Global QCD analysis of polarized PDFs status & prospects October 11th, 2007 IWHSS 09 International Workshop on Hadron Structure and Spectroscopy March 30 – April 1, 2009 Schloss Waldthausen, Mainz (Germany) Global QCD analysis of polarized PDFs status & prospects Marco Stratmann in collaboration with Daniel de Florian, Rodolfo Sassot,Werner Vogelsang

How to determine PDFs from data? information on nucleon (spin) structure available from DIS SIDIS hadron-hadron task: extract reliable pdfs not just compare some curves to data each reaction provides insights into different aspects and kinematics all processes tied together: universality of pdfs & Q2 - evolution need at least NLO for quantitative analyses; PDFs are not observables! information on PDFs “hidden” inside complicated (multi-)convolutions ! a “global QCD analysis” is required

PDFs data the charge: analyze a large body of data from many experiments on different processes with diverse characteristics and errors within a theoretical model with many parameters and hard to quantify uncertainties without knowing the optimum “ansatz” a priori

details & results of the DSSV global analysis toolbox comparison with data uncertainties: Lagrange multipliers vs. Hessian emerging picture next steps Global analysis of helicity parton densities and their uncertainties, PRL 101 (2008) 072001 (arXiv:0804.0422 [hep-ph])

theory “toolbox” QCD scale evolution due to resolving more and more parton-parton splittings as the “resolution” scale m increases the relevant DGLAP evolution kernels are known to NLO accuracy: Mertig, van Neerven; Vogelsang m - dependence of PDFs is a key prediction of pQCD verifying it is one of the goals of a global analysis

allows to separate universal PDFs from factorization e.g., pp ! p X allows to separate universal PDFs from calculable but process-dependent hard scatterring cross sections higher order QCD corrections essential to estimate/control theoretical uncertainties closer to experiment (jets,…) do not cancel in ALL scale uncertainty Jäger,MS,Vogelsang all relevant observables available at NLO accuracy except for charm/hadron-pair production at COMPASS, HERMES recent progress for Q2 ' 0 ! later

outline of a global QCD analysis start: choose fact. scheme (MS,…) & pert. order (NLO, …), select data sets, cuts, … parametrize quark and gluon PDFs a la Df(x,m0) ' xa (1-x)b at some initial scale m0 ' 1 GeV obtain PDFs at any x, m > m0 relevant for comparing with data compute DIS, pp, …cross sections judge goodness of current fit: optimum set of parameters {ai, bi, …} recent achievement: also quantify PDF uncertainties and properly propagate them to any observable of interest

global analysis: a computational challenge one has to deal with O(500) data points from many processes and experiments need to determine O(20) parameters describing PDFs at m0 NLO expressions often very complicated ! computing time becomes excessive ! develop sophisticated algorithms & techniques, e.g., based on Mellin moments Kosower; Vogt; Vogelsang, MS DSSV global analysis uses: “classic” inclusive DIS data routinely used in PDF fits ! Dq + Dq semi-inclusive DIS data so far only used in DNS fit ! flavor separation first RHIC pp data (never used before) ! Dg 467 data pts in total (¼10% from RHIC)

interlude: fragmentation functions crucial for pQCD interpretation (factorization!) of data with detected hadrons, e.g., SIDIS (HERMES, COMPASS), pp! pX (PHENIX, …) no local OPE ! no lattice formulation bi-local operator: Collins, Soper ’81, ’83 some properties of Dih(z,m) [very similar to PDFs]: non-perturbative but universal; pQCD predicts m–dep. describe the collinear transition of a parton “i” into a massless hadron “h” carrying fractional momentum z quark/gluon hadron z k k “leading particle” picture incompatible with inclusive definition of Dih global analysis & uncertainty estimates are a recent achievement DSS fit (de Florian, Sassot, MS) Phys. Rev. D75 (2007) 114010 Phys. Rev. D76 (2007) 074033

DSS: good global fit of all e+e-, ep, and pp hadron data main results: de Florian, Sassot, MS results for p§, K§, chg. hadrons full flavor separation for DiH(z) and DgH uncertainties (L.M.) well under control fits all LEP, HERMES, SMC, RHIC, … data supersede old fits based only on e+e- data

How can we use all this in a global PDF fit? several crucial differences w.r.t. an unpolarized fit: no sum rule which relates quarks and gluons (unpolarized: momentum sum) Df(x,m) not restricted to be positive; nodes possible “positivity bound” |Df(x,m)| · f(x,m) of limited use (valid only at LO !) much less data: DIS in limited x,Q2 range ! much less constrained gluon no nN-DIS data ! flavor separation relies on SIDIS data possible uncertainties from fragmentation pp data have to constrain Dg (more complicated to analyze than DIS scaling violations)

details & results of the DSSV global analysis toolbox comparison with data uncertainties: Lagrange multipliers vs. Hessian the emerging picture next steps

setup of DSSV analysis flexible, MRST-like input form possible nodes input scale simplified form for sea quarks and Dg: kj = 0 avoid assumptions on parameters {aj} unless data cannot discriminate take as from MRST; also use MRST for positivity bounds NLO fit, MS scheme need to impose: let the fit decide about F,D value constraint on 1st moments: 1.269§0.003 fitted (end up close to zero) 0.586§0.031

overall quality of the global fit very good! no significant tension among different data sets c2/d.o.f. ' 0.88 note: for the time being, stat. and syst. errors are added in quadrature

spin asymmetries in inclusive DIS [DNS: old analysis by de Florian, Navarro, Sassot] we account for kinematical “mismatches” in no need for any dynamical higher twist (contrary to Leader et al.)

spin asymmetries in semi-inclusive DIS impact of new FFs noticeable!

detour: DSS kaon FF’s DiK(z) RHIC pp data (BRAHMS, STAR) explain different Dg smaller u & larger s-frag. required by SIDIS note: some issues with K- data (slope!) await eagerly final HERMES data

gluons are key players at RHIC many QCD processes with a dominant gluon contribution already at the tree-level: high-pT jet, pion, heavy quark, … unpolarized “reference data” (p, jets, g) nicely agree with pQCD Jäger,MS,Vogelsang; Signer et al. Jäger,Schäfer,MS, Vogelsang; de Florian Bojak,MS; Riedl,Schäfer,MS Gordon,Vogelsang; Contogouris et al. all available at NLO decisive data start to emerge from RHIC …

RHIC pp data (inclusive p0 or jet) good agreement important constraint on Dg(x) despite large uncertainties ! later uncertainty bands estimated with Lagrange multipliers by enforcing other values for ALL

Dg in lepton-proton scattering gluons in DIS: a (small) NLO effect [they don’t couple directly to the photon] ! study processes sensitive to photon-gluon-fusion final states explored (data !!): one/two hadron production, charm COMPASS, HERMES Q2 large: “electroproduction” Q2 theory calculations more challenging than in pp: + if Q2' 0: “photoproduction” unknown photon structure NLO pQCD 1-hadron: X Jäger,MS,Vogelsang charm: X Bojak, MS (direct g) Riedl, Schäfer, MS (resolved g & MC) hadron pairs: Hendlmeier, Schäfer, MS (direct g) Jäger,Owens,MS,Vogelsang (resolved g) nothing for Q2 ¹ 0 almost done

DSSV gluon agrees well with model-dependent “LO” extractions of Dg/g not in global fit [NLO not available] a future global NLO fit will use measured ALL not derived Dg/g need to check unpolarized cross section as well

details & results of the DSSV global analysis toolbox comparison with data uncertainties: Lagrange multipliers vs. Hessian emerging picture next steps

estimating PDF uncertainties mainly two methods in use: [reshaped for PDF analyses by J. Pumplin and CTEQ] Hessian method: classic tool, explores vicinity of c2-minimum in quadratic approx.; often unstable for multi-parameter PDF analyses track c2 Lagrange multiplier: track how the fit deteriorates when PDFs are forced to give different predictions for selected observables; explores the full paramater space indep. of approximations issue: what value of Dc2 (tolerance) defines a 1-s error? non Gaussian errors, c2 “landscape” not parabolic uncertainties with diverse characteristics theor. errors correlated and poorly known data sets often marginally consistent for Dc2=1 we present uncertainties bands for both Dc2 = 1 and a more pragmatic 2% increase in c2

Hessian eigenvector PDF basis sets cartoon by CTEQ eigenvectors provide an optimized orthonormal basis near the minimum construct 2Npar eigenvector basis sets Sk§ by displacing each zk by § 1 the “coordinates” are rescaled such that Dc2 = åk zk2 sets Sk§ can be used to calculate uncertainties of observables Oi we will make 40 DSSV eigenvector sets available very soon

details & results of the DSSV global analysis toolbox comparison with data uncertainties: Lagrange multipliers vs. Hessian emerging picture next steps

DSSV sea polarizations indications for an SU(2) breaking of light u,d sea breaking of similar size than in unpol. case mainly determined by SIDIS data “bands”: error estimate from Lagr. mult. similar patterns in many models: large-NC, chiral quark soliton, meson cloud Thomas, Signal, Cao; Diakonov, Polyakov, Weiss; … c2 profiles for truncated moments:

DSSV sea polarizations – cont’d x a strange strangeness polarization Ds(x) always thought to be negative, but … mainly determined from SIDIS kaon data consistent with LO-type analyses by HERMES and COMPASS needs further studies – exp. & theory ! striking result, but relies on kaon fragmentation more data available soon (BELLE, …) unpolarized PDFs unpol. strangeness not well determined

similar Ds results in “LO” analyses by HERMES and COMPASS: s0.020.6 DS dx = 0.037 0.019(stat.)  0.027(syst.) COMPASS prel. from SPIN’08

of interest not only for nucleon structure enthusiasts: e.g. elastic scattering of SUSY dark matter arXiv:0801.3656

DSSV gluon polarization error estimates more delicate: small-x behavior completely unconstrained x study uncertainties in 3 x-regions RHIC range 0.05· x · 0.2 small-x 0.001· x · 0.05 large-x x ¸ 0.2 Dg(x) very small at medium x (even compared to GRSV or DNS) best fit has a node at x ' 0.1 huge uncertainties at small x find

prospects on Ds final HERMES data sets for SIDIS & DIS multiplicities crucial; more from COMPASS; can we distinguish Ds and Ds in the future? notoriously difficult in pp: two channels: W+charm (extremely rare probe) polarized L production issues to be addressed for L production: reliable NLO sets of DiL and DDiL DSV: de Florian, MS, Vogelsang, PRD 57 (1998) 5811 updated global analysis required, Dg too small (STAR data) AKK: Albino et al., arXiv:0803.2768v2 DSV: de Florian, MS, Vogelsang, PRD 57 (1998) 5811 sparse data; 3 models considered; update desirable feed-down from hyperon weak decays; effect on polarization? compute helicity-transfer subprocesses at NLO (work has started)

spin audit: 1st moments and the spin of the proton “helicity sum rule” Jaffe, Manohar; Ji; … A+ = 0 gauge, IMF partonic interpretation total u+d+s quark spin gluon spin angular momentum “quotable” properties of the nucleon ! total spin polarizations Sq and Sg ! helicity parton densities momentum fraction s dx x-moment 1 nothing is known yet about Lq and Lg lattice results for “angular momentum” are for a “different” sum rule (Ji’s version) w/o partonic interpretation – they cannot be mixed!

! case for a high-energy polarized ep-collider numerical results Q2 = 10 GeV2 Ds receives a large negative contribution at small x Dg: huge uncertainties below x'0.01 ! 1st moment still undetermined very difficult to give reliable estimates for full moments both quark and gluons may not contribute much to proton spin but we need to go to smaller x to settle this issue ! case for a high-energy polarized ep-collider

details & results of the DSSV global analysis toolbox comparison with data uncertainties: Lagrange multipliers vs. Hessian emerging picture next steps

getting ready to analyze new types of data from the next long RHIC spin run with O(50pb-1) and 60% polarization significantly improve existing inclusive jet + p0 data (plus p+, p-, …) first di-jet data from STAR ! more precisely map Dg(x) X the Mellin technique is basically in place to analyze also particle correlations challenge: much slower MC-type codes in NLO than for 1-incl. from 2008 RHIC spin plan

planning ahead: the 500GeV RHIC W-boson program just started flavor separation independent of SIDIS ! important x-check of present knowledge implementation in global analysis (Mellin technique) still needs to be done available NLO codes (RHICBos) perhaps too bulky; new results emerging de Florian, Vogelsang would be interesting to study impact with some simulated data soon further improving on uncertainties Lagrange multipliers more reliable than Hessian with present data Hessian method perhaps useful for Dc2 = 1 studies, beyond ?? include experimental error correlations if available work started together with help from the RHIC Spin Collaboration (aiming at a CTEQ-like collaboration of theory and experiment)

conclusions we have just explored the tip of the iceberg you are here Dutot, Ddtot Du, Dd Dg many avenues for further important measurements and theoretical developments Ds Lq,g spin sum rule