Measuring the Size of ProtonProton 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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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”...
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
Particle Accelerators allow us to study
aspects of the early universe in the lab
“Hadronization of the universe” occurred here
Perspectives on Temperature
NucleusNucleus 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
~106 K
Rhodium metal spin cooling (2000)
~1010 K
(LowT World Record!)
Trapped Ions
“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
“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 protonproton and nucleusnucleus collisions at all?
Protonproton (pp) collisions are the simplest case
of nucleusnucleus (AA) collisions...
pp collisions form the “baseline”
for AA collisions
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 headon at 0.99995c,
creating “little Big Bangs”!
between
when the hadrons
are formed and when they fly off
to be detected
Hadronization
1. SpaceTime Evolution of High Energy NucleusNucleus Collision
t
N
K
Thermal Freezeout
Hadron Gas
Mixed Phase
Projectile Fragmentation Region
QGP
Quark Formation & creation ~ 1fm/c
z
P
T
N
K
Measuring the extent of this
“spacetime 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
freestreaming towards the detector
Hadronization
2. SpaceTime Evolution of protonproton 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
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
HanburyBrown Twiss
Intensity Interferometry
(or just HBT for short)
The technique was originally developed by two English astronomers
Robert HanburyBrown and Richard Twiss (circa 1952)
(Sadly, RHB passed away just this January)
It’s form of “Intensity Interferometry”
 as opposed to “regular” amplitudelevel
(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?
(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
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 timeaverage
our measurement over many
fluctuations
rB1
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)
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 nonconstant expression!
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
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
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:
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
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 halfinteger spin particles.
Identical Fermions have an antisymmetric wave function 
only one particle may occupy a quantum state
Protons and electrons are examples of Fermions
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=p1p2
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 nonconstant C(Q) arises
because of
I) the symmetry of the twoparticle wave function
for identical bosons or fermions and
II) the kind of “statistics”
particles of a particular type obey
(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 soso for low Q
1/R=0.365 GeV
R~2.74 GeV1~ 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
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)
My current research related to this work
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. HanburyBrown
Quantum Optics Scully and Zubairy
Quantum Theory of Light Loudon
TwoParticle Correlations in Relativistic Heavy Ion Collisions Heinz and Jacak, nuclth/9902020
What have we learned?
HBT can be subtle and fun
Quark hadronization is complicated but
studying the size of protonproton collisions
using HBT may be able to tell us something about it
pp collisions are smaller than AA collisions!