Factorization of short- and long-range Interaction in Charged

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

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 Tanja Horn, CUA Colloquium

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 In this talk, will talk about layers of structure in nature each with its own symmetries and governing principles, all the way from the elementary particles up to the most complex, self-organizing systems described by chemistry and biology Physical objects are composed of matter, i.e. anything that occupies space and has mass, If an atom was of the size of a football field, the atomic nucleus would be of the size of a marble Though the atomic nucleus is tiny, it accounts for over 99% of the atoms mass Proton is a quantum mechanical system, so taking up space is not a good concept Clearly defined concepts here are mass, energy, matter The proton is a fermion One cannot understand a house by studying the bricks, and an understanding of the complex does not necessarily follow from a description of the elementary building blocks, but one can also not build a house without the bricks, and one needs to understand how nature manifests itself at all levels and how these levels are intertwined, example: nobel prize in atomic physics, where it turns out that the behavior of clusters of atoms in traps behave like atomic nuclei 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 Fermions whose number is conserved and which try to distinguish themselves from each other by following the Pauli principle, build up matter, while bosons, which behave in the opposite way, form the force carriers that keep it all together The identity crisis of fermions Where are the different forces important in nature? Tanja Horn, CUA Colloquium

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: The concept of virtual particles and force carriers Uncertainty principle: particles can exist if they disappear fast enough Even elephants may show up, if they disappear quickly enough Tanja Horn, CUA Colloquium

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 Illustrate how quarks combine into hadrons This static picture is somewhat simplified, and in reality quarks move around in the nucleon forming distributions that one would want to measure Tanja Horn, CUA Colloquium

The target and how we study it…
How do we measure the structure of particles that make up the atomic nucleus? We do not really know what’s inside, so may find a surprise….. Tanja Horn, CUA Colloquium

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

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 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 3 GeV 2 GeV 1 GeV photon Target proton d Wavelength must be smaller than object size or cannot scatter of it Need large energies: electrons typically have larger momentum/energy than Photons, their wavelength is smalller, so can see more structure Instead of photon energy, we typically use the four-momentum transfer Q2, This makes it easier for us to measure the energy Instead of photon energy, we typically use: Tanja Horn, CUA Colloquium

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 Relate all of this to a physical quantity Separate the process into a part that we want and one that we are not so I nterested in Spin 0 mesons (π+, K+) have electric charge form factor only Spin ½ nucleons have electric and magnetic form factors Tanja Horn, CUA Colloquium

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

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

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 2 3 p 1 2 3 1 2 3 x=P1/p x=P2/p 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 u d γ* e (E,p) e’ (E’,p’) (ν,Q2) 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

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

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

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

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 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) Gluons are the force carriers like photons in QED Strong force does not decrease with distance due to screening effect: in qcd, screening consists of gluons themselves, so always have some interaction, in qed, get screening effect as one moves away from the core Gluons carry a color charge, a quantum number that allows them to interact with themselves – different from photons QCD Tanja Horn, CUA Colloquium

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: ,2005 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 k' *  p p' e 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

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

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

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

e p  e’π+n Events ±1ns The time difference between the HMS and SOS reveals the interaction from the reaction of interest Electron and π+ are detected in the spectrometers The remaining neutron is identified through momentum and energy conservation e e’ p n π Time difference between the two spectrometers: measure the difference between when one particle arrives in one and int the other spectrometer Virtual pion cloud: forbidden, virtual particles that surround the proton. In reality, They are everywhere even inside the proton and pion Virtual Pion Cloud π* Tanja Horn, CUA Colloquium

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

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” Photon polarizations Typically learn about real photons in optics and apply simple concepts like Poynting/field vector Here, longitudinal photons, which have no classical analogue – they are vrtual and have mass The more virtual the system, the more longitudinal it is At higher Q2, longitudinal photons dominate 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

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

The Pion Form Factor: spatial quark distribution
T. Horn et al., Phys. Rev. Lett. 97 (2006) T. Horn et al., arXiv: (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? Thesis experiment that pushed to the highest energy possible and got high precision data Agree with low Q2 elastic data Explain what we would expect from this type of curve, e.g. agreement with The various models 300 GeV π+e elastic scattering data from CERN SPS Tanja Horn, CUA Colloquium

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

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 π electroproduction 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

Q2 dependence of σL and σT
Hall C data at 6 GeV Q2= GeV2 The Q-6 QCD 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= GeV2 σL σT T. Horn et al., arXiv: (2007) G. Huber, H. Blok, T. Horn et al., arXiv: (2008). Accepted by PRC Tanja Horn, CUA Colloquium

Fπ - a factorization puzzle?
T. Horn et al., Phys. Rev. Lett. 97 (2006) T. Horn et al., arXiv: (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 The puzzle – must emphasize it A.P. Bakulev et al, Phys. Rev. D70 (2004)] Tanja Horn, CUA Colloquium

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

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 Experiment Goal Comment Pion Form Factor Determine the distance scale where valence quarks dominate the π+ structure My thesis experiment Pion Factorization Check 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 Pions Understanding 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 Q2 Meson Electroproduction Imaging of gluons and sea quarks At a next generation facility Tanja Horn, CUA Colloquium

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

Q-n scaling after the Jlab Upgrade
Fit: 1/Qn QCD scaling predicts σL~Q-6 and σT~Q-8 Projected uncertainties for σL are improved by more than a factor of two compared to 6 GeV x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.31 0.1 0.40 0.2 0.55 0.5 Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics Tanja Horn, CUA Colloquium

Fπ,K after the JLab Upgrade
New experiment. Tie this in with the scaling studies again. The Q2 dependence of the kaon form factor gives the spatial quark distribution Normalization of the pion form factor 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…. Tanja Horn, CUA Colloquium

Nucleon with some momentum
May expect: 1 2 3 p 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 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 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 Tanja Horn, CUA Colloquium

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 Fraction x of Overall Proton Momentum Carried by Proton Momentum Fraction Times Parton Density 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 Tanja Horn, CUA Colloquium

Exclusive Processes at Collider Energies
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 Tanja Horn, CUA Colloquium

Backup Slides Tanja Horn, CUA Colloquium

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

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 x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.31 0.1 0.40 0.2 0.55 0.5 Tanja Horn, CUA Colloquium

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 x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.25 0.2 0.40 0.5 Tanja Horn, CUA Colloquium

Details of my π° experiment
VGG GPD-based calculation 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) 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

The other kinematic dependencies of the cross section
Fit: n=1.8 Fπ1 Fπ2 VGL σL VGL σT Cross section W-dependence given by: (W2-M2)n Earlier data suggest: n~2 An exponential t dependence describes the data from Jlab and earlier data from DESY W- and t-dependence of σπ as expected – what about Q2? Tanja Horn, CUA Colloquium

Extraction of Fπ from p(e,e’π+)n data
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(Q2) from L.  t-pole “extrapolation” is implicit, but one is only fitting data in the physical region Tanja Horn, CUA Colloquium

Check of the pion electroproduction technique
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 Q2 = 0.35 GeV2 consistent with extrapolation of SPS elastic data. Tanja Horn, CUA Colloquium

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