv}$, $O_S^{ss}$ from top to bottom on LHS). All angular distributions shown were generated using the CompHEP and LanHEP software packages [86, 87].

Figure 5

Angular distribution for the two leading energy jets produced in gluino decay of model A from Table  including all decay modes and secondary decays (solid) compared to the angular distribution of primary quarks in the channel where only two light quarks and the WIMP are produced (dashed). The secondary decays of top quarks and chargino/neutralinos are primarily responsible for the differences in the two distributions.

Figure 6

Average number of observed decays necessary to distinguish decay operators at 95% confidence level from the reference operator $O_{S2}^{ff}$, from Eq. (2) using the distributions for $m_{X0}/m_{X8}=10$. For each operator, from left to right the angular resolution is $\Delta \theta =10°$, 30°, 60°.