# Presentation: 626407

## K/π Fluctuations and the Balance Function

*K*/*π* Fluctuations and the Balance Function

- Gary Westfall
*Michigan State University*
*For the STAR Collaboration*
*INT Workshop on the QCD Critical Point*
*August 12, 2008*

## Fluctuations in the K/π Ratio

- Event-by-event fluctuations in *K*/*π* may give insight into the QCD critical point
- NA49 measured the fluctuations of *K*/*π* as a function of incident energy for central Pb+Pb collisions from*s**NN*1/2 = 6 to 17 GeV using the observable *σ*dyn
- measure the *K*/*π* ratio event-by-event
*K* = *K*+ + *K*-
*π* = *π*+ + *π*-
- produce histogram of the *K*/*π* ratio
- extract the width of *K*/*π* histogram to get *σ*data
- do the same for mixed event to get *σ*mixed

## K/π Fluctuations at the SPS

*K*/*π* Fluctuations at the SPS

- Define the dynamical fluctuations in terms of *σ*dyn

- C. Blume (NA49), hep-ph/0505137

- Divide by the mean and multiplity by 100 to get %

## K/π Fluctuations in STAR

- Study Au+Au collisions at *s**NN*1/2 = 20, 62, 130 and 200 GeV
- Extract the number of *K*+ + *K*- and *π*+ + *π*- event-by-event using energy loss and curvature in the STAR TPC
- Take kaons and pions with 0.2 < *p**t* < 0.6 GeV/c and |*η*| < 1.0
- kaons: *N**σ**,K* < 2, *N**σ**,**π* > 2
- pions: *N**σ**,**π* < 2, *N**σ**,K* > 2
- electrons are suppressed with *N**σ**,e* > 1

## K and π Identification in STAR

## K/π Histograms for Au+Au Collisions

*K*/*π* Histograms for Au+Au Collisions

- Mixed events are created by taking one track from different events to produce new events that have no correlations
- Mixed events are produced using 10 bins in centrality and 5 bins in vertex position
- The *K*/** distributions are wider for real events than for mixed events

## Excitation Function for σdyn

- Excitation Function for *σ*dyn

- Compare STAR results for central Au+Au collisions with SPS results for central Pb+Pb collisions

## Excitation Function for σdyn (2)

- STAR results for *σ*dyn are similar to those at the top SPS energies
- The statistical hadronization model (SH) of Torrieri [nucl-th/0702062 (2007)] for the light quark phase space density *γ**q* = 1 (equilibrium) under-predicts *σ*dyn at all energies
- The statistical hadronization model for a fitted *γ**q* (non-equilibrium) explains the STAR results but under-predicts the SPS measurements

## Different Fluctuations Measure

- The use of *σ*dyn is problematic for low multiplicities
- A better measure is *ν*dyn,*K**π*

**dyn was introduced to study net charge fluctuations (PRC 68, 044905 [2003])
**dyn,*K*** is insensitive to efficiency
**dyn,*K*** deals well with low multiplicities and does not require mixed events

## Are σdyn and νdyn,Kπ Different?

- Are *σ*dyn and *ν*dyn,*Kπ* Different?

- 200 GeV Au+Au

- Sergei Voloshin, J. Phys. Conf. 50, 111 (2006)

## νdyn,Kπ for Au+Au at 62 and 200 GeV

*ν*dyn,*K**π* for Au+Au at 62 and 200 GeV

- Centrality dependence of *K*/*π* fluctuations
- Inverse multiplicity dependence
- Relatively poor fit versus 1/*N*part
- NA49 results are all central Pb+Pb collisions
- Similar *N*part

- Au+Au

## Compare with NA49 using dN/d

- We can compare the results for the centrality dependence of *ν*dyn,*K**π* to the incident energy dependence of *σ*dyn in central collisions using the following method
- Use PHOBOS systematics ford*N*/d*η* versus *s**NN*1/2
- Use the identity *σ*dyn2 = *ν*dyn,*K**π*

## PHOBOS Systematics for dN/dηin Central Collisions

- B. Back et al. (PHOBOS Collaboration)
- Phys. Rev. C  **74**, 021902(R) (2006)

## νdyn,Kπ Plotted versus dN/dη

*ν*dyn,*K**π* Plotted versus d*N*/d*η*

- Better fit with 1/(d*N*/d*η*)than with 1/*N*part

- Au+Au

## Excitation Function for σdyn

- Excitation Function for *σ*dyn

- Scale centrality dependence of *ν*dyn,*K**π* to compare with excitation function of *σ*dyn in central collisions

## Addition of TOF to STAR

- STAR will add TOF for Run 10
- The TOF will provide excellent particle identification for *π*, *K*, and *p* for a large fraction of the measured particles event-by-event
- Improved *K*/*π* fluctuation measurements
- Improved balance functions with identified *π*, *K*, and *p*

- P. Sorensen

- Charged pions and kaons
- 0.2 < pt < 0.6 GeV/c

## Look at Charges Separately

- 200 GeV Au+Au

## HIJING Predictions - Separated Charges

- 200 GeV Au+Au

## Scale with dN/dη andCompare with HIJING

- Scale with d*N*/d*η* andCompare with HIJING

- Average *ν*dyn,*K*+/*π*+ and *ν*dyn,*K*-/*π*- to get Same
- Average *ν*dyn,*K*+/*π*- and *ν*dyn,*K*-/*π*+ to get Opposite

## Scale with dN/dη andCompare with AMPT

- Scale with d*N*/d*η* andCompare with AMPT

- AMPT (version 1.21, hard scattering) for summed charges is better than HIJING, but centrality dependence is not correct
- No difference between same and opposite

## Relation of K/π Fluctuations to Resonance Re-interaction

- Model of Torrieri, Jeon and Rafelski
- Predict *K*/*π* fluctuations and resonance production using statistical hadronization model
- _[www.gsi.de/documents/DOC-2007-Jul-101-1.pdf](http://www.gsi.de/documents/DOC-2007-Jul-101-1.pdf)_
- Jeon and Koch, PRL 83, 5435 (1999) (*π*+/*π*-)
- Relate *ν*dyn,*K*+/*π*- and *ν*dyn,*K*-/*π*- to *K**(892)/*K* ratio
- (3/4)<*N**π*>(*ν*dyn,*K*+/*π*- - *ν*dyn,*K*-/*π*-) ∼ *K**/*K*

## Resonance Reinteraction Compared with Thermal Model of Torrieri

- Au+Au

- T = 170 MeV

## Dependence on Acceptance

- Au+Au 200 GeV

## Balance Function

- Bass, Danielewicz, Pratt PRL 85 2689  (2000)

- Balance function represents charge balance of charge/anti-charge pairs
- Balance functions can be expressed in terms of **, *y*, *q**inv*, *q**out*, *q**side*, *q**long*, and **

## Balance Function

- 200 GeV Au+Au

- Data

- Shuffled

- Mixed

## Balance Function Widths - All Charged Particles

- 200 GeV

## Balance Function Widths - Pions and Kaons

- 200 GeV

## B(qinv) for Pions

*B*(*q**inv*) for Pions

- 200 GeV Au+Au

- Data

- Shuffled

## B(qinv) for Pions

- Charged pion pairs
- 0.2 < *p**t* < 0.6 GeV/c

## B(qinv) for Kaons

*B*(*q**inv*) for Kaons

- Charged kaon pairs
- 0.2 < *p**t* < 0.6 GeV/c

## B(qinv) for Pions and Kaonsfrom p+p at 200 GeV

- B(qinv) for Pions and Kaonsfrom p+p at 200 GeV

- B(qinv) for pions shows K0 and 0
- The 0 peak is shifted down as previously observed
- B(qinv) for kaons shows 

- Pions

- Kaons

## Balance Function Widths from B(qinv)

- Balance Function Widths from *B*(*q**inv*)

- Pions

- Kaons

## Balance Function - Excitation Function

- NA49
- Phys. Rev. **C** 76, 024914 2007

- Balance functions for
- Pb+Pb at *s**NN*1⁄2 =
- 6.3 to 17.3 GeV

- Balance functions for
- Au+Au at *s**NN*1⁄2 =
- 20 to 200 GeV

- STAR, QM 02, QM 04

## Balance Function Widths -Excitation Function

- NA49

- NA49
- Phys. Rev. **C** 76, 024914 2007

- Large *W* means narrow balance function

- UrQMD predicts wide balance function with no centrality dependence

## RHIC Low Energy Scan

- For central Au+Au and Pb+Pb collisions, **dyn for *K*/** fluctuations may show a deviation from the fluctuations predicted by a statistical hadronization model as a function of incident energy
- The width of the balance function in central Au+Au and Pb+Pb collisions decreases as the energy is increased until around 20 GeV, where it seems to stay constant
- These two observations hint at some kind of phase transition occurring between 7 and 20 GeV
- A comprehensive energy scan from 7 to 60 GeV with STAR and the new TOF will answer many questions

## Conclusions - K/

- Dynamical fluctuations in the *K*/*π* ratio in central Au+Au collisions represented by *σ*dyn show little incident energy dependence at RHIC energies within errors and compare reasonably with SPS results at the top energies
*ν*dyn,*K**π* seems to scale with d*N*/d*η*
- (d*N*/d*η*)*ν*dyn,*K**π* increases slightly with centrality
*ν*dyn*,K**π* for same sign particles is close to zero
*ν*dyn,*K**π* for opposite sign particles is negative
- HIJING overpredicts (d*N*/d*η*)*ν*dyn,*K**π* while AMPT seems to get the correct magnitude but not the centrality dependence
- Fluctuations of same and opposite sign particles may give us information about the re-interaction of kaons and pions

## Conclusions - Balance Function

- Balance function *B*(**) for all charged particles narrows in central Au+Au collisions
- HIJING shows no centrality dependence
- AMPT narrows in central collisions, but not as much as the data
- Balance function *B*(*y*) widths for pions and kaons are different
- Balance function *B*(*q**inv*) widths for pions and kaons are the same
- Central Au+Au widths scaled with shuffled events (*W*) are the same at 20, 62, 130, and 200 GeV
- Balance function *B*(*q**inv*) for pions shows the *K*0, but not the **0
- Widths extracted from *B*(*q**inv*) for pions  scale with d*N*/d**

## The End

## Extra Slides

## Balance Function with Identified Pions - Excitation Function

- Charged pion pairs
- 0.2 < *p**t* < 0.6 GeV/c

## B(qinv) Widths using Identified Pions - Excitation Function

*B*(*q**inv*) Widths using Identified Pions - Excitation Function

- Charged pion pairs
- 0.2 < *p**t* < 0.6 GeV/c

## Kinetic Temperatures as a Reference

## The QCD Phase Diagram

## The Search for the QCD Phase Transition

- The production of strangeness may be related to the onset of deconfinement
- Excitation function of<*K**+*>/<*π*+> shows “horn” around*s**NN*1/2 = 7 GeV
- The excitation function of <*K*->/<*π*-> is smooth

- C. Blume (NA49), hep-ph/0505137

## HBT-Coulomb Effects for B(qinv)

- Expanded scale in qinv
- Compare correlation function to B(qinv)

## RHIC Energy Scan

- Energies as low as sNN1/2 = 4.5 GeV (10 AGeV fixed target)

| (GeV) | (MeV) | Min Bias BBC Rate
(Hz) | Days/
Mevents | Number
Of Events

 | Number of
beam days |
| --- | --- | --- | --- | --- | --- |
| 4.6 | 570 | 5(5) | 9(4.6) | 5 | 45(23+2) |
| 6.3 | 470 | 7(50) | 4(0.5) | 5 | 20(3+1) |
| 7.6 | 410 | 13(150) | 2(0.2) | 5 | 10(1+1) |
| 8.8 | 380 | 20(300) | 1.5(<1) | 5(>5) | 7.5(1+1) |
| 12 | 300 | 54(1000) | 0.5(<1) | 5(>50) | 2.5(1+1) |
| 18 | 220 | >100(>1000) | 0.25(<1) | 5(>50) | 1.5(1+1) |
| 28 | 150 | >100(>1000) | 0.25(<1) | 5(>50) | 1.5(1+2) |

- T. Satogota, RHIC

## NA 49/61 Future Program

- M. Gazdzicki

## Proposed Energy and Mass Scans