1. Radiative Corrections to Neutrino-Deuteron Scattering Revisited
M. Fukugita (ICRR, Univ. of Tokyo)　and T.K.
(October 4, 2005 at “RADCOR 05”)
(i) Acta Physica Polonica B35 (2004 )1687
(ii) Phys. Letters B　598 (2004) 67
(iii) hep-ph/ ( to appear in Phys. Rev. D)

2. 1.Introduction Neutrino experiment after ~2000
 Precise measurement at low energy (1-10 MeV) weak processes
(i) KamLAND (Kamioka Liquid Scintillator Anti- Neutrino Detector)　
→　F. Suekane’s talk
(ii) SNO (Sudbury Neutrino Observatory)
(iii) etc., ……

3. Low-Energy Neutrino Reactions
KamLAND……
SNO………….

4. 1. Knowledge of the cross sections with 1 % accuracy or less is required for neutrino physics.
→ radiative corrections are important.
2. Clarify the electroweak radiative corrections in :

5. 2. Radiative Corrections
History
Neutron beta decay….. Kinoshita and Sirlin (’59)
(four-Fermi theory for nucleons)
Super-allowed Fermi transition ….. Sirlin (~’80)
(Weinberg-Salam theory)
KamLAND …. Vogel , Fayans (’84)
SNO………… Towner (’98) , Kurylov et al., (‘02)
One term has, however, eluded all of the
previous studies (in the Gamow-Teller part).

6. 3. Inverse beta decay Static nucleon limit, four-Fermi theory
　　　　positron energy, 　　　= positron velocity
Tree:
V-A Int.:

8. “Renormalization” effects
For CC processes
For NC processes

9. measurement of neutron beta decay asymmetry
　　　　　　　　　　　　　　　　　　　c.f. M.Fukugita and T.K. (’04)

10. Outer corrections・・・・・・
velocity-dependent,
UV-finite even in four-Fermi theory ,
unambiguously caculable (indep. of strong int.)
Inner corrections・・・・・・
just numbers
depend on strong interaction dynamics
UV-div. in four-Fermi-Theory
Missing in all of the previous studies

12. 4. Calulational Strategy
QED Corrections:
Use the four Fermi int. for nucleons,
M=UV cutoff
UV-divergent, IR convergent
(ii) Electroweak corrections:
Weinberg-Salam theory for quarks
Q: How to connect (i) and (ii) smoothly ?

15. Eliminating M-dependence
Eliminated by using Weinberg-Salam theory
(2) Eliminated by using a model of extended nucleon
　⇒　model dependent (nucleon form factor etc.)
The current algebra technique, CVC, and PCAC
make the classification into (1) and (2) unique.
　　　　 c.f., 　Sirlin, Abers et al. (’67) for Fermi-transition
　　　　　　　　 M. Fukugita and T.K. (’04) for GT-transition

16. Effects of Strong Dynamics appear only in:
(1) e.m. form factors
(2) weak form factor

17. The inner corrections:

18. ５．Neutral current phenomena
(SNO)
No vertex corrections, no bremsstrahlung
No outer corrections, no QED type corr.
only Weinberg-Salam type corrections
W. Marciano and A. Sirlin (1980)

22. Radiative Corrections to NC cross section:

23. 6. Summary
Established the strategy of calculating the inner corrections for G-T transitions
Clarified the meaning of
Showed how to include correctly the inner corrections in the SNO NC-cross section

28. 5. UV-divergences in four-Fermi theory
Naiive calulation (without Weinberg-Salam)

29. Universality of UV-divergence
(1) Abers et al. (’65)・・・ Fermi transition
CVC, current algebra ⇒　log-div. is independent of the strong dynamics
(2) Fukugita and TK (’04)・・・Gamow-Teller transition
　 PCAC, current algebra, BJL tech.⇒　log-div is
independent of the strong dynamics

30. 5. The Assymmetry measurement
Asymmetry in polarized neutron decay
Asymm= at tree level
at one-loop

31. 6. New SNO analyses The inner corrections were not correctly taken
nucl-ex/ (salt phase SNO data)
The inner corrections were not correctly taken
into account in their analysis.