# Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events

## Abstract

We critically examine the classic endpoint method for particle mass determination, focusing on difficult corners of parameter space, where some of the measurements are not independent, while others are adversely affected by the experimental resolution. In such scenarios, mass differences can be measured relatively well, but the overall mass scale remains poorly constrained. Using the example of the standard SUSY decay chain q ^{~}→χ ^{~} ^{0} _{2}→ℓ ^{~}→χ ^{~} ^{0} _{1} , we demonstrate that sensitivity to the remaining mass scale parameter can be recovered by measuring the two-dimensional kinematical boundary in the relevant three-dimensional phase space of invariant masses squared. We develop an algorithm for detecting this boundary, which uses the geometric properties of the Voronoi tessellation of the data, and in particular, the relative standard deviation (RSD) of the volumes of the neighbors for each Voronoi cell in the tessellation. We propose a new observable, Σ¯ , which is the average RSD per unit area, calculated over the hypothesized boundary. We show that the location of the Σ¯ maximum correlates very well with the true values of the new particle masses. Our approach represents the natural extension of the one-dimensional kinematic endpoint method to the relevant three dimensionsmore »

- Authors:

- Univ. of Florida, Gainesville, FL (United States). Physics Dept.
- Univ. of Hawaii, Honolulu, HI (United States). Dept. of Physics and Astronomy
- Univ. of Texas, Austin, TX (United States). Theory Group. Dept. of Physics. Texas Cosmology Center
- Univ. of Florida, Gainesville, FL (United States). Physics Dept.; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division

- Publication Date:

- Research Org.:
- Univ. of Florida, Gainesville, FL (United States); Univ. of Hawaii, Honolulu, HI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Korean Research Foundation (KRF)

- OSTI Identifier:
- 1424610

- Grant/Contract Number:
- SC0010296; SC0010504; PHY-1620610; PHY-0969510

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetry; phenomenology

### Citation Formats

```
Debnath, Dipsikha, Gainer, James S., Kilic, Can, Kim, Doojin, Matchev, Konstantin T., and Yang, Yuan-Pao.
```*Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events*. United States: N. p., 2017.
Web. doi:10.1007/JHEP06(2017)092.

```
Debnath, Dipsikha, Gainer, James S., Kilic, Can, Kim, Doojin, Matchev, Konstantin T., & Yang, Yuan-Pao.
```*Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events*. United States. doi:10.1007/JHEP06(2017)092.

```
Debnath, Dipsikha, Gainer, James S., Kilic, Can, Kim, Doojin, Matchev, Konstantin T., and Yang, Yuan-Pao. Mon .
"Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events". United States.
doi:10.1007/JHEP06(2017)092. https://www.osti.gov/servlets/purl/1424610.
```

```
@article{osti_1424610,
```

title = {Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events},

author = {Debnath, Dipsikha and Gainer, James S. and Kilic, Can and Kim, Doojin and Matchev, Konstantin T. and Yang, Yuan-Pao},

abstractNote = {We critically examine the classic endpoint method for particle mass determination, focusing on difficult corners of parameter space, where some of the measurements are not independent, while others are adversely affected by the experimental resolution. In such scenarios, mass differences can be measured relatively well, but the overall mass scale remains poorly constrained. Using the example of the standard SUSY decay chain q~→χ~02→ℓ~→χ~01 , we demonstrate that sensitivity to the remaining mass scale parameter can be recovered by measuring the two-dimensional kinematical boundary in the relevant three-dimensional phase space of invariant masses squared. We develop an algorithm for detecting this boundary, which uses the geometric properties of the Voronoi tessellation of the data, and in particular, the relative standard deviation (RSD) of the volumes of the neighbors for each Voronoi cell in the tessellation. We propose a new observable, Σ¯ , which is the average RSD per unit area, calculated over the hypothesized boundary. We show that the location of the Σ¯ maximum correlates very well with the true values of the new particle masses. Our approach represents the natural extension of the one-dimensional kinematic endpoint method to the relevant three dimensions of invariant mass phase space.},

doi = {10.1007/JHEP06(2017)092},

journal = {Journal of High Energy Physics (Online)},

number = 6,

volume = 2017,

place = {United States},

year = {Mon Jun 19 00:00:00 EDT 2017},

month = {Mon Jun 19 00:00:00 EDT 2017}

}

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