Measuring the Shape Proton Measuring the Shape Proton

Measuring the Shapeof theProtonmore than just a sphere!By:Adam J. Sarty(Saint Mary’s University)Pinch-Hit Talk presented at:AUPAC 2003 (at St. F.X.)(remember the alternative…nuthin)Physics & Atm. Science, Dalhousie (Nov. 2002)Physics Dept., U. Manitoba (Oct., 2002)TRIUMF, UBC (Oct. ,2002)Shape• One of the first questions askedwhen confronted with a newobject is:“What does it look like?”• For a physicist, this question isoften translated (that is, goingfrom normal-peoplepeople-languagelanguage tophysics-geekgeek-language):“What is the object’s shape?”• For a subatomic (nuclear)physicist, where the interest liesin the “fundamental” buildingblocks of all matter, the naturalquestion becomes:“What is the shape of the proton?”AJ Sarty (SMU): Shape of Proton (Fall 2002)Shape of the Proton• That protons are indeed “fundamentalbuilding blocks” of the atomic nucleushas been established since about 1930• And … since about 1970, we know protonshave an internal structure of 3 quarks … (butlet’s stick with protons since we can neverisolate one quark by itself, which will make itreally hard to measure it’s shape…)• What would we “expect”??- We have a feeling that“fundamental” objects should besimple (and symmetric) …SPHERICAL (like a ball)!• We do know the SIZE of the protonvery well (from electron scattering andfrom Atomic Lamb Shift):Proton charge radius = r p ≈ 0.9 fm• But what about “shape” … could theproton be deformed from spherical?AJ Sarty (SMU): Shape of Proton (Fall 2002)Defining “Shape”:Quadrupole Moment• To quantify how “non-spherical”anyobject’s mass distribution is, thetypical first-step step is to establish itsQuadrupole Moment:Q o = ∫ d 3 r ρ( ( r ) ( 3z 2 – r 2 )zPositive ≡ “prolate”(football shaped)Negative ≡ “oblate”(pancake shaped)zAJ Sarty (SMU): Shape of Proton (Fall 2002)

Quadrupole Momentof the Proton?• Unfortunately … we cannot evendefine the Quadrupole Moment for theproton (Quantum Mechanics gets inthe way!)• For proton, the Q.M. would be theexpectation value of the QuadrupoleMoment operator:< Q o > = < p | Q o | p > ≡ 0 !Proton w.f.:J = ½Quad. Moment Operator:Rank “2” (J = 2)Proton w.f.:J = ½• Angular Momentum Selection Rulesdictate this is zero ( J= ½ and J = 2cannot couple to give J= ½ ).AJ Sarty (SMU): Shape of Proton (Fall 2002)Proton Shape another Way?…the Transition Quadrupole Moment• To access the proton’s intrinsic“shape” information, we need toby-passthis angular momentumselection rule problem …• Look at “shape” of Transitions to ahigher-J J excited state (been doing thiswith “heavy” J = 0 and J = ½ nucleifor about 40-50 years!).• The 1 st excited state of the proton isthe ∆(1232), and it has J = 3/2 :< ∆ | Q o | p > = ? (shape info!)Delta w.f.:J = 3/2Quad. Moment Operator:Rank “2” (J = 2)Proton w.f.:J = ½• No angular momentum problem:( J=3/2 ) ⊗ ( J=2 ) → ( J= ½ ) AJ Sarty (SMU): Shape of Proton (Fall 2002)Accessing (Experimentally)the Transition Quadrupole Moment• Unfortunately (again!) … easier towrite “” ” than to measure!• The (ok… “my” !) preferred method:ELECTROMAGNETICALLY excitethe proton to its first excited state, the∆ (1232), using real photons (gammarays) or virtual photons (electronscattering).As a Short “Aside” …Proton Shape even makes theNEWS…pγ *γ * + p → ∆(1232)∆(1232)• Incident particle is“shapeless”• EM interaction known• Excitation from “QuadrupolePhotons”(L = 2) will be a direct signature for aQuadrupole Transition Moment!AJ Sarty (SMU): Shape of Proton (Fall 2002)Sept. 22, 2002: USA Today –“Physicists thrown for a loop” …Story on shape of the proton being not exactly spherical!Based on interpretation of Jefferson Lab Hall A dataon elastic electron scattering from proton, byG. Miller (PRC 66, 032201(R), 2002):“Light front cloudy bag model:Nucleon electromagnetic form factors”AJ Sarty (SMU): Shape of Proton (Fall 2002)

Outline for (the rest of)the Talk…• Models (simple) of the Proton- Basis for understanding meaning of“shape” of proton- Explanations of the needed jargon(e.g. “multipoles“multipoles”)• Electron Scattering basics- Response Functions – and relationto multipoles- Status of World’s Data• Overview of 2 Experimental Projects:- “OOPS” at MIT-Bates- “FPP” in Hall A at Jefferson LabAJ Sarty (SMU): Shape of Proton (Fall 2002)A Starting Pointfor discussing proton structure:The Constituent Quark Model• Basis: : 3 “heavy” valence quarks,each with spin-parity:parity: S π = ½ +• Angular Momentum Coupling:Proton (J(π = ½ + ) ∆ (J π = 3/2 + )J = L ⊗ SS = [ ( ½ ⊗ ½ ) 0 , 1 ⊗ ½ ] = ½ or 3/2L: 0, 1, or 2 could work…PARITY:π = (π(q-1 )(π q-2 )(π q-3 )(−1) L= (+)(+)(+)(−1) L = (−1)(LSo: L = 0 or 2½ = 0 ⊗ ½ “spherical” 3/2 = 0 ⊗ 3/2½ = 2 ⊗ 3/2 3/2 = 2 ⊗ ( ½, , 3/2)“deformed”AJ Sarty (SMU): Shape of Proton (Fall 2002)Simplest Structure:Spherical (L = 0)• Complete Spherical Symmetry:L = 0 in both proton and Deltaone quarkspin flipJ π = ½ + J π = 3/2 +• Indeed … the dominantly observedtransition is this simple spin-flip …• So, the proton is “mostly spherical”• The issue is to measure how muchL=2 component exists in thesestates – this is the measure of“deformation from spherical”.• Let’s now examine EM excitationof the transition (allowing for theL=2 components) …AJ Sarty (SMU): Shape of Proton (Fall 2002)What “kind” (MULTIPOLE) of Photoncan Excite p → ∆?γ * + p → ∆(1232)(L π γ ⊗ ½ + = 3/2 + )• Conserve Parity: : Final π is +, so …π initial = (π(γ )(π proton ) = (π(γ )(+) ) = +• So photon’s s parity is Even.• Recalling Parity of EM Multipoles:- Electric: EL = (-1)(L- Magnetic: ML = (-1)(L+1- Scalar (or Coulomb): CL = (-1)(L• So…L π γ = 1 + ⇔ M1 (magnetic dipole)orL π γ = 2 + ⇔ E2, C2 (quadrupole!)• M1 is dominant (spin flip!)• Let’s s see “meaning” of E2 and C2 …AJ Sarty (SMU): Shape of Proton (Fall 2002)

Existence of E2 or C2:Implies L=2 (“Deformation”) !• In the simple CQM:Let the |N> and |∆> | > w.f. be linearcombinations of the 3 valence quarksin L=0 and L=2 statesWhat Physics do we Learn byStudying “Deformation”(the L=2 states)?• Valence Quark picture (CQM):- “ColourHyperfine Interaction”:a tensor force (analogous to theNN tensor force introducingmixing of L=0 and L=2 states inthe deuteron)(mechanism: 1-gluon 1exchange?)Beyond the Simple CQM …Non-Valence Quark D.O.F. (qqor π’s!)(from Buchmann & Henley, PRC 63, 015202)AJ Sarty (SMU): Shape of Proton (Fall 2002)Valence (1-quark)Non-Valence (2-quark)AJ Sarty (SMU): Shape of Proton (Fall 2002)Physics of Deformation (continued):Quark Interactions vs. Pion Cloud• Existence of E2 or C2 excitations maynot mean L=2 valence quarkcomponents (i.e. may not be probingdirect quark-quark interaction)• Possible presence of 2-quark 2currentsallows E2 or C2 with L=0 valence q’sPhysics of Deformation (continued):Quark Interactions vs. Pion Cloud• However, existence of E2 or C2 excitationsstill means “deformed“proton”…• A popular model of the 2-quark 2currents is the presence of a(deformed) “PION CLOUD”surrounding the valence quarks.(from Buchmann & Henley, PRC 63, 015202)AJ Sarty (SMU): Shape of Proton (Fall 2002)• Rationale: : long-range structuredetermined by lightest GoldstoneBoson (again, not dissimilar to thecase in the deuteron!)AJ Sarty (SMU): Shape of Proton (Fall 2002)

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)

One Last Model Prediction!Sato/Lee, PRC 63 (2001) 055201:Pion-exchange modelIm( M 1+ )Letting the Cat out of the Bag:Real Photons show Deformation!1997No pion cloudIm( E 1+ )Full calc.Im( S 1+ )At Low Q 2 :Sensitive to long-range structure: Pion cloudAs Q 2 increases:Pion cloud effects ↓, Valence quark effects ↑AJ Sarty (SMU): Shape of Proton (Fall 2002)• Won’t discuss these here…but they usedSPIN (Polarized Photon Asym) ) in a wayanalogous to what I’ll show with γ * .AJ Sarty (SMU): Shape of Proton (Fall 2002)Pursuing the Details of Deformation:Electron Scattering! (still many exps)Existing Data for SMR & EMRas of 2000:SMREMR• Q 2 dependence maps out dynamics ofrelevant d.o.f. at varying distance scales(e.g. pion cloud to valence quarks)• Can only get C2 information from γ*‣Gives more direct access to w.f.structure (direct probe of charge dist.)AJ Sarty (SMU): Shape of Proton (Fall 2002)

Response Definitions:• Each Response (and Polarization)provides unique combinations ofcontributing multipoles.Response Functions → MultipolesWrite relations for R’s that do not needrecoil proton polarization:Measure φ depend. or p polarization to separate!18 R’s!AJ Sarty (SMU): Shape of Proton (Fall 2002)• Once R’s are isolated (through(measuredφ dependence), need also opening angle(θ) distribution to decomposemultipoles...AJ Sarty (SMU): Shape of Proton (Fall 2002)Response Functions → MultipolesSome General Comments• Too many competing multipoles toextract them model independently fromthe cross section angular dist’s.• To minimize model dependence indetermination of the multipoles,Either:- Measure more R’s, since each R has aunique combination of multipoles (dothis by measuring recoil protonpolarization! 13 more R’s accessible)Or- Make an approx. truncated expansion• ALL of the World’s CMR,EMR data sofar have used a simplified expansion:- Keep only terms with an M 1+- Use only l = 0, 1EXPERIMENT OVERVIEW #1:The Out-of-Plane Spectrometers(OOPS)At MIT-Bates Linear Accelerator• Focus on Low-Q2 region(beam energy is 1 GeV maximum)• Can access the 5 R’s obtainable withoutmeasuring recoil pol.:- Use polarized beam, measureazimuthal (φ)) distribution• Getting the φ distribution is hard!- Not a large CMS→LAB“kinematicfocusing” boost effect- So “cone” of emitted protons isphysically big (full 180 degrees ofproton opening angle in CMS folds toaround 50 degrees in LAB).AJ Sarty (SMU): Shape of Proton (Fall 2002)AJ Sarty (SMU): Shape of Proton (Fall 2002)

Place 4 Identical Spectrometers at keyAzimuthal Angles (φ) at Fixed θThe Real OOPS!4 Identical Spectrometers and aSophisticated Support SystemAJ Sarty (SMU): Shape of Proton (Fall 2002)AJ Sarty (SMU): Shape of Proton (Fall 2002)Proof I once worked on OOPS!OOPS: Sensitivity to “Deformation” inthe R LT ResponseMertz et al., PRL 86 (2001) 2963Kunz, MIT PhD (2000); in prep for PRLThanks to I. Nakagawa, C.Kunz, andA. Bernstein for use of OOPS slides in this talk.AJ Sarty (SMU): Shape of Proton (Fall 2002)• This is a comparison to one particularphenomenological isobar model … BUTmodel-toto-model comparisons still unclear.AJ Sarty (SMU): Shape of Proton (Fall 2002)

OOPS: Model Dependence inthe R LT ResponseMertz et al., PRL 86 (2001) 2963• No model can successfully describe theW-dependence of all acquired data.• Relevance: : resonant and non-resonantcontributing multipoles have differentdependence of W.AJ Sarty (SMU): Shape of Proton (Fall 2002)EXPERIMENT OVERVIEW #2:Recoil Proton Polarization usingthe High Resolution Spectrometersin Hall A at Jefferson Lab• E91-011 at JLab: : data acquired May-August 2000 (preliminary(results today)• Higher Q 2 ( = 1.0 GeV 2 ): largerCMS→LAB“kinematicfocusing” boostmakes getting the φ distribution easier(no need for multiple OOPS’s!)• Use Recoil Proton Polarimetry to accessmany more R’s! R• Measure a full θ distribution also tofacilitate reduction in model dependenceof multipole extraction!• Note: : the polarization R’s R s allow accessto “phase information” of thecontributing multipoles (by beingsensitive to Imaginary parts).AJ Sarty (SMU): Shape of Proton (Fall 2002)Collaboration List…Spokespeople and PhD StudentsAJ Sarty (SMU): Shape of Proton (Fall 2002)

Hall A Facility for Performing Measurement• Beam Polarization mid-high 70%’s• Average current (whole run) = 45 µA(143 C): HIGHEST: 108.2 µA, P=79%Hall AFocal Plane Polarimeter:(FPP)Tools in Hall A:• 2 Hi-Res Specs(6 msr each)• FPP• High I, high Pol.cw beam• 15 cm LH2cryotarget• E 0 up to 5 GeVAJ Sarty (SMU): Shape of Proton (Fall 2002)Hall A E91-011 MeasuredCross Section Angular Distributions(PRELIMINARY!)UPDATED World’s Data forEMR & CMR (as of now!)• Each “box” above is a bin in φ, , showingopening angle (θ)() distribution.• With JUST this cross section data, we cando the same “simplified” EMR & CMRextraction as earlier experiments …AJ Sarty (SMU): Shape of Proton (Fall 2002)• A LOT of NEW data from Hall B’s“CLAS” at JLab (Jooet al., PRL, 2002) –from extensive cross section distributions• Our Prelim points from Cross SectionsOnly (blue(points) ) in agreement …AJ Sarty (SMU): Shape of Proton (Fall 2002)

BUT! We now have the Recoil ProtonPolarization Measurements!6 components:3 for “induced” Polarization3 for “transferred” PoalrizationHelicity-Dependent Polarized R’s(“transferred” – need pol. Beam)• The small differences between the twophenomenological models shown(“SAID” and “MAID”) dominated byresonant “1+” amplitudes.AJ Sarty (SMU): Shape of Proton (Fall 2002)AJ Sarty (SMU): Shape of Proton (Fall 2002)Helicity-Independent Polarized R’s(“induced” – don’t need pol. Beam)PRELIMINARY Attempt to ExtractMultipoles from ALL of E91-011 Data(cross section and polarization angulardistributions!)• EPIPROD program by J.J. Kelly, U. Maryland• The now larger differences between thetwo phenomenological models shown(“SAID” and “MAID”) arises from lackof knowledge of the non-resonantmultipole amplitudes (“background”).AJ Sarty (SMU): Shape of Proton (Fall 2002)AJ Sarty (SMU): Shape of Proton (Fall 2002)

SUMMARY• The Proton is not purely spherical!• There continue to be ongoingexperimental efforts to fullycharacterize the amount of“quadrupoledeformation”.• Challenging experimentally:- Full angular distributions needed- Polarized electron beam needed- Recoil proton polarimetry needed- Need to separate resonant and non-resonant contributions• When completed…will provide new& valuable insight into our vision ofthe proton’s structure.AJ Sarty (SMU): Shape of Proton (Fall 2002)