Longitudinal Spin Physics at RHIC and a Future eRHIC Brian Page Brookhaven National Laboratory CIPANP 2015 – Vail, CO

Outline RHIC Measurements Intrinsic Gluon Spin (∆G) Theory and Results: Jets and π 0 s Flavor Separated Quark Helicities (∆Σ): W Bosons Future eRHIC Motivation ∆G in DIS: Q 2 Evolution of g 1 (x,Q 2 ) Charged Current Interactions as a Probe of Quark Helicities Summary Brian Page - CIPANP 20152

Piecing Together the Proton Spin Helicity Distributions: Δq, Δg Simple picture of proton composed of three valence quarks superseded by complex interaction of quarks, antiquarks, and gluons The proton’s spin must arise from combination of intrinsic and orbital angular momenta of these components This talk will deal only with the intrinsic components: ∆G and ∆Σ Brian Page - CIPANP 20153

RHIC: First Polarized pp Collider Brian Page - CIPANP 20154

RHIC: First Polarized pp Collider Time Projection Chamber (TPC) Charged Particle Tracking |η|<1.3 Barrel Electromagnetic Calorimeter (BEMC): |η|<1 Endcap Electromagnetic Calorimeter: 1<η<2 η = 0 η = 1 Brian Page - CIPANP 20155

Intrinsic Gluon Contribution: ∆G Kinematic reach of polarized DIS measurements Brian Page - CIPANP 20156

Accessing ∆G at RHIC: A LL p T (GeV) Partonic fractions in jet production at 200 GeV For most RHIC kinematics, gg and qg dominate, making A LL for jets and hadrons sensitive to gluon polarization. Parton Level Asymmetry Brian Page - CIPANP 20157

STAR 2009 Inclusive Jet A LL 2009 results have factor of 3 to 4 better statistical precision than 2006 results Result divided into two pseudorapidity ranges which emphasize different partonic kinematics Result lies consistently above the 2008 DSSV fit and is consistent with the LSS10p fit arXiv: Brian Page - CIPANP 20158

PHENIX Inclusive π 0 A LL PHENIX π 0 results from 2005, 2006, and 2009 shown in upper panels along with several theory curves PHENIX π 0 and STAR inclusive jet results are completely consistent as shown on bottom left. Note the different p T scales Brian Page - CIPANP Phys. Rev. D arXiv:

New DSSV Results Uncertainty on integral over low x region is still sizable Uncertainty shrinks substantially from DSSV* to new DSSV fit Brian Page - CIPANP Phys. Rev. Lett. 113,

New NNPDF Results Brian Page - CIPANP Nucl. Phys. B 887, 276 (2014)

Data Sets in the Pipeline High statistics data sets from 2012 and 2013 are being analyzed 200 GeV longitudinal run recently concluded Expected effect of data sets taken after 2009 on uncertainty of ∆g running integral shown Integral of ∆g(x,Q 2 ) from x min to 1 as a function of x min 200 GeV: x min > GeV + Forward Rapidity: x min > Brian Page - CIPANP arXiv:

Flavor-Separated Quark Contribution x x DIS probes all quark and anti-quark flavors so ∆Σ well constrained Constraints on individual quark and anti- quark distributions are weaker due to uncertainty in fragmentation functions needed in SIDIS extractions Expect flavor symmetric light sea, but observe u̅ ≠ d Comparing anti-quark helicity distributions important for discriminating between models of light sea generation _ Brian Page - CIPANP Phys. Rev. D 80, (2008)

Probing the Sea Quarks W boson production at RHIC provides complimentary measurements to SIDIS: Data at high Q 2 and no dependence on fragmentation functions V-A structure of weak interaction leads to perfect spin separation Structure of asymmetry allows for enhancement of a given flavor based on decay kinematics Forward Scatter Backward Scatter Brian Page - CIPANP

STAR W Results Asymmetries extracted from combination of 2011 and 2012 data using Profile Likelihood method A L from W + is consistent with predictions from the 2008 DSSV polarized PDF set A L from W - is systematically higher than DSSV predictions at negative lepton η This region has enhanced sensitivity to ∆u̅ contribution Brian Page - CIPANP Phys. Rev. Lett. 113, (2014)

PHENIX W Results PHENIX presents asymmetries from W & Z bosons decaying into e + and e - at mid-rapidity Results from 2011 (500 GeV), 2012 (510 GeV), and 2013 (510 GeV) are being finalized At forward rapidity, W to muon decay channel is utilized Preliminary results from 2013 have been presented and work continues on reducing systematic uncertainties Forward measurements especially difficult as W cross section drops sharply Brian Page - CIPANP arXiv:

Impact on Global Analyses STAR W A L data from included in preliminary DSSV analysis (DSSV++) and recent NNPDF analysis (NNPDFpol1.1) STAR W data shifts best fit values for first moments of ∆u̅(x,Q 2 ) and ∆d̅(x,Q 2 ) for x > 0.05 ∆u̅ best fit value changes sign between DSSV+ and new DSSV++ and the node which existed in DSSV08 is absent in NNPDFpol1.1 Brian Page - CIPANP arXiv: Nucl. Phys. B 887, 276 (2014)

eRHIC: Polarized ep Collider Brian Page - CIPANP

Hera Jlab, Compass & HERMES RHIC eRHIC: Polarized ep Collider Colliders: Large kinematic coverage DIS: Kinematic precision Polarization: Spin observables eRHIC! Brian Page - CIPANP

eRHIC: Accessing ∆G Several observables are sensitive to ∆G in DIS but golden measurement at an eRHIC would be scaling violation of g 1 (x,Q 2 ) Current DIS constraints on ∆G hampered by limited x & Q 2 coverage eRHIC would greatly expand kinematic reach and precision of g 1 (x,Q 2 ) measurements! Current Data Brian Page - CIPANP arXiv:

eRHIC: Impact on ∆G eRHIC will have the ability to vastly reduce the uncertainty on ∆G, especially at low x where constraints from data are virtually non-existent The excellent statistical precision achievable with an eRHIC means control of systematics will be critical Above plot shows how the constraint on ∆G is affected by systematic uncertainty Brian Page - CIPANP arXiv:

Gluon Quarks orbital angular momentum 1/2 - - = eRHIC: Solving the Spin Puzzle Above plot shows the running integral of ∆g(x,Q 2 ) from x min to 1 as a function of x min Large reduction in uncertainty on ∆G from eRHIC can be seen eRHIC will also reduce the uncertainty on the quark contribution to the proton spin No assumptions about hyperon beta decay in eRHIC uncertainty Constraints on gluon and quark contributions will provide independent check of orbital angular momentum component of proton spin Brian Page - CIPANP arXiv:

eRHIC: Probing the Sea DIS largely 1-photon exchange, but can also proceed via charged current (CC) interaction mediated by W boson CC interactions in polarized DIS give access to quark / antiquark helicity distributions as well as unique structure functions Because W is virtual, can access lower values of Q 2 to overlap with and provide cross check to SIDIS measurements Brian Page - CIPANP arXiv:

eRHIC: Quark / Anti-Quark Constraints ∆d̅∆u̅ ∆d∆u eRHIC with 5 GeV electrons colliding with 100 and 250 GeV protons greatly reduce uncertainty on u and d anti- quark helicity distributions See significant reduction in uncertainty on first moment of quark/anti-quark helicity distributions for x > 0.05 from 20 x 250 GeV electron on proton collisions Brian Page - CIPANP 2015 arXiv:

Summary Polarized p+p data from RHIC gives access to gluon interactions at leading order and has placed strong constraints on ∆G for x > 0.05 Real W production at RHIC provides a unique probe of the flavor separated light quark and anti-quark distributions Many other observables investigated at RHIC including di-jets/di- hadrons, charged pions, etc, which give consistent picture while A future eRHIC, would be the ultimate laboratory for detailed studies of QCD and would provide the most stringent constraints on the intrinsic quark, anti-quark, and gluon spin contributions to the spin of the proton Brian Page - CIPANP

Backup Slides Brian Page - CIPANP

Jet Reconstruction Detector GEANT PYTHIA Particle Jet LevelsMC Jets Anti-K T Algorithm: Radius = 0.6 Less sensitive to underlying event and pile-up effects Implemented using FastJet Used in both data and simulation Parton STAR Detector has: Full azimuthal coverage Charged particle tracking from TPC for |η| < 1.3 E/BEMC provide electromagnetic energy reconstruction for -1 < η < 2.0 STAR well suited for jet measurements Brian Page - CIPANP

2006 Inclusive Jet A LL Run 6 data rules out GRSV-Min and GRSV-Max Large gluon polarization in the accessible region disfavored Phys. Rev. D (2012) Brian Page - CIPANP

2006 vs 2009 Inclusive Jet A LL Run 9 results are a factor of 3 or greater more precise than Run 6 results Data falls between DSSV and GRSV-STD Brian Page - CIPANP

DSSV Global Fit de Florian et al., PRL 101, (2008) First global NLO analysis which includes DIS, SIDIS, and RHIC pp data Strong constraint on Δg in the range 0.05 < x < 0.2 Low x range still poorly constrained STAR Brian Page - CIPANP

2009 Di-jet Cross Section Results Thickness of blue box represents error on theory determined by changing factorization and renormalization scales by factor of 0.5 and 2 Thickness of vertical black hashing represents size of statistical error on the measurement Green hatched box is symmetric about data point and is the quadrature sum of all systematic errors 31Brian Page - CIPANP 2015

2009 Di-jet A LL Errors 32 Di-jet statistical and systematic errors shown for two unique topologies and the combination which probe different partonic kinematics Systematics include contributions from JES, residual transverse polarization, and trigger / reconstruction biases Red curve shows 2008 DSSV best fit for A LL and blue curve shows GRSV-STD fit Brian Page - CIPANP 2015

33 PHENIX π + π - A LL Phys. Rev. D 91, (2015)

STAR π + π - A LL In Run 5, STAR measured A LL for inclusive charged pions A LL (π+) - A LL (π-) is sensitive to the sign of ΔG Trigger using neutral jet patch -> Introduces significant trigger bias (charged pions often subleading particles in jets) 34Brian Page - CIPANP 2015

35 eRHIC Layout Luminosity > ~10 33 – cm -2 s -1 (depending on √s)