single spin asymmetries in hard reactions
DESCRIPTION
Los Alamos 5 Aug. 2002. single spin asymmetries in hard reactions. P.J. Mulders Vrije Universiteit Amsterdam [email protected]. Content. Observables in (SI)DIS in field theory language l ightcone/lightfront correlations Relation to lightcone wave functions - PowerPoint PPT PresentationTRANSCRIPT
single spin asymmetries inhard reactions
P.J. MuldersVrije Universiteit
Amsterdam
Los Alamos5 Aug. 2002
05/08/2002 lightcone2002 p j mulders
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Content Observables in (SI)DIS in field theory language
lightcone/lightfront correlations Relation to lightcone wave functions Single-spin asymmetries in hard reactions
T-odd correlations T-odd in final (fragmentation) and initial state
(distribution) correlations Conclusions and further work
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Soft physics in inclusive deep inelastic leptoproduction
(calculation of) cross sectionDIS
Full calculation
+ …
+ +
+PARTONMODEL
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Leading order DIS In limit of large Q2 only result
of ‘handbag diagram’ survives
Isolate part encoding soft physics
? ?
Lightcone dominance in DIS
Distribution functions
Parametrization consistent with:Hermiticity, Parity & Time-reversal
SoperJaffe Ji NP B 375 (1992) 527
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
Bacchetta Boglione Henneman MuldersPRL 85 (2000) 712
= ½
Sum over lightcone wf
squared
Lightfront quantization
Kogut & Soper
• Good fields are independent, satisfying CCR’s• Suitable to define the partons in QCD
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.
chiral-odd functions
diagonalin transversespin basis
Color gauge link in correlator
Diagrams containing correlator A+ produce the gauge link U(0,) in quark-quark lightcone correlator
(x) subleading
include M/P+ parts gives M/Q terms in T-odd only for FF in e.g. e+e
Jaffe Ji NP B 375 (1992) 527Jaffe Ji PRL 71 (1993) 2547
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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 f1
q(x) = q(x), g1q(x) =q(x), h1
q(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
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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
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Leading order SIDIS In limit of large Q2 only result
of ‘handbag diagram’ survives
Isolating parts encoding soft physics
? ?
Lightfront dominance in SIDIS
Lightfront dominance in SIDIS
Three external momentaP Ph q
transverse directions relevantqT = q + xB P – Ph/zh
orqT = -Ph/zh
Lightfront correlator(distribution)
Lightfront correlator (fragmentation)+
no T-constraintT|Ph,X>out = |Ph,X>in
Collins SoperNP B 194 (1982) 445
distribution functions in SIDIS
Constraints from Hermiticity & Parity Dependence on …(x, pT
2) T-invariance: h1
= f1T = 0?
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!
Distribution functions in SIDISRalston 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)
= ½
Sum over lightcone wf
squared
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
Matrix representationfor M = [(x,pT) +]T
pT-dependent functions
T-odd: g1T g1T – i f1T and h1L
h1L + i
h1
Matrix representation for M = [(z,kT) ]T
pT-dependent functions
FF’s: f D g G h H
No T-inv constraints H1
and
D1T
nonzero!
Matrix representation for 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
Distribution and fragmentation functions
pT-integrated
pT-dependent
no T-odd
T-odd ?
Mulders TangermanNP B 461 (1996) 197
Sample azimutal asymmetryLTO
example of a leading azimuthal asymmetry without appropriate weights this would be a convolution instead of a factorized expression
Tangerman MuldersPL B 352 (1995) 129
KotzinianNP B 441 (1995) 234
Sample single spin asymmetryOTO
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
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Summarizing SIDIS 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) Fragmentation functions are not
constrained by time-reversal invariance This allows T-odd functions H1
and D1T,
appearing in single spin asymmetries
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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
What about T-invariance and (x,pT)?
Color gauge link in correlator
?
Diagrams containing correlator A+ produce the gauge links U(0,-) and U(-,) in quark-quark matrix element
Boer MuldersNP B 569 (2000) 505hep-ph/9906223
Distribution
for plane waves T|P> = |P> But...T U
T = Uthis does not affect (x) it does affect (x,pT) appearance of T-odd functions in (x,pT) color gauge inv requires leading transverse gluons
?
including the gauge link
From AT(-)y m.e.?
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T-odd phenomena T-invariance does not constrain (x,pT) Effects are connected to gauge link
They require ‘leading’ pT-effects
They change of sign from SIDIS to DY
They spoil density interpretation of functions and relation to lc wf
Phenomenology of T-odd functions exist
Similar T-odd effects exist at subleading (twist-3) level Experiment can give answers via specific experiments
Brodsky Hwang Schmidt hep-ph/0201296
Ji Yuan hep-ph/0206057
Collins hep-ph/0204004
Brodsky Hoyer PR D 65 (2002) 114025
Boer Mulders TeryaevPR D 57 (1998) 3057hep-ph/9710223
Qiu Sterman
Schaefer Teryaev
Related work:
Mulders Tangerman NP B 461 (1996) 197
Single spin asymmetriesOTO
T-odd fragmentation function (Collins function) or T-odd distribution function (Sivers function) Both of the above can explain pp X SSA Different asymmetries in leptoproduction!
Boer MuldersPR D 57 (1998) 5780
Boglione MuldersPR D 60 (1999) 054007
CollinsNP B 396 (1993) 161
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Conclusions Hard reactions with two hadrons (DY, SIDIS)
offer possibilities to access parton transverse momenta pT
Experimental access via azimuthal asymmetries, often also requiring polarization
T-odd phenomena occur in single-spin asymmetries
These are natural for fragmentation functions and seem possible for pT-dependent distribution functions involving necessary AT pieces in gauge link