Measuring the Shape Proton Measuring the Shape Proton

ELECTRON SCATTERING:How do we Really access this information??• Pick a “final state” (∆ doesn’t live long!)• Detect more than just scattered e’• need to disentangle L=0, L=2 …M1, E2 or C2CMS energy (4-mom. Transfer) 2AJ Sarty (SMU): Shape of Proton (Fall 2002)The “Rest of the Story”on Multipoles…• We now need “more” than just thephoton’s M1, E2 or C2 properties:Ensure “final state” from ∆(1232) decay∆(1232) → p + π 0J π = 3/2 + → [ (½ + ⊗ 0 - ) s ⊗ l ]S π = ½ +• So, Constraints on l(the relative angular momentum ofthe pπp0 pair in Final State):1. Can have: l + ½ = 3/2 (i.e. l = 1)or l – ½ = 3/2 (i.e. l = 2)2. MUST conserve Parity: : final π = +π final = (π(π )(π proton ) (-1)(l = (+)(-) (-1)l+ = (-1)l +1 … so: l = ODD∴ l = 1AJ Sarty (SMU): Shape of Proton (Fall 2002)The Full Multipole Labelsfor Pion Electroproduction from the Proton:• The Dominant “Spherical” (single-quark spin-flip) Transition:l = 1Magnetic photon(must be M1)M 1+• The smaller “Deformed” (quadrupole(quadrupole)Transitions:E 1+ and S 1+(with E meaning “electric“electric” ” photon,and S meaning “scalar“scalar” ” photon)- The “S” can also be written “L”“(“longitudinallongitudinal” ” photon)J = l + ½• Represent COMPLEX Tx Amplitudes• Strength of “Quadrupole“Quadrupole” multipolesdefined with reference to dominantamp:EMR ~ E 1+ / M 1+CMR ~ S 1+ / M 1+AJ Sarty (SMU): Shape of Proton (Fall 2002)Isolating ∆-Excitation(the RESONANT M 1+ , E 1+ , S 1+ )• Can use:• polarization (spin)• Complete angular distributionsTo isolate desired multipole pieces(more on this in a minute!)AJ Sarty (SMU): Shape of Proton (Fall 2002)