Shifted peak: Resolving nearly degenerate particles at the LHC

We propose a method for determining the mass difference between two particles, ${\tilde{l}}_1$ and ${\tilde{l}}_2$, that are nearly degenerate, with $\Delta m\equiv m_2-m_1\ll m_1$. This method applies when (a) the ${\tilde{l}}_1$ momentum can be measured, (b) ${\tilde{l}}_2$ can only decay to ${\tilde{l}}_1$, and (c) ${\tilde{l}}_1$ and ${\tilde{l}}_2$ can be produced in the decays of a common mother particle. For small $\Delta m$, ${\tilde{l}}_2$ cannot be reconstructed directly, because its decay products are too soft to be detected. Despite this, we show that the existence of ${\tilde{l}}_2$ can be established by observing the shift in the mother particle invariant-mass peak, when reconstructed from decays to ${\tilde{l}}_2$. We show that measuring this shift would allow us to extract $\Delta m$. As an example, we study supersymmetric gauge-gravity hybrid models in which ${\tilde{l}}_1$ is a metastable charged slepton next-to-lightest supersymmetric particle and ${\tilde{l}}_2$ is the next-to-lightest slepton with $\Delta m\sim 5\mathrm{GeV}$.

Figure 1

Reconstructed ${\tilde{l}}_1$ with $0.6<\beta <0.8$ after smearing ${\tilde{l}}_1$ momenta with a Gaussian with $\sigma =0.05|{\overrightarrow{p}}_{{\tilde{l}}_1}|$ centered on the true momentum and after smearing $\beta$ with a Gaussian with $\sigma =0.02$.

Figure 2

The $p_T$ distribution of leptons produced by the three-body decays of ${\tilde{l}}_2$.

Figure 3

The ${\tilde{l}}_1^{\pm }{e}^{\mp }$ invariant-mass distribution. The fit parameters $\sigma$, $a$, $f_{\mathrm{sig}}$, and mean are defined in Eq. (28).

Figure 4

The ${\tilde{l}}_1^{\pm }{\mu }^{\mp }$ invariant-mass distribution. The fit parameters $\sigma$, $a$, $f_{\mathrm{sig}}$, and mean are defined in Eq. (28).

Figure 5

The ${\tilde{l}}_1^{\pm }{e}^{\pm }$ invariant-mass distribution. The fit parameters $\sigma$, $a$, $f_{\mathrm{sig}}$, and mean are defined in Eq. (28).

Figure 6

The ${\tilde{l}}_1^{\pm }{\mu }^{\pm }$ invariant-mass distribution. The fit parameters $\sigma$, $a$, $f_{\mathrm{sig}}$, and mean are defined in Eq. (28).