Spin Physics results at HERMES with Longitudinally Polarized

Spin Physics results at HERMES with Longitudinally Polarized Targets Alessandra Fantoni (on behalf of the HERMES Collaboration) 1. The spin puzzle & the HERMES experiment 2. Polarised structure function g 1 3. Flavor decomposition & polarised quark distribution functions 4. New 5 -flavor extraction 5. New isoscalar extraction s 6. High-p. T hadrons, g 7. DVCS for probing GPD’s 8. Hint for Excl. processes International Workshop on Hadron Structure and Spectroscopy (IWHSS ’ 08) with Recoil Detector st nd Torino March 31 –April 02 , 2008

HERa MEasurement of Spin (DESY) 180 Researchers from 30 Institutions of 12 Countries Study of nucleon structure • double spin asymmetries (inclusive, seminclusive) • single spin asymmetries Data taking 1995 -2007 (seminclusive, transversity and exclusive processes)

1. The Nucleon Spin Structure and the HERMES experiment QPM: gluons are important ! G sea quarks: qs EMC 1988: zzle u p n S=0. 123± 0. 094± 0. 138 i p s don’t forget the orbital angular momentum! SLAC, CERN, DESY: S 0. 2 -0. 4 Polarised Deep Inelastic Scattering (DIS)

The Nucleon Structure HERMES: polarised DIS Unpolarised DIS • q from measurements on longitudinally polarised targets √ * √ • dq from measurements on transversely polarised targets • G from measurements on high p. T * • L from exclusive measurements (GPDs) * * first measurements only recently

Characteristiques of the HERMES experiment 27. 5 Ge. V (e+/e-) <Pb>~ 53± 2. 5 % Stern-Gerlach separation • resolution: dp/p~2%, dq<1 mrad • PID: leptons with e~98%, contam. <1% hadrons dual RICH: p, K, p 2<Eh<15 Ge. V 1 H→ <|P |> ~ 85 % t 2 H→ <|P |> ~ 84 % t 1 H <|Pt|> ~ 74 % gaseus atomic target, high polarisation, non diluited

2. Polarised Structure Functions g 1 [HERMES Collaboration PRD 75 (2007)] HERMES data set precise and complete

Polarised Structure Functions: g 1 [Q 2>1 Ge. V 2 data only] Use only deuteron data! MS assume saturation of S = G 1 d : theory from hyperon beta decay MS(a 8=0. 586± 0. 031) a 0= S (theory) x (exp) (evol) = 0. 330 ± 0. 011 ± 0. 025 ± 0. 028 ωD=0. 05± 0. 05 theory

q and G from inclusive data • uv and dv (quite) well determined: uv >0, dv <0 • q and G weakly constraint by data

How to further proceed ? • q and G from inclusive DIS data via evolution equations : requires wide kinematic range in Q 2 and x only fixed target spin experiments so far … need polarised collider to extend kinematic coverage OR: need more direct probes unpolarised DIS

Polarised semi-inclusive DIS Flavor tagging p+ ud K- p- Partonic Distribution Function (PDF) us ud Fragmentation Function (FF) z=Eh/(E-E’)

3. Polarised Quark Distribution Functions Polarised Parton Distribution Functions qf(x)=q+(x)-q-(x) Hadronic asymmetries to be measured known quantities Purity Functions

Polarised Quark Distribution Functions [HERMES Coll. PRL 92(2004), PRD 71(2005)] First measurements of q by flavour decomposition

Polarised Quark Distribution Functions [HERMES Coll. PRL 92(2004), PRD 71(2005)] u quarks: large positive polarisation d quarks: negative polarisation - sea quarks (u, d, s, s): compatibile with 0 First direct 5 -flavor separation of polarised PDFs

4. Future: 5 -Flavor q(x) Extraction Revisited There’s still room for improvement: • Statistical uncertainties Not all possible asymmetries were utilized. Some may have significant leverage over the sea quarks (ks) • Systematic uncertainties The published Monte Carlo related systematic uncertainty was “hopefully conservative”. Confirm rigorously Potentially reduce!

Comparison of Uncertainties of Old and New Asymmetries: 2 -4 Ge. V deuterium gives additional pions and kaons Additional asymmetries available: Proton Deuteron Target HH+, HHP, P Ks, p 0, and L • Published • New

Correlating MC tune and q(x) systematic uncertainty 68% Contour Best MC Tune 1. Scan 2 surface around best Monte Carlo tune. Fit with quadratic Polynomial. 2. Find 68% contour. Two factors: c 2 • Height of 68% of ddimensional Gaussian Distribution. 2 min+C • The height of 2 minimum to accommodate model imperfection. PDG does something like this. pa parj a rj b 2 min 3. Compute Dq(x) along contour: Use Hessian method to sample along uncorrelated parameter directions. CTEQ does something like this. Puritie s Dq(x)

In reality… Scan the 2 surface around the best Monte Carlo tune. • Correlations are quite clear between parameters • Generate and diagonalize the matrix of 2 nd derivatives to find linear combinations that are uncorrelated Jetset/Lund c 2 surface in Fragmentation Parameter Basis • Blue ellipses represent 68% contour • Colored lines represent uncorrelated parameter directions

MC Multiplicities • Black dots are generated at the best Monte Carlo tune. • Colored dots are generated at the 68% contour in the uncorrelated parameter directions • 9 Hessian vectors 18 parameter sets to include So, where are the new q(x) uncertainties? ! Results not yet released, but should be greatly reduced (>50% in some bins).

5. New “Isoscalar” extraction of S [HERMES Collaboration ar. Xiv: 0803. 2993 submitted to Phys. Rev. Lett. ]

Isoscalar extraction - formalism

Isoscalar Formalism – cont’d

Extraction of ∫D(z)dz ’s Multiplicity corrected to 4 p of charged kaons in SIDIS from D target Curves: Continuous = calculated from x. S(x) Dashed = non-strange quark contribution to multiplicity Dash-dotted = strange quark contribution to multiplicity Dotted = best fit of ∫ D(z)dz using CTEQ 6 L PDFs 0. 2<z<0. 8

Experimental inclusive and kaon spin asymmetries Lepton-nucleon polarised cross section asymmetries A||, d(x) for inclusive DIS and A||, d. K(x) for SIDIS by a D target as a function of x for identified charged kaons Kaon asymmetry small and “slightly” positive

Non strange & quark helicity distributions 0. 02<xbj <0. 6 measured range Q 02 = 2. 5 Ge. V 2 a 8=∫ q 8=0. 586± 0. 031 from hyperon b decay assuming SU(3) deficit: violation First moments of helicity distributions: SU(3) symmetry or error octet Q = 0. 359 ± 0. 026∫ ±S(x)dx 0. 018 is 0 withinmissing strength at x below Earlier HERMES conclusions S = 0. 037 ± 0. 019 ± 0. 027 measured range of unpolarised sea confirmed q 8 = Q – 2 S = 0. 285 ± 0. 046 ± 0. 057

6. High p. T hadrons and sensitivity to g First HERMES g/g measurement [HERMES Collaboration, Phys. Rev. Lett. 84 (2000) 2584] Top cite 100+ First longitudinal double spin asymmetries for 2 hadrons Historical plot : first HERMES data and future projections

g/g extraction: methods I and II • Method I: – Factorize – Assumes • No sign change in â(x) • “flat” g/g(x) – No information on <x> of measurement – Gives average g/g over covered x range (0. 07<x<0. 7) • Method II: – Fit: find a g/g(x) such that – Assumes functional form for g/g(x) – Only small range in p. T – Gives g/g(x) and average x of measurement

G from method I Assuming g(x)/g(x) const over x : h+, h- antitagged: 4 points between 1. 05<p. T<2. 5 Ge. V h+, h- tagged: 1 point for p. T>1 Ge. V Pairs: 1 point for Ge. V 2 Only statistical errors are shown • Results for different data samples (diff. mixtures) agree within statistics • Consistency between the two hadron charges and the two targets • Dominating sample: Deuteron antitagged -> Used for Method II and syst. error analysis (charge combined)

G from method II (Anti-tagged only) • Several test functions • Final 2 functions used are polynomials with 1(2) free parameters • Fix: - g/g x for x 0 - g/g 1 for x 1 • | g/g(x)|<1 for all x • Difference between functions is a systematic uncertainty • Light shaded area: range of all data • Dark shaded area: fit center of gravity (span of the 4 pt bins)

G from method II 2/ndf 5 mainly due to highest p. T point • Model systematic is not included in fit • 1 -2 parameter function is too smooth • function 1 used as default and function 2 for systematics

Model systematic PYTHIA 6. 2 has been tuned: • fair agreement in tagged region (see plot vs kinematic variables) • less agreement in anti-tagged region • some failures in pt dependence • checks with LO p. QCD (collinear) • Uncertainties from each group (PYTHIA params. / PDFs / low-p. T asym. ) summed linearly to “Models” uncertainty • Experimental (stat. +syst. ) added in quadrature: syst. uncertainty (beam&target) from 4% scaling uncertainty to 14% on g/g

g/g results vs world data • Black and blue curves: p. QCD fits to g 1 • Black data points: CERN exp results • Red data point: Prel. HERMES Method I • Red curves: Prel. HERMES Method II: fit Δg(x)/g(x) with 2 functions such that g/g=0. 071 ± 0. 034 ± 0. 010 [HERMES Coll. Paper in progress]

7. GPDs and Exclusive Processes Q 2>>, t<< Q 2 • high Q 2 hard regime • high luminosity s~1/Q 4, 1/Q 6 • high resolution exclusivity t Quantum number of final state selects different GPDs: Vector mesons (r, w, f): H E ~ ~ Pseudoscalar mesons (p, h): H E ~ ~ DVCS (g) depends on H, E, H, E polarisation provides new observables sensitive to different (combinations) GPDs

Exclusive processes at HERMES e+/e 27. 5 Ge. V No recoil particle identification Identification exclusive events by missing mass Mx : …background estimated by MC

Deeply Virtual Compton Scattering (DVCS) A R HE t ly a Beam Spin Asymmetry on Beam Charge Asymmetry azimuthal asymmetries [HERMES Coll. PRL 87(2001)] Top cite 100+ [HERMES Coll. PRD 75 (2007)]

[HERMES Collaboration ar. Xiv: 0802. 2499 submitted to JHEP]

Exclusive processes at HERMES > 2006 e+/e 27. 5 Ge. V Statistics with Recoil larger than pre-Recoil data taking With Recoil, DVCS events measured directly, bkgr rejected Installed Dec 05, commissioned and Pre-Recoil results can be later refined fully working Dedicated to exclusive processes New results expected soon 2006: 7 M DIS events e 20 M DIS events e+ 2007: 20 M DIS events e+

Conclusions • Inclusive data analysis on g 1 completed • Results from semi-inclusive DIS from purity analysis • Idea of new 5 -flavor extraction Takes full advantage of the HERMES longitudinal target data statistical power by incorporating many new asymmetries. Addresses (and will reduce considerably!) Monte Carlo related systematic uncertainties in a rigorous way. • New Isoscalar Extraction of s(x) Excellent confirmation of Monte Carlo based 5 -flavor extraction Suggests exciting new physics for s(x) in the x<0. 02 range • High-p. T hadrons with sensitivity to g • Possibility to probe GPD’s with Longitudinal and Transverse pol. targets • First hint for future Exclusive Results with Recoil Detector