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Radiative Corrections to Neutrino-Deuteron Scattering Revisited

M. Fukugita (ICRR, Univ. of Tokyo) and T.K. (October 4, 2005 at “RADCOR 05”). Radiative Corrections to Neutrino-Deuteron Scattering Revisited. (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

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Radiative Corrections to Neutrino-Deuteron Scattering Revisited

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  1. M. Fukugita (ICRR, Univ. of Tokyo)and T.K. (October 4, 2005 at “RADCOR 05”) Radiative Corrections to Neutrino-Deuteron Scattering Revisited (i) Acta Physica Polonica B35 (2004 )1687 (ii) Phys. Letters B598 (2004) 67 (iii) hep-ph/0509123 ( 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.:

  7. “Renormalization” effects • For CC processes • For NC processes

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

  9. 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

  10. 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 ?

  11. EliminatingM-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

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

  13. The inner corrections:

  14. 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)

  15. Radiative Corrections to NC cross section:

  16. 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

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

  18. 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

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

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

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