Factorization of short- and long-range Interaction in Charged Pion Production Tanja Horn Jefferson Lab Washington, DC 24 September 2008 Colloquium at the Catholic University of America 1 Tanja Horn, CUA Colloquium

Outline Matter and its building blocks The distribution of the building blocks inside the nucleon How do we relate them to a physical quantity when nothing is moving? Probing the building blocks if they are moving (momentum distributions) Interactions between the building blocks (quarks and the strong force) Studies of the three valence quarks in the nucleon at Jefferson Lab Case study: the pion Current results and of a little mystery The quest: how do we understand the puzzle posed by current data Outlook Summary 2 Tanja Horn, CUA Colloquium

Fundamental Matter The proton internal structure is complex No exact definition for quantum mechanical reasons Typically use concept of mass, energy, and particles Over 99.9% of the atom’s mass is concentrated in the nucleus Ordinary matter (atoms and molecules) is made up of protons, neutrons and electrons 3 Tanja Horn, CUA Colloquium

Matter and Forces Fermions are the building blocks Conserve particle number Try to distinguish themselves from each other by following the Pauli principle Bosons form the force carriers that keep it all together 4 Tanja Horn, CUA Colloquium

Exchanged/thrown particles can create attractive and repulsive forces These particles are not real, but virtual Virtual particles can exist by the Heisenberg principle: Virtual Particles as Force Carriers Even elephants may show up, if they disappear quickly enough 5 Tanja Horn, CUA Colloquium

Hadrons are composed of quarks with: Flavor: u, c, t (charge +2/3) and d, s, b (charge -1/3) Color: R, G, B Spin: ½ (fermions) Two families of hadrons: Baryons: valence qqq Mesons: valence Hadrons 6 Tanja Horn, CUA Colloquium

How do we measure the structure of particles that make up the atomic nucleus? The target and how we study it… 7 Tanja Horn, CUA Colloquium

Scattering Experiments Measure the substructure of matter Mass of target particles Light: small deflections Heavy: large deflections Measure scattering cross sections, dσ= probability for beam particles to scatter by an angle θ Shapes of target particles: 8 Tanja Horn, CUA Colloquium

Elastic Electromagnetic Scattering The higher the beam energy, and the shorter the wavelength of the photon, the more detail in the target structure is revealed Visible light  λ=500 nm=5x10 -7 m, E γ =2 eV BUT we want to study nucleons=protons and neutrons, whose radius is about m! Need photons with E=1 keV∙nm/λ=10 9 eV=1 GeV The solution: Accelerating charged particles emit photons Accelerate electrons to 3 GeV and scatter them off a proton target Electrons deflected (accelerated), and emits a 1 GeV photon 3 GeV 2 GeV 1 GeV photon Target proton d Instead of photon energy, we typically use: 9 Tanja Horn, CUA Colloquium

Elastic Form Factors The spatial distribution (form factor) is a Fourier transform of the charge distribution Spin 0 mesons ( π +, K + ) have electric charge form factor only Spin ½ nucleons have electric and magnetic form factors The elastic scattering cross section can be factorized into that of a point object and a part that gives information about the spatial distribution of the constituents 10 Tanja Horn, CUA Colloquium

Atomic and Nuclear Substructure Rutherford AtomProton Form Factor Scattering Angle Lab Scattering Angle (deg) Experimental curve falls off faster than the one for a point charge 11 Tanja Horn, CUA Colloquium

Now we know about the spatial distribution of the quarks in the nucleon, but how fast do they move? A little more dynamic 12 Tanja Horn, CUA Colloquium

Nucleon with some momentum Now that we know how to measure the spatial distribution of quarks in the nucleon, what about their momentum? x is the fraction of momentum carried by a quark in a nucleon momentum moving quickly to the right p x=P 1 /px=P 2 /p 13 Tanja Horn, CUA Colloquium

Deep Inelastic Scattering Cross section can be factorized into that of a point object and a part that gives information about the momentum distribution of the constituents in the nucleon By measuring quark distribution functions, one cannot say anything about the momentum fraction perpendicular to the direction of motion The longitudinal momentum distribution is given by the quark distribution functions u u d u u d γ*γ* e (E,p) e ’ (E’,p’) (ν,Q2)(ν,Q2) 14 Tanja Horn, CUA Colloquium

Combine spatial and momentum information into one study We can do even better! 15 Tanja Horn, CUA Colloquium

Interference pattern x = 0.01x = 0.40x = 0.70 Generalized Parton Distributions (GPDs) Is there a way of combining the information about spatial and momentum distributions including the transverse dimension? Wigner quantum phase space distributions provide a correlated, simultaneous description of both position and momentum distribution of particles The closest analogue to a classical phase space density allowed by the uncertainty principle GPDs are Wigner distributions and give information about the 3-D mapping of the quark structure of the nucleon 16 Tanja Horn, CUA Colloquium

Before we measure GPDs, what can hadron structure tell us about the strong force, the glue that holds hadrons together Back to basics 17 Tanja Horn, CUA Colloquium

The Strong Force Has a property called confinement The strong force does not get weaker with large distances (opposite to the EM force), and blows up at distances around m, the radius of the nucleon We never see a free quark Two types of strong interaction with very different potentials Quark-quark (colored objects) Hadron-hadron (van der Waals type) Gluons are the messengers for the quark-quark interactions Quantum Chromo Dynamics (QCD) is the theory that governs their behavior QED QCD 18 Tanja Horn, CUA Colloquium

Quark-quark interactions in QCD W. Melnitchouk et al., Phys.Rept.406: ,2005 QCD coupling α s At infinite Q 2 (short distances), quarks are asymptotically free –Equivalent to turning off the strong interaction At low Q 2 (long distances), these calculations are complex, because quarks are confined in hadrons –Need to resort to QCD based models We know how to calculate these short distance quark-quark interactions –Perturbative QCD (pQCD) 19 Tanja Horn, CUA Colloquium

Probing Generalized Quark Distributions in the Nucleon Analogous to the form factor measurements, we need to find a process, which we can describe by factorizing it into: a known part that we can calculate, and one that contains the information we are after For some reactions it has been proven that such factorization is possible, but only under very extreme conditions In order to use them, one needs to show that they are applicable in “real life” A decisive test is to look at the scaling of the cross section (interaction probability) as a function of Q 2, and see if it follows the QCD prediction for scattering from a cluster of point-like objects k'k' **  p p'p' e GPD Known process 20 Tanja Horn, CUA Colloquium

Studies of the three (valence) quarks in the nucleon at JLab To the point: how do we do all of this practically? Put a cat in a quantum box? 21 Tanja Horn, CUA Colloquium

Two superconducting Linacs –Three experimental Halls operating concurrently E~ 5.7 GeV –Hadron-parton transition region C.W. beam with currents of up to 100 uA –Luminosity (Hall C) ~10 38 Jefferson Lab 22 Tanja Horn, CUA Colloquium

Experimental Setup HMS: 6 GeVSOS: 1.7 GeV Magnetic fields bend and focus beams of charged particles Hall C has two magnetic spectrometers for particle detection Short Orbit Spectrometer (SOS) for short lived particles High Momentum Spectrometer (HMS) for high momentum particles Electron beam interacts with hadrons in the cryogenic target H.P. Blok, T. Horn et al., arXiv: (2008). Accepted by PRC. 23 Tanja Horn, CUA Colloquium

e p  e’ π + n Events The time difference between the HMS and SOS reveals the interaction from the reaction of interest ±1ns Electron and π + are detected in the spectrometers The remaining neutron is identified through momentum and energy conservation e e’ pn π π*π* Virtual Pion Cloud 24 Tanja Horn, CUA Colloquium

Pick one simple process to illustrate the concepts of form factors: the pion Simple is good… 25 Tanja Horn, CUA Colloquium

Interference terms Pion Electroproduction The photon in the e p  e’ π + n reaction can be in different polarization states, e.g. along or at 90° to the propagation direction The interaction probability includes all possible photon polarization states “Transverse Photons” Interference terms are also allowed in this quantum mechanical system Longitudinal photons have no classical analog (must be virtual) Dominate at high Q 2 (virtuality) “Longitudinal Photons” 26 Tanja Horn, CUA Colloquium

Pion and Kaon Form Factors At low Q 2 <0.3 GeV 2, F π and F K can be measured exactly using the high energy π + / K + scattering from atomic electrons [S.R. Amendolia et al., NP B277 (1986)] No “free pion” target, so to extend the measurement to larger Q 2 values, must use the “virtual pion cloud” of the proton 27 Tanja Horn, CUA Colloquium

The Pion Form Factor: spatial quark distribution T. Horn et al., Phys. Rev. Lett. 97 (2006) T. Horn et al., arXiv: (2007). 300 GeV π +e elastic scattering data from CERN SPS At low Q 2 : good agreement with elastic data At higher Q 2 many models describe the data How do we know which one is right? My thesis experiment! Highest possible value of Q 2 with 6 GeV beam at JLab 28 Tanja Horn, CUA Colloquium

In order to combine the spatial and momentum distributions of quarks in the nucleon in our studies of the pion, we still need to check if the factorization conditions hold Watch out for speed traps… σ L ~Q Tanja Horn, CUA Colloquium

Tests of the Handbag Dominance In order to study the combined spatial and momentum distributions of the quarks in the nucleon, need to study GPDs –But before can say anything, we must demonstrate that the conditions for factorization apply One of the most stringent tests of factorization is the Q 2 dependence of the π electroproduction cross section –σ L scales to leading order as Q -6 –σ T scales as Q -8 –As Q 2 becomes large: σ L >> σ T Factorization Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997] Q 2 ? 30 Tanja Horn, CUA Colloquium

Q 2 dependence of σ L and σ T The Q -6 QCD scaling prediction is consistent with the current JLab σ L data The expectations: σ L >>σ T and σ T ~Q -8 are not consistent with the 6 GeV data Data at higher Q 2 are needed to draw a definite conclusion T. Horn et al., arXiv: (2007) Hall C data at 6 GeV Q 2 = GeV 2 Q 2 = GeV 2 σLσL σTσT G. Huber, H. Blok, T. Horn et al., arXiv: (2008). Accepted by PRC 31 Tanja Horn, CUA Colloquium

Q 2 >1 GeV 2 : Q 2 dependence of F π is consistent with hard-soft factorization prediction (Q -2 ) Factorization condition seems to hold BUT globally F π data still far from hard QCD calculations –Factorization condition does not hold –Or something else is missing in the calculation T. Horn et al., Phys. Rev. Lett. 97 (2006) T. Horn et al., arXiv: (2007). A.P. Bakulev et al, Phys. Rev. D70 (2004)] F π - a factorization puzzle? Studying the kaon could provide additional information New experiment needed 32 Tanja Horn, CUA Colloquium

How can we solve the factorization puzzle presented by the current data? We are on a quest! 33 Tanja Horn, CUA Colloquium

The road to a hard place… ExperimentGoalComment Pion Form FactorDetermine the distance scale where valence quarks dominate the π + structure My thesis experiment Pion FactorizationCheck if the conditions of factorization apply at JLab, and if they do, study the 3-dimensional image of the nucleon Approved JLab experiment (E ) Kaon Electroproduction Test the reaction mechanism with a heavier quark system. This may also help solving the form factor puzzle. Proposal will be submitted to next JLab PAC Neutral PionsUnderstanding the neutral pion reaction mechanism would allow a more reliable interpretation of the charged pion data Letter of intent will be submitted to next JLab PAC High Q 2 Meson Electroproduction Imaging of gluons and sea quarksAt a next generation facility Need to understand if we are already scattering from clusters of point-like objects (current data are ambiguous), and if not, when this occurs 34 Tanja Horn, CUA Colloquium

SHMS The 12 GeV JLab and Hall C New opportunities at JLab with twice as much energy in the near future In Hall C, we are building the Super High Momentum Spectrometer (SHMS) HMS During my time in Hall C, I have been actively involved in the SHMS development Bender magnet, spectrometer optics, shield house design For my high Q 2 meson production experiments, the large momentum (and small angle) capability is essential 35 Tanja Horn, CUA Colloquium

QCD scaling predicts σ L ~Q -6 and σ T ~Q -8 Projected uncertainties for σ L are improved by more than a factor of two compared to 6 GeV Q -n scaling after the Jlab Upgrade Fit: 1/Q n Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) Tanja Horn, CUA Colloquium

F π,K after the JLab Upgrade The Q 2 dependence of the kaon form factor gives the spatial quark distribution Normalization of the pion form factor 37 Tanja Horn, CUA Colloquium

GPD studies beyond JLab At JLab we can learn about the three (valence) quarks that make up the nucleon, but the story does not end there…. 38 Tanja Horn, CUA Colloquium

Nucleon with some momentum May expect: Might expect the 3 valence quarks to carry all of the momentum of the nucleon Actually, one gets: There is something else in the nucleon, which carries at least half of the nucleon’s momentum p Tanja Horn, CUA Colloquium

Gluons Gluons carry a significant fraction of the nucleon’s momentum Gluons are essential components of protons and nucleons Gluons provide the “glue”, which keeps the quarks inside the nucleon They are the carriers of the strong force 40 Tanja Horn, CUA Colloquium

Sea quarks The pion cloud around the nucleon from which we knocked out the virtual pion is really part of the nucleon itself In fact, the three valence quarks move in a sea of virtual quarks and gluons. These virtual quark-antiquark pairs carry the rest of the nucleons momentum As with all virtual particles, they exist only long enough such that the Heisenberg principle is not violated 41 Tanja Horn, CUA Colloquium

Quark Momentum Distributions Fraction x of Overall Proton Momentum Carried by Proton Momentum Fraction Times Parton Density Where do we look for gluons in the nucleon? – at low x!! This is also the place to look for strange sea quarks 42 Tanja Horn, CUA Colloquium

GPD studies beyond JLab To study gluons and sea quarks, we need to make measurements at small x, where valence quarks are not dominant Best way to do this is at a electron-proton collider Physics interest closely related to JLab studies of the three (valence) quarks that make up the nucleon 43 Tanja Horn, CUA Colloquium

Exclusive Processes at Collider Energies 44 Tanja Horn, CUA Colloquium

Summary The past decades have seen good progress in developing a quantitative understanding of the electromagnetic structure of the nucleon New puzzles have emerged as a result of high precision data Progress in both theory and experiment now allow us for the first time to make 3-dimensional images of the internal structure of the proton and other strongly interacting particles Quark-valence structure from JLab Gluon and sea quark contributions at an electron-proton collider The next decades will see exciting developments as we begin to understand the structure of matter 45 Tanja Horn, CUA Colloquium

Backup Slides 46 Tanja Horn, CUA Colloquium

S.J. Brodsky, G.P. Lepage “Perturbative QCD”, A.H. Mueller, ed., An early pQCD Prediction: Scaling Dimensional Scaling at large Q 2 (short distance) At infinite Q 2, quarks are asymptotically free –The hadron becomes a collection of free quarks with equal longitudinal momenta In this limit, the form factor is expected to scale like: 47 Tanja Horn, CUA Colloquium

Details of my pion production program (E ) xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) Phase space for L/T separations with SHMS+HMS Provides a Q 2 coverage, which is a factor of 3-4 larger compared to 6 GeV Provides the first separated cross section data above the resonance region Essential for studies of the reaction mechanism 48 Tanja Horn, CUA Colloquium

Details of my kaon production program Provides the first systematic measurement of the separated K + Λ ( Σ 0 ) cross section above the resonance region –Essential as relative importance of σ L not well known Q 2 dependence of the cross section will provides important additional information about the reaction mechanism –May shed light on the pion form factor puzzle –Will identify missing elements in existing calculations of σ kaon xQ 2 (GeV 2 ) W (GeV) -t (GeV/c) Tanja Horn, CUA Colloquium

Compare σL in π + n and π° p to separate pole and non-pole contributions –Essential to access to the spin structure of the nucleon and to apply SU(3) 00 ++ VGG GPD-based calculation pole non-pole Details of my π° experiment Measurement of σ L for  0 could help constrain pQCD backgrounds in the extraction of F π –Would allow for access to larger Q 2 –JLab 6 GeV PAC31 proposal (T. Horn et al.) 50 Tanja Horn, CUA Colloquium

other kinematic dependencies of the cross section The other kinematic dependencies of the cross section Cross section W-dependence given by: (W 2 -M 2 ) n –Earlier data suggest: n~2 Fit: n=1.8 Fπ1Fπ1 Fπ2Fπ2 VGL σ L VGL σ T An exponential t dependence describes the data from Jlab and earlier data from DESY W- and t-dependence of σ π as expected – what about Q 2 ? 51 Tanja Horn, CUA Colloquium

π + electroproduction can only access t<0 (away from pole) Early experiments used “Chew- Low” technique –measured –t dependence –Extrapolate to physical pole This method is unreliable – different fit forms consistent with data yet yield very different FF A more reliable approach is to use a model incorporating the  + production mechanism and the `spectator’ nucleon to extract F  (Q 2 ) from  L.  t-pole “extrapolation” is implicit, but one is only fitting data in the physical region Extraction of F π from p(e,e’ π + )n data 52 Tanja Horn, CUA Colloquium

Does electroproduction really measure the physical form-factor since we are starting with an off- shell pion? This can be tested making p(e,e’  + )n measurements at same kinematics as  +e elastics Looks good so far: –Ackermann electroproduction data at Q 2 = 0.35 GeV 2 consistent with extrapolation of SPS elastic data. Check of the pion electroproduction technique 53 Tanja Horn, CUA Colloquium