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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”)

(i) Acta Physica Polonica B35 (2004 )1687

(ii) Phys. Letters B 　 598 (2004) 67

(iii) hep-ph/0509123 ( to appear in Phys. Rev. D)

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1.Introduction

Neutrino experiment after ~2000 Precise measurement at low energy (1-1

0 MeV) weak processes

(i) KamLAND (Kamioka Liquid Scintillator Anti- Neutrino Detector) 　

→ 　 F. Suekane’s talk

(ii) SNO (Sudbury Neutrino Observatory)

(iii) etc., ……

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Low-Energy Neutrino Reactions

KamLAND……

　　　　　　　　　　　　　　　　　　　

　　　　　　　　SNO………….

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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 :

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2. Radiative Corrections

• HistoryNeutron 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).

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3. Inverse beta decay

Static nucleon limit, four-Fermi theory

　　　　 positron energy, 　　　 = positron velocity

Tree:

V-A Int.:

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“Renormalization” effects

• For CC processes

• For NC processes

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• measurement of neutron beta decay asymmetry

　　　　　　　　　　　　　　　　　　　 c.f. M.Fukugita and T.K. (’04)

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• 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

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4. Calulational Strategy

(i) 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 ?

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Eliminating　M-dependence

(1) 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

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Effects of Strong Dynamics appear only in:

(1) e.m. form factors

(2) weak form factor

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The inner corrections:

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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)

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Radiative Corrections to NC cross section:

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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

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5. UV-divergences in four-Fermi theory

Naiive calulation (without Weinberg-Salam)

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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

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5. The Assymmetry 　 measurement

Asymmetry in polarized neutron decay

Asymm= at tree level

at one-loop

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6. New SNO analyses

nucl-ex/0502021 (salt phase SNO data)

The inner corrections were not correctly taken

into account in their analysis.