Transcript Lectures on Polarized DIS

Cahn and Sivers effects in the target
fragmentation region of SIDIS
Aram Kotzinian
Torino University & INFN
On leave in absence from YerPhI, Armenia and JINR, Russia
hep-ph/0504081
Introduction
Hadronization in SIDIS
Cahn and Sivers asymmetries in the current fragmentation
regions
Cahn and Sivers asymmetries in LEPTO
Discussion & Conclusions
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SIDIS in LO QCD: CFR
h
q
Dqh ( z)
q
fq N ( x)
p
N
d lN lhX   fq ( x, k T , sq ;S N )  d lqlq  Dqh ( z, pT ; sq )
q
Well classified correlations in TMD distr. and fragm. functions
ˆ T )  f1T Sivers distribution
ST  (p×k
(k T  sT )(pˆ  SL )  h1L Mulders distribution
ˆ T )  h1 Boer distribution
sT  (p×k
SL  sL  g1L Helicity distribution
ˆ hT )  H1 Collins effect in quark fragmentation
sT  (q×p
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Cahn effect in CFR
M.Anselmino, M.Boglione, U.D’Alesio, A.K., F.Murgia and A.Prokudin: PRD 71, 074006 (2005);
Azimuthal modulation of lepton-quark hard scattering cross section in unpolarized SIDIS
Quadratic in zh
Linear in zh and proportional to k 2
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Sivers Effect in CFR
Azimuthal modulation of quark transverse momentum in a transversely polarized nucleon
 Siv
ST
N
q
k
ΦSiv =  -ΦS
M.Anselmino, M.Boglione, U.D’Alesio,
A.K., F.Murgia and A.Prokudin:
PRD 71, 074006 (2005);
hep-ph/0507181
Parameters were extracted
from combined analysis of
HERMES and COMPASS
data (details in the talk of
A. Prokudin)
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Ed. Berger criterion (separation of CFR &TFR)
The typical hadronic correlation length in rapidity is
Illustrations from P. Mulders:
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SIDIS in LO QCD: TFR
q
M hq N ( x, z)
h
N
d lN lhX   d lqlq M hq N ( x, z)
q
1994: Trentadue & Veneziano; Graudenz; … Fracture functions:
conditional probability of finding a parton q with momentum
fraction x and a hadron h with the CMS energy fraction z
More correlations for TMD dependent FracFuncs M hq N ( x, k T , sq ; z, pTh ; SN )
S L  (p Th × k T )
s L  (p Th × k T )
(S T  p Th )  (s T × k T )...
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SIDIS Event Generators and
LUND String Fragmentation
Parton DF, hard X-section & Hadronization are factorized
d lN lhX   fq ( x, k T , sq ; S N )  d lqlq Hhq N ( x, k T , sq ; xF , pTh ; S N )
ρ+
π-
d
u
K+
u
s
R
(ud)
s

Rank from quark
d
qq
π0
d
Rank from diquark
d
h
q
R
Soft Strong Interaction
u
q
R
Implemented in PHYTIA and LEPTO + JETSET (hadronization)
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Quark kT in MC generators PYTHIA and LEPTO
- Generate virtual photon – quark scattering in collinear configuration:
- Before
- After hard scattering
- Generate intrinsic transverse momentum of quark (Gaussian kT)
kT
- Rotate in l-l’ plane
zˆ
- Generate uniform azimuthal distribution of quark (flat by default)
q
- Rotate around virtual photon
zˆ
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l  l  plane
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l+l- + X
Sivers effect in pp
ST
p
fq N  ( x, k T )
q
q
p

fq N ( x, kT )

*

One class of nonperturbative input:
only distribution functions, no hadronization effects are present
d
h1 h2 l  l  X
  f q h1 ( x1 , k T1; S h1 ) f q h2 ( x2 , k T 2 )  d
qq l  l 
q
Modify PYTHIA to include Sivers effect: azimuthal correlations of the parton
transverse momentum and transverse spin on nucleon in distribution functions
Siv
kT
zˆ
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ST
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Sivers effect in pp
l+l- + X
p   p      X
q
p
q
p
at s =14.4 GeV
p   p      X
 *
at s =200 GeV
Similar values as in Anselmino et al: hep-ph/0507181
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Implementing Cahn and Sivers effects in LEPTO
The common feature of Cahn and Sivers effects
Unpolarized initial and final quarks
Fragmenting quark-target remnant system is similar to that in
default LEPTO but the direction of z is now modulated
Cahn:
Sivers:
Generate the final quark azimuth
according to above distributions
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Results: Cahn
Charged hadrons azimuth
EMC Collaboration (280GeV)
Imbalance of measured
in TFR and CFR: neutrals?
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Results: Sivers
z, xBj and PT dependences
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Predictions for xF-dependence at
JLab 12 GeV
Red triangles with error bars – projected
statistical accuracy for 1000h data taking
(H.Avagyan).
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Results: Sivers JLab 12 GeV
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Bjorken variable dependence of “FFs” in LEPTO
Cuts:
Q 2  1GeV 2
W 2  10GeV 2
y<0.85;
0.023<x<0.6
E>3.5GeV
z  0.2
x F >0.1
x  0.1
Q 2  1.5GeV 2
x  0.1
The dependence of “FFs” on x
Q 2  3.4GeV 2
cannot be attributed to Q2 evolution
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Dependence on target remnant spin state
(unpolarized LEPTO)
Example: valence u-quark is removed from proton. Default LEPTO:
the remnant (ud) diquark is in 75% (25%) of cases scalar (vector)
{(ud )0 u},
{(ud )1 u},
w  1.
w  1.
Even in unpolarized LEPTO
there is a dependence on target
remnant spin state
(ud)0: first rank Λ is possible
(ud)1: first rank Λ is impossible
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Target remnant in Polarized SIDIS
JETSET is based on SU(6) quark-diquark model
90% scalar
100% vector
Probabilities of different string spin configurations depend on
quark and target polarizations, target type and process type
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Polarized SIDIS & HF
Spin dependence of hadronization: A.K. (hep-ph/0410093, EPJ C, 2005)
d lN lhX   fq ( x, k T , sq ; S N )  d lqlq Hhq N ( x, k T , sq ; xF , pTh ; S N )
q
 Nh  
l N
and
H qh/ N q N
are the spin dependent
cross section and HFs
In contrast with FFs, HFs in addition to z depend on x and target type and on struck
quark and target polarization:
Hqh N  0 double spin effect (struck quark & target), as in DFs.
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Asymmetries
h
2
2


H
(
x
,
z
,
Q
)

q
(
x
,
Q
)
q/ N
2
2
h
2 
q eq q( x, Q ) H q / N ( x, z,Q ) q( x, Q 2 )  H h ( x, z, Q 2 ) 
q/ N


A1h ( x, z , Q 2 ) 
2
h
2


q
(
x
,
Q
)

H
(
x
,
z
,
Q
)
q/ N
2
2
h
2 
q eq q( x, Q ) H q / N ( x, z,Q )1  q( x, Q 2 ) H h ( x, z, Q 2 ) 
q/ N


The standard LO expression for helicity asymmetry of SIDIS is obtained when
and
For TMD dependent HFs the new spin-azimuth correlations depending on both
transverse momentum of quark in nucleon and final hadron are possible:
S L  (p Th ×k T )

Unpolarized lepton, long. polarized target
sL  (p Th ×k T )

Unpolarized target, long. polarized lepton
(S T  p Th )  (s T ×k T ) 
Unpolarized lepton, trans. polarized target
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Conclusions
Hadronization functions provide a general description of SIDIS in the
whole kinematics of hadrons
Both Cahn and Sivers effects are implemented in LEPTO. Possible
polarization effects in hadronization were neglected.
Existing data in the CFR are well described by modified LEPTO
The measured Cahn effect in the TFR is not well described
It is important to perform new measurements of Cahn, Sivers and
other azimuthal asymmetries in the TFR (JLab, HERMES, Electron
Ion Colliders)
This will help better understand spin dynamics in hadronization:
Do neutral hadrons compensate the Cahn effect in CFR?
Are there asymmetries present in TFR that compensate the Sivers effect in CFR?
Do there exist any other spin-dependent azimuthal asymmetries in TFR?
The access to TFR opens a new field both for theoretical and
experimental investigations
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additional slides
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p+
p-
K+
K-
P+
P-
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MC tuning
Monti Carlo:
Lepto in combination with
JETSET;
PDF: CTEQ-6L
Fragmentation parameters
tuned to HERMES
multiplicities in the
acceptance
Data:
Q2>1GeV2, W2>10GeV2,
z>0.2, 2GeV <p< 15GeV (p,
K, and P)
Excellent Agreement even at the
cross section level
DATA/MC <10%!
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HERMES check
xF ?
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xF > 0.1
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