Marco Stratmann

October 11th, 2007

Global QCD analysis of polarized

PDFs

status & prospects

IWHSS 09 International Workshop on Hadron Structure and Spectroscopy March 30 – April 1, 2009Schloss Waldthausen, Mainz (Germany)

in collaboration withDaniel de Florian, Rodolfo Sassot,Werner Vogelsang

How to determine PDFs from data?

task: extract reliable pdfs not just compare some curves to data

information on nucleon (spin) structure available from

DIS SIDIS hadron-hadron

! a “global QCD analysis” is required

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

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 increases

the relevant DGLAP evolution kernels are known to NLO accuracy:Mertig, van Neerven; Vogelsang

dependence of PDFs is a key prediction of pQCD

verifying it is one of the goals of a global analysis

factorization

allows to separate universal PDFs from

calculable but process-dependent

hard scatterring cross sections

e.g., pp ! X

higher order QCD corrections

essential to estimate/control

theoretical uncertainties

closer to experiment (jets,…)

do not cancel in ALLscale uncertainty

Jäger,MS,Vogelsang

all relevant observables available at NLO accuracy

except for charm/hadron-pair production at COMPASS, HERMESrecent 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 f(x,0) ' x (1-x) at

some initial scale 0 ' 1 GeV

optimum set of parameters {i, i, …}

obtain PDFs at any x, > 0

relevant for comparing with data

compute DIS, pp, …cross sections judge goodness of current fit:

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

• NLO expressions often very complicated ! computing time becomes excessive ! develop sophisticated algorithms & techniques, e.g., based on Mellin moments

• need to determine O(20) parameters describing PDFs at 0

Kosower; Vogt; Vogelsang, MS

DSSV global analysis uses:

semi-inclusive DIS dataso far only used in DNS fit

! flavor separation

“classic” inclusive DIS dataroutinely used in PDF fits

! q + q

first RHIC pp data (never used before)

! g

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! X (PHENIX, …)

global analysis & uncertainty estimates are a recent achievement

DSS fit (de Florian, Sassot, MS)Phys. Rev. D75 (2007) 114010

Phys. Rev. D76 (2007) 074033

no local OPE ! no lattice formulation

• bi-local operator:Collins, Soper ’81, ’83

some properties of Dih(z,) [very similar to PDFs]:

• non-perturbative but universal; pQCD predicts –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 Di

h

DSS: good global fit of all e+e-, ep, and pp hadron data

de Florian, Sassot, MSmain results:

• results for §, K§, chg. hadrons

• full flavor separation for DiH(z) and Dg

H

• 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)

f(x,) not restricted to be positive; nodes possible

“positivity bound” |f(x,)| · f(x,) of limited use (valid only at LO !)

much less data:

• DIS in limited x,Q2 range ! much less constrained gluon

• no N-DIS data ! flavor separation relies on SIDIS data

possible uncertainties from fragmentation

• pp data have to constrain g

(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

input scale

possible nodes

simplified form for sea quarks and g: j = 0

• avoid assumptions on parameters {aj} unless data cannot discriminate

• take s 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

2/d.o.f. ' 0.88

note: for the time being, stat. and syst. errorsare added in quadrature

very good!

no significant tensionamong different data sets

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, …

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 …

unpolarized “reference data” (, jets, ) nicely agree with pQCD

RHIC pp data (inclusive 0 or jet)

good agreement

important constraint

on g(x) despite

large uncertainties! later

uncertainty bands estimatedwith Lagrange multipliers byenforcing other values for ALL

g 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, charmCOMPASS, HERMES

+

if Q2' 0: “photoproduction”

unknown photon structure

Q2 large: “electroproduction”

Q2

theory calculations more challenging than in pp:

NLOpQCD

1-hadron: X Jäger,MS,Vogelsangcharm: X Bojak, MS (direct ) Riedl, Schäfer, MS (resolved & MC)hadron pairs: Hendlmeier, Schäfer, MS (direct ) Jäger,Owens,MS,Vogelsang (resolved )

nothingfor Q2 0

almost done

DSSV gluon agrees well with model-dependent “LO” extractions of g/g

not in global fit[NLO not available]

a future global NLO fit will use measured ALL not derived g/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:

Hessian method: classic tool, explores vicinity of 2-minimum in

quadratic approx.; often unstable for multi-parameter PDF analyses

track 2

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

[reshaped for PDF analyses by J. Pumplin and CTEQ]

issue: what value of 2 (tolerance) defines a 1- error?

• non Gaussian errors, 2 “landscape” not parabolic• uncertainties with diverse characteristics• theor. errors correlated and poorly known• data sets often marginally consistent for 2=1

we present uncertainties bands

for both 2 = 1 and

a more pragmatic 2% increase

in 2

Hessian eigenvector PDF basis sets

• 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 2 = k zk2

cartoon by CTEQ

• 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 cloudThomas, Signal, Cao; Diakonov, Polyakov, Weiss; …

2 profiles for truncated moments:

DSSV sea polarizations – cont’d

a strange strangeness polarization

s(x) always thought to be negative, but …

mainly determined from SIDIS kaon data

consistent with LO-type analyses by

HERMES and COMPASS

x

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 s results in “LO” analyses by HERMES and COMPASS:

HERMES

s0.020.6 S dx = 0.037 0.019(stat.)

0.027(syst.)

COMPASSprel. from SPIN’08

of interest not only for nucleon

structure enthusiasts:

e.g. elastic scattering of SUSY dark matter

arXiv:0801.3656

error estimates more delicate: small-x behavior completely unconstrained

x

study uncertainties in 3 x-regions

RHIC range0.05· x · 0.2

small-x0.001· x · 0.05

large-xx ¸ 0.2

g(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

DSSV gluon polarization

prospects on s final HERMES data sets for SIDIS & DIS multiplicities crucial;

more from COMPASS; can we distinguish s and s in the future?

notoriously difficult in pp: two channels: W+charm (extremely rare probe)

polarized production

issues to be addressed for production:

• reliable NLO sets of Di and Di

• feed-down from hyperon weak decays; effect on polarization?

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

• compute helicity-transfer subprocesses at NLO (work has started)

spin audit: 1st moments and the spin of the proton

“helicity sum rule”

total u+d+s quark spin

gluon spin

angularmomentum

Jaffe, Manohar; Ji; …

“quotable” properties of the nucleon !

total spin polarizations Sq and Sg !helicity parton densities

momentum fraction

s dx

x-moment

1

0

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!

A+ = 0 gauge, IMFpartonic interpretation

Q2 = 10 GeV2

s receives a large negative contribution at small x g: huge uncertainties below x'0.01 ! 1st moment still undetermined

numerical results

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 + 0 data (plus +, -, …)

first di-jet data from STAR ! more precisely map g(x)

X the Mellin technique is

basically in place to analyzealso 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 2 = 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

many avenues for further important measurements and theoretical developments

we have just explored the tip of the iceberg

you are here

Lq,g

s

g

utot, dtot

u, d

spin sum rule