1. James L. Drachenberg For the STAR Collaboration October 1, 2013 OUTLINE Introduction Event Selection Analysis Description Systematic Uncertainties Preliminary Results Conclusions Transverse Single-spin Asymmetries from p ↑ + p jet + X and p ↑ + p jet + π ± +X at √s = 500 GeV at RHIC STAR

2. Contributions to Proton Spin Structure Consider proton moving right Δq(x) Δg(x) Proton spin   Spin sum rule: Polarized DIS: ~ 0.3 coming into focus: h 1 (x) Proton spin    Transversity – data over limited kinematic range: x Bj ≤ 0.3 1 Transverse-spin Jet Asymmetries - Drachenberg poorly constrained arXiv:nucl-ex/1304.0079

3. 2 Transverse-spin Jet Asymmetries - Drachenberg Separate Sivers and Collins: Go beyond inclusive production - e.g. Jets, correlations, direct photons Sivers ~ sin(φ S )Collins ~ sin(φ S -φ h ) φ S —angle between spin and event planeφ h —angle of hadron around jet axis Sensitivity to Orbital Motion and Transversity? S P ⋅ (p × k T,parton ) ≠ 0 S q ⋅ (p × k T,π ) ≠ 0 Sivers mechanism: asymmetry in the forward jet or γ production SPSP k T,parton p p Collins mechanism: asymmetry in the forward jet fragmentation SPSP p p SqSq k T, π Sensitive to proton spin – parton transverse motion correlations (needs L z ) Sensitive to transversity ( h 1 ) π ± Kinematic Variables z = p π / p jet j T (k T, π ) = π p T relative to jet axis

4. Transverse Jet Asymmetries 3 Transverse-spin Jet Asymmetries - Drachenberg ΦhΦh –p beam p beam S⊥S⊥ pπpπ P JET jTjT ΦSΦS F. Yuan, PRL 100, 032003 (2008) D’Alesio et al., PRD 83, 034021 (2011) Transverse Momentum Dependent (TMD) Approach Asymmetry moments sensitive to various contributions (analogous moments sensitive to gluon scattering) A UT – Transverse single-spin asymmetry (also written A N ) Transversity Boer-Mulders FF Pretzelocity Boer-Mulders FF Sivers Boer-Mulders Collins

5. Transversity Boer-Mulders FF Pretzelocity Boer-Mulders FF Sivers Boer-Mulders Collins Transverse Jet Asymmetries 4 Transverse-spin Jet Asymmetries - Drachenberg ΦhΦh –p beam p beam S⊥S⊥ pπpπ P JET jTjT ΦSΦS F. Yuan, PRL 100, 032003 (2008) D’Alesio et al., PRD 83, 034021 (2011) Transverse Momentum Dependent (TMD) Approach Asymmetry moments sensitive to various contributions (analogous moments sensitive to gluon scattering) A UT – Transverse single-spin asymmetry (also written A N )

6. Phys. Rev. D 86 32006 (2012) STAR Transverse Jet Asymmetries at Central Pseudorapidity 5 Transverse-spin Jet Asymmetries - Drachenberg STAR measured transverse single-spin asymmetries for inclusive jet production at central pseudorapidity and √s = 200 GeV (2006) : consistent with zero : hints of non-zero asymmetry with charge-sign dependence Similarly, di-jet and π 0 A N at central psuedorapidity and 200 GeV consistent with zero PRL 99, 142003, PRL. 95, 202001, arXiv:hep-ex/1108.0911 R. Fersch, DNP2011 Collins Asymmetry A ≣ 2 vs. j T Collins Asymmetry A ≣ 2 vs. z 0.2 0.4 0.6 0.8 z -0.1 0.1 2 10 -1 1 10 j T (GeV)

7. STAR Transverse Jet Asymmetries at Central Pseudorapidity 6 Transverse-spin Jet Asymmetries - Drachenberg 2012 STAR data provide opportunity for higher precision and greatly reduced systematic uncertainties at √s = 200 GeV 2011 STAR data provide opportunity for first measurements of central pseudorapidity inclusive jet asymmetries at √s = 500 GeV  Increased sensitivity to gluonic subprocesses p T [GeV/c] Aschenauer, JLab UGM 2013 R. Fersch, DNP2011

8. Moments of Jet Asymmetries at 500 GeV 7 Transverse-spin Jet Asymmetries - Drachenberg Various contributions to polarized jet+π cross section (TMD approach) Phys. Rev. D 83, 034021 (2011)

9. Moments of Jet Asymmetries at 500 GeV 8 Transverse-spin Jet Asymmetries - Drachenberg Negligible under maximized scenario! Various contributions to polarized jet+π cross section (TMD approach)

10. Phys. Rev. D 83, 034021 (2011) Moments of Jet Asymmetries at 500 GeV 9 Transverse-spin Jet Asymmetries - Drachenberg Possible non-zero contributions, expected to be quite small e.g. Phys. Rev. Lett. 95, 202001 (2005); Phys. Rev. Lett 99, 142003 (2007); Phys. Rev. D 86, 032006 (2012); arXiv:hep-ex/1108.0911 projections for √s = 500 GeV D’Alesio et al. Various contributions to polarized jet+π cross section (TMD approach)

11. Moments of Jet Asymmetries at 500 GeV 10 Transverse-spin Jet Asymmetries - Drachenberg “Collins-like” asymmetry: Sensitive to linearly polarized gluons Completely unconstrained! Phys. Rev. D 83, 034021 (2011) Maximized contribution for √s = 500 GeV D’Alesio et al. Various contributions to polarized jet+π cross section (TMD approach) Gluon helicity density matrix Off-diagonal terms related to linear polarization in (xy) plane at angle φ to x-axis Phys Rev. D 73, 014020 (2006)

12. Solenoidal Tracker at RHIC 11 Transverse-spin Jet Asymmetries - Drachenberg Jet reconstruction utilizes TPC + Barrel + Endcap EMC Minbias Trigger: coincidence in vertex position detector (VPD) -Pb+plastic scintillator with PMT readout -570 cm from interaction point -4.24 < |η| < 5.1, J. Zhou, M.S. Thesis

13. Jet Reconstruction in STAR 12 Transverse-spin Jet Asymmetries - Drachenberg Anti-k T algorithm JHEP 0804, 063 (2008) Radius parameter R = 0.6 Use PYTHIA + GEANT to quantify detector response STAR Di-jet event at detector-level     e-e- e+e+ Detector GEANT PYTHIA Data jets MC jets Particle Parton π ± Kinematic Variables z – π momentum / jet momentum j T – π p T relative to jet axis

14. 2011 STAR Event Selection 13 Transverse-spin Jet Asymmetries - Drachenberg Center of mass energy, √s = 500 GeV Total integrated luminosity of 25 pb -1 for all transverse runs Polarization for present analysis: 54±3% Good event vertex with |z vertex | < 30 cm Jet Reconstruction: -N hits, track > 12 -Track association with event vertex -Minimum track p T > 0.2 GeV/c -Minimum tower energy > 0.2 GeV Jet requirements: -No charged particles with p T > 30 GeV/c -Total charged-particle p T > 0.5 -Neutral-energy fraction < 0.98 -|η jet | < 1.0 (and within detector acceptance of BEMC+TPC) -6 < p T,jet < 55 GeV/c Pion Requirements: -Restriction on dE/dx: -1 < n σ (π) < 2.5 (contamination < 3%) -(η jet -η ch ) 2 + (φ jet -φ ch ) 2 > (0.1) 2 -N hits, dE/dx > 5

15. Studies with Embedded Monte Carlo 14 Transverse-spin Jet Asymmetries - Drachenberg Systematic shifts in reconstructed kinematic variables and azimuthal resolutions evaluated by comparing to Monte Carlo embedded in real zero-bias data simulate effects of real, out-of-time pile-up Detector-level jets matched both to parton and particle jets with matched event vertex Kinematic shifts evaluated at particle level Corresponding parton-jet p T ~ 0.6-1.4 GeV/c lower jet p T track z track j T

16. Sources of Systematic Uncertainty 15 Transverse-spin Jet Asymmetries - Drachenberg Pion contamination < 3% Dominant systematic uncertainty from reconstructed jets unassociated with parton jets  Take difference between measured A UT and A UT assuming dilution Further systematic uncertainties: Resolution of relevant azimuthal angles  corrected as dilution to measured asymmetry “leak-through” of other moments of A UT Pion contamination from K/p and e ± (< 3%) Polarization uncertainty (correlated vertical scale uncertainty, σ(P)/P = 5.6%) Angular resolution corrected as dilution

17. Asymmetry Measurements 16 Transverse-spin Jet Asymmetries - Drachenberg For uniform acceptance: α and β yields are functions of integrated over half of detector

18. Estimating Leak-through Systematic 17 Transverse-spin Jet Asymmetries - Drachenberg Acceptance inefficiencies can allow non-zero effects to “leak through” and distort desired observable Quantify distortion by event-weighting unpolarized data yields and calculating resulting asymmetries Reasonable acceptance + small observed asymmetries  Small upper-limits on “leak-through” systematic 0.2 < z reco < 0.3 Assuming 10% Sivers asymmetry For 10%, upper-limit ~ 0.0021 For 2%, upper-limit ~ 0.0004

19. Sivers Asymmetries 18 Transverse-spin Jet Asymmetries - Drachenberg No sign of sizable azimuthal asymmetry in jet production at √s = 500 GeV Consistent with expectation from inclusive jets, di-jets, and neutral pions at √s = 200 GeV Asymmetries shown as function of particle-jet p T Corresponding parton-jet p T lower by 0.6-1.4 GeV/c Horizontal errors include uncertainties from statistics, calorimeter gains, efficiencies, track momentum, and tracking efficiency p T [GeV/c]

20. Sivers Asymmetries 19 Transverse-spin Jet Asymmetries - Drachenberg Measured asymmetries shown in η-bins No sign of sizable asymmetry Asymmetries shown as function of particle-jet p T Corresponding parton-jet p T lower by 0.6-1.4 GeV/c Horizontal errors include uncertainties from statistics, calorimeter gains, efficiencies, track momentum, and tracking efficiency p T [GeV/c]

21. Collins Asymmetries 20 Transverse-spin Jet Asymmetries - Drachenberg Increased gluonic subprocesses at √s = 500 GeV lead to expectation of small Collins asymmetry until larger z Present data do not have sufficient statistics at high-z to observe Collins asymmetry of order 1% D’Alesio et al.

22. Collins Asymmetries 21 Transverse-spin Jet Asymmetries - Drachenberg Present model predictions expect negligible effects for A UT vs. j T integrated over z > 0.1 Measured asymmetries shown for x F > 0 (i.e. 0 < η jet < 1) in z-bins No sign of non-zero asymmetry as a function of j T or jet p T Similarly, no sign of positive effect for backward region (x F < 0), as expected

23. Collins-like Asymmetries 22 Transverse-spin Jet Asymmetries - Drachenberg Maximized contribution for √s = 500 GeV Model predictions shown for “maximized” effect, saturated to positivity bound Until now, Collins-like asymmetries completely unconstrained  Sensitive to linearly polarized gluons D’Alesio et al.

24. Collins-like Asymmetries 23 Transverse-spin Jet Asymmetries - Drachenberg Measured asymmetries shown for -1 < η < 1 in z-bins Consistently below 2% maximum from model D’Alesio et al.

25. Collins-like Asymmetries 24 Transverse-spin Jet Asymmetries - Drachenberg Similarly, no large effect observed as a function of jet p T Measured asymmetries shown for -1 < η < 1 in z-bins

26. Summary 25 Transverse-spin Jet Asymmetries - Drachenberg STAR data from 2011 provide first measurements of transverse spin asymmetries for jet production at central pseudorapidity and √s = 500 GeV

27. Summary 26 Transverse-spin Jet Asymmetries - Drachenberg STAR data from 2011 provide first measurements of transverse spin asymmetries for jet production at central pseudorapidity and √s = 500 GeV Increased gluonic subprocesses at √s = 500 GeV provide unique sensitivity to Collins-like asymmetry from linearly polarized gluons

28. Summary 27 Transverse-spin Jet Asymmetries - Drachenberg STAR data from 2011 provide first measurements of transverse spin asymmetries for jet production at central pseudorapidity and √s = 500 GeV Increased gluonic subprocesses at √s = 500 GeV provide unique sensitivity to Collins-like asymmetry from linearly polarized gluons No observation of large asymmetry from gluon Sivers effect, consistent with expectations from previous measurements of jet and π 0 asymmetries at √s = 200 GeV

29. Summary 28 Transverse-spin Jet Asymmetries - Drachenberg STAR data from 2011 provide first measurements of transverse spin asymmetries for jet production at central pseudorapidity and √s = 500 GeV Increased gluonic subprocesses at √s = 500 GeV provide unique sensitivity to Collins-like asymmetry from linearly polarized gluons No observation of large asymmetry from gluon Sivers effect, consistent with expectations from previous measurements of jet and π 0 asymmetries at √s = 200 GeV No observation of large asymmetry from Collins effect, consistent with expectations from decreased quark subprocesses at √s = 500 GeV

30. Summary 29 Transverse-spin Jet Asymmetries - Drachenberg STAR data from 2011 provide first measurements of transverse spin asymmetries for jet production at central pseudorapidity and √s = 500 GeV Increased gluonic subprocesses at √s = 500 GeV provide unique sensitivity to Collins-like asymmetry from linearly polarized gluons No observation of large asymmetry from gluon Sivers effect, consistent with expectations from previous measurements of jet and π 0 asymmetries at √s = 200 GeV No observation of large asymmetry from Collins effect, consistent with expectations from decreased quark subprocesses at √s = 500 GeV First measurements of Collins-like asymmetries will help place constraints on model predictions beyond maximal projections from positivity bounds

31. Looking Forward 30 Transverse-spin Jet Asymmetries - Drachenberg Additional data from 2011 jet-patch triggers will allow much greater precision for higher jet p T (above 7 GeV/c) High precision measurements from 2012 at √s = 200 GeV will allow greater sensitivity to effects from quark subprocesses STAR Preliminary Results at √s = 500 GeV Sivers AsymmetriesCollins AsymmetriesCollins-like Asymmetries