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Measuring the Size of Proton-Proton Collisions. Thomas D. Gutierrez University of California, Davis March 14, 2002 Department of Physics Sonoma State University. Quarks knocked loose during a collision quickly form bound states through a process called “ hadronization ”.

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measuring the size of proton proton collisions

Measuring the Size of Proton-Proton Collisions

Thomas D. Gutierrez

University of California, Davis

March 14, 2002

Department of Physics

Sonoma State University

slide2

Quarks knocked loose during a collision

quickly form bound states through a process

called “hadronization”...

Hadrons = Made of quarks

Free quarks have

never been observed!

This is interesting and

strange…

Baryon = qqq

p = uud

n = dud

Meson = qq

p+ = ud

K+ = us

“A neutron is a dud…”

Particle Physics at a Glance

http://particleadventure.org

slide3

Particle Accelerators allow us to study

aspects of the early universe in the lab

“Hadronization of the universe” occurred here

slide4

Graphic courtesy JLK

Perspectives on Temperature

Nucleus-Nucleus collisions

~1012 K

~109 K

Neutron Star Thermonuclear Explosion

(Terrestrial Nuclear explosions)

~107 K

~106 K

Solar Interior

~ 120 MeV

~6000 K

Solar Surface

Room Temperature ~ 1/40 eV

~300 K

Cosmic Microwave Background

~3 K

~10-6 K

Rhodium metal spin cooling (2000)

~10-10 K

(Low-T World Record!)

Trapped Ions

slide5

Particle Key

“Projectile”

“Target”

Baryons (p,n,,,…)

Mesons (,K,,,…)

Note the length contraction of the nuclei

along the direction of motion!

This is because v~c

Nuclear Collisions in Action

slide6

“AA” is used to evoke the image of “Atomic Number”

…and by colliding nuclei, the bulk properties

of nuclear matter can be studied under extreme conditions...

“material science”

This is akin to

colliding blocks

of ice to study the

phase diagram of water!

Density of the system compared to

normal nuclear density (0.13/fm3)

High energy pp collisions

tend to be somewhere in here

Collisions fling normal nuclear matter into exotic states

Why study proton-proton and nucleus-nucleus collisions at all?

Proton-proton (pp) collisions are the simplest case

of nucleus-nucleus (AA) collisions...

pp collisions form the “baseline”

for AA collisions

slide7

But why is that?

Let’s look at two situations

While AA collisions probe the

material science of nuclear matter (phase diagrams, etc.)

pp collisions more directly probe hadronization

Why collide protons at all?

The Relativistic Heavy Ion Collider (RHIC)

on Long Island, NY slams gold nuclei head-on at 0.99995c,

creating “little Big Bangs”!

slide8

Lots of stuff happens

between

when the hadrons

are formed and when they fly off

to be detected

Hadronization

1. Space-Time Evolution of High Energy Nucleus-Nucleus Collision

t

N

K

Thermal Freeze-out

Hadron Gas

Mixed Phase

Projectile Fragmentation Region

QGP

Quark Formation & creation ~ 1fm/c

z

P

T

slide9

N

K

Measuring the extent of this

“space-time surface

of hadronization” is what is meant

by the “size of the collision”

Because the system size is so small,

there are very few interactions from

the moment of impact

to when particles are

free-streaming towards the detector

Hadronization

2. Space-Time Evolution of proton-proton Collision

t

That’s why pp collisions are

a cleaner probe of what is going

on during hadronization

Quark scattering and creation

z

P

T

slide10

Measuring the size of pp collisions gives information

about what the collision looked like when the hadrons

were created -- this gives us insight into the mysterious

process of “hadronization”

Ok. But...

HOW do you measure the size?

Why measure the size of pp collisions?

Source sizes are measured using a technique called

Hanbury-Brown Twiss

Intensity Interferometry

(or just HBT for short)

slide11

What is HBT?

The technique was originally developed by two English astronomers

Robert Hanbury-Brown and Richard Twiss (circa 1952)

(Sadly, RHB passed away just this January)

It’s form of “Intensity Interferometry”

-- as opposed to “regular” amplitude-level

(Young or Michelson) interferometry --

and was used to measure the angular sizes of stars

The method had far reaching consequences!

A quantum treatment of HBT generated much controversy and

led to a revolution in quantum optics (photons can act strangely!)

Later it was used by high energy physicists to measure

source sizes of elementary particle or heavy ion collisions

But how does HBT work? And why use it instead of “regular” interferometry?

slide12

L >> d

(brackets indicate time average -- which is what is usually measured)

Two slit interference (between coherent sources at A and B)

rA1

P1

A

Plane wave

rB1

d

Monochromatic Source

B

“source geometry” is related to interference pattern

slide13

A

d

B

L >> d

(brackets again indicate time average)

“Two slit interference” (between incoherent sources at A and B)

P1

rA1

Two monochromatic but incoherent sources

(i.e.with random, time dependent phase)

produce no interference pattern

at the screen --

assuming we time-average

our measurement over many

fluctuations

rB1

slide14

Average of I over a very short time

Average of I over a medium time

Average of I over a fairly long time

For very long time averages we get

Long/Short compared to what?

The time scale of the random fluctuations

What does <I> mean?

Position on the screen in radians (for small angles)

slide15

P1

rA1

rB1

R

rA2

d

P2

rB2

L >> (d & R)

HBT Example (incoherent sources)

A

As before...

B

But if we take the product before time averaging...

where

(will be related to source and detector geometry)

Difference of the path length differences

Important: The random phase terms completely dropped out

and left us with a non-constant expression!

slide16

Time average of the product

This quantity is known as a correlation function

Product of the time averages

It is important to note that for coherent sources

(remembering in that case <I>=I)

so

C=1

slide17

If I1 and I2 tend to increase together

beyond their averages

over the fluctuation times...

This gives a big correlation

A plot of I1*I2

with the I’s treated

as variables

If I1 and I2 both tend to stick around their

individual averages

over the fluctuation times…

the correlation tends towards one

If either I1 or I2 (or both) tend to be below their

averages or are near zero

over the fluctuation times…

the correlation tends towards zero

What does C mean?

If we independently monitor the

intensity as a function of time at two

points on the screen...

<I2>

I1

<I1>

I2

It’s not exactly the usual “statistical correlation function”…

but it is related

slide18

Two interesting limits (with a “little” algebra)...

If d>>R (like an astronomy experiment):

If R>>d (like an elementary particle experiment):

ˆ

ˆ

D

-

D

-

k

(

r

r

)

~

kd

k

k

1

2

1

2

For two incoherent point sources….

Recall

The momentum difference is called:

slide19

Increasing angular size

Increasing source size d

Notice that the “widths” of these correlation functions are

inversely related to the source geometry

source

Width w

A source can also be a continuous distribution

rather than just points

The width of the correlation function

will have a similar inverse relation to the source size

Width ~1/w

Correlation function

Astronomy

For fixed k

Particle physics

I’ll drop

slide20

The HBT effect at the quantum level is deeply

related to what kind of particle

we are working with

Bosons and Fermions

Bosons are integer spin particles.

Identical Bosons have a symmetric two particle wave function --

any number may occupy a given quantum state...

Photons and pions are examples of Bosons

Fermions are half-integer spin particles.

Identical Fermions have an antisymmetric wave function --

only one particle may occupy a quantum state

Protons and electrons are examples of Fermions

slide21

At the quantum level:

Joint probability of measuring a

particle at both detectors 1 and 2

Probability of measurement at 1 times

probability of a measurement at 2

The correlation function for Gaussian source distributions

can be parameterized like:

C

Thermal Bosons

2

Partly coherent bosons+contamination

Chaoticity parameter

Coherent sources (like lasers)

are flat for all Q

~

1/R

1

Q=|p1-p2|

Momentum difference

Fermions exhibit anticorrelation

Fermions

0

More about

Correlation

functions

Than is probably healthy

A series of independent events should give C=1 (same as a coherent source)

At the quantum level

a non-constant C(Q) arises

because of

I) the symmetry of the two-particle wave function

for identical bosons or fermions and

II) the kind of “statistics”

particles of a particular type obey

slide22

HBT Summary and Observations

  • The correlation function contains information about the source geometry
  • The width of the correlation function goes like 1/(source width)
  • The HBT correlation function is insensitive to random phases that would normally destroy “regular” interference patterns
slide23

Back to pp Collisions

  • Pions (also bosons) are used in the HBT rather than photons
  • Basic idea is the same: Correlation function contains information about pion emission source size in the collision and may give clues about the nature of hadronization
slide24

(preliminary analysis this year by TG)

I may be a theorist sort

but what can I say…real data is fun!

Gaussian fit is only so-so for low Q

1/R=0.365 GeV

R~2.74 GeV-1~ 0.55fm

lam=0.358

Q

GeV

Real Data!

500k pp events from Experiment NA49 at CERN

1. signal

1. Generate a cumulative signal histogram by taking the momentum

difference Q between all combinations of pion pairs in one pp event; repeat this for all pp events

2. Generate a random background histogram by taking the momentum

difference Q between pions pairs in different events

3. Generate a correlation function by taking the ratio of signal/random

Q

GeV

2. random

Q

GeV

3. correlation

Q

GeV

slide25

NA44 at CERN

NPA610 240 (96)

R really increases with system size!

Just for comparison...

C(Q)

C is narrower so R is bigger

Typical AA Data

This isn’t my analysis

Q (MeV/c)

From Craig Ogilvie

(2 Dec 1998)

slide26

My current research related to this work

  • Analysis: HBT for pp collisions at NA49 (at CERN) and STAR (at RHIC)
  • Evaluate phase space density of the pp system, extract temperature!
  • Current pure theory project (mostly unrelated to particle physics): What are theoretical correlation functions for parastatistical particles and anyons?
  • Lots of room for student involvement at various levels!
slide27

I guess we expected this :)

Lots more interesting work to be done!

More reading for the interested viewer...

Boffin: A Personal Story of the Early Days of Radar, Radio Astronomy, and Quantum Optics R. Hanbury Brown

Intensity Interferometry R. Hanbury-Brown

Quantum Optics Scully and Zubairy

Quantum Theory of Light Loudon

Two-Particle Correlations in Relativistic Heavy Ion Collisions Heinz and Jacak, nucl-th/9902020

What have we learned?

HBT can be subtle and fun

Quark hadronization is complicated but

studying the size of proton-proton collisions

using HBT may be able to tell us something about it

pp collisions are smaller than AA collisions!