Counting dark matter particles in LHC events

We suggest trying to count the number of invisible particles produced in missing energy events at the LHC, arguing that multiple production of such particles provides evidence that they constitute stable dark matter and that counting them could yield further insights into the nature of dark matter. We propose a method to count invisible particles, based on fitting the shapes of certain transverse- or invariant-mass distributions, discuss various effects that may affect the measurement, and simulate the use of the method to count neutrinos in standard model processes and dark matter candidates in new physics processes.

Figure 1

Normalized, phase-space distribution of $m_T^2$ for $n\in \{1,\dots ,4\}$ for the process $M\to P+nX$, i.e. the decay of a parent particle of mass $M$ into a visible particle $P$ and $n$ invisible particles $X$.

Figure 2

Normalized, phase-space distribution of $m_T^2$ for $n\in \{1,\dots ,4\}$ for the process $M\to 2P+nX$, i.e. the decay of a parent particle of mass $M$ into two visible particles $P$ and $n$ invisible particles $X$.

Figure 3

Normalized, phase-space distribution of $m_T^2$ for the cascade decay process $M\to P+Y\to 2P+X$ for various values of the intermediate mass ratio $z=m_Y^2/M^2$.

Figure 4

Normalized, phase-space distribution of $m_V^2$ for $n\in \{1,\dots ,4\}$ for the process $M\to 2P+nX$.

Figure 5

Normalized, phase-space distribution of $m_{T2}^2$ for $(k,l)\in \{(1,1),(1,2),(2,2),(1,3)\}$ for the process $2M\to 2P+(k+l)X$.

Figure 6

Phase-space distribution of $m_T$ for the process $2M\to 2P+1X$, for a massive invisible particle of mass $m_X$ for various values of the mass ratio $x=m_X^2/M^2$.

Figure 7

Phase-space distribution of $m_T$ for the process $M\to P+nX$, with fractional width $y=\Gamma /M$, for $n=1$, 2.

Figure 8

Standard model examples with final state neutrinos, along with the best and next-best fits for distribution of transverse mass variables near endpoint. The fits are to the relevant endpoint power law (see Table ) convolved with a Breit-Wigner, with fractional width set to the true value. Details of Monte Carlo event generation are given in the text.

Figure 9

Best and next-best fits for the SUSY cascade process in 28 with 6 visible particles and a pair of 115 GeV neutralinos in the final state. The fits are to the endpoint behavior of generated $(3+k)+(3+l)$-body phase space, where $k+l=n$, with varying invisible mass and convolved with a Breit-Wigner of fixed fractional width. Details of the Monte Carlo event generation are given in the text.