# Presentation: 803632

## Predictions for two-pion correlations for sqrt(s)=14 TeV proton-proton collisions

- Tom Humanic
- Ohio State University

## Outline of the talk

- Introduction
- Simple geometric model to give “baseline” predictions for HBT from pp@LHC
- Reality check of model by comparing with Tevatron HBT experiment
- Results of model calculations for sqrt(s)=14 TeV
- Summary
- (work to appear in Phys. Rev. C, or see nucl-th/0612098v2)

**p+p and Pb+Pb @ LHC**

**LHC ring in**
**Geneva area**

## CERN Large Hadron Collider (LHC)

- * Located in Switzerland and France – 27 km circumference ring
- * Maximum C. M. energies and luminosities of colliding beams:
- 	proton + proton:	14 TeV @ 1034 collisions/(sec*cm2)
- 	lead + lead:		5.5 ATeV @ 1027 collisions/(sec*cm2)
- * First p-p beam for physics expected by Summer, 2008
-    First Pb-Pb beam by ~ end of 2009 (we hope!)
-              better have some interesting p-p physics to do while waiting
-              for Pb-Pb: e.g. HBT, mini-BH, ........
- * Will be the highest energy particle accelerator in the world!
-     (Tevatron presently running at Fermilab has a maximum
-       C.M. energy for p-p of 2 TeV)

## ALICE setup

**ALICE setup**

- _[ITS](file:///ITS.ppt)_

- _[TPC](file:///TPC.ppt)_

- _[TRD](file:///TRD.ppt)_

- _[TOF](file:///TOF.ppt)_

- _[PHOS](file:///PHOS.ppt)_

- _[HMPID](file:///HMPID.ppt)_

- _[MUON SPEC.](file:///DIMUON.ppt)_

- _[PMD](file:///PMD.ppt)_

- _[FMD](file:///Forward.ppt)_

## What do we expect to see from pion HBT with p+p @ LHC?

**Pion HBT with p+p @ STAR**
**Zbigniew Chajecki QM05**

**Jet model for HBT with p+p @ FNAL/LHC**
**Guy Paic and Piotr Skowronski**
**J. Phys. G: Nucl. Part.. Phys. 31 (2005)**

- p

- p

- jet

- jet

**Finds R increases as**
**dN/dy increases, as seen**
**In FNAL data**

## Goals of the present work

- Use a very simple model to make “baseline predictions” for pion HBT in pp@LHC --> differences between these predictions and LHC data could point to the presence of new physics
- Calculate the 1-d invariant two-pion correlation function C(Qinv), where Qinv = |p1-p2| and p1 and p2 are pions 4-momenta, to make the predictions simpler to compare with data
- Include final-state hadronic rescattering effects since large hadronic multiplicites  (e.g. > 300) are possible at the LHC -- concentrate on events with high multiplicity to enhance this effect
- Do a reality check of the model by comparing results with a Tevatron HBT experiment (Experiment E735) --> if the model fails miserably here already, it’s time for the junk pile!

## Simple geometric model for HBT from p+p

- p

- p

-  i-th particle

- * Assume all particles have the same proper time for hadronization, ****, so that
- the hadronization space-time for each particle is given by “causality”, i.e.
-             ti = Ei/mi   ;  xi = xoi +  pxi/pi   ;  yi = yoi +  pyi/pi   ;  zi =  pzi/pi
-     (similar to Csorgo and Zimanyi, Nucl. Phys. A512 (1990) applied to e+-e-)
- * Take into account hadronic rescattering using a full Monte Carlo rescattering calculation

- Initial “ thin disk”
- of radius **r = 1 fm**

## Other details of the model....

- Use PYTHIA v.6326 to generate hadrons for 1.8 TeV p-pbar or 14 TeV p+p “minimum bias” events
**       **“final” hadrons from PYTHIA to use:  K, N, ’
- Monte Carlo hadronic rescattering calculation:
**      **Let hadrons undergo strong binary collisions until the system gets so dilute (since it is expanding) that all collisions cease.
-      --> (i,j) from Prakash, etc..
-      Record the time, mass, position, and momentum of each hadron when it no  longer scatters.   freezout condition.
- Calculate C(Qinv) ~ Nreal(Qinv)/Nback(Qinv) by binning symmetrized pairs of pions assuming plane waves in Nreal to put in HBT correlations (usual method).
- Fit Gaussian (Tevatron)  or more general function (LHC) to C(Qinv) to extract parameters R and  **or** R, , B, and 
-      C(Qinv) = 1+ exp(-R2Qinv2) **or** C(Qinv) = 1+cos(BQinv2) exp(-RQinv)
- Carry out calcuations for several  values to see effect on HBT -- expect the smaller values of to have the largest rescattering effects

## How long does it take to collect a “reasonable” data sample of, for example, -- pairs for events with total mult>300 in a detector at the LHC?

- Assumptions:
-      * reasonable data sample of -- pairs for HBT: ~106
-      * detector: ALICE ITS+TPC (~accept. 0.1<pT, -1<y<1; DAQ rate 100Hz)
-      * 1st-year LHC p-p luminosity @ 14 TeV: L~1030 cm-2 s-1
-      * ~40% of charged particles reconstructed in an event are -’s
- From PYTHIA p-p minimum bias run @ 14 TeV
-      * total ~ 50 mb,        m>300) = 0.1 total ~ 5 mb
-      * charged hadron multiplicity in ALICE acceptance for m>300: ~ 50/event
- Result:
-      * events/sec=  L (m>300) ~ 5000 > DAQ rate --> 100 events/sec
-      * -- pairs obtained per event ~ (0.4*50)2/2 = 200 --> 20,000 pairs/sec
-      --> running time to obtain 106 pairs = 106/20,000 = 50 seconds ~ 1 minute

## Compare model predictions with Tevatron data as a reality check on the model

- Compare with Experiment E735 which extracted  HBT @ sqrt(s)=1.8 TeV in p-pbar collisions using a spectrometer (T. Alexopoulos et al., Phys. Rev. D48,1931(1993))
- Make kinematic cuts on pT and rapidity to simulate experimental acceptance in the model
- Fit the Gaussian function to C(Qinv) to extract R an  from the model since this was the procedure used in the experiment
- Compare model calculations with =0.1, 0.5 and 1.0 fm/c to experiment to see if the data favor one of them over the others

##    and pT distributions from PYTHIA for p-pbar @ 1.8 TeV for 1) direct, 2) with “y-pT hole”, 3) hole+rescatt. (=0.1 fm/c)

## Sample model 2- correlation functions for =0.1, 0.5, 1.0 fm/c for 1.8 TeV p-pbar

## Comparisons of Gaussian fit paramters between E735 and model for =0.1 fm/c

## Comparisons of Gaussian fit paramters between E735 and model for =0.5 fm/c

## Comparisons of Gaussian fit paramters between E735 and model for =1.0 fm/c

## Summary of results for model comparison with Tevatron experiment

- Model best describes the the pT and multiplicity dependences of the  E735 Gaussian HBT parameters for the case of =0.1 fm/c with rescattering turned on
- Suggests that hadronization time short in these collisions, i.e. <<1 fm/c, and that significant hadronic rescattering effects are present

## Model predictions for LHC p-p collisions at 14 TeV

- Make predictions for =0.1 and 0.5 fm/c cases
- Employ same “y-pT hole” method as used for Tevatron calculations
- Fit more general function to C(Qinv):    (see Csorgo and Zimanyi)
-         C(Qinv) = 1+cos(BQinv2) exp(-RQinv)
-          where,
-          R = “size” parameter
-            = “strength” parameter
-          B  = “oscillatory” parameter, B ~  for present model,
-                  normally not observed for cases where R>>
- since exp term dominates and quickly damps  	       oscillations
-            = “degree of function fall-off” parameter

##   and pT distributions from PYTHIA for p-p @ 14 TeV for 1) direct and 2) hole+rescatt. (=0.1 fm/c)

## Sample model 2- correlation functions for =0.1 fm/c for 14 TeV p-p with fit to general function

## Sample model 2- correlation functions for =0.5 fm/c for 14 TeV p-p with fit to general function

## General fit function parameters versus pT and multiplicity for model with =0.1 fm/c for 14 TeV p-p

## General fit function parameters versus pT and multiplicity for model with =0.5 fm/c for 14 TeV p-p

## Summary of general fit parameter behavior predicted by model for 14 TeV p-p

- R -- largest variation for =0.1 fm/c case, can increase by 3x for increasing m and decrease by 3x for increasing pT
- -- weak dependencies on kinematical cuts which tend to be opposite those of R; <0.5 due to presence of long-lived resonances
- B -- tends to follow the behavior B ~ since noticeable baseline oscillations are seen for the =0.5 fm/c case
-  -- similar kinematical dependencies as , tends to have values in range 0.7<<1.5 for both =0.1 and 0.5 fm/c

## Summary

- Within the context of this simple model, results from two-pion HBT @ Tevatron and LHC energies strongly depend on the hadronization proper time, 
- Comparison of the model with Tevatron data looks reasonable and favors a short hadronization time, ~0.1 fm/c
- Final-state hadronic rescattering effects appear to be observable for <0.5 fm/c in high-energy p-p and p-pbar collisions
- Significant dependences of the HBT parameters on particle multiplicity and pT bin are predicted by the model to be seen for LHC p-p collisions -- these are enhanced for short 