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Rutherford Scattering Acknowlegements: The E158, HAPPEX, PREX and MOLLER Collaborations www.particleadventure.org Electrons are Not Ambidextrous: New Insights from a Subatomic Matter of Fact Krishna Kumar Stony Brook University, SUNY Physics Colloquium BNL, November 4, 2014 Electroweak Nuclear Physics Outline ✦ Electron Scattering & Subatomic Structure ✦ Electron Scattering and the Weak Force ★ Electrons in the scattering process are NOT ambidextrous ✦ Parity-Violating Electron Scattering ✦ Two Modern Applications ★ The Neutron Skin of a Heavy Nucleus • PREX: First direct electroweak measurement (Phys.Rev.Lett. 108 (2012) 112502)! • PREX-II: Followup precision measurement scheduled for 2016! ★ Search for New Superweak Forces • MOLLER: Proposed ultra-precise weak mixing angle measurement! ✦ Outlook Electrons are Not Ambidextrous 2 Krishna Kumar, November 4 2014 Electroweak Nuclear Physics Outline Fundamental Symmetries, Nuclear Structure, Hadron Physics ✦ Electron Scattering & Subatomic Structure ✦ Electron Scattering and the Weak Force ★ Electrons in the scattering process are NOT ambidextrous ✦ Parity-Violating Electron Scattering ✦ Two Modern Applications ★ The Neutron Skin of a Heavy Nucleus • PREX: First direct electroweak measurement (Phys.Rev.Lett. 108 (2012) 112502)! • PREX-II: Followup precision measurement scheduled for 2016! ★ Search for New Superweak Forces • MOLLER: Proposed ultra-precise weak mixing angle measurement! ✦ Outlook Electrons are Not Ambidextrous 2 Krishna Kumar, November 4 2014 Electron Scattering and the Subatomic Structure ~ 1910 Rutherford Scattering The first fixed target scattering experiment Rutherford devised a scattering experiment involving a beam of alpha particles scattering off a gold foil differential cross section dσ ⌦ dΩ ⇥ ✓ ◆ # alphas scattered into solid angle per unit time Incident beam intensity Electrons are Not Ambidextrous 4 Krishna Kumar, November 4 2014 ~ 1910 Rutherford Scattering The first fixed target scattering experiment Rutherford devised a scattering alpha particles & gold atom’s positive charge: experiment involving a beam of alpha interaction governed by Maxwell’s equations particles scattering off a gold foil d⇤ Z Z α 2 = 1 2 dΩ 2mv2 sin2(⇥/2) ✓ ◆ ✓ ◆ Atom’s positive charge: static differential cross section EM potential dσ ⌦ dΩ ⇥ ✓ ◆ # alphas scattered into solid angle per unit time Incident beam intensity Electrons are Not Ambidextrous 4 Krishna Kumar, November 4 2014 ~ 1910 Rutherford Scattering The first fixed target scattering experiment Rutherford devised a scattering alpha particles & gold atom’s positive charge: experiment involving a beam of alpha interaction governed by Maxwell’s equations particles scattering off a gold foil d⇤ Z Z α 2 = 1 2 dΩ 2mv2 sin2(⇥/2) ✓ ◆ ✓ ◆ Atom’s positive charge: static differential cross section EM potential dσ ⌦ dΩ ⇥ ✓ ◆ # alphas scattered into solid angle per unit time Incident beam intensity Electrons are Not Ambidextrous 4 Krishna Kumar, November 4 2014 ~ 1910 Rutherford Scattering The first fixed target scattering experiment Rutherford devised a scattering alpha particles & gold atom’s positive charge: experiment involving a beam of alpha interaction governed by Maxwell’s equations particles scattering off a gold foil d⇤ Z Z α 2 = 1 2 dΩ 2mv2 sin2(⇥/2) ✓ ◆ ✓ ◆ Atom’s positive charge: static differential cross section EM potential dσ ⌦ dΩ ⇥ ✓ ◆ •Established that atoms have a tiny nuclear # alphas scattered into core ~ 10-14 m, << atomic size of 10-10 m solid angle per unit time •Revolutionized experimentation: particle Incident beam intensity scattering as a microscope Electrons are Not Ambidextrous 4 Krishna Kumar, November 4 2014 A femtoscope Electron Scattering At nuclear scales, particles behave mostly like waves Particle How to produce femtometer Accelerators wavelengths in the laboratory? Electrons are Not Ambidextrous 5 Krishna Kumar, November 4 2014 A femtoscope Electron Scattering Electron interactions are well-understood At nuclear scales, particles behave mostly like waves Particle How to produce femtometer Accelerators wavelengths in the laboratory? Quantum Electrodynamics Dirac: relativistic motion of electrons with spin 1/2 Electron scattering: electromagnetic interaction E’ described as an exchange of a virtual photon. θ E N Electrons are Not Ambidextrous 5 Krishna Kumar, November 4 2014 A femtoscope Electron Scattering Electron interactions are well-understood At nuclear scales, particles behave mostly like waves Particle How to produce femtometer Accelerators wavelengths in the laboratory? Quantum Electrodynamics Dirac: relativistic motion of electrons with spin 1/2 Electron scattering: electromagnetic interaction E’ described as an exchange of a virtual photon. θ Mott: spin 1/2 electrons E scattering off infinitely N heavy point spinless nucleus 2 2 θ q2: (4-momentum)2 of the virtual photon q = −4EE # sin 2 Electrons are Not Ambidextrous 5 Krishna Kumar, November 4 2014 € A femtoscope Electron Scattering Electron interactions are well-understood At nuclear scales, particles behave mostly like waves Particle How to produce femtometer Accelerators wavelengths in the laboratory? Quantum Electrodynamics Dirac: relativistic motion of electrons with spin 1/2 Electron scattering: electromagnetic interaction E’ described as an exchange of a virtual photon. θ Mott: spin 1/2 electrons E scattering off infinitely N heavy point spinless nucleus 2 2 θ q2: (4-momentum)2 of the virtual photon q = −4EE # sin 2 Powerful technique: high statistics and precise event-by-event kinematic determination Electrons are Not Ambidextrous 5 Krishna Kumar, November 4 2014 € The Size of a Nucleus e Heavy, spinless d⇥ 4Z2α2E2 e γ = nucleus dΩ Mott q4 ⇥ Electrons are Not Ambidextrous 6 Krishna Kumar, November 4 2014 If Q sufficiently large (wavelength < 10 fm) , nuclear size modifies formula The Size of a Nucleus Increase momentum transfer -> shorter wavelength -> higher resolu6on -> smaller scales e Heavy, spinless d⇥ 4Z2α2E2 e γ = 208Pb nucleus dΩ Mott q4 ⇥ Differential Cross Section dσ dσ 2 = F (q) dΩ dΩ ⇥ ⇤Mott 1 2 3 q (fm)-1 Electrons are Not Ambidextrous 6 Krishna Kumar, November 4 2014 If Q sufficiently large (wavelength < 10 fm) , nuclear size modifies formula The Size of a Nucleus Increase momentum transfer -> shorter wavelength -> higher resolu6on -> smaller scales e Heavy, spinless d⇥ 4Z2α2E2 e γ = 208Pb nucleus dΩ Mott q4 ⇥ Differential Cross Section dσ dσ 2 = F (q) dΩ dΩ ⇥ ⇤Mott The point-like sca>ering probability modified: Introduce a “form factor” F (q)= eiqrρ(r)d3r Form factor is the Fourier transform of 1 2 charge distribuon 3 q (fm)-1 Electrons are Not Ambidextrous 6 Krishna Kumar, November 4 2014 If Q sufficiently large (wavelength < 10 fm) , nuclear size modifies formula The Size of a Nucleus Increase momentum transfer -> shorter wavelength -> higher resolu6on -> smaller scales e Heavy, spinless d⇥ 4Z2α2E2 e γ = 208Pb nucleus dΩ Mott q4 ⇥ Differential Cross Section dσ dσ 2 = F (q) dΩ dΩ ⇥ ⇤Mott F (q) ρ(r) 1 2 3 q (fm)-1 Electrons are Not Ambidextrous 6 Krishna Kumar, November 4 2014 If Q sufficiently large (wavelength < 10 fm) , nuclear size modifies formula The Size of a Nucleus Increase momentum transfer -> shorter wavelength -> higher resolu6on -> smaller scales e Heavy, spinless d⇥ 4Z2α2E2 e γ nuclear = nucleus dΩ Mott q4 charge ⇥ Differential Cross Section densities dσ dσ 2 = F (q) dΩ dΩ ⇥ ⇤Mott F (q) ρ(r) Electrons are Not Ambidextrous 6 Krishna Kumar, November 4 2014 The Size of the Proton Otto Stern (1932) measured the proton magnetic moment µp~ 2.5 µBohr : First indication that the proton was not just a positive, structureless electron (Nobel prize 1943) Electrons are Not Ambidextrous 7 Krishna Kumar, November 4 2014 Precise e-p cross section measurements at various scattering angles The Size of the Proton Otto Stern (1932) measured the proton magnetic moment µp~ 2.5 µBohr : First indication that the proton was not just a positive, structureless electron (Nobel prize 1943) Stanford U. Mark III Accelerator McAllister and Hofstadter, Physical Review 102 (1956) 851. Electrons are Not Ambidextrous 7 Krishna Kumar, November 4 2014 Precise e-p cross section measurements at various scattering angles The Size of the Proton Otto Stern (1932) measured the proton magnetic moment µp~ 2.5 µBohr : First indication that the proton was not just a positive, structureless electron (Nobel prize 1943) Stanford U. Mark III Accelerator McAllister and Hofstadter, Physical Review 102 (1956) 851. Electrons are Not Ambidextrous 7 Krishna Kumar, November 4 2014 Precise e-p cross section measurements at various scattering angles The Size of the Proton Otto Stern (1932) measured the proton magnetic moment µp~ 2.5 µBohr : First indication that the proton was not just a positive, structureless electron (Nobel prize 1943) Stanford U. Mark III Accelerator McAllister and Hofstadter, Physical Review 102 (1956) 851. Electrons are Not Ambidextrous 7 Krishna Kumar, November 4 2014 Precise e-p cross section measurements at various scattering angles The Size of the Proton Otto Stern (1932) measured the proton magnetic moment µp~ 2.5 µBohr : First indication that the proton was not just a positive, structureless electron (Nobel prize 1943) Stanford U. Mark III Accelerator McAllister and Hofstadter, Physical Review 102 (1956) 851. It isn’t Mott, nor Dirac, nor modified Dirac with a larger magnetic moment… Electrons are Not Ambidextrous 7 Krishna Kumar, November 4 2014 Precise e-p cross section measurements at various scattering angles The Size of the Proton
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