The QCD structure of the nucleon
description
Transcript of The QCD structure of the nucleon
The QCD structure of the nucleon
P.J. MuldersVrije Universiteit
Amsterdam
FrascatiMay 2003
Universality of T-odd effects in single spin and azimuthal asymmetries, D. Boer, PJM and F. Pijlman, hep-ph/0303034
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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
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Introducing the nucleon: from global view to quarks
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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
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A real look at the proton
+ N ….
Nucleon excitation spectrumE ~ 1/R ~ 200 MeVR ~ 1 fm
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A virtual look at the proton N N + N N
_
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Spacelike form factor global density
charge
current
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Nucleon e.m. form factors
GEp GMp/p GMn/n Gdipole
Gdipole = (1+Q2/2)-2
2 = 0.71 GeV2
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Nucleon form factors
Present-day status (TJNAF)
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Nucleon densities
proton neutron
• charge density 0• u more central than d?• role of antiquarks?• n = n0 + p+ … ?
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Another (weak) look at the nucleon
n p + e +
= 900 s Axial charge GA(0) = 1.26
Different weights depending on processes
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Information on substructure
quark numberanom.mag.mom
axial charge
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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)
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A hard look at the proton Hard virtual momenta ( q2 = Q2 ~ many
GeV2) can couple to (two) soft momenta
+ N jet jet + jet
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DIS event
ZEUS@DESY
Hitting quarks in the proton
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Soft physics in inclusive deep inelastic leptoproduction
(calculation of) cross sectionDIS
Full calculation
+ …
+ +
+PARTONMODEL
Lightcone dominance in DIS
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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
Distribution functions
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
Distribution functions
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
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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
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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
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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
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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
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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
Bacchetta, Boglione, Henneman & MuldersPRL 85 (2000) 712
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
Bacchetta, Boglione, Henneman & MuldersPRL 85 (2000) 712
Positivity and bounds
Positivity and bounds
Matrix representationfor M = [(z,kT) ]T
pT-dependent functions
FF’s: f D g G h H
No T-inv constraints H1
and
D1T
nonzero!
Matrix representationfor M = [(z,kT) ]T
pT-dependent functions
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
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Process dependence and universality
Difference between [+] and [-]
Integrateover pT
Difference between [+] and [-]
integrated quarkdistributions
transverse moments
measured in azimuthal asymmetries
±
Difference between [+] and [-]
gluonic pole m.e.
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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 [-]
Distribution functions
(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
Distribution functions
(x,pT)
= (x,pT) ± G
(omitting mass terms)
Sivers effect in SIDISand DY opposite in sign
Collins hep-ph/0204004
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Time reversal constraints for fragmentation functions
Time reversalout(z,pT)
in(z,pT)
G
T-even(real)
T-odd(imaginary)
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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
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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