Precision fragmentation function measurements at Belle Freiburg, June 6 2007 R. Seidl (University of Illinois and RBRC) Outline: •Why QCD and spin physics? •Transversity and the Collins function •Transversity as thirsd leading twist distribution function •Access to transversity over Collins fragmentation function •Collins function measurements at Belle •The Belle detector •Improved statistics with on_resonance data •First global analysis from SIDIS and Belle data •Interference fragmentation function measurements •unpolarized fragmentation function measurements
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Precision fragmentation function measurements at Belle Freiburg, June 6 2007 R. Seidl (University of Illinois and RBRC) Outline: Why QCD and spin physics?
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Precision fragmentation function measurements at Belle
Freiburg, June 6 2007
R. Seidl (University of Illinois and RBRC)
Outline:•Why QCD and spin physics?•Transversity and the Collins function
•Transversity as thirsd leading twist distribution function•Access to transversity over Collins fragmentation function•Collins function measurements at Belle
•The Belle detector•Improved statistics with on_resonance data
•First global analysis from SIDIS and Belle data
•Interference fragmentation function measurements•unpolarized fragmentation function measurements
R.Seidl: Fragmentation function measurements at Belle 2 Freiburg, June 6th
Why QCD and spin physics?
• QCD as the right theory of quarks and gluons,
• Perturbative part well understood
• Nucleon as simplest bound state of QCD poorly understood (though building block of most matter in universe)
• Significant surprises when including spin:
Spin crisis: Quarks contribute only ~30% to nucleon spin
Large transverse single spin asymmetries which are forbidden by perturbative QCD observed
“You think you understand something? Now add spin ...” – R. Jaffe
R.Seidl: Fragmentation function measurements at Belle 3 Freiburg, June 6th
R.Seidl: Fragmentation function measurements at Belle 4 Freiburg, June 6th
q(x), G(x)
Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton(known from fixed target (SI)DIS experiments)
q(x),G(x)
Sum of quarks with parallel and antiparallel polarization relative to proton spin(well known from Collider DIS experiments)
q(x)
Quark distributions
Difference of quarks with parallel and antiparallel polarization relative to transversely polarized proton(first results from HERMES and COMPASS – with the help of Belle)
Unpolarized distribution function q(x)
Helicity distribution function q(x)
Transversity distribution function q(x)
R.Seidl: Fragmentation function measurements at Belle 5 Freiburg, June 6th
Cross sections in (semi)inclusive pp and DIS, factorization
fq(x1) fq(x2) Dh(z) TdP
d
fq(x1) Dh(z) 2dQ
d•Hard scales PT and Q2
•Convolution integrals over all involved momenta
•Factorization of involved distribution and fragmentation functions
•(kT)-dependent distribution and fragmentation functions
k
k’
Q
2P
1P
1P
PS
lS
1PS
2PS
R.Seidl: Fragmentation function measurements at Belle 6 Freiburg, June 6th
Transversity properties
• Helicity flip amplitude• Chiral odd • Since all interactions
conserve chirality one needs another chiral odd object
• Does not couple to gluons different QCD evolution than q(x)
• Valence dominated Comparable to Lattice calculations, especially tensor charge
Positivity bound:
Soffer bound:
xqxδq
xqxqxδq 21
R.Seidl: Fragmentation function measurements at Belle 7 Freiburg, June 6th
Finding another chiral odd object in SIDIS Collins fragmentation function
functions of many final states Important input for general QCD physics and
helicity structure measurements• Measure other interesting QCD-related
quantities at Belle:– Chiral-odd -fragmentation function– Event shapes– R-ratio with ISR
R.Seidl: Fragmentation function measurements at Belle 36 Freiburg, June 6th
Backup Slides
Belle
R.Seidl: Fragmentation function measurements at Belle 37 Freiburg, June 6th
• Similar to previous method• Observe angles 1R2R
between the event-plane (beam, two-pion-axis) and the two two-pion planes.
• Theoretical guidance by Boer,Jakob,Radici
Interference Fragmentation – “ “ method
R2R1221111 m,zHm,zHA cos
R2
R1
1hP
2hP
3hP
4hP
2h1h PP
4h3h PP
R.Seidl: Fragmentation function measurements at Belle 38 Freiburg, June 6th
What would we see in e+e-?
Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning
m1
m1
m2
m2
“Jaffe” “Radici”
R.Seidl:The W physics program at PHENIX 39 PVSA, BNL April 27th
Sivers interpretation
Taken from H. Tanaka in Trento’04
•Attractive rescattering of hit quark by gluon creates transverse momentum•M.Burkardt [hep-ph0309269] – impact parameter formalism•Orbital angular momentum at finite impact parameter•observed and true x differ•Observable left/right asymmetry