# Presentation: 120680

##   Neutral Kaon Interferometry at RHIC

**  ****Neutral Kaon Interferometry at RHIC**
**Selemon Bekele**
**The Ohio State University**
* *

## Introduction
Heavy Ion Collisions
Phase Transitions
Neutral Kaon Correlations
Summary

- Introduction
- Heavy Ion Collisions
- Phase Transitions
- Neutral Kaon Correlations
- Summary

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## Introduction

**The Phase diagram of Matter**

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**Introduction**

## How to create quark matter

-   **The Relativistic Heavy Ion Collider**   (**RHIC) will create extremely high **
**temperatures and pressures by colliding atomic nuclei together **
**at high speeds. **
**  ****When they hit, the nuclei may create just the right conditions for quark-gluon plasma to form. **

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**Evolution of a heavy ion collision**

## Phase Transitions

**A thermalised bulk system **
**is characterized by the equations**

- Schematic diagram showing a phase
- transition using bag model calculation
- B~200 MeV is the bag constant

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## Phase transition from Lattice QCD

-   **T****c**** depends on treatment of quark flavors**
** ****The pressure divided by T****4**** changes fast around     the critical temperature Tc~170 ± 20 MeV**
** ****The energy density divided by T****4** **also** **changes**
** ****very rapidly over a small interval around the **
**critical temperature**

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- Deviation from Stefan-Boltzmann (SB) limit
- indicates substantial interactions among
- quarks and gluons

- (F. Karsch, hep-lat/0106019)

- (F. Karsch, hep-lat/0106019)

## of a particle with momentum k at  x. The two particle 

**Where  ***A(x**,**,k)*** is the production amplitude for the production **
**of a particle with momentum ***k*** at  ***x. ***The two particle **
**momentum distribution is given by**

**For identical bosons one has to symmetrize the two**
**Particle wave function**

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**HBT (Hanbury-Brown and Twiss) interferometry**

**A method developed in the early 1950s**
**to determine the size of distant stars using**
**photon intensity correlations**

## Measurable!

- with the effective source distribution is given by

- For a Gaussian source, the correlation function is usually parametrized as

- Fourier transform of
- particle source

- the correlation function becomes

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## RHIC HBT Puzzle

**Models predict  ****R****out****/R****side**** > 1**
**Experiments   ****R****out****/R****side**** ~ 1**

- Radius parameters from
- pion correlation functions

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## Neutral Kaon Correlations

- Motivations
- Pion correlations are affected by Coulomb interactions, Resonance contributions
- Resonance effects are small
- No coulomb effects
- Less multi-particle effects  due to small kaon density
- Particle identification possible to higher transverse momentum using decay topology methods
- No significant measurements in heavy ion experiments

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## Neutral Kaon (         ) correlations

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- A general neutral kaon wave function may be written as

- The

- are  produced by the strong interaction

- The

- are what are measured in experiments

- Neglecting CP violation, one may write

- The

- is then a linear combination of

- One can form a symmetric combination from

## The correlation function is given by

- where

- are production amplitudes

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## For a Gaussian distribution

- One can see that the correlation function mixes space and time. In the case of insufficient statistics experimental correlation functions are fit to the form

- If the source function

- and the production amplitudes

- are identical  for both particles, one gets the simple expression

- , one gets

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## Neutral particle Identification

**Neutral particle Identification**

- A schematic diagram of a neutral particle decaying inside the TPC

**The important geometrical cuts**
**to identify a neutral particle coming**
**from the primary interaction vertex**

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## K0s K0s Correlation Function

**K****0****s**** K****0****s**** Correlation Function**

**Gives the values **
**λ****= 0.99******** 0.27**
**R****inv**** = 5.62 ******** 0.69**

**Fitting the fully corrected correlation function to a gaussian**

- K0s invariant mass

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- STAR Preliminary

**The strong interaction makes**
**the source bigger than the quantum**
**statistics case**

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## MT Systematics

**The measured HBT radii correspond to the size of the region from which particles with similar momenta are emitted. This means the HBT radii will**
**Exhibit a dependence on the pair momentum. The plot  below shows the invariant radius parameter as a function of **

**M****T**** Systematics**

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## 1D K0sK0s  correlations
Absence of Coulomb final state effects makes it a powerful tool in HBT studies
The λ parameter is consistent with unity as one expects for a system with small resonance contribution
Our analysis shows that radius  is bigger than what one would expect at Mt~1 GeV if the effect of the strong interaction is neglected
With more statistics 3D K0sK0s correlations will be an important next step

- 1D K0sK0s  correlations
- Absence of Coulomb final state effects makes it a powerful tool in HBT studies
- The λ parameter is consistent with unity as one expects for a system with small resonance contribution
- Our analysis shows that radius  is bigger than what one would expect at Mt~1 GeV if the effect of the strong interaction is neglected
- With more statistics 3D K0sK0s correlations will be an important next step

- Summary

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