SLIDE 1 Parity-Violation in Neutron Deuteron Scattering in Pionless Effective Field Theory
Jared Vanasse Duke University
SLIDE 2 Parity Violation
Parity violation in weak force proposed by Lee and Yang to explain puzzle Madame Wu discovered parity-violation in the beta decay of
60Co
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DDH Potential
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SLIDE 6 Low Energy Nucleon-Nucleon Parity- Violation
Conservation of angular momentum, and possible isospin transitions tell us
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EFT Ingredients
Identity degrees of freedom Write down all possible operators that obey symmetry of underlying theory using degrees of freedom Obtain power counting scheme to order terms in powers of (p/Λ)n Calculate all terms up to a given order (p/Λ)N
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The Lagrangian for Pionless EFT is The Lagrangian can be rewritten in the more useful form Spin and Isospin Projectors are
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Effective range expansion (ERE) is Partial wave expansion gives Reexpanding about deuteron pole ERE becomes
Effective Range Expansion
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Dressed deuteron propagator is Single nucleon bubble gives Resulting dressed deuteron propagator is Matching onto the ERE we find
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Parity Conserving nd Scattering
At LO and infinite sum of diagrams in needed in the Quartet channel Deuteron has spin 1 and neutron is spin ½, thus nd scattering has a Quartet and Doublet channel
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Quartet Channel
After projection integral equation is Where Ql(a) is related to Legendre polynomial of second kind up to factor (-1)l
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Doublet Channel
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Parity-Violation in EFT
The parity-violating Lagrangian contains five terms and is given by
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Parity-Violating nd Scattering
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Focus on single diagram Diagram is given by where
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Partial wave series is Where the spin angle functions are given by Terms are projected out by
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Projecting amplitude leads to integral where Focusing on first term we find
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Expression has simple solution
SLIDE 21 Beam Asymmetry nd Scattering
Vanasse
SLIDE 22 Vanasse
Target Asymmetry nd Scattering
SLIDE 23 nd Spin Rotation
Griesshammer, Schindler, and Springer Vanasse
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Asymmetry Results
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Spin Rotation Results
Spin rotation Comparison of different results for spin rotation
SLIDE 26 Future Directions
Resolve factor of two Carry calculation to higher orders Calculate pd scattering Ay puzzle
3He photodisintegration
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Summary
We can calculate nd scattering PV amplitudes to LO. Estimates for the PV LEC's can be obtained by matching onto DDH estimates. Using LEC estimates and PV amplitudes we can predict any PV observable in nd scattering.
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Thank You
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Numerical Techniques
Integrals are discretized using quadrature. Gives set of linear equations to solve. In order to avoid singularities amplitude is evaluated along path C'B.
SLIDE 30 Girlanda Reduction
Girlanda showed nucleon-nucleon parity-violation is described by only five LEC's. There are twelve possible unique relativistic parity-violating nucleon-nucleon terms
SLIDE 31 Using Fierz identities and equations of motion one can find six relations between
Taking the non-relativistic reduction we find two operators are the same and get Lagrangian
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LEC Estimates
