By: Mark Parra-‐Shostrand

Faculty Mentor: Dr. Sean Gavin

Graduate Student: Christopher Zin

REU Project

Study two-‐particle correlations as a function of

pseudorapidity due to jet production in high energy

proton-‐proton collisions

Specifically, I studied three statistical observables R, D,

and

δp t1

δp t 2

Studied charged particles in a pseudorapidity range -‐6 to

6 and transverse momentum .15 to 2.

Pseudorapidity (eta)

It’s a function of a particles angle of emission from the

beam axis

In other words, eta is the speed along the beam axis

and relates position with speed

Eta. Image credit Wikipedia

In terms of momentum

Eta cont.

Pz= momentum directed down the beam axis

Pt= transverse momentum perpendicular to the beam

axis

Therefore,

tanθ =

P t

P z

η = 1 2 ln ⎛ P + P ⎞

z

⎜

⎝ P − P

⎟

z ⎠

when simplified,

⎡ ⎛

η = −ln tan θ ⎞ ⎤

⎢

⎣ ⎝ 2⎠

⎥

⎦

Why study Pseudorapidity Dependence?

Two production

mechanisms

-‐jets

-‐flux tubes/string

fragmentation

Jets are peaked in

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*+,)"-)."/012"314+56,('78"/(&89+7,&:#7"

&#$"

&"

%#$"

%"

!#$"

Flux tubes are not

peaked

!"

'(" ')" '*" '&" !" &" *" )" ("

+,-."/-0123/4567"+487916/8:;6"

Correla=on Measurements

Earliest evidence of jet quenching came from

measurements of two particle correlations

I used pseudorapidity dependence over a rapidity

range

Statistical quantities used for one and two-‐body

densities are[1]:

ρ 1

η ( ) = dN

dη

ρ 2 ( η 1

,η 2 ) = d 2 N

dη 1

dη 2

Correla=on Meas. Cont.

To write multiplicity in range of eta

N =

∫

Δη

ρ 1 ( η)dη

Here represents the average of the number of

charged particles per event

Fluctuations of the particle number are found by

integrating the two-‐particle density to get the average

number of pairs per event

( ) = ρ 2

η 1

,η 2

N N −1

∫

Δη

( )dη 1

dη 2

R

You may recognize a statistical measurement for the

particle fluctuation as the variance.

In equilibrium the events follow a Poisson

distribution so

variance as [1]

σ 2 eq

= N

. So we define this robust

R = σ 2 − N

= N 2 − N 2 − N

N 2 N 2

This tells us how far the events are from being in

equilibrium

What’s D?

D allows us to distinguish between Jets and Flow

We argue if D is positive we expect Jets to dominate

and if D is negative we expect Flow

D = NP t

− N P t

− p t

N 2 − N 2

( )

N 2

= average number charged particles

= average total transverse momentum

= /

Think of as average covariance per particle pair

Goal of calculation is to see how particles

characteristics change together

δp t1

δp t 2

measures transverse momentum

fluctuations [2]

δp t1

δp t 2

δp t1

δp t 2

=

∑ i≠ j

δp ti

δp tj

N ( N −1)

δp t1

δp t 2

Cont.

Where

δp ti

=

p ti

− p t

p t

= P t

P = ∑ p

N t i ti

What this tells us is:

-‐If the quantity approaches zero, we can say all the

particles transverse momentum is about average

-‐If not close to zero we may have explosive jets

one million events

)(

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!#!*"

!#!)"

!#!("

!#!'"

!#!&"

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!#!$"

!"

,+" ,)" ,'" ,%" !" %" '" )" +"

!#!!*"

!#!!)"

!#!!("

!#!!'"

!#!!&"

!"#$%$&'(

-"

%&'"&'"($

-‐one million events

-‐the sta=s=cal

uncertain=es are so small

the ploCed line covers it

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+," +)" +'" +%" !" %" '" )" ,"

!"#$

-./0./01"

Results

If you examine R, D, and you can see they are

not flat. This implies our data does not follow Poisson

distribution

Our data illustrates the production of jets

Our findings at

-‐D ~ . 068 GeV

-‐R ~ .854

η = 0

:

-‐ ~ .0067 GeV 2

δp t1

δp t 2

δp t1

δp t 2

Future Sugges=ons

For a future experiment one could use other programs

such as HIJING to simulate heavy-‐ion collisions.

Expand the pseudorapidity range past -‐6 to 6

One could also increase the event size from one

million to ten million

Find a way to eliminate or turn off jets in PYTHIA 8 to

test D

SoGware Used

I used PYTHIA 8 a Monte Carlo event generator. It

replicates interactions between charged particles to

illustrate the elementary particles during collisions[3].

PYTHIA 8 only uses proton-‐proton collisions, therefore

only a few dozen particles result from the collision.

PYTHIA 8 is not designed to produce radial flow.

Additionally, I used ROOT. ROOT is a data analysis

program that creates histograms, plots and many more

data analysis methods. I had ROOT run through PYTHIA

and analyze this vast amount of data to portray a

histogram of R, D, and δp t1

δp t 2

Acknowledgements/References

I would like to thank George Moschelli and Rajendra

Pokharel for discussions and additional guidance.

[1] C. Pruneau, S. Gavin and S. Voloshin, Phys. Rev. C 66,

044904 (2002) [arXiv:nucl-ex/0204011].

[2] S. Gavin and G. Moschelli, (2011) [arXiv:

1107.3317v2 [nucl-th]].

[3] T. Sjostrand and M. van Zijil, Phys. Rev. D 36, 2019

(1987).