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

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

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

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 ~ 10-25 e-cm x sinjCP(1 TeV/M)2

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

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)

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

Free Neutron Energy Distribution G.J. Russell, Spallation physics–an overview, Proceedings of ICANS-XI, KEK-Report Vol. 90-25, 291–299, 1991 But: fast neutrons disappear quickly

Use moderator (e.g. elastic scattering) to slow down neutrons: Room Temp. Neutron Moderator @ Room Temp Fast neutron Use moderator (e.g. elastic scattering) to slow down neutrons: After 20-100 collisions En ~ 1/40 eV (Room Temp) Slowing down takes ~ 100 ms Neutrons then in thermal equilibrium

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)

Basic Ground State Neutron Properties Mass: mn = 939.5654133(58) MeV/c2 Measured e.g. via n + p  d + g Magnetic Moment: mn = -1.91304373(45) mN Precession in B-field Charge: qn < 10-21 e Neutron deflection by strong E-field (60 kV/cm over 9 m) Mass difference: mn – mp = 1.29333205(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)

Neutron Lifetime Puzzle Shannon, Steven L. Reading-Ikkanda/Quanta Magazine;  Sources: pre-2017, Particle Data Group; Serebrov 2017, arxiv:1712.05663; Pattie, 2018, arxiv:1707.01817

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

Electromagnetic Structure (Non-Rel): Charge Distribution: 𝜌 𝑟 = 1 2𝜋 3 𝐺 𝐸 𝑛 (𝑞) 𝑒 −𝑖 𝑞 ∙ 𝑟 𝑑 3 𝑞 Magnetization Distribution: 𝑗 (𝑟)= 1 2𝜋 3 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)

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, 065206, 2017 𝐺 𝐷 = 1 1+ 𝑄 2 Λ 2 where Λ=0.71𝐺𝑒 𝑉 2

Neutron’s Charge Distribution Fully relativistic treatment: Charge densities of the neutron and proton By: Miller, Gerald A. PHYSICAL REVIEW LETTERS , 99, 112001, 2007 b is transverse impact parameter in “Infinite Momentum Frame” 𝑏 𝜌 𝑏 ( fm −1 )

Electromagnetic Properties: Neutron Charge Radius: 𝑟 𝐸 2 =-0.1161(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

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.)

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

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

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)

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

UCN Properties g 3m UCN

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 200 - 1000 0.4 - 2 20 Ultra Cold Neutrons < 8 > 50 ~ 0.005 Geza

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

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

Height Selects Vertical Velocity Neutron Energy Levels in Gravity UCN @ ILL Height Selects Vertical Velocity

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

Gravity at short distance 1 mm Jenke, et al, PRL 112, 151105 (2014) Hartmut

Student Exercises: UCN Gravity states

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

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

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

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 = -0.33 ± 0.03  a “10” measurement

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

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

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

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

Polarized Neutron decay æ 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

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

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

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

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 http://www.iamatechie.com

Particle Physics Solution of the Matter-Antimatter Asymmetry of the Universe http://scienceworld.wolfram.com 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

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

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

Sensitivity of Neutron EDM Searches CN UCN

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 10-100 TeV scale. A new direct neutron edm experiment is planned at Oak Ridge National Laboratory. “

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 !! 

Extra Slides …

Fermi Pseudopotential ℏ 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

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

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

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)

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)

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

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”

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, 095017 (2015). Very high mass scale for particular models: Few x 10-28 e-cm EDM sensitive to 150 – 600 TeV

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

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

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)