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→
PAVI06 2
.I
.II
.III
.IV
.V
→ →
→ →
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, , …
PC vertex
PV vertex
* One-meson exchange PV interactions
PAVI06 Background 4
* 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 • • • • • •
PAVI06 Background 6
* 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