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

Christine Aidala, Sambamurti Lecture, 7/22/ 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. 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,... Proton spin is what makes MRI possible!

Christine Aidala, Sambamurti Lecture, 7/22/ s+1 Energy Levels Any particle with spin 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) Stern-Gerlach Experiment Apply a magnetic field

Christine Aidala, Sambamurti Lecture, 7/22/ 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/ 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/ 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! (~ m)

Christine Aidala, Sambamurti Lecture, 7/22/ 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 Chromodynamics (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/ 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/ For More Information For more info on quarks, gluons, and the strong force, see (Many pictures on previous pages borrowed from this site)

Christine Aidala, Sambamurti Lecture, 7/22/ 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/ Proton Structure and Momentum Fraction Halzen and Martin, “Quarks and Leptons,” p. 201 x Bj /3 x Bj 1/3 1 Valence Sea A point particle 3 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/ 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/ Proton Surprising data from late 1980’s! 1987: Only 14% +- 23% of proton’s spin carried by quarks’ spins! The Proton Spin Crisis begins!! Spin Quark Spin Gluon Spin Orbital Angular Momentum 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/ 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/ 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 ½ + ½ - ½ = ½, but numbers don’t add up! Sea quarks just add to our difficulties!! Can gluon spin account for what’s missing?? x Bj We’re trying to find out at RHIC!

Christine Aidala, Sambamurti Lecture, 7/22/ 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/ 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/ 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/ AGS LINAC BOOSTER Polarized Source Spin Rotators 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H jet) P HENIX P HOBOS B RAHMS & PP2PP S TAR AGS pC Polarimeter Partial Snake Siberian Snakes Helical Partial Snake Strong Snake Spin Flipper RHIC as a Polarized p+p Collider maintain measure Various equipment to maintain and measure beam polarization through acceleration and storage

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

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

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

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

Christine Aidala, Sambamurti Lecture, 7/22/ 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/ 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/ Hard Scattering Process X q(x 1 ) g(x 2 ) 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) Universality Can use factorized perturbative QCD (pQCD) to calculate particle production at high-energy facilities

Christine Aidala, Sambamurti Lecture, 7/22/ How Well Does Factorized pQCD Work at RHIC? g2g2 gqgq q2q2  Fraction pions produced  ~90 o from beam 00 p T (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/ 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/ Hard Scattering in Polarized p+p Hard Scattering Process 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/ Some Spin Asymmetry Measurements A LL : “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/ A LL 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/ A LL 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/ 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/ 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/ Gluon Spin from Various Global Analyses x Δ g(x) at Q 2 = 10 GeV 2 Latest analysis!

Christine Aidala, Sambamurti Lecture, 7/22/ 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/ 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/ 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?? Spin Quark Spin Gluon Spin Orbital Angular Momentum

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

Christine Aidala, Sambamurti Lecture, 7/22/ 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/ 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/ A LL of  0 at Two Energies

Christine Aidala, Sambamurti Lecture, 7/22/  +,  - A LL 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 A LL of  + and  - differ measurably This difference can allow us to determine the sign of  g

Christine Aidala, Sambamurti Lecture, 7/22/ A LL of Charged Pions (STAR)