[PPT] - Hadronic Parity Violation in Effective Field Theory Matthias R. PowerPoint Presentation

SLIDE 1

Hadronic Parity Violation in Effective Field Theory

Matthias R. Schindler

University of South Carolina

The 19th Particles and Nuclei International Conference July 24–29, 2011

Collaborators: H. W. Grießhammer, D. R. Phillips, R. P . Springer

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SLIDE 2

Hadronic parity violation and effective field theory Two-nucleon sector Three-nucleon sector Conclusion & Outlook

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SLIDE 3

Hadronic parity violation

Weak interaction between quarks induces parity-violating component in nucleon-nucleon (NN) interaction Effects highly suppressed ∼ 10−6 − 10−7 Parity violation to isolate weak component Range of weak quark-quark interactions ∼ 0.002 fm Probe of nonperturbative QCD

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SLIDE 4

Few-nucleon experiments

Complex nuclei: enhancement up to ∼ 10% effect Relation to NN interaction? Theoretically difficult Two-nucleon system

pp scattering (Bonn, PSI, TRIUMF

, LANL)

np → dγ (SNS, LANSCE, Grenoble)
np spin rotation?

Few-nucleon systems

nα spin rotation (NIST)
pα scattering (PSI)

3He(

n, p)3H (SNS)

nd → tγ (SNS?)
nd spin rotation?

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SLIDE 5

Theory goals

Variety of experiments Unified framework Model-independent Check consistency of results Defendable theoretical errors

Two- and few-body systems

Energies 10s of MeV Ideally suited for pionless effective field theory [EFT(π /)]

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SLIDE 6

Pionless EFT

Model-independent framework Lagrangian with all terms allowed by symmetries At very low energy cannot resolve pion exchange NN contact terms with increasing number of derivatives Leading-order parity-conserving Lagrangian L =N†(i∂0 +

∇2

2M )N − 1 8C(1S0) (NTτ2τaσ2N)†(NTτ2τaσ2N) − 1 8C(3S1) (NTτ2σ2σiN)†(NTτ2σ2σiN) + . . . ,

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SLIDE 7

Parity violation in EFT(π /)

At leading order: 5 independent PV NN contributions1 Experimental input to determine 5 coefficients LPV = −

C(3S1−1P1)

NTσ2 στ2N † ·

NTσ2τ2i

↔

∇N

+ C(1S0−3P0)

(∆I=0)

NTσ2τ2

τN † ·

NTσ2

σ · τ2 τi

↔

∇N

+ C(1S0−3P0)

(∆I=1)

ǫ3ab NTσ2τ2τ aN † NTσ2 σ · τ2τ b↔ ∇N

+ C(1S0−3P0)

(∆I=2)

Iab NTσ2τ2τ aN † NTσ2 σ · τ2τ bi

↔

∇N

+ C(3S1−3P1) ǫijk

NTσ2σiτ2N † NTσ2σkτ2τ3

↔

∇

j

N

+ h.c.

1

Savage, Springer (1998); Zhu et. al. (2005); Girlanda (2008); Phillips, MRS, Springer (2009)

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Nucleon-nucleon scattering

Simplest process

NN cross section

Strong contribution does not depend on helicity Weak contribution does depend on helicity Consider asymmetry in N + N AL = σ+ − σ− σ+ + σ− Interference between strong and weak

P S + P S

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Leading-order results: pp/nn

2

App/nn

L

= 8k App/nn C

1S0

App = 4

C(1S0−3P0)

(∆I=0)

+ C(1S0−3P0)

(∆I=1)

+ C(1S0−3P0)

(∆I=2)

Ann = 4
C(1S0−3P0)

(∆I=0)

− C(1S0−3P0)

(∆I=1)

+ C(1S0−3P0)

(∆I=2)

No Coulomb interaction for pp (∼ 3% at 15 MeV)

Depends on ratio of PV and PC constant ⇒ Renormalization point-dependence of App/nn dictated by C

1S0 2

Phillips, MRS, Springer (2009)

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SLIDE 10

Leading-order results: np

Anp

L = 8k

 

dσ

1S0

dΩ dσ

1S0

dΩ + 3dσ3S1 dΩ

A

1S0

np

C

1S0

+

dσ

3S1

dΩ dσ

1S0

dΩ + 3dσ3S1 dΩ

A

3S1

np

C

3S1

  A

1S0

np = 4

C(1S0−3P0)

(∆I=0)

− 2C(1S0−3P0)

(∆I=2)

A

3S1

np = 4

C(3S1−1P1) − 2C(3S1−3P1)

dσ dΩ = 1 a 2 + k2 −1 Measure at 2 different energies: disentangle A

1S0

np and A

3S1

np

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SLIDE 11

np spin rotation
np scattering amplitude related to spin rotation angle3

1 ρ dφPV dl = M 2k 1 2

mp=± 1

2

Re [M+(mp) − M−(mp)] Rotation angle at NLO with g(X−Y) =

32π

M C(X−Y) CX

: 1 ρ dφnp

PV

dl =

(18.1 ± 1.8) g(3S1−3P1) + (9.0 ± 0.9) g(3S1−1P1)

+ (−37.0 ± 3.7) g(1S0−3P0)

(∆I=0)

+ (74.4 ± 7.4) g(1S0−3P0)

(∆I=2)

rad

MeV

1 2

dφnp

PV

dl

≈
10−6 − 10−7 rad

m

3

Grießhammer, MRS, Springer

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SLIDE 12

Electromagnetic processes

Asymmetry in np → dγ Aγ = 32 3 M κ1(1 − γa

1S0)

C(3S1−3P1) C

3S1

NPDGamma @ SNS Related to deuteron anapole moment through C(3S1−3P1)4 Circular polarization in np → d γ Pγ ∼ aC(3S1−1P1) C

3S1

+ b C(1S0−3P0)

(∆I=0)

− 2C(1S0−3P0)

(∆I=2)

C

1S0

Experimental result consistent with Pγ = 0 Use high-intensity free electron lasers for γd → np?

4

Savage (2001); MRS, Springer (2009); Knyazkov (1983)

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Three-nucleon systems

Parity-conserving sector Describe 3N systems with NN interactions only? Na¨ ıve power counting: |2N| > |3N| > |4N| > . . . Analysis of nd scattering in 2S 1

2 wave5

3N interaction at leading order for renormalization Additional experimental input (e.g. scattering length) Parity-violating sector Na¨ ıve power counting: 3N interaction higher order If not: even more experiments needed

5

Bedaque, Hammer, van Kolck (1999)

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Parity violation in 3N sector

Analyze high-momentum behavior of loop integrals, e.g., Parity-conserving amplitude known Include leading-order PV 2N interaction6 No PV 3N interaction at LO and NLO

6

Grießhammer, MRS (2011)

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nd spin rotation
nd scattering amplitude at NLO7

Verified that no PV 3NI required for renormalization 1 ρ dφnd

PV

dl =

(15.9 ± 1.6) g(3S1−1P1) − (36.6 ± 3.7) g(3S1−3P1)

+(4.6 ± 1.0) (3g(1S0−3P0)

(∆I=0)

− 2g(1S0−3P0)

(∆I=1)

)

rad

MeV

1 2

dφnd

PV

dl

≈ 10−[6...7] rad

m

7

Grießhammer, MRS, Springer

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SLIDE 16

Cutoff dependence

g3S11P1

200 500 1000 2000 5000 5 10 15 MeV cg 3 S1 1 P1 rad MeV

12

200

500 1000 2000 5000 1 2 3 4 5 MeV c rad MeV

12

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SLIDE 17

Conclusion & Outlook

Hadronic parity violation Probe nonperturbative QCD phenomena: inside-out probe Current and proposed experiments Low-energy Few-nucleons Need consistent analysis and interpretation

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Conclusion & Outlook

EFT for parity-violating NN interactions 5 independent operators at LO in EFT(π /) 2-body observables

pp scattering,

np spin rotation, np ↔ dγ Not enough information PV 3 body sector No PV 3-body operators at LO and NLO

nd spin rotation
nd → tγ

Few-body observables Parity-conserving: EFT(π /) up to A=6 No Core Shell Model, Resonating Group Method8 Lattice

8

Stetcu, Barrett, van Kolck (2007), (2010); Kirscher, Grießhammer, Shukla, Hofmann (2010); Beane, Savage (2002)

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Coulomb corrections

Coulomb corrections can be included in EFT(π /)9 Coulomb parameter η = Mα

2p

Integrals for cross section over finite range θ1 ≤ θ ≤ θ2 For Tlab = 0.1 MeV: η ≈ 0.26 ⇒ expand in η App

L = 8p App

C

1S0

1 + η
1

aS(µ)p

1

cos θ1 − cos θ2 ln 1 − cos θ1 1 − cos θ2

+O(η)2

9

Kong and Ravndal (1999)

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SLIDE 20

Comparison with experiment

pp scattering experiments (23o < θlab < 52o)10 A

pp L (E = 13.6 MeV) = (−0.93 ± 0.21) × 10−7

A

pp L (E = 45 MeV) = (−1.50 ± 0.22) × 10−7

From result at E = 13.6 MeV: App C

1S0

= (−1.5 ± 0.3) × 10−10 MeV−1 Coulomb correction ∼ 3 percent Use to ‘predict’ asymmetry at 45 MeV A

pp L (E = 45 MeV) = (−1.69 ± 0.38) × 10−7

In agreement with experiment

10

Eversheim (1991); Kistryn (1987)

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Higher-order corrections

At E = 45 MeV center-of-mass momentum p > mπ Resum higher-order corrections in PC sector Re-analyze low-energy pp measurement (no Coulomb) App(µ = mπ) C

1S0

= (−1.1 ± 0.25) × 10−10 MeV−1 ∼ 30% difference “Prediction” for E = 45 MeV A

pp L (E = 45MeV) = (−2.6 ± 0.6) × 10−7

Compare to −1.69 × 10−7: > 50% difference

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