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/0509123 ( to appear in Phys. Rev. D)

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., ……

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

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 :

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).

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

“Renormalization” effects For CC processes For NC processes

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

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

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 ?

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

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

The inner corrections:

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)

Radiative Corrections to NC cross section:

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

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

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

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

6. New SNO analyses The inner corrections were not correctly taken nucl-ex/0502021 (salt phase SNO data) The inner corrections were not correctly taken into account in their analysis.