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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Thomas D. Gutierrez
University of California, Davis
March 14, 2002
Department of Physics
Sonoma State University
quickly form bound states through a process
Hadrons = Made of quarks
Free quarks have
never been observed!
This is interesting and
Baryon = qqq
p = uud
n = dud
Meson = qq
p+ = ud
K+ = us
“A neutron is a dud…”
Particle Physics at a Glance
aspects of the early universe in the lab
“Hadronization of the universe” occurred here
Perspectives on Temperature
Neutron Star Thermonuclear Explosion
(Terrestrial Nuclear explosions)
~ 120 MeV
Room Temperature ~ 1/40 eV
Cosmic Microwave Background
Rhodium metal spin cooling (2000)
(Low-T World Record!)
Note the length contraction of the nuclei
along the direction of motion!
This is because v~c
Nuclear Collisions in Action
…and by colliding nuclei, the bulk properties
of nuclear matter can be studied under extreme conditions...
This is akin to
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
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”!
when the hadrons
are formed and when they fly off
to be detected
1. Space-Time Evolution of High Energy Nucleus-Nucleus Collision
Projectile Fragmentation Region
Quark Formation & creation ~ 1fm/c
Measuring the extent of this
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
2. Space-Time Evolution of proton-proton Collision
That’s why pp collisions are
a cleaner probe of what is going
on during hadronization
Quark scattering and creation
about what the collision looked like when the hadrons
were created -- this gives us insight into the mysterious
process of “hadronization”
HOW do you measure the size?
Why measure the size of pp collisions?
Source sizes are measured using a technique called
(or just HBT for short)
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?
(brackets indicate time average -- which is what is usually measured)
Two slit interference (between coherent sources at A and B)
“source geometry” is related to interference pattern
L >> d
(brackets again indicate time average)
“Two slit interference” (between incoherent sources at A and B)
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
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)
L >> (d & R)
HBT Example (incoherent sources)
But if we take the product before time averaging...
(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!
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)
beyond their averages
over the fluctuation times...
This gives a big correlation
A plot of I1*I2
with the I’s treated
If I1 and I2 both tend to stick around their
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...
It’s not exactly the usual “statistical correlation function”…
but it is related
If d>>R (like an astronomy experiment):
If R>>d (like an elementary particle experiment):
For two incoherent point sources….
The momentum difference is called:
Increasing source size d
Notice that the “widths” of these correlation functions are
inversely related to the source geometry
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
For fixed k
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
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:
Partly coherent bosons+contamination
Coherent sources (like lasers)
are flat for all Q
Fermions exhibit anticorrelation
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
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
I may be a theorist sort
but what can I say…real data is fun!
Gaussian fit is only so-so for low Q
R~2.74 GeV-1~ 0.55fm
500k pp events from Experiment NA49 at CERN
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
NPA610 240 (96)
R really increases with system size!
Just for comparison...
C is narrower so R is bigger
Typical AA Data
This isn’t my analysis
From Craig Ogilvie
(2 Dec 1998)
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!