# Presentation: 200126

## UMass Amherst

- Christine A. Aidala

***The Whole Story ******Behind a Half:******The Quest to Understand the Proton’s Spin***

- Sambamurti Memorial Lecture
- BNL
- July 22, 2008

## What is Spin?

- Spin is a quantum mechanical property of fundamental particles or combinations of particles.
- It’s called “spin” because it’s a type of angular momentum and is described by equations treating angular momentum.

***?***

- In a magnetic field, different spin states split into different energy levels.

*Proton spin is what makes MRI possible!*

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Stern-Gerlach Experiment

- 2*s*+1 Energy Levels

*Stern-Gerlach Experiment*

- Apply a magnetic field

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Looking Inside the Proton:The Quark-Parton Model

- Similarly to Rutherford’s 1911 experiment in which the scattering of alpha particles at large angles off of gold revealed a hard atomic core (the nucleus), in the late 1960’s at SLAC, scattering of electrons at large angles off of protons revealed “hard” subcomponents in the proton
- Protons weren’t solid lumps of positive charge as previously believed!
- The pointlike constituents that make up the proton are called “quarks,” or slightly more generally, “partons.”

- Quark

**Quarks, like protons, have spin 1/2.**

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Quark-Parton Model (cont.)

*Quark-Parton Model (cont.)*

- But these quarks are not completely free in the nucleon!
- Bound by force-carrier particles called “gluons.”
- “Sea quarks” are also present:  short-lived quark-antiquark pairs from quantum mechanical fluctuations.
- As you hit the proton with more energy, you resolve shorter-lived fluctuations:  gluons and sea quarks.

- The simplest model says a proton’s made of three “valence” quarks:  2 up quarks and 1 down quark.

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Strong Force

- How does the nucleus stay together?  The electromagnetic force should cause the protons to repel one another . . .
- Protons and neutrons interact via the *strong force*, carried by gluons
- Much stronger than the electromagnetic force (thus the name!)
- But very short range! (~10-15 m)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Color Charge and QCD

*Color Charge and QCD*

- Strong force acts on particles with *color* charge
- Quarks, plus gluons themselves!  (Contrast with photons, which are electrically neutral)
- “Color” because three different “charges” combine to make a neutral particle: red+blue+green = white
- Quantum *C**h**r**o**m**o*dynamics (QCD)—theory describing the strong force

- Note that quarks also carry *fractional* electromagnetic charge!
- Proton = up + up + down quarks
-       +1 = +2/3 + +2/3 + -1/3
- Neutron = down + down + up
-            0 = -1/3 + -1/3 + +2/3

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Quark Confinement

*Quark Confinement*

- Never see quarks or gluons directly!
*Confined* to composite, color-neutral particles
- Groups of three quarks (rgb), called *baryons*, or quark-antiquark pairs (red-antired, . . .), called *mesons*
- If you try to pull two quarks apart, energy between them increases until you produce a new quark-antiquark pair (recall *E=mc**2*)

- “D- meson”

- “D+ meson”

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## For More Information

- For more info on quarks, gluons, and the strong force, see
- http://www.particleadventure.org/
- (Many pictures on previous pages borrowed from this site)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Studying Proton Structure

- If can’t see individual quarks and gluons (“partons”), how to determine the proton’s structure?
- Inelastic scattering—shoot a high-energy beam (e.g. of electrons) at the proton to break it up, and try to understand what happens
- Electron exchanges a photon with quarks, because quarks carry electromagnetic charge as well as color

- Describe proton structure in terms of *parton distribution functions* (pdf’s)
-  - Probability of scattering off of a parton carrying a particular fraction of the proton’s momentum (“Bjorken-x” variable)
- (Recall that even if protons are in a stationary target, have non-zero momentum in center-of-mass frame)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Proton Structure and Momentum Fraction

*Proton Structure and Momentum Fraction*

- Halzen and Martin, “Quarks and Leptons,” p. 201

- xBj

- xBj

- 1

- xBj

- 1

- 1

- 1/3

- 1/3

- xBj

- 1/3

- 1

- Valence

- Sea

- A point particle

- 3 valence quarks

- 3 bound valence quarks

- 3 bound valence quarks
- and some slow sea quarks

- Slow

- What momentum fraction would the scattering particle carry
- if the proton were made of ...

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## What Have We Learned?

- Conclusions from decades of inelastic scattering data investigating proton momentum structure:
- 3 “valence” quarks carry (on average) the largest single momentum fractions of the proton
- But lots of gluons and “sea” quark-antiquark pairs in the proton as well!  Gluons carry ~50% of total momentum of proton.

- What about the *spin* structure of the proton?
- - Do inelastic scattering with *polarized* protons!  (spin directions all aligned)

**~**

**~ ?**

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## The Proton Spin Crisis

- Surprising data from late 1980’s!
- 1987:  Only 14% +- 23% of proton’s spin carried by quarks’ spins!
**The Proton Spin Crisis begins!!**

*The Proton Spin Crisis*

- Say you have a proton with total spin +1/2 along some axis.  Most naively, you’d expect it to contain two quarks with spin +1/2 and one with spin -1/2.
- 1/2 + 1/2 - 1/2 = +1/2

- gluon

*These haven’t been easy to measure!*

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Polarized Parton Distribution Functions

- Describe spin structure in terms of *polarized* parton distribution functions
- Helicity distributions—*difference* in probability of scattering off of a quark or gluon with *same vs. opposite helicity* of proton

- Helicity:  Projection of spin vector onto momentum vector for particles polarized longitudinally, i.e. parallel to direction of motion.
- Either positive or negative.

- Positive helicity

- Negative helicity

- vs.

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Quark and Gluon Helicity Distributions

**up quarks**

**down quarks**

**sea quarks**

**gluon**

- EMC, SMC at CERN
- E142 to E155 at SLAC
- HERMES at DESY

- In valence region (*x**Bj*>~0.1), note  *up* quarks have large spin contribution in *same* direction as proton spin and *down* quarks have (smaller) contribution *opposite* to proton
-    - Reminiscent of
-      1⁄2 + 1⁄2 - 1⁄2 = 1⁄2,
- but numbers don’t add up!
- Sea quarks just add to our difficulties!!
- Can *gluon* spin account for what’s missing??

- xBj

- xBj

- We’re trying to find out at RHIC!

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## The Relativistic Heavy Ion Collider

- Two main physics programs: Proton spin structure + QCD at high energies and densities
- Heavy-ion program: Search and discovery mission for quark-gluon plasma, state of matter believed to have existed 10 millionths of a second after the Big Bang.
- First polarized proton collider in world!  Special magnets and other equipment installed to maintain and measure polarization.

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## RHIC at Brookhaven National Laboratory

*RHIC at Brookhaven National Laboratory*

- The Relativistic Heavy Ion Collider
- located at Brookhaven National Laboratory
- Long Island,
- New York

- Christine Aidala, Sambamurti Lecture, 7/22/2008

**Notes:**
RHIC is (was) visible from space and is located on Eastern Long Island

## The Relativistic Heavy Ion Collider

- Heavy ions, *polarized* protons
- Most versatile collider in the world!  Nearly any species can be collided with any other.
- asymmetric species possible due to independent rings with separate steering magnets (unlike matter-antimatter colliders)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## RHIC as a Polarized p+p Collider

**AGS**

**LINAC**

**BOOSTER**

-   Polarized Source

- Spin Rotators

-   200 MeV Polarimeter

-  AGS Internal Polarimeter

-   Rf Dipole

-  RHIC pC Polarimeters

**P****HENIX**

**P****HOBOS**

**B****RAHMS & PP2PP**

**S****TAR**

- AGS pC Polarimeter

- Partial Snake

- Siberian Snakes

- Siberian Snakes

-  Spin Flipper

*RHIC as a Polarized p+p Collider*

- Various equipment to *maintain* and *measure* beam  polarization through acceleration and storage

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## RHIC’s Experiments

*RHIC’s Experiments*

- Transverse spin only
- (No rotators)

- Longitudinal or transverse spin

- Longitudinal or transverse spin

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## PHENIX

*PHENIX*

*** ******14 Countries;  69 Institutions;  ***
***> 500 Participants as of July 2007***

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## PHENIX Detector

*PHENIX Detector*

**2 central arms**
**- ****Track charged particles and detect electromagnetic processes **

**2 forward arms**
**- ****Identify and track muons (“heavy electrons”)**

_**Philosophy:**_
-  **Fast data acquisition & high granularity**
** ****Trade-off area covered**

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## PHENIX Detector

*PHENIX Detector*

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Au+Au Collision in PHENIX Central Arms

*Au+Au Collision **in PHENIX Central Arms*

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Fixed-Target Vs. Collider Experiments

- Earliest experiments studying proton structure used electron beams to probe stationary (“fixed”) proton targets (think of tube of hydrogen gas)
- Typically easier and cheaper to perform fixed-target experiments
- Collider experiments allow you to reach higher energy
- Can use different theoretical tools to interpret results (“perturbative QCD” = “pQCD”)
- Can produce heavier particles (*E=mc**2* again!)
- Can access different kinematic region (e.g. lower momentum fraction, *x**Bj*)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Proton-Proton Scattering Vs. Electron-Proton Scattering

- Studying the proton by breaking it up with another proton is much more complicated than probing it with an electron beam!
- Two composite objects colliding and breaking up
- Rely on some input from experiments performed in simpler systems
- One specific advantage: *Direct access to gluons*, which cannot be probed directly via electron beams (no electromagnetic charge)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Understanding Particle Production in p+p Collisions

*Understanding Particle Production in p+p Collisions*

- Particle production rates can be calculated using pQCD from:
- Parton distribution functions (from experiment)
- pQCD partonic scattering rates (from theory)
- “Fragmentation functions” (from experiment)

- Can use *factorized* perturbative QCD (pQCD) to calculate particle production at high-energy facilities

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## How Well Does Factorized pQCD Work at RHIC?

*How Well Does Factorized pQCD Work at RHIC?*

- Fraction pions produced

- ~90o from beam

- 0

- pT (GeV/c)

- pQCD calculations describe polarization-averaged cross-section measurements well at RHIC!

*p**T**: Transverse momentum.*
*Interesting because if scattered quarks and gluons change direction sharply with respect to the beam direction, we know there was a “hard” interaction! (Think of Rutherford)*

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## How Can We Investigate the Proton’s Spin at RHIC?

- Collide polarized protons in different configurations and see what we observe in our detector
- Most often examining *asymmetries*
*e.g*. difference in the number of a certain particle produced when the beams have the same vs. opposite polarization
- Same number produced gives asymmetry = 0.
- All from one configuration and none from the other gives +1 or -1.
- Knowing what partonic processes (involving quarks and gluons) led to production of the observed particle gives us a handle on the quarks’ and gluons’ contribution to the spin.

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Hard Scattering in Polarized p+p

*Hard Scattering in ****Polarized**** p+p*

- Measure asymmetries, input q as measured by previous experiments, then use pQCD to “solve for” g, the gluon spin contribution to the proton’s spin

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Some Spin Asymmetry Measurements

- ALL: “double-longitudinal” asymmetry measurement, taken with both beams longitudinally polarized, sensitive to the gluon spin contribution to the proton’s spin

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## ALL of Neutral Pions

- Data show asymmetry close to zero.
- Different curves are theoretical predictions assuming different values of g.

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## ALL of Charged Pions

- Prediction of ordering of pion asymmetries depending on sign of gluon spin contribution.

- Not yet clear.  Need more data! ...

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Measuring Asymmetries at Other Energies

- Measuring asymmetries at different energies accesses different ranges of momentum fraction
- Lower energies  Higher momentum fractions
- Higher energies  Lower momentum fractions
- So far most data taken at 200 GeV
- Short run in 2006 at 62.4 GeV
- Future running at 500 GeV planned

- Also working on charged particle asymmetry

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## A Global Effort

- No single measurement can determine proton spin structure
- Trying to map out these polarized parton distribution *functions*, need to measure the functions at different momentum fraction values
- RHIC spin experiments are continuing the work of earlier ones, which started in the mid-1980s
- Two other spin experiments ongoing
- HERMES (Hamburg, Germany): electron-proton fixed-target
- COMPASS (Geneva, Switzerland): muon (heavy electron)-proton fixed-target
- Future experiments
- Proposed Electron-Ion Collider at RHIC or Jefferson Lab
- . . .

- Hope to pin down the parton distribution functions by putting all world data together

**up quarks**

**down quarks**

**sea quarks**

**gluon**

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Gluon Spin from Various Global Analyses

*Gluon Spin from Various Global Analyses*

***x*****Δ*****g*****(*****x*****) at**
***Q*****2**** = 10 GeV****2**

- Latest analysis!

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Latest Global Analysis of Helicity Distributions

- “DSSV” the first global analysis to include RHIC data on an equal footing with all other world data
- Finds small gluon spin contribution, with distribution crossing zero near *x* ~ 0.1!

- de Florian, Sassot, Stratmann, Vogelsang

***Look forward to even better knowledge of gluon spin contribution to proton spin as further RHIC (and other) data become available!***

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Longitudinal vs. Transverse Spin Structure

- Transverse spin structure of the proton cannot be deduced from longitudinal (helicity) structure
- Spatial rotations and Lorentz boosts don’t commute
- Relationship between longitudinal and transverse structure provides information on the relativistic nature of partons in the proton
- Transverse spin structure of the proton remains much less well understood than longitudinal, but field advancing rapidly!
- Measurements in p+p increasingly valuable, as necessary “input” quantities from simpler systems become available

- Quark “transversity” distribution

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## The Whole Story??

- Not yet!  A number of years to go . . .
- Present RHIC data suggest gluon spin contribution to proton spin can’t make up what’s missing!
- Proton Spin Crisis continues!!!
***If*** there are no surprises at low momentum fractions, orbital angular momentum of quarks and gluons the only possibility left, but nobody knows how to measure it directly!
- Any suggestions??

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Extra Slides

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Fermions include most of the familiar matter around us, such as electrons, protons, and neutrons, as well as others. 

*Fermions and Bosons*

- All particles can be classified into two categories depending on their spin: *fermions* and *bosons*.

- Bosons include force-carrier particles such as the photon (electromagnetic force) and gluon (strong force), plus composite particles made of an even number of fermions.

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## Factorization in pQCD

*Factorization in pQCD*

- Parton distribution functions (need experimental** input**)
- 	- probability of scattering off of a gluon or particular flavor quark carrying a certain momentum fraction of the proton momentum
- 	- easiest to measure in electron-proton scattering measurements
- pQCD hard scattering rates (calculable in pQCD)
- 	- scattering rates for quarks on quarks, quarks on gluons, or gluons on gluons
- 	- calculate theoretically
- Fragmentation functions (need experimental input)
- 	- probability of a particular flavor quark “fragmenting” into (becoming) a particular final-state particle (remember you never see an individual quark!)

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## ALL of 0 at Two Energies

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## +, - ALL and g

- At transverse momentum  > ~5 GeV/c, pions are dominantly produced via qg scattering
- The tendency of +        to fragment from an up quark and -         from a down quark and the fact that u and d have opposite signs make ALL of + and - differ measurably
- This difference can allow us to determine the sign of g

- Christine Aidala, Sambamurti Lecture, 7/22/2008

## ALL of Charged Pions (STAR)

- Christine Aidala, Sambamurti Lecture, 7/22/2008