Next-to-Leading Order Parity-Violating Potential and

Chang Ho HyunSungkyunkwan University

In collaboration withS. Ando and B. Desplanques

PAVI06 Milos, GreeceMay 19, 2006

→ γ→

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.I

.II

.III

.IV

.V

→ →

→ →

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, , …

PC vertex

PV vertex

* One-meson exchange PV interactions

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* DDH potential : one-meson exchange PV potential of , , mesons

S, D, … ↔ P, F, …

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* Weak coupling constants : Theory

* Quark model : B. Desplanques et al., Ann. Phys. 124 (1980)

* Soliton : N. Kaiser, U.G. Meissner, Nucl. Phys. A499 (1989)

* QCD sum rule : E. M. Henley et al., Phys. Lett. B 367 (1996)

× 107 ’

Quark model 4.6 -11.4 0 -0.2 -9.5 -1.9 -1.1

Soliton 1.0 -3.7 -2.2 -0.1 -3.3 -1.4 -1.0

Sum rule 3.0 • • • • • •

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* Weak coupling constants : Experiment

* Measurement of PV asymmetry in

γ = - (0.6 ± 2.7) × 10-7 Cavaignac et al., Phys. Lett. B 67 (1977)

γ = - (1.5 ± 4.8) × 10-8 Alberi et al., Can. J. Phys 66 (1988)

1

→ →

Forbidden decay of 18F : | 1≤×

Anapole moment of 133Cs : 1×

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→ →

∝ 1 + γ dd

Non-zero γ : PV E1 transition

E1 operator : = (I = 1, L = 1, S = 0)

Photon momentumNeutron

polarization

Neutron momentum

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Scattering : 1S0, 3S1+3D1

Deuteron: 3S1+3D1

* PC transition : 1S0 → 3S1+3D1 (M1 isovector)

3S1+3D1 → 3S1+3D1 (M1 isoscalar)

* PV transition : 3PJ5 → 3S1+3D1

3S1+3D1 → 3PJ5

* Isovector PV potential produces 3PJ5 admixture to 3S1+3D1.

→γ determined by

L = 1, S = 0)

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* Result with one-meson exchange

× 108

(DDH best)

Bonn -0.117 -0.001 0.003 -5.42

Bonn B -0.117 -0.001 0.002 -5.41

Av18 -0.117 -0.001 0.002 -5.41

If ’s ~ 10-7,

more than 97% of γ from pion.

γ

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* Heavy baryon chiral perturbation theory

• Lagrangian satisfying the symmetries of QCD

• Nucleon treated as a heavy field

• SSB : pion is a Goldstone boson

• Expansion in powers of /

• Counting rule : systematic expansion in powers of / Counting rule

* Meson propagator ~ -2

* Nucleon propagator ~ -1

* Loop integral ~ 4

* Derivative or external field ~ 1

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* PV potential : Isovector

LO

NLO

0

-2

~

~

Two-pion exchange (TPE) Contact term(CT)

-1

4

-1

-2 -2

-1

-2

4-2

0

4

-1

-1

-2

-2

0 0

… …

PV

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Contact term

Calculated from underlying theory or

Adjusted to experiments

NNLO ~

+• •

• 4-2 -2`

4-2 -2

-1

No calculation, no experiment

Approximation : (2 + 2V)-1 ~ -2

V + (2)CT term at

LO

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LO

NLO

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Fourier transformation

Form factor and cutoff : -/

Need control at high

Dispersion relation

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Form factor and cutoff

PV

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Dispersion relation

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OPEP + TPEP

OPE

OPE+TP

E

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OPEP + TPEP + CT

OPE+TP

E

OPE+TPE+C

T

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-0.117

= 400 MeV -0.108

= 600 MeV -0.116

= 800 MeV -0.118

γ =

→ →

± 10 % sub 1 %

-0.102

-0.119

-0.123

-0.117

-0.107

-0.116

-0.118

PV potential calculated with heavy baryon chiral perturbation theory up to next-to-leading order

γ calculated with OME and effective NLO potentials

Heavy OME to γ : ~ 1 %

TPE to γ: ~ 10 %

CT to γ : sub 1 %

How to achieve cutoff independence ; V low k?

One-pion exchange ; Dominant with 10% uncertainty

Measurement of γ; Crucial for 1

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Other NLO diagram

-20PC

~ 0

-1

-1

4

0

Can be absorbed in CT term by redefining 0

PV

1/ correction at LO

`

† (∙ ∂ ∙) → ∙ ∙

~ 2/N ~ 10-2 eV