1. Jiro Kodaira and QCD Analysis of Structure Functions
Dedicated to the memory of Jiro Kodaira
T. Uematsu (Kyoto Univ.)
at KEK workshop “Towards precision QCD physics” March 10, 2007

2. Jiro Kodaira’s Personal History
Born　in　Nagano，Japan in 1951
Graduated from Kyoto Univ. in 1974
Finished Ph.D in 1979
1979 －1980　 RA at YITP, Kyoto Univ.
1980 － JSPS Fellow at SLAC
1982 － RA at Kobe University
1983 － RA & AP at Hiroshima Univ.
2005 － Professor at KEK

3. Asymptotic freedom ’73
Kodaira’s paper
EMC effects ’88
LHC starting ’07
1951
’70
’74
1979
2005
2006
’80
’82
’83
under grad.
SLAC
Hiroshima
KEK
Born in Nagano
Graduate course
in Kyoto Univ.
Kobe
Yukawa
Inst.

4. Kodaira’s contributions to perturbative QCD
QCD higher order corrections to the polarized deep inelastic scattering
　Kyoto Group
　flavor-singlet nucleon polarized structure function Kodaira 1979
Soft gluon resummation
Kodaira & Trentadue
Spin correlation in top quark production
　　　　　　　 Kodaira & Parke, …
Axial Anomaly plays an important role
NLL order

5. QCD Higher Order Effects
Physical quantity
Anomalous dim.
Next-Leading-log
Leading-log
Kyoto Group
Kodaira et al
flavor non-singlet
Phys.Rev.D20 (1979) 627; Nucl.Phys. B159 (1979) 99

6. Polarized DIS & Structure Functions
nucleon
spin
incident lepton
scattered quark
scattered lepton or
Structure tensor
Unpolarized structure fns.
polarized structure fns.

8. Flavor Singlet Case Axial anomaly Kodaira QCD correction
Axial vector current
Flavor Singlet　Case
Axial anomaly
Triangle anomaly
2-loop anomalous dim. does not vanish
+ other diagram
Kodaira
Nucl.Phys. B165 (1980)129
: # of flavors
QCD correction

9. Parton distribution functions are scheme-dependent
1988 EMC at CERN “Spin Crisis”
Altarelli-Ross
Phys. Lett B212 (1988) 391
Gluon polarization contributes due to anomaly Or
Parton distribution functions are scheme-dependent
J. Kodaira and T. U. Nucl. Phys. B141 (1978) 497

10. Kodaira’s other contributions to pQCD
Twist-3 effects & BC sum rule in
Yasui, Tanaka, Nasuno, Tochimura; Sasaki, Matsuda, T.U.
Twist-4 effects in
Kawamura, Yasui, T.U.
Spin correlation in top quark production
Parke, Nasuno, Kiyo, Hori, Morii
Polarized Drell-Yan processes
Kawamura, Tanaka, Shimizu, Yokoya
Small-x of in resummation
Kiyo, Tochimura

11. Higher-twist effects in polarized structure fns.
Twist-3 and twist-4 operators
Tanaka's talk
characteristics of higher-twist operators
Represents quark and gluon correlations
The number of relevant composite operators increases as n　increases
Renormalization of higher-twist operators
　 Operator mixing through renormalization becomes quite complicated

12. Twist-3 effects in twist-2 twist-3 quark-gluon operators
Mixing very complicated
Burkhardt-Cottingham sum rule

13. Twist-4 effects on spin structure fn
Flavor non-singlet
Twist-4 effects
Flavor singlet
Off-shell Green’s functions in covariant gauge

14. KEK
An expert in the field of pQCD and expected to advise experimentalists about physics at LHC and ILC from deep understanding of the theory
Leader’s role of “Minami-Tateya” (numerical analysis) group doing automatic computation of Feynman graphs and various simulations for the analyses of data from collider experiments
International collaborations just started
LAPTH Annecy, NIKHEF (GRACE-FORM project), …

15. Kodaira’s connections in the world
SLAC S. Parke (Fermilab), L. Trentadue (Parma),
　　　　　　　　　L. Dixon, S. Drell, S. Brodsky,…
RIKEN-BNL R.L.Jaffe (MIT), X.Ji (Maryland),
W. Vogelsang, D. Boer, M. Stratmann,..
DESY Zeuthen J. Bluemlein, S. Moch, …
NIKHEF J. Vermaseren, …
LAPTH D. Perret-Gallix, F. Boudjema,..
CERN G. Altarelli, ….
Firenze S. Catani, …
Collaboration with KEK Minami-tateya Group

16. 7th International Symposium on Radiative Corrections
APPLICATION OF QUANTUM FIELD THEORY TO PHENOMENOLOGY
Shonan Village, Japan October 2-7, 2005

17. Concluding remarks Very sad but his achievements will remain
Take over Kodaira’s spirit for the research in high-energy physics and pass it to the younger generations
Efforts should be taken toward precisions of QCD as well as Electro-weak physics
Promote the international collaborations
as Jiro Kodaira had tried to establish

18. Conclusion QCD is a Theory of Strong Interaction
From Jiro’s Slide in Aug06
Conclusion
QCD is a Theory of Strong Interaction
Non-abelin Gauge Theory　
One of the “most” beautiful The. in 20th Century
Forced to solve (at least) two problems now
1. do calculation for practical purpose (LHC, ILC, …)
2. reveal dynamics of gauge theory
using the simplest but the most difficult one
namely QCD