Finding The Spin of the Proton Douglas Fields University of New Mexico

Outline Review of Problem Spin physics at RHIC Brief Review of Deep Inelastic Scattering Spin “Crisis” Spin physics at RHIC RHIC and PHENIX Measurements of ΔG “Measurements” of ΔL PHENIX upgrades and future measurements February 4, 2009 LANL P-25 Seminar

Motivation Hadron Physics: Standard Model Tests: Forget all of that Understanding of the structure of the nucleon. Understanding of nuclear interactions. Tests of QCD. Standard Model Tests: Use spin as a tool to test Standard Model predictions. Search for exotics (SUSY, PV…). Forget all of that Spin is as fundamental as charge or mass! February 4, 2009 LANL P-25 Seminar

Spin Effects Polarized pp elastic scattering at 197MeV. Ay ~ (NL – NR)/ (NL + NR) Shows that the strong (nuclear) force depends strongly on the spin orientation. p NL NR February 4, 2009 LANL P-25 Seminar

“Naïve Quark Model” Protons are spin ½ objects composed of three spin ½ objects. Since Quarks are fermions, total wavefunction must be antisymmetric February 4, 2009 LANL P-25 Seminar

Strong Spin Dependence Deltas are spin 3/2 objects composed of three spin ½ objects. Mass is ~300MeV greater than proton! February 4, 2009 LANL P-25 Seminar

Predictions Baryon magnetic moments are well predicted by the Naïve Quark Model mu = md ~ 1/3mp ms given by L magnetic moment (but mu=4MeV, md=7MeV)? February 4, 2009 LANL P-25 Seminar

Caveat… Quarks (and anti-quarks) only account for ½ of nucleon momentum and it is dependent on at what scale you observe. I like the fractal analogy: At low resolving power, one sees three quarks in the nucleon At higher resolving power, one sees more and more detail of what a quark is, namely a collection of quarks, antiquarks and gluons. Resolving power (smaller scales) February 4, 2009 LANL P-25 Seminar

What Does the Proton Look Like? The distribution of partons in the proton was not very well understood 10 years ago Today, the picture is different… J.D. Bjorken, Collisions Of Constituent Quarks At Collider Energies SLAC-PUB-95-6949 (1995) February 4, 2009 LANL P-25 Seminar

Probing the Proton EM interaction Strong interaction Weak interaction Photon Sensitive to electric charge2 Insensitive to color charge Strong interaction Gluon Sensitive to color charge Insensitive to flavor Weak interaction Weak Boson Sensitive to weak charge ~ flavor Insensitive to color February 4, 2009 LANL P-25 Seminar

Missing Ingredients Longitudinal momentum fraction (x) Transverse position (b) Intrinsic transverse momentum (kT) Correlations of above (x┴ x kT) P.H. Hägler, et. al. February 4, 2009 LANL P-25 Seminar

Parton Distribution Functions Quark Distributions unpolarized distribution q(x,Q2)= = helicity distribution Dq(x,Q2)= g(x,Q2)= Dg(x,Q2)= No Transverse Gluon Distribution in 1/2 Gluon Distributions transversity distribution dq(x,Q2)= February 4, 2009 LANL P-25 Seminar

Sum Rules Momentum Sum Rule Helicity Sum Rule: ΔΣ measured in DIS experiments and found to be small (0.1 – 0.3)… February 4, 2009 LANL P-25 Seminar

“Spin Crisis” “Not-so-Naïve” quark model and comparison to results Predicted from EJSR Measured in DIS February 4, 2009 LANL P-25 Seminar

Not Really a Crisis… Remember the more complicated possibilities… But Leptons don’t scatter off gluons (at first order) How do we probe the gluons? February 4, 2009 LANL P-25 Seminar

(longitudinal polarization) RHIC Spin BRAHMS & PP2PP STAR AGS LINAC BOOSTER Pol. H- Source Spin Rotators (longitudinal polarization) Solenoid Partial Siberian Snake Siberian Snakes 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H jet) AGS pC Polarimeters Strong AGS Snake Helical Partial Siberian Snake PHOBOS Spin flipper PHENIX February 4, 2009 LANL P-25 Seminar

PHENIX Detector Philosophy: High resolution at the cost of acceptance High rate capable DAQ Excellent trigger capability for rare events Central Arms: ||<0.35, =2900 Charged particle ID and tracking; photon ID. EM Calorimetry. Muon Arm: 1.2<||<2.4 Muon ID and tracking. Global Detectors Collision trigger Collision vertex characterization Relative luminosity Local Polarimetry February 4, 2009 LANL P-25 Seminar

“Measurements” of ΔG Example: choose channel with high statistics p + p → π0 + X Complicated mixture of amplitudes Compare with: February 4, 2009 LANL P-25 Seminar

Solution Factorization between hard and soft physics Soft: Hard: Example: q + g → π0 + X Soft: q(x), Δq(x), D(z) Hard: NLO pQCD cross-sections – spin dependent Missing ingredients: Δg(x) beam polarization Soft Physics from universal fits to data Hard Physics σ ~ momenta and helicities D February 4, 2009 LANL P-25 Seminar

Status of Ingredients Status of Pol. PDFs (2004) Valence quark fairly well determined from DIS ΔG and sea quarks poorly known February 4, 2009 LANL P-25 Seminar

pQCD Check pp0 X : PRD76,051106 Next step: Measure cross-section as a test for perturbative QCD at Run 6, pushes p0 cross-section to 20 GeV/c. Agreement with pQCD over broad range of pT. Does this mean that QCD works for spin sorted in this same range? February 4, 2009 LANL P-25 Seminar

Where Are We So Far? Factorization between hard and soft physics Soft: Example: q + g → π0 + X Soft: q(x), Δq(x), D(z) Hard: NLO pQCD cross-sections – spin dependent Missing ingredients: Δg(x), P – beam polarization ☺ ☺ ☺ Soft Physics from universal fits to data ☺ Hard Physics σ ~ momenta and helicities D ☺ February 4, 2009 LANL P-25 Seminar

π0 ALL arXiv:0810.0694 Put all ingredients into a NLO pQCD calculation with assumed values of ΔG, Monte Carlo the results with the detector acceptance, and compare to data to determine allowed values of ΔG. February 4, 2009 LANL P-25 Seminar

From ALL to G (with GRSV model) Generate g(x) curves for different (with DIS refit) Compare ALL data to curves (produce 2 vs G) arXiv:0810.0694 Calculate ALL for each G February 4, 2009 LANL P-25 Seminar

Update to Pol. PDFs Using the π0 results from PHENIX, one can recalculate allowed values of the pol. PDFs. Much improved limits on ΔG. February 4, 2009 LANL P-25 Seminar

ΔL ΔG is appearing to be small (although it may be enough to solve the Spin Crisis) What is next? ΔL… Theory tells us it should be there anyway. Anomalous magnetic moment Sivers Effect February 4, 2009 LANL P-25 Seminar

Sivers Effect Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon For a positive Siver’s function, there will be net parton kT to the left (relative to direction of proton, assuming spin direction is up). SP kT,q p FSI : SIDIS ISI : Drell-Yan February 4, 2009 LANL P-25 Seminar

How can you get a net kT? Nice conceptual picture from D. Sivers (talk given at UNM/RBRC Workshop on Parton Orbital Angular Momentum). Summary: Sivers effect requires orbital motion. Is process dependent. I would like to just follow this conceptual picture to see where it may lead. February 4, 2009 LANL P-25 Seminar

Sivers Effect No Sivers Effect without interaction with absorber. February 4, 2009 LANL P-25 Seminar

Fields Effect Think of rotating (longitudinal) water balloons, or… February 4, 2009 LANL P-25 Seminar

Origin of Jet kT Another Possibility: Net transverse momentum of a di-hadron pair in a factorization ansatz Di-hadron pT kT initial – e.g., fermi motion of the confined quarks or gluons, initial-state gluon radiation… hard – final-state radiation (three-jet)… frag – fragmentation transverse momentum jT Another Possibility: Spin-correlated transverse momentum – partonic orbital angular momentum Can examine the helicity dependence of each term: February 4, 2009 LANL P-25 Seminar

Like Helicity (Positive on Positive Helicity) Peripheral Collisions Larger Peripheral Collisions Larger Measure jet Integrate over b, left with some residual kT Central Collisions Smaller February 4, 2009 LANL P-25 Seminar

Un-like Helicity (Positive On Negative Helicity) Peripheral Collisions Smaller Integrate over b, left with some different residual kT Central Collisions Larger February 4, 2009 LANL P-25 Seminar

Integrating over Impact Parameter Drell-Yan pair production in polarized p+p collisions. (Meng Ta-Chung et al. Phys. Rev. D 1989) kTR kPR Like Helicity Un-like Helicity Averaging over D(b): Integrating over impact parameter b: February 4, 2009 LANL P-25 Seminar

Measuring jet kT – di-hadron correlation o- h± azimuthal correlation Trigger on a particle, e.g. o, with transverse momentum pTt. Measure azimuthal angular distribution w.r.t. the azimuth of associated (charged) particle with transverse momentum pTa. The strong same and away side peaks in p-p collisions indicate di-jet origin from hard scattering partons. February 4, 2009 LANL P-25 Seminar

How does PHENIX measure kt? near Zero kT Non-Zero kT Intra-jet pairs angular width : near  jT Inter-jet pairs angular width : far  jT  kT far Drawings by A. Zimmerman February 4, 2009 LANL P-25 Seminar

Jet Kinematics For details, see: Phys. Rev. D 74, 072002 (2006) February 4, 2009 LANL P-25 Seminar

Correlation Function Red – real (raw Δφ) Blue – background (mixed events) February 4, 2009 LANL P-25 Seminar

Fit Function Blue – real (raw Δφ) Red – Fit from above equation February 4, 2009 LANL P-25 Seminar

Spin sorted dihadron correlations Fit Results Red – Like helicity (++ & --) Blue – Unlike helicity (+- & -+) February 4, 2009 LANL P-25 Seminar

Need <zt> and xh <k2T> asymmetry results are not sensitive to this xh and <zt> values – only needed to set the scale. ^ xh and <zt> are determined through a combined analysis of the π° inclusive cross section and using jet fragmentation function measured in e+e- collisions. Ref. PRD 74, 072002 (2006) ^ February 4, 2009 LANL P-25 Seminar

kT results for unpolarized case kT = 2.88 +/- 0.02 (stat) +/- 0.12 (syst) GeV jT = 607.5 +/- 0.8 (stat) +/- 0.3 (syst) MeV February 4, 2009 LANL P-25 Seminar

Preliminary Results Take the difference Like – Unlike helicities. Normalized by beam polarizations. <j2T > asymmetry small (-6 ± 6 MeV out of ~607 MeV for unpolarized). <k2T > asymmetry also small (-8 ± 90 MeV out of ~2.9 GeV for unpolarized). February 4, 2009 LANL P-25 Seminar

Interpretation The small asymmetry in jT verifies our assumption that the third term is suppressed. The second term may be constrained from current knowledge of the π0 ALL. February 4, 2009 LANL P-25 Seminar

Interpretation The first term can be related in the “Meng conjecture” to partonic transverse momentum: where cij give the initial state weights and Wij give the impact parameter weighting. Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%), We can interpret this as a constraint on the gluon orbital angular momentum. Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions. February 4, 2009 LANL P-25 Seminar

What Next? February 4, 2009 LANL P-25 Seminar

PHENIX VTX Detector Upgrade Main physics goal to discriminate heavy-flavor production via displaced vertices. I would like to use it to better determine jet kT. Needs simulation and study. February 4, 2009 LANL P-25 Seminar

Summary We have an analysis tool – di-hadron azimuthal correlations - that allows us to measure kT. We are studying this in helicity-sorted collisions to see if there is a spin-dependent, coherent component of kT. In our kinematic range, we find jT RMS = -6 ± 6 MeV, and kT RMS = -8 ± 90 MeV. While this is consistent with other measurements related to gluon OAM, the connection to parton OAM needs theoretical guidance! February 4, 2009 LANL P-25 Seminar

Summary Our group has made significant contributions to the RHIC Spin program and to the PHENIX experiment. We are currently leading the investigation of an interesting, albeit speculative, physics analysis. We will continue significant contributions to the PHENIX upgrade plan with an eye on our research thrust. I look forward to an invigorated nuclear/particle group with the addition of active theorists. February 4, 2009 LANL P-25 Seminar

Backups February 4, 2009 LANL P-25 Seminar

How do you measure the quark spins? ~ l-q elastic scattering k k/ Leading order diagram. + Radiative corrections + NLO corrections + Higher twist… n, q X February 4, 2009 LANL P-25 Seminar

eμ Elastic Scattering e-(p2,s2) m-(p4,s4) m-(p3,s3) e-(p1,s1) Initial State Potential Final State Probability to happen: February 4, 2009 LANL P-25 Seminar

Feynman Prescription… EM coupling strength e EM coupling strength e Electric interaction Magnetic interaction February 4, 2009 LANL P-25 Seminar

Now, for e-quark scattering eq scattering Now, assume: So that, Modified by the quark fractional charge Modified by the quark mass February 4, 2009 LANL P-25 Seminar

Step towards protons… Sum over quark flavors and integrate over x weighted by f(x), the probability to have momentum fraction x: Electric STRUCTURE Function Magnetic STRUCTURE Function February 4, 2009 LANL P-25 Seminar

Structure Functions Structure functions in the scaling limit Spin independent Spin dependent (= 0 when sum over spins) This is related to the elastic scattering off parton with momentum fraction p = xP February 4, 2009 LANL P-25 Seminar

Nosecone Calorimeter Main physics goals to measure γ-jet events and isolate muons from W-decay I would like to use it to better determine jet kT. Needs simulation and study. Tungsten absorber Pb absorber Pad readout Stripixel readout Cu skin 15 mm February 4, 2009 LANL P-25 Seminar