Factorization of short- and long-range Interaction in Charged Pion Production

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

2. 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 Tanja Horn, CUA Colloquium

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

4. 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 Tanja Horn, CUA Colloquium

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

6. Hadrons • 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 Tanja Horn, CUA Colloquium

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

8. Scattering Experiments • Measure the substructure of matter • Shapes of target particles: • 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 Tanja Horn, CUA Colloquium

9. 2 GeV 3 GeV 1 GeV photon Target proton 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, Eγ=2 eV • BUT we want to study nucleons=protons and neutrons, whose radius is about 10-15 m! • Need photons with E=1 keV∙nm/λ=109 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 d • Instead of photon energy, we typically use: Tanja Horn, CUA Colloquium

10. Elastic 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 • 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 Tanja Horn, CUA Colloquium

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

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

13. 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 1 1 1 p 3 3 3 2 2 2 x=P1/p x=P2/p Tanja Horn, CUA Colloquium

14. 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 e’ (E’,p’) e (E,p) (ν,Q2) γ* u u u d d u • The longitudinal momentum distribution is given by the quark distribution functions • By measuring quark distribution functions, one cannot say anything about the momentum fraction perpendicular to the direction of motion Tanja Horn, CUA Colloquium

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

16. 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 x = 0.01 x = 0.40 x = 0.70 Interference pattern • GPDs are Wigner distributions and give information about the 3-D mapping of the quark structure of the nucleon Tanja Horn, CUA Colloquium

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

18. The Strong Force • Gluons are the messengers for the quark-quark interactions • Quantum Chromo Dynamics (QCD) is the theory that governs their behavior • The strong force does not get weaker with large distances (opposite to the EM force), and blows up at distances around 10-15 m, the radius of the nucleon • We never see a free quark QED • Has a property called confinement • Two types of strong interaction with very different potentials • Quark-quark (colored objects) • Hadron-hadron (van der Waals type) QCD Tanja Horn, CUA Colloquium

19. Quark-quark interactions in QCD QCD coupling αs • At infinite Q2 (short distances), quarks are asymptotically free • Equivalent to turning off the strong interaction • We know how to calculate these short distance quark-quark interactions • Perturbative QCD (pQCD) • At low Q2 (long distances), these calculations are complex, because quarks are confined in hadrons • Need to resort to QCD based models W. Melnitchouk et al., Phys.Rept.406:127-301,2005 Tanja Horn, CUA Colloquium

20. e k'  * p' p 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 Known process • 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” GPD • A decisive test is to look at the scaling of the cross section (interaction probability) as a function of Q2, and see if it follows the QCD prediction for scattering from a cluster of point-like objects Tanja Horn, CUA Colloquium

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

22. Jefferson Lab • 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) ~1038 Tanja Horn, CUA Colloquium

23. HMS: 6 GeV SOS: 1.7 GeV Experimental Setup H.P. Blok, T. Horn et al., arXiv:0809.3161 (2008). Accepted by PRC. • 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 Tanja Horn, CUA Colloquium

24. 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 π Virtual Pion Cloud π* p n Tanja Horn, CUA Colloquium

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

26. 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 “Longitudinal Photons” • Longitudinal photons have no classical analog (must be virtual) • Dominate at high Q2 (virtuality) • Interference terms are also allowed in this quantum mechanical system Tanja Horn, CUA Colloquium

27. Pion and Kaon Form Factors • At low Q2<0.3 GeV2, Fπ and FK 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 Q2 values, must use the “virtual pion cloud” of the proton Tanja Horn, CUA Colloquium

28. The Pion Form Factor: spatial quark distribution T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. T. Horn et al., arXiv:0707.1794 (2007). • My thesis experiment! • Highest possible value of Q2 with 6 GeV beam at JLab • At low Q2: good agreement with elastic data • At higher Q2 many models describe the data • How do we know which one is right? 300 GeV π+e elastic scattering data from CERN SPS Tanja Horn, CUA Colloquium

29. Watch out for speed traps… σL~Q-6 • 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 Tanja Horn, CUA Colloquium

30. 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 Q2 dependence of the πelectroproduction cross section • σL scales to leading order as Q-6 • σT scales as Q-8 • As Q2 becomes large: σL >> σT Factorization Q2 ? • Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons[Collins, Frankfurt, Strikman, 1997] Tanja Horn, CUA Colloquium

31. Q2 dependence of σL and σT Hall C data at 6 GeV • The Q-6QCD scaling prediction is consistent with the current JLab σL data • The expectations: σL>>σT and σT~Q-8 are not consistent with the 6 GeV data • Data at higher Q2 are needed to draw a definite conclusion Q2=2.7-3.9 GeV2 Q2=1.4-2.2 GeV2 σL σT T. Horn et al., arXiv:0707.1794 (2007) G. Huber, H. Blok, T. Horn et al., arXiv:0809.3052 (2008). Accepted by PRC Tanja Horn, CUA Colloquium

32. Fπ - a factorization puzzle? T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. T. Horn et al., arXiv:0707.1794 (2007). • Q2>1 GeV2: Q2 dependence of Fπ is consistent with hard-soft factorization prediction (Q-2) • Factorization condition seems to hold • BUT globally Fπ data still far from hard QCD calculations • Factorization condition does not hold • Or something else is missing in the calculation • Studying the kaon could provide additional information • New experiment needed A.P. Bakulev et al, Phys. Rev. D70 (2004)] Tanja Horn, CUA Colloquium

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

34. The road to a hard place… • Need to understand if we are already scattering from clusters of point-like objects (current data are ambiguous), and if not, when this occurs Tanja Horn, CUA Colloquium

35. 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) SHMS HMS • For my high Q2 meson production experiments, the large momentum (and small angle) capability is essential • During my time in Hall C, I have been actively involved in the SHMS development • Bender magnet, spectrometer optics, shield house design Tanja Horn, CUA Colloquium

36. Fit: 1/Qn Q-n scaling after the Jlab Upgrade • QCD scaling predicts σL~Q-6and σT~Q-8 • Projected uncertainties for σL are improved by more than a factor of two compared to 6 GeV • Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics Tanja Horn, CUA Colloquium

37. Fπ,K after the JLab Upgrade The Q2 dependence of the kaon form factor gives the spatial quark distribution Normalization of the pion form factor Tanja Horn, CUA Colloquium

38. 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…. Tanja Horn, CUA Colloquium

39. Nucleon with some momentum • May expect: p • Might expect the 3 valence quarks to carry all of the momentum of the nucleon • Actually, one gets: 1 3 2 • There is something else in the nucleon, which carries at least half of the nucleon’s momentum Tanja Horn, CUA Colloquium

40. 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 Tanja Horn, CUA Colloquium

41. 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 Tanja Horn, CUA Colloquium

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

43. 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 Tanja Horn, CUA Colloquium

44. Exclusive Processes at Collider Energies Tanja Horn, CUA Colloquium

45. 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 Tanja Horn, CUA Colloquium

46. Backup Slides Tanja Horn, CUA Colloquium

47. An early pQCD Prediction: Scaling • Dimensional Scaling at large Q2 (short distance) • At infinite Q2, 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: S.J. Brodsky, G.P. Lepage “Perturbative QCD”, A.H. Mueller, ed., 1989. Tanja Horn, CUA Colloquium

48. Details of my pion production program (E12-07-105) Phase space for L/T separations with SHMS+HMS • Provides the first separated cross section data above the resonance region • Essential for studies of the reaction mechanism • Provides a Q2 coverage, which is a factor of 3-4 larger compared to 6 GeV Tanja Horn, CUA Colloquium

49. Details of my kaon production program • Provides the first systematic measurement of the separated K+Λ (Σ0) cross section above the resonance region • Essential as relative importance of σL not well known • Q2 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 σkaon Tanja Horn, CUA Colloquium

50. 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) Details of my π° experiment VGG GPD-based calculation pole • Measurement of σL for p0 could help constrain pQCD backgrounds in the extraction of Fπ • Would allow for access to larger Q2 • JLab 6 GeV PAC31 proposal • (T. Horn et al.) non-pole p+ p0 Tanja Horn, CUA Colloquium