12004, torinoaram kotzinian outline why l ? transverse polarization of l data models transversity...

2004, Torino Aram Kotzinian 1

OutlineWhy Transverse polarization of

DataModels

Transversity

Longitudinal polarization of LEP data

models

Semi-inclusive DIS (SIDIS) Target and current fragmentation

Production mechanism and models


Large branching ratio in charged hadrons channel:

Long decay length due to weak decay

Well separated primary and decay vertexes


Consider reaction Xplcpbla N )()'()()(In our case ba

Kinematics in the Lab. frame

Normal to production plane

Which Component of polarization are permitted?

yn is invariant with

respect to boosts along momentum or axisz

l

z

x

ny

'llq

'l

l


The cross-section is Lorentz scalar

P-invariance of strong and EM interactions

Reaction probability is linear function of spin

We have 4 independent vectors:

Possible scalars:

General Constraints

ppll N and ,',

pplS N1

pplS N'2

pllS '3

NpllS '4

polarization to the coefficient of iP

iS *


Inclusive production. Unpolarized Beam and Target

Xppbqa N )()()(

Lab system, production plane

Go to rest frame (*)

*q*NP

*x

*z

qq*Note:

||qq

q P

)( Sinqq

z


With this choice of axis in rest frame

The normal components:

And with simplest algebra we get:

02*2* qpN

***0 NpqSm

1***10 NpqSm

****0 ppqS N

1*3*2*1*3*2*2310 NN pqSmpqSm

It is important to note that if transverse momentum

is equal to 0 then , and we have no nonzero

pseudo-vector to contract spin pseudo-vector

Thus, in this case only normal polarization is allowed

0* 3q

)(2 SinPP n


Semi-inclusive production

Xplcpbla N )()'()()(

In the lepton scattering plane

We need expressions of in the rest frame

q

lq

x

z

))(,0),(,(),,,( 03210

CoslSinlllllll

;310 llll )0,0,0,( 0

0 ll

);0,0,,0( 11 ll ),0,0,0( 3

3 ll

'x

'y

l

P

l

Lepton scattering plane

productionplane

x

' and ll

In the transverse to plane rotate to productionplaneq

)0,0,0,( 00

)1(0 lll

)0),(),(,0( 11)1(1 SinlCosll

),0,0,0( 33

)1(3 lll


In the productionplane rotate to new axis:

)0,0,0,( 00

)1(0

)2(0 llll

))()(),(),()(,0( 111)2(1 CosCoslSinlCosSinll

P

q zz '

''x'x

''z

))(,0),(,0( 33)2(3 SinlCosll

So, in the Lab. Frame with coordinates

),,,( 131130 CosCoslSinlSinlCosSinlCoslll

''


Go to rest frame (*), ( – Lorentz factors in Lab. Frame)

In is evident that for scattered lepton momentum we have similar expression

)

,

,

,(

13

1

013

130*

CosCoslSinl

Sinl

lCosSinlCosl

CosSinlCoslll

)( 3*2*2*3*1*1***101 lSlSpmplSmpplS NNN

)( 3'*2*2'*3*1*1*'**10

'2 lSlSpmplSmpplS NNN

)](

)()([2'*1*1'*2*3*

1'*3*3'*1*2*3'*2*2'*3*1*'3

llllS

llllSllllSmpllS

)()([)](

)()([2'*0*0'*2*3*0'*3*3'*0*2*11'*2*2'*1*3*

2'*1*1'*3*2*2'*3*3'*2*1*0'4

llllSllllSpllllS

llllSllllSppllS

N

NN


Azimuthal Dependence of Polarization

SinllP

aCosllP

P

2'23

3'32

1

21

,

1,

0

,

2''

2'1

2

,3

2

1

43

SinaSinP

bCosCosaP

aSinSinP

We see that after integration over azimuth only normal polarization survives

2

21

2

3

2

1

4321Unp

aSinSinP

bCosaCosP

aSinSinPSo, for unpolarized SIDIS we get the following azimuthal dependence

(Sideway)

(Long.)

(Normal)


Virtual Photon Spin Density Matrix

Even for unpolarized lepton virtual photon is polarized!


Polarized Beam and Unpolarized Target We have new additional scalar:

**Pol BBSS SS

In our case the beam is longitudinally polarized

so, in the rest frame all components of

lS toparallel is B

0* BS

)'1(

)1(

3*3

2*2

1*1

Pol

CosaSP

SinSP

aCosSP

B

B

B

After azimuthal integration only sideway and longitudinal components of transferred polarization survives

(Sideway)

(Long.)

(Normal)


Phys. Rev. Letters 90 (2003) 131804-1


CLAS Results


New pseudovector, new scalars:

Polarized Beam and Target

TS

T

TB

TB

NTB

TB

SS

lSSS

lSSS

pSSS

pSSS

10

'9

8

7

6

Good home exercise: find all possible (lepton plane, target transverse polarization) azimuthal dependences

Azimuth-integrated results of Tangerman and Mulders


Polarized Beam, Target. Integrated over azimuth


Conclusions

In (polarized) SIDIS, in principle, all components of polarization are allowed by General Principles

The azimuthal dependence of polarization is dictated by General Principles

It is important to pay attention to azimuthal dependence of acceptance


Transverse Polarization of

PPPP

nBeam

Beam

n

z

xNormal to production plane

TFT PxSEmpiric relation:


Models for Transverse Polarization

DeGrand & Miettinen model (1981)Quark recombination

Anderson, Gustafson & Ingelman (1979)String fragmentation

Barni , Preparata & Ratcliffe (1992)Diffractive triple-Regge model

Anselmino, Boer, D’Alesio & Murgia (2001)New polarizing Fragmentation Functions


DeGrand&Miettinen model

An empirical rule for spin direction of recombining quark:Slow partons – Down, fast partons – UpSU(6) wave functions for baryons

Semiclassical dynamic is based on Thomas precession

New term in effective interaction Hamiltonian:

where Thomas frequency is


Anderson, Gustafson & Ingelman model

Semiclassical string fragmentation modelVacuum quantum numbers of quark-antiquark pair: -state0

3P

ud

LPss

TP

Normal to production plane – out of picture

-pair orbital moment is compensated by spinNegative transverse polarization of

ss


Interference between diagrams with different intermediate baryons give rise to polarization

Barni , Preparata & RatcliffeTS


Polarizing Fragmentation Functions

In unpolarized quark fragmentation with nonzero transverse momentum, , can be polarized

n

k

qp

Probabilistic interpretation – no interference effects

k


Some Open Questions

No transverse polarization observed at LEP

Positive transverse polarization at HERMESQualitatively can be explained in DM model with VMD approach

Parton model: u-quark dominance? Compare with neutrino data.


Transverse polarization of quarks in the transversely polarized nucleon: measurement

Transverse polarization transfer from quark to

Transversity

TargetSS

)(1 xh q

Lepton scattering planeTargetS

S

s-quark dominance in polarization transfer as in SU(6)?


SIDIS


Longitudinally polarized quark fragmentation into


Longitudinally polarized quark sources


Longitudinal Polarization of in quark fragmentationCharged lepton SIDIS:


Longitudinal Polarization of CFR

Spin transfer in the longitudinally polarized quark fragmentationSpin transfer coefficient:

NQM:

Burkardt & Jaffe: SU(3)&polarized DIS data

Ma, Schmidt, Soffer & Yang: quark-diquark model with SU(6) breaking& pQCD; Boros, Londergan & Thomas: MIT bag model

Bigi; Gustafson & Hakkinen: SU(6)+LUND fragmentation q → B → Λ


LEP data

HERMES data


TFR of SIDIS

Trentadue & Veneziano: fracture function

– probability of finding a parton q with momentum fraction x and a hadron h with the CMS energy fraction

in the proton.


Melnitchouk & Thomas:

100 % anticorrelated with target polarization contradiction with neutrino data for unpolarized target

Longitudinal polarization of in the TFR

Meson Cloud Model


Karliner, Kharzeev , Sapozhnikov, Alberg,Ellis & A.K.nucleon wave function contains an admixture with

component:

π,K masses are small at the typical hadronic mass scale ⇒ a strong attraction in the − channel.

pairs from vacuum in state

Intrinsic Strangeness Model

ss

0PJqq 0

3P

Polarized proton:Spin crisis: 1.0s


Ed. Berger criterion

The typical hadronic correlation length in rapidity is

Illustrations from P. Mulders:


production in 500 GeV/c π−-Nucleon Production

Fermilab E791 Collaboration, hep-ph/0009016


Production in String Fragmentation Model

NOMAD CC data


qq q

Rank from diquark

Rank from quark

Tagging scheme for a hyperonWhich contains:Struck quark Remnant

diquark

Rq=1 (A)

Rq1 & Rqq1 (B)

Rqq=1 (A)

Rqq1 & Rq1 (B)

NOMAD (43.8 GeV) COMPASS (160 GeV)


Small mass system: isotropic decay

Removed sea u-quark event: target remnant is split


Building SU(6)=SU(3)F x SU(2)S non relativisticwave functions of octet baryons:

p, n, +,0, -, 0, 0, -

Cyclic permutations…)


SU(6) quark-diquark wave functions of baryons

unpolarized nucleon


Strange baryons: octet


Strange baryons: decuplet


J.Ellis, A.K. & D.Naumov (2002)


Λ polarization in quark & diquark fragmentation

Λ polarization from the diquark fragmentation

Λ polarization from the quark fragmentation


The struck quark polarization


Spin Transfer

We use Lund string fragmentation model incorporated in LEPTO6.5.1 and JETSET7.4.

We consider two extreme cases when polarization transfer is nonzero:

model A: the hyperon contains the stuck quark: Rq = 1

the hyperon contains the remnant diquark: Rqq = 1

model B: the hyperon originates from the stuck quark: Rq ≥ 1

the hyperon originates from the remnant diquark:Rqq ≥ 1


Fixing free parameters

We vary two correlation coefficients ( and ) in order to fit our models A and B to the NOMAD Λ polarization data.

We fit to the following 4 NOMAD points to find our free parameters:


Results


Predictions for COMPASS

12004, torinoaram kotzinian outline why l ? transverse polarization of l data models transversity...

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normal slide

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axis slide

azimuth slide

coefficient of slide