Magnetic Mapping for the 6He ExperimentREU Final Presentation

Jessie Thwaites1

Mentor: Alejandro Garcıa2

1College of Saint Benedict/Saint John’s University

2CENPA, University of Washington

15 August 2018

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Outline

1 Motivation

2 BackgroundWeak InteractionHelicity and ChiralityFierz Interference

3 My ContributionGadgetMultipole Expansion

4 Discussion

5 Further Investigation

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Motivation

Search for Beyond theStandard Model (BSM)physics through precisionexperiment

predicted by other theories:supersymmetry, GrandUnified Theories

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Background - Weak Interaction

Weak interaction - fundamentalforce

responsible for β decay

6He→ 6Li + e− + νe

mediated by W− boson

new physics: interactions

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Background - Parity Violation

Parity is the inversion of spatial coordinates

(ct, x , y , z)→ (ct,−x ,−y ,−z)

P~r = −~rP~L = (−~r)× (−~p) = ~r × ~p

Parity shows symmetry under theinversion of spatial coordinates

with parity: expected both right-and left-handed particles

Chien Sheng-Wu 1957 -left-handed particles only

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Helicity and Chirality

Helicity:

H =~p · ~s|~p||~s|

= ±1

Helicity not Lorentz invariant→ solution: define Chirality

eL =

√1+ p

E2 eH=−1 +

√1− p

E2 eH=+1

eR =

√1− p

E2 eH=−1 +

√1+ p

E2 eH=+1

eReL =√

1− ( pE )2 = m

E

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Interaction Hamiltonian

Interaction Hamiltonian for 6He beta decay:

Hint = ψf γµγ5ψi (2CAe

−Lγµγ5νLe ) +

ψf σµνψi [(CT − C ′T )e−Lσµνν

Re + (CT + C ′T )e−Rσµνν

Le ]

Search for tensor currents (σµν)

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Chirality-flipping - Fierz Interference

terms that include RH & LHare chirality flipping

show small distortions tospectrum

dW = dW0(1 + a pe ·pνEeEν

+ b ΓmeEe

)

b ≈ (CT +C ′T )

CA

m/K0 1 2 3 4 5 6 7

) [a

.u.]

-2(b

=10

E/d

Γd

0

2

4

6

8

10

610×

m/K0 1 2 3 4 5 6 7

(b=

0)-1

E/d

Γ)/

d-2

(b=

10E

/dΓd

2−

0

2

4

6

83−10×

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Measuring the β spectrum - CRES technique

need precision measurements of the entire spectrum

6 GHz bandwidth, tune magnet

Cyclotron Radiation Emission Spectroscopy (Project 8)

m/K0 1 2 3 4 5 6 7

E/d

Nd

0

2

4

6

8

10

610× = 1 TB

= 2 TB

= 4 TB

= 6 TB

ωc =qBc2

Ee

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My ContributionMagnetic Modeling

1. adapt NMR probe2. multipole expansion

3. position mapping

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The Gadget

Place the probe in the magnet at a particular location (r , θ, z)

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Nuclear Magnetic Resonance (NMR) Principles

start with a sample in a magnetic field, B0

perturb with a small oscillating field, B1

at resonance, induces an energy transitionby flipping magnetization

produces a strong signal at this frequency- characteristic of magnetic field seen bynucleus

use this magnitude measurement & fit tomultipole expansion

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Multipole Expansion

Laplace’s Equation:∇2φm = 0

Solutions: Taylor Expansion with spherical harmonics:

φm =∞∑l=0

l∑m=−l

(aml rl + bml r

−(l+1))Yml

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Theodolite Mapping

accurate positionmeasurements for probe

position accuracy impactsaccuracy of Linear LeastSquares fit in code

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Position mapping: z=-20 cm

Mean (x,y) values for set r

colors show r-value

Additional measurements:z=0 and z=+20 cm (notyet finished)

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Future Investigation

Finish position mapping of magnet

Automate gadget & Teslameter data collection process

Improvements on multipole model

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Acknowledgements

NSF and INT REU Program

Dr. Alejandro Garcia and his group

Deep, Gray, Cheryl and Linda

References[1] A. Abragam. Principles of Nuclear Magnetism. Clarendon Press, 1961.

[2] D. M. Asner, R. F. Bradley, L. de Viveiros, P. J. Doe, J. L. Fernandes, M. Fertl, E. C. Finn, J. A. Formaggio,D. Furse, A. M. Jones, J. N. Kofron, B. H. LaRoque, M. Leber, E. L. McBride, M. L. Miller, P. Mohanmurthy,B. Monreal, N. S. Oblath, R. G. H. Robertson, L. J. Rosenberg, G. Rybka, D. Rysewyk, M. G. Sternberg, J. R.Tedeschi, T. Thuemmler, B. A. VanDevender, and N. L. Woods (Project 8 Collaboration). Single-ElectronDetection and Spectroscopy via Relativistic Cyclotron Radiation. Phys. Rev. Lett., 114(16), Apr. 2015.

[3] C. Boettcher. Theory of Electric Polarization. Elsevier Publishing Co., 1952.

[4] M. Fertl, B. Graner, A. Garcia, M. Guigue, D. Hertzog, P. Kammel, A. Leredde, P. Mueller, N. S. Oblath,R. G. H. Robertson, G. Rybka, G. Savard, D. Stancil, H. E. Swanson, B. A. VanDevender, and A. Young.Detection of cyclotron radiation applied to searches for chirality-flipping interactions. Not yet published, 2018.

[5] R. Hong, M. G. Sternberg, and A. Garcia. Helicity and nuclear beta decay correlations. Am. J. Phys., 85(45),2017.

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