Como, September 7, 2005 Aram Kotzinian 1 Cahn and Sivers effects in the target fragmentation region of SIDIS Introduction Hadronization in SIDIS Cahn and Sivers asymmetries in the current fragmentation regions Cahn and Sivers asymmetries in LEPTO Discussion & Conclusions Aram Kotzinian Torino University & INFN On leave in absence from YerPhI, Armenia and JINR, Russia hep-ph/ 0504081
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Cahn and Sivers effects in the target fragmentation region of SIDIS
Cahn and Sivers effects in the target fragmentation region of SIDIS. Introduction Hadronization in SIDIS Cahn and Sivers asymmetries in the current fragmentation regions Cahn and Sivers asymmetries in LEPTO Discussion & Conclusions. Aram Kotzinian Torino University & INFN - PowerPoint PPT Presentation
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Como, September 7, 2005 Aram Kotzinian 1
Cahn and Sivers effects in the target fragmentation region of SIDIS
Introduction Hadronization in SIDISCahn and Sivers asymmetries in the current fragmentation regions
Cahn and Sivers asymmetries in LEPTODiscussion & Conclusions
Aram Kotzinian
Torino University & INFNOn leave in absence from YerPhI, Armenia and JINR, Russia
hep-ph/0504081
Como, September 7, 2005 Aram Kotzinian 2
SIDIS in LO QCD: CFR
( , ;( , ) ), hq q
lN lhXq q N
q
lq lqd f dx D z T Tp sk s ;S
Well classified correlations in TMD distr. and fragm. functions
1ˆ Tf T TS (p×k ) Sivers distribution
1ˆ h T Ts (p×k ) Boer distribution
1Lg L LS s Helicity distribution
1ˆ H h
T Ts (q×p ) Collins effect in quark fragmentation
( )q Nf x N
( )hqD z
qq
h
p
1ˆ( )( ) Lh T T Lk s p S Mulders distribution
Como, September 7, 2005 Aram Kotzinian 3
Cahn effect in CFR
Quadratic in hz
M.Anselmino, M.Boglione, U.D’Alesio, A.K., F.Murgia and A.Prokudin: PRD 71,
074006 (2005);
Linear in and proportional to 2khz
Azimuthal modulation of lepton-quark hard scattering cross section in unpolarized SIDIS
Como, September 7, 2005 Aram Kotzinian 4
Sivers Effect in CFRAzimuthal modulation of quark transverse momentum in a transversely polarized nucleon
SivTS
N
qk
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)
Siv SΦ = -Φ
Como, September 7, 2005 Aram Kotzinian 5
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
( , )qh NM x z N
q
h
( , )lN lhX lq l
q
qh N
q Md d x z
( , , , ; )q hh N q NM x zT Tk s ; p S
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
s
( ) ...
h
h
h
L T T
L T T
T T T T
S (p ×k )
(p ×k )
S p (s ×k )
Como, September 7, 2005 Aram Kotzinian 7
SIDIS Event Generators and LUND String Fragmentation
( , ,( , , ) , ; )q hh N q F
lqlN lhN N
qXq q
q
ld x xd Hf x T TTk s ; pS k s ; S
u
( ud)
R
R
R
u
u
d
d
d
s
d
s
+ρ
0π
-π
+K
Soft
Str
ong
Inte
ract
ion
qq
q
Ran
k f
rom
diq
uark
Ran
k f
rom
qu
ark
h
Parton DF, hard X-section & Hadronization are factorized
Implemented in PHYTIA and LEPTO + JETSET (hadronization)
Como, September 7, 2005 Aram Kotzinian 8
Quark kT in MC generators PYTHIA and LEPTO
- Generate virtual photon – quark scattering in collinear configuration:
- Before
- After hard scattering
- Rotate in l-l’ plane
- Generate intrinsic transverse momentum of quark (Gaussian kT)
- Generate uniform azimuthal distribution of quark (flat by default)
- Rotate around virtual photon
Tk z
q
zplane ll
Como, September 7, 2005 Aram Kotzinian 9
Sivers effect in pp l+l- + X
Siv
z TS
Tk
1 2
11 21 1 2 2( , ) ( , ) qq l lh
h h l l Xq h q h
q
d f x f dx T T; kSk
One class of nonperturbative input:
only distribution functions, no hadronization effects are present
Modify PYTHIA to include Sivers effect: azimuthal correlations of the parton
transverse momentum and transverse spin on nucleon in distribution functions
( , )q N
f x Tk
ST
( , )q Nf x Tk*
p
p
q
q
Como, September 7, 2005 Aram Kotzinian 10
Sivers effect in pp l+l- + X
at =14.4 GeV
p p X
s
q p
q p
*
at =200 GeV
p p X
s
Similar values as in Anselmino et al: hep-ph/0507181
Como, September 7, 2005 Aram Kotzinian 11
Implementing Cahn and Sivers effects in LEPTO
The common feature of Cahn and Sivers effects Unpolarized initial and final quarksFragmenting quark-target remnant system is similar to that in default LEPTO but the direction of is now modulatedz
Cahn:
Sivers:
Generate the final quark azimuth according to above distributions
Como, September 7, 2005 Aram Kotzinian 12
Results: Cahn
Imbalance of measured in TFR and CFR: neutrals?
Charged hadrons azimuth
EMC Collaboration (280GeV)
Como, September 7, 2005 Aram Kotzinian 13
Results: Sivers
Predictions for xF-dependence at JLab 12 GeV
Red triangles with error bars – projected statistical accuracy for 1000h data taking
(H.Avagyan).
z, xBj and PT dependences
Como, September 7, 2005 Aram Kotzinian 14
Results: Sivers JLab 12 GeV
Como, September 7, 2005 Aram Kotzinian 15
Bjorken variable dependence of “FFs” in LEPTO
2 2
0.1
1.5
x
Q GeV
2 2
0.1
3.4
x
Q GeV
2 2
2 2
F
Cuts:
Q 1
W 10
y<0.85;
0.023<x<0.6
E >3.5
0.2
x >0.1
GeV
GeV
GeV
z
The dependence of “FFs” on x
cannot be attributed to Q2 evolution
Como, September 7, 2005 Aram Kotzinian 16
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)
Even in unpolarized LEPTO there is a dependence on targetremnant spin state
0{( ) }, 1.ud u w
1{( ) }, 1.ud u w
(ud)0: first rank Λ is possible(ud)1: first rank Λ is impossible
Como, September 7, 2005 Aram Kotzinian 17
Target remnant in Polarized SIDIS
JETSET is based on SU(6) quark-diquark model
Probabilities of different string spin configurations depend on quark and target polarizations, target type and process type
90% scalar
100% vector
Como, September 7, 2005 Aram Kotzinian 18
Polarized SIDIS & HF
In contrast with FFs, HFs in addition to z depend on x and target type and on struck quark and target polarization:
are the spin dependent cross section and HFs
hN Nl
hNq Nq
H /and
0hq NH double spin effect (struck quark & target), as in DFs.
Spin dependence of hadronization: A.K. (hep-ph/0410093, EPJ C, 2005)
( , ,( , , ) , ; )q hh N q F
lqlN lhN N
qXq q
q
ld x xd Hf x T TTk s ; pS k s ; S
Como, September 7, 2005 Aram Kotzinian 19
),,(),(
),,(),(1),,(),(
),,(
),,(
),(),(
),,(),(
),,(
2/
2
2/
22
/22
2/
2/
2
22
/22
21
QzxHQxq
QzxHQxqQzxHQxqe
QzxH
QzxH
QxqQxq
QzxHQxqe
QzxA
hNq
hNq
q
hNqq
hNq
hNq
q
hNqq
h
Asymmetries
The standard LO expression for helicity asymmetry of SIDIS is obtained when
and
s
( )
h
h
h
L T T
L T T
T T T T
S (p ×k )
(p ×k )
S p (s ×k )
For TMD dependent HFs the new spin-azimuth correlations depending on both
transverse momentum of quark in nucleon and final hadron are possible:
Unpolarized lepton, long. polarized target
Unpolarized target, long. polarized lepton
Unpolarized lepton, trans. polarized target
Como, September 7, 2005 Aram Kotzinian 20
ConclusionsHadronization functions provide a general description of SIDIS in the whole kinematics of hadronsBoth 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 LEPTOThe 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
Como, September 7, 2005 Aram Kotzinian 21
additional slides
Como, September 7, 2005 Aram Kotzinian 22
MC tuningMonti 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 (, K, and P)
Excellent Agreement even at the cross section level