The QCD structure of the nucleon

The QCD structure of the nucleon

P.J. MuldersVrije Universiteit

Amsterdam

[email protected]

FrascatiMay 2003

Universality of T-odd effects in single spin and azimuthal asymmetries, D. Boer, PJM and F. Pijlman, hep-ph/0303034

19/20 May 2003 Frascati p j mulders 2

Content Introduction: From global view to quarks Observables in (SI)DIS in field theory language lightcone/lightfront correlations

Single-spin asymmetries in hard reactions T-odd correlations

T-odd observables in final (fragmentation) and initial state (distribution) correlations

Structure functions and parton densities Universality of T-odd phenomena


Introducing the nucleon: from global view to quarks


Global properties of nucleons

mass charge spin magnetic moment isospin,

strangeness baryon number

Mp Mn 940 MeV

Qp = 1, Qn = 0 s = ½ gp 5.59, gn -

3.83 I = ½: (p,n) S =

0 B = 1


A real look at the proton

+ N ….

Nucleon excitation spectrumE ~ 1/R ~ 200 MeVR ~ 1 fm


A virtual look at the proton N N + N N

_


Spacelike form factor global density

charge

current


Nucleon e.m. form factors

GEp GMp/p GMn/n Gdipole

Gdipole = (1+Q2/2)-2

2 = 0.71 GeV2


Nucleon form factors

Present-day status (TJNAF)


Nucleon densities

proton neutron

• charge density 0• u more central than d?• role of antiquarks?• n = n0 + p+ … ?


Another (weak) look at the nucleon

n p + e +

= 900 s Axial charge GA(0) = 1.26

Different weights depending on processes


Information on substructure

quark numberanom.mag.mom

axial charge


A hard look at the proton

For hard momenta, it is improbable that system survives. One needs additional hard interactions

Best deal is hitting elementary or pointlike objects

G(Q2) ~ (Q2R2)(n-1)


A hard look at the proton Hard virtual momenta ( q2 = Q2 ~ many

GeV2) can couple to (two) soft momenta

+ N jet jet + jet


DIS event

ZEUS@DESY

Hitting quarks in the proton


Soft physics in inclusive deep inelastic leptoproduction

(calculation of) cross sectionDIS

Full calculation

+ …

+ +

+PARTONMODEL

Lightcone dominance in DIS


Leading order DIS In limit of large Q2 the result

of ‘handbag diagram’ survives … + contributions from A+ gluons

A+

A+ gluons gauge link

Ellis, Furmanski, PetronzioEfremov, Radyushkin

Color gauge link in correlator Matrix elements

A+ produce the gauge link U(0,) in leading quark lightcone correlator

A+

Distribution functions

Parametrization consistent with:Hermiticity, Parity & Time-reversal

SoperJaffe & Ji NP B 375 (1992) 527


M/P+ parts appear as M/Q terms in T-odd part vanishes for distributions but is important for fragmentation

Jaffe & Ji NP B 375 (1992) 527Jaffe & Ji PRL 71 (1993) 2547

leading part


Jaffe & JiNP B 375 (1992) 527

Selection via specific probing operators(e.g. appearing in leading order DIS, SIDIS or DY)

Lightcone correlator

momentum density

= ½

Sum over lightcone wf

squared

Basis for partons

‘Good part’ of Dirac space is 2-dimensional

Interpretation of DF’s

unpolarized quarkdistribution

helicity or chiralitydistribution

transverse spin distr.or transversity

Off-diagonal elements (RL or LR) are chiral-odd functions Chiral-odd soft parts must appear with partner in e.g. SIDIS, DY

Matrix representation

Related to thehelicity formalism

Anselmino et al.

Bacchetta, Boglione, Henneman & MuldersPRL 85 (2000) 712


Summarizing DIS Structure functions (observables) are identified with

distribution functions (lightcone quark-quark correlators) DF’s are quark densities that are directly linked to

lightcone wave functions squared There are three DF’s

f1q(x) = q(x), g1

q(x) =q(x), h1q(x) =q(x)

Longitudinal gluons (A+, not seen in LC gauge) are absorbed in DF’s

Transverse gluons appear at 1/Q and are contained in (higher twist) qqG-correlators

Perturbative QCD evolution


Soft physics in semi-inclusive (1-particle incl) leptoproduction

SIDIS cross section

variables hadron tensor

(calculation of) cross sectionSIDIS

Full calculation

+

+ …

+

+PARTONMODEL

Lightfront dominance in SIDIS

Lightfront dominance in SIDIS

Three external momentaP Ph q

transverse directions relevantqT = q + xB P – Ph/zh

orqT = -Ph/zh


Leading order SIDIS In limit of large Q2 only result

of ‘handbag diagram’ survives

Isolating parts encoding soft physics

? ?

Lightfront correlator(distribution)

Lightfront correlator (fragmentation)+

no T-constraintT|Ph,X>out = |Ph,X>in

Collins & SoperNP B 194 (1982) 445

Jaffe & Ji, PRL 71 (1993) 2547;PRD 57 (1998) 3057

Distribution

From AT() m.e.

including the gauge link (in SIDIS)A+

One needs also AT

G+ = +AT

AT()= AT

() +d G+

Ji, Yuan, PLB 543 (2002) 66Belitsky, Ji, Yuan, hep-ph/0208038

Distribution

A+

A+including the gauge link (in SIDIS or

DY)SIDIS

SIDIS [-]

DYDY [+]hep-ph/0303034

Distribution

for plane waves T|P> = |P> But... T U

T = U

this does affect (x,pT) it does not affect (x) appearance of T-odd functions in (x,pT)

including the gauge link (in SIDIS or DY)

Parameterizations including pT

Constraints from Hermiticity & Parity Dependence on …(x, pT

2) Without T: h1

and f1T

nonzero! T-odd functions

Ralston & SoperNP B 152 (1979) 109

Tangerman & MuldersPR D 51 (1995) 3357

Fragmentation f D g G h H No T-constraint: H1

and D1T

nonzero!

Integrated distributions

T-odd functions only for fragmentation

Weighted distributions

Appear in azimuthal asymmetries in SIDIS or DY

T-odd single spin asymmetry

example of a leading azimuthal asymmetry T-odd fragmentation function (Collins function) T-odd single spin asymmetry involves two chiral-odd functions Best way to get transverse spin polarization h1

q(x)

Tangerman & MuldersPL B 352 (1995) 129

CollinsNP B 396 (1993) 161

example:OTO inep epX

Single spin asymmetriesOTO

T-odd fragmentation function (Collins function) or T-odd distribution function (Sivers function) Both of the above can explain SSA in pp X Different asymmetries in leptoproduction!

Boer & MuldersPR D 57 (1998) 5780

Boglione & MuldersPR D 60 (1999) 054007

CollinsNP B 396 (1993) 161

SiversPRD 1990/91


Summarizing SIDIS Beyond just extending DIS by tagging quarks

… Transverse momenta of partons become relevant,

effects appearing in azimuthal asymmetries DF’s and FF’s depend on two variables, (x,pT) and (z,kT) Gauge link structure is process dependent ( pT-dependent distribution functions and (in general)

fragmentation functions are not constrained by time-reversal invariance

This allows T-odd functions h1 and f1T

(H1 and D1T

) appearing in single spin asymmetries


Structure functions are parton densities

Distribution functions with pTRalston & SoperNP B 152 (1979) 109

Tangerman & MuldersPR D 51 (1995) 3357

Selection via specific probing operators(e.g. appearing in leading order SIDIS or DY)

Lightcone correlator

momentum density


Remains valid for (x,pT)

… and also after inclusion of links for (x,pT)

Sum over lightcone wf

squared

Brodsky, Hoyer, Marchal, Peigne, Sannino PR D 65 (2002) 114025

Interpretation

unpolarized quarkdistribution

helicity or chiralitydistribution

transverse spin distr.or transversity

need pT

need pT

need pT

need pT

need pT

T-odd

T-odd

Collinear structure of the nucleon!

Matrix representationfor M = [(x)+]T

pT-dependent functions

T-odd: g1T g1T – i f1T and h1L

h1L + i

h1

Matrix representationfor M = [(x,pT)+]T


Positivity and bounds

Positivity and bounds

Matrix representationfor M = [(z,kT) ]T


FF’s: f D g G h H

No T-inv constraints H1

and

D1T

nonzero!

Matrix representationfor M = [(z,kT) ]T


FF’s after kT-integration

leaves just the ordinary D1(z)

R/L basis for spin 0 Also for spin 0 a T-odd function exist, H1

(Collins function)

e.g. pion


Process dependence and universality

Difference between [+] and [-]

Integrateover pT


integrated quarkdistributions

transverse moments

measured in azimuthal asymmetries

±


gluonic pole m.e.


Time reversal constraints for distribution functions

Time reversal(x,pT) (x,pT)

G

T-even(real)

T-odd(imaginary)

Consequences for distribution functions

(x,pT) = (x,pT) ± G

Time reversal

SIDIS[+]

DY [-]


(x,pT)

= (x,pT) ± G

Sivers effect in SIDISand DY opposite in sign

Collins hep-ph/0204004

Relations among distribution functions

1. Equations of motion2. Define interaction dependent functions3. Use Lorentz invariance


(x,pT)

= (x,pT) ± G

(omitting mass terms)

Sivers effect in SIDISand DY opposite in sign

Collins hep-ph/0204004


Time reversal constraints for fragmentation functions

Time reversalout(z,pT)

in(z,pT)

G

T-even(real)

T-odd(imaginary)


Time reversal constraints for fragmentation functions

G out

out

out

out

T-even(real)

T-odd(imaginary)

Time reversalout(z,pT)

in(z,pT)

Fragmentation functions

(x,pT)

= (x,pT) ± G

Time reversal does not lead to constraints

Collins effect in SIDISand e+e unrelated!

If G = 0

Fragmentation functions

(x,pT)

= (x,pT) ± G

Collins effect in SIDISand e+e unrelated!

including relations


T-odd phenomena T-invariance does not constrain fragmentation

T-odd FF’s (e.g. Collins function H1)

T-invariance does constrain (x) No T-odd DF’s and thus no SSA in DIS

T-invariance does not constrain (x,pT) T-odd DF’s and thus SSA in SIDIS (in combination with

azimuthal asymmetries) are identified with gluonic poles that also appear elsewhere (Qiu-Sterman, Schaefer-Teryaev)

Sign of gluonic pole contribution process dependent In fragmentation soft T-odd and (T-odd and T-even) gluonic pole

effects arise No direct comparison of Collins asymmetries in SIDIS and e+e

unless G = 0

Documents

The QCD structure of the nucleon