Presentation on theme: "12004, TorinoAram Kotzinian Outline Why L ? Transverse polarization of L Data Models Transversity Longitudinal polarization of L LEP data models Semi-inclusive."— Presentation transcript:
12004, TorinoAram Kotzinian Outline Why L ? Transverse polarization of L Data Models Transversity Longitudinal polarization of L LEP data models Semi-inclusive DIS (SIDIS) Target and current fragmentation Production mechanism and models
52004, TorinoAram Kotzinian Consider reaction In our case Kinematics in the Lab. frame Normal to production plane Which Component of polarization are permitted? is invariant with respect to boosts along momentum or axis
62004, TorinoAram Kotzinian 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 polarization to the coefficient of
72004, TorinoAram Kotzinian Inclusive production. Unpolarized Beam and Target Lab system, production plane Go to rest frame (*) Note:
82004, TorinoAram Kotzinian With this choice of axis in rest frame The normal components: And with simplest algebra we get: 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
92004, TorinoAram Kotzinian Semi-inclusive production In the lepton scattering plane We need expressions of in the rest frame Lepton scattering plane production plane In the transverse to plane rotate to production plane
102004, TorinoAram Kotzinian In the production plane rotate to new axis: So, in the Lab. Frame with coordinates
112004, TorinoAram Kotzinian Go to rest frame (*), ( – Lorentz factors in Lab. Frame) In is evident that for scattered lepton momentum we have similar expression
122004, TorinoAram Kotzinian Azimuthal Dependence of Polarization We see that after integration over azimuth only normal polarization survives So, for unpolarized SIDIS we get the following azimuthal dependence (Sideway) (Long.) (Normal)
132004, TorinoAram Kotzinian Virtual Photon Spin Density Matrix Even for unpolarized lepton virtual photon is polarized!
142004, TorinoAram Kotzinian Polarized Beam and Unpolarized Target We have new additional scalar: In our case the beam is longitudinally polarized so, in the rest frame all components of After azimuthal integration only sideway and longitudinal components of transferred polarization survives (Sideway) (Long.) (Normal)
172004, TorinoAram Kotzinian New pseudovector, new scalars: Polarized Beam and Target Good home exercise: find all possible (lepton plane, target transverse polarization) azimuthal dependences Azimuth-integrated results of Tangerman and Mulders
182004, TorinoAram Kotzinian Polarized Beam, Target. Integrated over azimuth
192004, TorinoAram Kotzinian 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
202004, TorinoAram Kotzinian Transverse Polarization of L L n z x Normal to production plane Empiric relation:
212004, TorinoAram Kotzinian 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, DAlesio & Murgia (2001) New polarizing Fragmentation Functions
222004, TorinoAram Kotzinian DeGrand&Miettinen model An empirical rule for spin direction of recombining quark: Slow partons – Down, fast partons – Up SU(6) wave functions for baryons Semiclassical dynamic is based on Thomas precession New term in effective interaction Hamiltonian: where Thomas frequency is
232004, TorinoAram Kotzinian Anderson, Gustafson & Ingelman model Semiclassical string fragmentation model Vacuum quantum numbers of quark-antiquark pair: -state Normal to production plane – out of picture -pair orbital moment is compensated by spin Negative transverse polarization of L
242004, TorinoAram Kotzinian Interference between diagrams with different intermediate baryons give rise to polarization Barni, Preparata & Ratcliffe
252004, TorinoAram Kotzinian Polarizing Fragmentation Functions In unpolarized quark fragmentation with nonzero transverse momentum,, L can be polarized L n Probabilistic interpretation – no interference effects
262004, TorinoAram Kotzinian Some Open Questions No transverse polarization observed at LEP Positive transverse polarization at HERMES Qualitatively can be explained in DM model with VMD approach Parton model: u-quark dominance? Compare with neutrino data.
272004, TorinoAram Kotzinian Transverse polarization of quarks in the transversely polarized nucleon: measurement Transverse polarization transfer from quark to L Transversity Lepton scattering plane s-quark dominance in polarization transfer as in SU(6)?
312004, TorinoAram Kotzinian Longitudinal Polarization of L in quark fragmentation Charged lepton SIDIS:
322004, TorinoAram Kotzinian Longitudinal Polarization of L: CFR Spin transfer in the longitudinally polarized quark fragmentation Spin 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
332004, TorinoAram Kotzinian LEP data HERMES data
342004, TorinoAram Kotzinian 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.
352004, TorinoAram Kotzinian Melnitchouk & Thomas: 100 % anticorrelated with target polarization contradiction with neutrino data for unpolarized target Longitudinal polarization of L in the TFR Meson Cloud Model
362004, TorinoAram Kotzinian 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 Polarized proton: Spin crisis:
372004, TorinoAram Kotzinian Ed. Berger criterion The typical hadronic correlation length in rapidity is Illustrations from P. Mulders:
382004, TorinoAram Kotzinian L production in 500 GeV/c π-Nucleon Production Fermilab E791 Collaboration, hep-ph/0009016
392004, TorinoAram Kotzinian L Production in String Fragmentation Model NOMAD CC data
402004, TorinoAram Kotzinian qqq Rank from diquark Rank from quark Tagging scheme for a hyperon Which contains: Struck quarkRemnant diquark R q =1 (A) R q 1 & Rqq 1 (B) R qq =1 (A) R qq 1 & Rq 1 (B) NOMAD (43.8 GeV)COMPASS (160 GeV)
412004, TorinoAram Kotzinian Small mass system: isotropic decay Removed sea u-quark event: target remnant is split
422004, TorinoAram Kotzinian Building SU(6)=SU(3) F x SU(2) S non relativistic wave functions of octet baryons: p, n, +, 0, -, 0, 0, - Cyclic permutations…)
462004, TorinoAram Kotzinian J.Ellis, A.K. & D.Naumov (2002)
472004, TorinoAram Kotzinian Λ polarization in quark & diquark fragmentation Λ polarization from the diquark fragmentation Λ polarization from the quark fragmentation
482004, TorinoAram Kotzinian The struck quark polarization
492004, TorinoAram Kotzinian 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
502004, TorinoAram Kotzinian 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:
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