# Charged Particle Pseudorapidity Distributions Measured with the STAR EPD

## Abstract

**:**

## 1. Introduction

#### 1.1. The EPD

## 2. Methodology

#### 2.1. Charged Particle Pseudorapidity Measurement with the EPD

**p**of the particle and the beam. Instead, a more convenient3 quantity, the pseudorapidity $\eta $ is used, which is defined as:

#### 2.2. From Raw EPD Data to Pseudorapidity Distribution [$\mathrm{d}N/\mathrm{d}\eta $]

`HIJING`Monte Carlo event generator combined with

`Geant4`to simulate the precise geometry of the EPD. In the following, the abbreviation MC will indicate data from these simulations. Such a response matrix can be seen in Figure 3.

`HIJING`, which are, in reality, inevitable with heavy-ion collisions. However, this shortfall should not change the results significantly, according to PHOBOS results [9]: the contribution from light ion fragments causes at least an order of magnitude smaller contribution to $\mathrm{d}N/\mathrm{d}\eta $ than the results in this analysis (see Section 4).

`RooUnfold`[10] framework, implemented in C++, running within the

`ROOT`environment [11]. The package itself defines classes for the different unfolding algorithms—among others, the Bayesian iterative unfolding.

`Number of hits from 1 primary`($\eta $) distribution), or by weighing the values filled in response matrix such that it could compensate for the multiple counts during the unfolding. In this analysis, the first method was used.

#### 2.3. Extracting Charged Particle Pseudorapidity Distribution

`Fake()`method. In this analysis, the following methods were used as the charged factor correction:

- Bin-by-bin correction of the already unfolded $\mathrm{d}N/\mathrm{d}\eta $ using the charged particle fraction ${N}_{charged}\left(\eta \right)/{N}_{all}\left(\eta \right)$ from MC data;
- Bin-by-bin correction of the raw EPD data via ${N}_{charged}\left({i}_{\mathrm{Ring}}\right)/{N}_{all}\left({i}_{\mathrm{Ring}}\right)$ from MC data; then unfolding of the EPD charged particle distribution.7
- Mark neutral particles as background and fill the response matrix as in the second method, except that the hits from neutral primaries are considered as “fake”.

#### 2.4. Consistency Check of the Unfolding Methods

## 3. Systematic Checks

#### 3.1. Dependence on Input MC Distribution

#### 3.1.1. Tightening and Shifting the Input MC $\mathrm{d}N/\mathrm{d}\eta $

#### 3.1.2. Broadening the Input MC $\mathrm{d}N/\mathrm{d}\eta $

#### 3.2. Changing the Charged Fraction in the MC Training Dataset

#### 3.3. Changing the ${p}_{T}$ Slope of the MC Training Dataset

#### 3.4. Centrality and z-Vertex Selection

#### 3.5. z-Vertex Choice

#### 3.6. Unfolding Method Choice

#### 3.7. EPD Related Uncertainties

## 4. Results

#### Comparison with the PHOBOS Results

## 5. Discussion

`Geant4`simulation, unfolding procedure from the STAR part, and the PHOBOS data itself.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

QGP | quark–gluon plasma |

RHIC | Relativistic Heavy-Ion Collider |

STAR | Solenoidal Tracker |

EPD | Event Plane Detector |

BES | Beam Energy Scan |

MIP | minimum ionizing particle |

ADC | analog-to-digital converter |

MC | Monte Carlo (simulation) |

QCD | quantum chromodynamics |

## Notes

1 | The EPD is more sensitive to charged particles, as detailed subsequently. |

2 | The rings are numbered from 1 to 32 in the following manner: the innermost East EPD ring is the #1 which follows outward until #16; then, the #17 continues on the West EPD side’s outermost ring until #32 being the innermost one. |

3 | In the ultrarelativistic limit, it approaches to rapidity (in $c=1$ unit system, c being the speed of light): $\eta \approx y\equiv \frac{1}{2}ln\left(\frac{E+{p}_{z}}{E-{p}_{z}}\right)$, with E being the energy of the particle. |

4 | Fill(${x}_{\mathrm{measured}}$, ${x}_{\mathrm{truth}}$); naturally, “measured” and “truth” here stand for the training datasets obtained from MC (simulation). |

5 | Miss(${x}_{\mathrm{truth}}$) and Fake(${x}_{\mathrm{measured}}$). |

6 | Caused by both primary and secondary particles. |

7 | In this case, another type of response matrix has to be used that was filled only with the charged particles’ data. |

8 | Note that the mentioned unfolding procedure was at this stage still done on the MC EPD ring distribution and thus on the training sample. |

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**Figure 1.**Example multi-MIP Landau fit of ADC count distribution in ring #16, with ADC counts in arbitrary units. Blue points with error bars represent the data, red continuous line shows the fitted function.

**Figure 2.**(

**a**) Vertices of particles registered by the EPD, based on a

`HIJING`[6] +

`Geant4`[7] MC detector simulation. The plots shows the vertex distribution in the x–y plane, integrated along the z axis, revealing the detector structure and surrounding materials. (

**b**) Distribution of various types of simulated primary particles hitting EPD, ring-by-ring, where rings in the backward direction are in the left hand part of this panel, while rings in the forward direction are in the right hand side—ordered by apparent spatial rapidity of the given ring.

**Figure 3.**Heatmap visualization of the R response matrix, connecting bins containing numbers of EPD ring hits (caused by either primary or secondary particles) with bins corresponding to primary particles at given $\eta $ pseudorapidity. The left side corresponds to East EPD wheel, the right side to West EPD wheel. It is worth noting that many primaries create hits even in the opposite side EPD via secondaries, as seen in upper left and bottom right quarters.

**Figure 4.**Consistency check of the three different methods to get $\mathrm{d}{N}_{ch}/\mathrm{d}\eta $ from MC EPD ring distribution. The difference is shown as unfolded $\mathrm{d}{N}_{ch}/\mathrm{d}\eta $ over MC “truth”, the distributions divided bin-by-bin. Blue marker represents the first method ($\eta $-dependent charged factor correction), black shows the second method (EPD ring number dependent charged factor correction), and red represents the third method (marking neutral particles), relative to MC truth’s $\mathrm{d}{N}_{ch}/\mathrm{d}\eta $. The errorbars are only plotted for informative purposes: they were calculated using the

`ROOT`’s

`TH1`class’ default square root of sum of squares of weights.

**Figure 5.**Tightening and shifting the MC input distribution using random selection based on Gaussian distribution of $\sigma $ width and ${\eta}_{0}$ curve peak position. (

**a**) Demonstration of the Gaussian suppression factors used. (

**b**) The $\mathrm{d}{N}_{ch}/\mathrm{d}\eta $ of the distorted MC input samples.

**Figure 6.**Broadening the MC input distribution using random selection based on Gaussian distribution of ${\sigma}_{\mathrm{broad}}$ width.

**Figure 7.**Charged particle pseudorapidity distributions measured with STAR EPD on RHIC energy $\sqrt{{s}_{NN}}=19.6$ GeV. The data was processed in eight centrality classes, presented with the different markers. The statistical uncertainties, marked by errorbars, are not visible on this plot, as the markers themselves are larger. The colored area indicates the systematic uncertainties of the measurement.

**Figure 8.**Charged particle pseudorapidity distributions measured with STAR EPD on RHIC energy $\sqrt{{s}_{NN}}=27.0$ GeV. The data were processed in eight centrality classes, presented with the different markers. The errorbars represent the statistical uncertainty, and the colored area indicates the systematic uncertainties of the measurement.

**Figure 9.**Charged particle pseudorapidity distributions measured in PHOBOS (hollow circles) and STAR (star markers). Note that on the upper left graph, the centrality class of the PHOBOS experiment’s result is actually 6–10%.

Source | Systematic Uncertainty |
---|---|

MC input $\mathrm{d}{N}_{\mathrm{ch}}/\mathrm{d}\eta $ tightening, shifting | 6% |

MC input $\mathrm{d}{N}_{\mathrm{ch}}/\mathrm{d}\eta $ broadening | 4% |

Charged fraction in MC | 6% |

${p}_{T}$ slope change in MC | 1% |

Centrality selection | 2% |

z-vertex selection | negligible |

z-vertex choice | 1% |

Unfolding method choice | 8% |

EPD related uncertainties, electronics, efficiency | negligible |

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**MDPI and ACS Style**

Molnár, M., for the STAR Collaboration.
Charged Particle Pseudorapidity Distributions Measured with the STAR EPD. *Universe* **2023**, *9*, 335.
https://doi.org/10.3390/universe9070335

**AMA Style**

Molnár M for the STAR Collaboration.
Charged Particle Pseudorapidity Distributions Measured with the STAR EPD. *Universe*. 2023; 9(7):335.
https://doi.org/10.3390/universe9070335

**Chicago/Turabian Style**

Molnár, Mátyás for the STAR Collaboration.
2023. "Charged Particle Pseudorapidity Distributions Measured with the STAR EPD" *Universe* 9, no. 7: 335.
https://doi.org/10.3390/universe9070335