The Whole Story Behind a Half The Quest

The Whole Story Behind a Half: The Quest to Understand the Proton’s Spin Christine A. Aidala UMass Amherst Sambamurti Memorial Lecture BNL Christine Aidala, Lecture, 7/22/2008 July. Sambamurti 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. The units of angular momentum are the same as Planck's constant, h, and can only have values that are integer : 0, 1, 2, 3, . . . or half-integer: 1/2, 3/2, 5/2, . . . In a magnetic field, different spin states split into different energy levels. Christine Aidala, Sambamurti Lecture, 7/22/2008 Proton spin is what makes MRI possible! 2

Stern-Gerlach Experiment Any particle with spin Apply a magnetic field Spin ½ particle (e. g. 107 Ag or 1 H) Spin 1 particle (e. g. 2 H) Spin 3/2 particle (e. g. 7 Li) 2 s+1 Energy Levels Christine Aidala, Sambamurti Lecture, 7/22/2008 3

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. ” Quarks, like protons, have spin 1/2. Christine Aidala, Sambamurti Lecture, 7/22/2008 4

Quark-Parton Model (cont. ) The simplest model says a proton’s made of three “valence” quarks: 2 up quarks and 1 down quark. • But these quarks are not completely free in the nucleon! – Bound by force-carrier particles called “gluons. ” – “Sea quarks” are also present: short-lived quarkantiquark pairs from quantum mechanical fluctuations. • As you hit the proton with more energy, you resolve shorter-lived fluctuations: gluons and sea quarks. Christine Aidala, Sambamurti Lecture, 7/22/2008 5

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 6

Color Charge and QCD • Strong force acts on particles with color charge – Quarks, themselves! (Contrastcharge! with Note that quarksplus alsogluons carry fractional electromagnetic electrically neutral) Protonphotons, = up + upwhich + downare quarks +1 = +2/3 because + +2/3 + -1/3 • “Color” three different “charges” combine to+make neutral Neutron = down +aup 0 = -1/3 + +2/3 red+blue+green = white particle: • Quantum Chromodynamics (QCD)—theory describing the strong force Christine Aidala, Sambamurti Lecture, 7/22/2008 7

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 8

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 9

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 Christine Aidala, Sambamurti Lecture, 7/22/2008 momentum in center-of-mass frame) 10

Proton Structure and Momentum Fraction What momentum fraction would the scattering particle carry if the proton were made of … 3 bound valence quarks A point particle x. Bj 1/3 1 3 bound valence quarks and some slow sea quarks Sea 3 valence quarks x. Bj 1 Valence 1/3 1 x. Bj Halzen and Martin, “Quarks and Leptons, ” p. 201 Christine Aidala, Sambamurti Lecture, 7/22/2008 Slow 1/3 x. Bj 11 1

What Have We Learned? • Conclusions fromspin decades of inelastic scattering What about the structure of the proton? data investigating proton momentum structure: – 3 -“valence” quarks carry (on average) the largest Do inelastic scattering with polarized single momentum fractions of protons! (spin directions allthe aligned) – But lots of gluons and “sea” quark-antiquark pairs in the proton as well! Gluons carry ~50% of total momentum of proton. ~ ~? Christine Aidala, Sambamurti Lecture, 7/22/2008 12

The Proton Spin Crisis gl n o u Proton 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 Surprising data from late 1980’s! 1987: Only 14% +- 23% of proton’s spin carried by quarks’ spins! The Proton Spin Crisis begins!! These haven’t been easy to measure! Quark Spin Gluon Spin Orbital Angular Momentum Christine Aidala, Sambamurti Lecture, 7/22/2008 13

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 Positive helicity Helicity: Projection of spin vector onto momentum vector for particles polarized longitudinally, i. e. parallel to direction of motion. Either positive or negative. Negative helicity vs. Christine Aidala, Sambamurti Lecture, 7/22/2008 14

Quark and Gluon Helicity Distributions EMC, SMC at CERN E 142 to E 155 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 ½ + ½ - ½ = ½, but numbers don’t add up! We’re trying to find out at RHIC! up quarks gluon Sea quarks just add to our difficulties!! sea quarks down quarks x. Bj Can gluon spin account for what’s missing? ? Christine Aidala, Sambamurti Lecture, 7/22/2008 15

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 16

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 17

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 matterantimatter colliders) Christine Aidala, Sambamurti Lecture, 7/22/2008 18

RHIC as a Polarized p+p Collider RHIC p. C Polarimeters Absolute Polarimeter (H jet) Siberian Snakes BRAHMS PHOBOS & PP 2 PP Siberian Snakes Spin Flipper PHENIX STAR Spin Rotators Partial Snake Strong Snake Polarized Source LINAC 200 Me. V Polarimeter BOOSTER Helical Partial Snake AGS Rf Dipole AGS Internal Polarimeter AGS p. C Polarimeter Christine Aidala, Sambamurti Lecture, 7/22/2008 Various equipment to maintain and measure beam polarization through acceleration and storage 19

RHIC’s Experiments Transverse spin only (No rotators) Longitudinal or transverse spin Christine Aidala, Sambamurti Lecture, 7/22/2008 20

PHENIX 14 Countries; 69 Institutions; > 500 Participants as of July 2007 Christine Aidala, Sambamurti Lecture, 7/22/2008 21

PHENIX Detector Philosophy: ü Fast data acquisition & high granularity Ø Trade-off area covered 2 central arms - Track charged particles and detect electromagnetic processes 2 forward arms - Identify and track muons (“heavy electrons”) Christine Aidala, Sambamurti Lecture, 7/22/2008 22

PHENIX Detector Christine Aidala, Sambamurti Lecture, 7/22/2008 23

Au+Au Collision in PHENIX Central Arms Christine Aidala, Sambamurti Lecture, 7/22/2008 24

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” = “p. QCD”) – 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 25

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 26

Understanding Particle Production in p+p Collisions q(x 1) Hard Scattering Process Can use factorized perturbative QCD (p. QCD) to calculate particle production at X high-energy facilities g(x 2) Particle production rates can be calculated using p. QCD from: Christine Aidala, Sambamurti Lecture, 7/22/2008 Universality – Parton distribution functions (from experiment) – p. QCD partonic scattering rates (from theory) – “Fragmentation functions” (from experiment) 27

How Well Does Factorized p. QCD Work at RHIC? p. QCD calculations p describe polarizationp 0 averaged cross-section measurements well at Dg Dg. Dq Dq RHIC! 0 2 2 Fraction pions q~90 o from beam produced 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) p. T (Ge. V/c) Christine Aidala, Sambamurti Lecture, 7/22/2008 28

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 29

Hard Scattering in Polarized p+p Hard Scattering Process Measure asymmetries, input Dq as measured by previous experiments, then use p. QCD to “solve for” Dg, the gluon spin contribution to the proton’s spin Christine Aidala, Sambamurti Lecture, 7/22/2008 30

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 31

ALL of Neutral Pions Data show asymmetry close to zero. Different curves are theoretical predictions assuming different values of Dg. Christine Aidala, Sambamurti Lecture, 7/22/2008 32

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 33

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 Ge. V • Short run in 2006 at 62. 4 Ge. V • Future running at 500 Ge. V planned Christine Aidala, Sambamurti Lecture, 7/22/2008 Also working on charged particle asymmetry 34

A Global Effort • No single canparton determine proton spin Hope tomeasurement pin down the distribution structure functions by putting all world data together – Trying to map out these polarized parton distribution functions, need to measure the functions at different momentum fraction values up quarks • RHIC spin experiments are continuing the work of gluon earlier ones, which started in the mid-1980 s • 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 sea quarks down quarks –. . . Christine Aidala, Sambamurti Lecture, 7/22/2008 35

Gluon Spin from Various Global Analyses xΔg(x) at Q 2 = 10 Ge. V 2 Latest analysis! Christine Aidala, Sambamurti Lecture, 7/22/2008 36

Latest Global Analysis of Helicity Distributions 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! • “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! Christine Aidala, Sambamurti Lecture, 7/22/2008 37

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! Quark “transversity” distribution – Measurements in p+p increasingly valuable, as necessary “input” quantities from simpler systems become available Christine Aidala, Sambamurti Lecture, 7/22/2008 38

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 Quark Spin Gluon Spin directly! – Any suggestions? ? Spin Orbital Angular Momentum Christine Aidala, Sambamurti Lecture, 7/22/2008 39

Extra Slides Christine Aidala, Sambamurti Lecture, 7/22/2008 40

Fermions and Bosons All particles can be classified into two categories depending on their spin: fermions and bosons. • Fermions include most of the familiar matter around us, such as electrons, protons, and neutrons, as well as others. • 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 41

Factorization in p. QCD 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 p. QCD hard scattering rates (calculable in p. QCD) - 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 42

ALL of p at Two Energies 0 Christine Aidala, Sambamurti Lecture, 7/22/2008 43

p p ALL and Dg +, - • At transverse momentum > ~5 Ge. V/c, pions are dominantly produced via qg scattering • The tendency of p+ to fragment from an up quark and pfrom a down quark and the fact that Du and Dd have opposite signs make ALL of p+ and p- differ measurably • This difference can allow us to determine the sign of Dg Christine Aidala, Sambamurti Lecture, 7/22/2008 44

ALL of Charged Pions (STAR) Christine Aidala, Sambamurti Lecture, 7/22/2008 45