1. Overview of Neutron Properties
Introduction to Summer School Topics
Importance of Neutron Properties beyond Nuclear Physics
How to study Neutron Properties
Basic ground state Neutron Properties
Neutron Properties studied via Fundamental Interactions (and Vice Versa!)
EM, Strong, Gravitational & Weak
Summary
B. Filippone
NCSU: 7/16/18

2. Importance of Neutron Properties beyond Nuclear Physics
Neutrons interact via all known forces (Strong, Weak, EM & Gravity)
Provides basic input & tests for Strong & Electroweak Standard Model
Provides access to possible new interactions Beyond Standard Model (BSM) as well as gravity
Susan
Examples
Big Bang Nucleosynthesis
Searching for New Charge-Parity Violation

3. Importance of Neutron Properties beyond Nuclear Physics: Big Bang
Nucleosynthesis p
Source:
Particle Data Group (PDG-2018)

4. Neutron EDM & New Physics
Small EDM in standard model (CKM – see later) provides negligible “background” signal
New CP violation “natural” in new physics
e.g. dn ~ e-cm x sinjCP(1 TeV/M)2

5. Similar Physics at Enormously Different Energy Scales
Neutron Electric Dipole Moment + - 𝐸 𝑑
“Next LHC” Collision Energy
LHC Collision Energy
Proton Rest Mass Energy
Neutron Beta Decay Energy
Neutrino Rest Mass Energy
𝐸= 𝑑 ∙ 𝐸
1014 eV
10-23 eV
1013 eV
109 eV
106 eV
10-1 eV
We now step down to very low energies. This is the energy of the neutron’s electric dipole moment in an electric field at the future sensitivity. No EDM has yet been observed in neutron, proton, quark, muon, electron, tau …
Higgs Boson

6. How to study Neutron Properties
Many (but not all) properties are determined using free neutrons
Where do we get free neutrons ?
For “neutron” targets can also use
Deuteron (bound n+p) n=d-p
Polarized 3He: 3He  ppn (spin-dependent effects mostly due to the neutron)

7. How to Produce Free Neutrons
Reactors via Fission
Accelerators via Spallation
~ 2-3 neutrons/fission
Protons
Proton Beam
Tungsten Nucleus Target
~ 20 neutrons/spallation
for 800 MeV proton beam
Secondary Neutrons
Neutrons
Takeyasu

8. Free Neutron Energy Distribution
G.J. Russell,
Spallation physics–an overview,
Proceedings of ICANS-XI,
KEK-Report Vol , 291–299, 1991
But: fast neutrons disappear quickly

9. Use moderator (e.g. elastic scattering) to slow down neutrons:
Room
Temp.
Neutron
Room Temp
Fast neutron
Use moderator (e.g. elastic scattering) to slow down neutrons:
After collisions En ~ 1/40 eV (Room Temp)
Slowing down takes ~ 100 ms
Neutrons then in thermal equilibrium

10. Where are Neutrons for Fundamental Physics?
SNS Oak Ridge
TRIUMF
PNPI
ILL
NIST NCNR
JPARC
FRMII
PULSTAR
NCSU
RCNP
PSI
LANSCE
Los Alamos
Research Reactors
Proton Accelerators (spallation sources)

11. Basic Ground State Neutron Properties
Mass: mn = (58) MeV/c2
Measured e.g. via n + p  d + g
Magnetic Moment: mn = (45) mN
Precession in B-field
Charge: qn < e
Neutron deflection by strong E-field (60 kV/cm over 9 m)
Mass difference: mn – mp = (51) MeV/c2
Lifetime: tn = 880.2(1.0) sec
Count Nn(t) or dNn/dt
𝜇 𝑁 = 𝑒ℏ 2 𝑚 𝑝
Source:
Particle Data Group
(PDG – 2018)

12. Neutron Lifetime Puzzle
Shannon, Steven
L. Reading-Ikkanda/Quanta Magazine; 
Sources: pre-2017, Particle Data Group;
Serebrov 2017, arxiv: ;
Pattie, 2018, arxiv:

13. Neutron Properties studied via Fundamental Interactions
Electromagnetic Scattering at High Energy
Characterized by EM form factors 𝐺 𝐸 𝑛 𝑞 , 𝐺 𝑀 𝑛 𝑞

14. Electromagnetic Structure (Non-Rel):
Charge Distribution:
𝜌 𝑟 = 1 2𝜋 𝐺 𝐸 𝑛 (𝑞) 𝑒 −𝑖 𝑞 ∙ 𝑟 𝑑 3 𝑞
Magnetization Distribution:
𝑗 (𝑟)= 1 2𝜋 𝑖( 𝑞 × 𝑟 )𝐺 𝑀 𝑛 (𝑞) 𝑒 −𝑖 𝑞 ∙ 𝑟 𝑑 3 𝑞
With 𝐺 𝐸 𝑛 0 =0 (neutron total charge)
𝐺 𝑀 𝑛 0 = 𝜇 𝑛 (neutron magnetic moment)

15. Can measure 𝐺 𝐸 𝑛 𝑄 2 , 𝐺 𝑀 𝑛 𝑄 2 via:
𝑄 2 = 𝑞 2 − 𝜈 2 (rel. invariant)
𝑟 𝑐 2 = lim 𝑄 2 →0 − 1 6 𝑑 𝐺 𝑛 𝐸 𝑄 2 𝑑 𝑄 2
Ye, et al. PHYSICS LETTERS B  777, 8, 2018
Sukolsky, et al, PhysRevC 96, , 2017
𝐺 𝐷 = 𝑄 2 Λ 2
where Λ=0.71𝐺𝑒 𝑉 2

16. Neutron’s Charge Distribution
Fully relativistic treatment:
Charge densities of the neutron and proton
By: Miller, Gerald A.
PHYSICAL REVIEW LETTERS , 99, , 2007
b is transverse impact parameter in “Infinite Momentum Frame”
𝑏 𝜌 𝑏 ( fm −1 )

17. Electromagnetic Properties:
Neutron Charge Radius: 𝑟 𝐸 2 = (22) fm2
Magnetization Radius: 𝑟 𝑀 2 =0.864(8) fm
Polarizabilities from Compton Scattering:
Electric Polarizability: an=11.8(1.1) x 10-4 fm3
Magnetic Polarizability: bn=3.7(1.2) x 10-4 fm3
All above are determined by Strong Interaction/QCD

18. Neutron Properties studied via Fundamental Interactions
Electromagnetic Scattering at High Energy
Characterized by form factors (EM Structure)
Strong Interaction Scattering at Low Energy
At low energy scattering is s-wave
Characterized by scattering lengths
E.g. n-e, n-n, n-p, n-A, … for neutron charge radius (EM), neutron-nucleon & n-nucleus (Strong Int.)

19. Strong Interaction Scattering
Bob
Recall (for short-range potential):
At low energies (kr0<<1; eg s-wave) elastic scattering determined solely by scattering length a
For k 0
selas = 4pa2

20. Thus attractive V0 can give both positive and negative a
Scattering Length
Repulsive Potential
Weak Attractive Potential
Strong Attractive Potential
Thus attractive V0 can give both positive and negative a
 Fermi
Can get a>0 for both attractive and repulsive V

21. Slow Neutron Strong Interaction
Slow neutrons with deBroglie wavelength >> inter-atomic spacing see a “step” potential
They can be guided and trapped (for a > 0)
Analogous to light in medium
But here “index of refraction” of medium is
𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 = 1− 𝑉 𝑒𝑓𝑓 𝐸 𝑛 and can have 𝑛 𝑣𝑎𝑐 > 𝑛 𝑚𝑒𝑑
Can make guides and total “external” reflection
Works for Cold Neutrons (CN) and Ultra-Cold Neutrons (UCN)

22. Potential step analogous to index of
refraction in optics
Neutron kinetic energy
And if a > 0 can have total external reflection
Stefan, Fred
For UCN E < V0 for all angles q

23. UCN Properties g 3m
UCN

24. Slow Free Neutrons Cold Neutrons (CN) and Ultra-Cold Neutrons (UCN)
CN are typically guided “beams” of neutrons
UCN are typically trapped “gas” of neutrons
Velocity (m/s)
Wavelength (nm)
“Temperature” K
Cold Neutrons 20
Ultra Cold Neutrons
< 8
> 50
~ 0.005
Geza

25. Neutron Properties studied via Fundamental Interactions
Electromagnetic Scattering at High Energy
Characterized by form factors (EM Structure)
Strong Interaction Scattering at Low Energy
At low energy scattering is s-wave
Characterized by scattering lengths
E.g. n-e, n-n, n-p, n-A, … for neutron charge radius (EM), neutron-nucleon & n-nucleus (Strong Int.)
Gravitational Quantum States

26. Bound Quantum States in a Gravitational Field
1-d Schrödinger potential problem
V(z) z
mgz
neutron in ground state
“bounces” ~ 15 mm high

27. Height Selects Vertical Velocity
Neutron Energy Levels in Gravity
ILL
Height Selects Vertical Velocity

28. UCN Transmission vs. absorber height
Classical expectation
Nesvizhevsky, et al,
Nature 2002

29. Gravity at short distance
1 mm
Jenke, et al, PRL 112, (2014)
Hartmut

30. Student Exercises:
UCN Gravity states

31. Neutron Properties studied via Fundamental Interactions
Electromagnetic Scattering at High Energy
Characterized by form factors (EM Structure)
Strong Interaction Scattering at Low Energy
At low energy scattering is s-wave
Characterized by scattering lengths
E.g. n-e, n-n, n-p, n-A, … for neutron charge radius (EM), neutron-nucleon & n-nucleus (Strong Int.)
Gravitational Quantum States
Weak Interaction Studies via Discrete Symmetry Tests and Neutron Decay Properties

32. Discrete Transformations & Symmetries
Charge Conjugation
Time Reversal
Parity
Symmetries:
If the Hamiltonian respects this Symmetry,
e.g. 𝑃 𝐻=𝐻
then a process and its transform are both equally likely
Note:
A fundamental theorem – the CPT Theorem – requires interaction Hamiltonians (in QFT) to respect the product operation – C•P•T
Not so for C, P, T, CP, PT, TC

33. Parity Violation in the Electroweak Interaction
T.D. Lee
C.N. Yang
Consider beta-decay of polarized neutron
Polarization = spin = angular momentum = axial vector  𝑟 x 𝑝
Polarized neutron 𝑝 e
If this experiment ≠ this experiment
then Parity is not Conserved 𝑝 e q
spin
Which implies Ne = 1 + a cos
a = asymmetry

34. Experimental Confirmation of Parity Violation
C.S. Wu, R.W. Hayward, D.D. Hoppes, R.P. Hudson
Phys Rev 105, 1413 (1957)
R.L. Garwin, L.M. Lederman, M.Weinrich
Phys. Rev. 105, 1415 (1957)
a ~ -0.2 ± 0.02  a “10” measurement
a = ± 0.03  a “10” measurement

35. Neutron Beta Decay or in quark picture… p u d e- W- ne n
Weak interaction arises in
Leptonic reactions (muon decay)
Semi-leptonic reactions (neutron/nuclear decay)
Non-leptonic reactions (hadronic parity violation)
or in quark picture… u d ne e- n p W-
John, Jason, Mike, Leah

36. Quark Weak Interaction
Standard Model of Quark Weak interaction has weak eigenstates different from mass eigenstates
Neutron can provide precise measurement of Vud
< 0.3% measurements can be sensitive to new physics (from loops in electroweak field theory) ÷ ø ö ç è æ = b s d V tb ts td cb cs cd ub us ud w
Weak eigenstates
Mass eigenstates
Single complex phase
is possible
(gives “CP” Violation
-more later)
a.k.a. Radiative Corrections

37. Sensitivity to New Physics
Quark weak coupling in Standard Model via Vud
(from m vs b-decay)
New particles produce loop corrections W- e-
GWVud m- nm GW d u ne m- nm W- e- ne m ~ n c0 d u

38. Neutron Decay in the Standard Model
GF = Fermi Constant (known from m decay)
Vud = up-down quark weak coupling
GA = Axial vector weak coupling constant
GV = Vector weak coupling constant
f = phase space integral
DR = Electroweak radiative correction
Note: Z0 Boson (M=91 GeV) gives 2% correction!
GA/GV from parity violating decay asymmetry in n decay

39. Polarized Neutron decayæ n . σ r ö e m p . p e n E p . σ A n . σ p p x p d G = G ç + + 1 b a e ν + + B ν + D e n ÷ ç n E E E E è E ø e e ν ν e
Gn =1/tntotal decay rate (depends on GA and GV)
Correlations a, A and B depend on GA and GV
Coefficient b (Fierz) requires new Scalar or Tensor interaction
Coefficient D violates Time Reversal Invariance
Must measure two observables to extract GA and GV (eg. tn and A)
Hirohiko, Brad

40. CP Violation for neutron EDM
Charge Conjugation
Parity
Time Reversal
123
123 - + B J E d m T P
P-even
T-even
P-odd
T-odd
Non-zero d violates T, P
But CPT Theorem of Quantum Field Theory says C x P x T is conserved
 non-zero d also violates CP

41. How big is the neutron EDM?l
d = e x l
u-quark
+2/3e
if l ~ 0.1 rn
-2(1/3e)
dn ~ 4x10-14 e-cm
d-quarks
Experiment says dn < 3x10-26 e-cm

42. Note: Neutron EDM also appears in Electron Scattering
Neutron EM current:
F3 related to neutron EDM:
P&T even
P odd
P&T odd

43. Why is CP Violation Interesting
Why is CP Violation Interesting?  There’s a Big Puzzle in the Early Universe:
You might expect equal amounts of matter & antimatter in the Universe after the Big Bang
These symmetries are important when we discuss another problem with the Standard Model associated with matter production in the early universe.
Energy/photons can produce matter and antimatter – in equal amounts, but when we look around we don’t see anti-matter galaxies – via collisions.
 But 𝑀 ≪𝑀

44. Particle Physics Solution of the Matter-Antimatter Asymmetry of the Universe
Sakharov Conditions (1967)
Total number of quarks must change
- Possible in Standard Model in Big Bang
Departure from Thermal Equilibrium
- Phase Transitions can do this
CP & C violation
- Weak interaction violates C & CP
- But CP violation in the Standard Model is TOO small
A. Sakharov
New particles/interactions are needed to provide larger CP violation

45. Where should we look for EDMs?
Neutral systems are easiest
charged particles are accelerated in E-field
Electrons & muons
Electrons in atoms/molecules, muons in storage rings
Strongly interacting particles
Free neutrons, protons in storage rings, atoms with paired electrons (e.g. diamagnetic)
Stephanie, Kent, Beatrice

46. Searches for a Neutron EDM
E.M. Purcell and N.F. Ramsey, Phys. Rev. 78, 807 (1950)
Searching for Parity Violation in Neutron Scattering
Pioneered Neutron Beam Magnetic Resonance

47. Sensitivity of Neutron EDM SearchesCN
UCN

48. Neutron EDM searches remain highly motivated
Particle Physics Project Prioritization Panel Report
“ Among the most powerful probes of new physics that does not conserve CP are the electric dipole moments (EDM’s) of the neutron, electron and proton … sensitive to contributions from new particle masses at the TeV scale. A new direct neutron edm experiment is planned at Oak Ridge National Laboratory. “

49. Summary
Neutron properties are fundamental input for characterizing all known forces & searching for new ones
Precision neutron measurements can search for new physics (i.e. new particles) at very high mass scales (MNEW >> mn) beyond the Standard Model as well as anomalous gravity
You have 5 days & lots of lectures lectures to digest all of this …
Have Fun !! 

50. Extra Slides …

51. Fermi Pseudopotentialℏ
Then for many nuclei in a solid:
And if ai = a and
l >> atomic spacing: ℏ ℏ
n0 is the nuclear number density
Effective Step Potential

52. Ultra-Cold Neutrons (UCN) (Fermi/Zeldovich)
Are very slow neutrons
(v < 8 m/s , l > 500 Å )
that cannot penetrate into
certain materials
Neutrons can be
trapped in bottles
or by magnetic
field

53. What about HUGE Molecular EDMs!
H20: d = 0.4 x 10-8 e-cm
NaCl: d= 1.8 x 10-8 e-cm
NH3: d = 0.3 x 10-8 e-cm J J
But NH3 EDM is not T-odd
or CP-odd since d J d d J J d
Ground state is actually a
superposition

56. Violation of Time Reversal Symmetry for EDM
Existence of EDM for neutron (or electron, proton) implies a violation of Time Reversal Invariance
Consider a neutron with EDM
If Time Reversal Symmetry is respected:
both time forward and time-backward
neutron states are equally present
But then rotational invariance implies four distinguishable neutrons:
EDM up, spin up,
EDM up, spin down,
EDM down, spin up
EDM down, spin down
But only two distinguishable neutron states exist!! via the Pauli Principle
Thus if EDM≠0  Time Reversal Symmetry is violated (and BTW Parity Violation)

57. Experimental EDMs
Present best limits come from atomic systems and the free neutron
Paramagnetic atoms like 205Tl & polar molecules (ThO) are primarily sensitive to electron EDM
Diamagnetic atoms (e.g. 199Hg) and the free neutron are primarily sensitive to hadronic EDM
Future best limits may come from
Molecular Ions (HfF-, ThF-)
Liquids (129Xe)
Solid State systems (high density)
Storage Rings (Muons, Deuterons, Protons)
Radioactive Atoms (225Ra, 223Rn)
New Technology for Free Neutrons (PSI, ILL, SNS)

58. Weak Decays nm Consider muon decay e- m- ne
Can calculate muon lifetime GF
LIPS = Lorentz Invariant Phase Space

59. Are there new sources of CP violation Beyond the Standard Model to account for matter/antimatter asymmetry?
Where to search for new sources of CP Violation?
Quarks/Gluons
Neutron/Proton EDM: Allows production of matter-antimatter asymmetry via “Baryogenesis”
Leptons (e, m, t, ni)
Lepton EDMs
Neutrino mixing suggests possibility of new CP violation in leptons
Allows production of matter-anti-matter asymmetry via “Leptogenesis”

60. Impact of non-zero EDM Must be new Physics Sharply constrains
Present neutron EDM limit
Must be new Physics
Sharply constrains
models beyond the
Standard Model
(especially with
LHC data)
May account for matter-antimatter asymmetry of the universe
Amin Aboubrahim, Tarek Ibrahim, Pran Nath, The Neutron Electric Dipole Moment and Probe of PeV Scale Physics, Phys. Rev. D , 91, (2015).
Very high mass scale for particular models:
Few x e-cm EDM sensitive to 150 – 600 TeV

61. Weak Decays Ignoring small kinematic corrections
Key feature of Electroweak Standard Model is
UNIVERSALITY - lepton and quark weak interactions
are identical ... modulo the CKM matrix. Thus

62. Measuring Energy Levels
Vibrating mirror
Jenke, et al. NATURE PHYSICS  7, 468 (2011)

63. Effective Potential depends on Scattering Length a
EUCN
The coherent nuclear potential can lead to repulsive effective potential for a > 0
For En < V0, neutrons are trapped  UCN
Bouncing at walls can lead to neutron absorption
but often Lmfp >> ln (thus can have probability per bounce < 10-5)