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

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

1Tanja Horn, CUA Colloquium

User

OutlineOutline• 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


Fundamental MatterFundamental 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


Matter and ForcesMatter 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


• 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 Virtual Particles as Force CarriersCarriers

2ΔEΔt

• Even elephants may show up, if they disappear quickly enough


• 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

HadronsHadrons

qq


• How do we measure the structure of particles that make up the atomic nucleus?

The target and how we study The target and how we study it…it…


Scattering ExperimentsScattering 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:


Elastic Electromagnetic Elastic Electromagnetic ScatteringScattering

• 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

3 GeV

2 GeV

1 GeV photon

Target proton

222 EpQ

d

• Instead of photon energy, we typically use:


Elastic Form FactorsElastic Form Factors

22|)F(Q|

dΩdσ

dΩdσ

objectpoint

• 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

rdρ(r)e)F(Q3r/iq2


Atomic and Nuclear Atomic and Nuclear SubstructureSubstructure

Rutherford Atom Proton Form Factor

Scattering Angle

Lab Scattering Angle (deg)

Experimental curve falls off faster than the one for a point charge


• Now we know about the spatial distribution of the quarks in the nucleon, but how fast do they move?

A little more dynamicA little more dynamic


Nucleon with some momentumNucleon 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

p1

2 3

1

2 3

1

2 3

x=P1/p x=P2/p


Deep Inelastic ScatteringDeep 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

)(x)q(x)(qex(x)FFi

ii2i22

)QR(x,2(1

/EQy

2E

Mxyy1

x

)Q(x,F

Q

4ππ

dxdQ

σd2

22222

4

2

2

2

uu

d

u

u

d

γ*

e (E,p)

e’ (E’,p’)

(ν,Q2)


• Combine spatial and momentum information into one study

We can do even better!We can do even better!


Interference pattern

x = 0.01 x = 0.40 x = 0.70

Generalized Parton Distributions Generalized Parton Distributions (GPDs)(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


• Before we measure GPDs, what can hadron structure tell us about the strong force, the glue that holds hadrons together

Back to basicsBack to basics


The Strong ForceThe 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 10-15 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


Quark-quark interactions in QCDQuark-quark interactions in QCD

W. Melnitchouk et al., Phys.Rept.406:127-301,2005

QCD coupling αs

• At infinite Q2 (short distances), quarks are asymptotically free

– Equivalent to turning off the strong interaction

• At low Q2 (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)


Probing Generalized Quark Probing Generalized Quark Distributions in the NucleonDistributions 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 Q2, and see if it follows the QCD prediction for scattering from a cluster of point-like objects

k'

*

p p'

e

GPD

Known process


• Studies of the three (valence) quarks in the nucleon at JLab

To the point: how do we do all of this To the point: how do we do all of this practically?practically?

Put a cat in a quantum box?


• 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

Jefferson LabJefferson Lab


Experimental SetupExperimental Setup

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

H.P. Blok, T. Horn et al., arXiv:0809.3161 (2008). Accepted by PRC.


e p e p e’ e’ππ++n Eventsn 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’

p n

π

π*

Virtual Pion Cloud


• Pick one simple process to illustrate the concepts of form factors: the pion

Simple is good…Simple is good…


Interference terms

Pion ElectroproductionPion 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

πNNg

• Longitudinal photons have no classical analog (must be virtual)• Dominate at high Q2 (virtuality)

dt

dσε

dt

dσ LT cos2φdt

dσεcosφ

dt

dσ)(12

dtdφ

dσ2π TTLT

“Longitudinal Photons”


t),(QF(t)g)m(t

Qt

dt

dσ 22

π

2

πNN2

π

2

L

Pion and Kaon Form FactorsPion 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

πNNg

dt

dσε

dt

dσ LT cos2φdt

dσεcosφ

dt

dσ)(12

dtdφ

dσ2π TTLT

12

2

θτ)tan2(11ε


The Pion Form Factor: spatial The Pion Form Factor: spatial quark distributionquark distribution

T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

T. Horn et al., arXiv:0707.1794 (2007).

300 GeV π+e elastic scattering data from CERN SPS

• At low Q2: good agreement with elastic data

• At higher Q2 many models describe the data

• How do we know which one is right?

• My thesis experiment!

• Highest possible value of Q2 with 6 GeV beam at JLab


• 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…Watch out for speed traps…

σL~Q-6


Tests of the Handbag Tests of the Handbag DominanceDominance

• 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

H H~E E

~• Factorization theorems for meson

electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997]

Q2 ?

dt

dσε

dt

dσ LT cos2φdt

dσεcosφ

dt

dσ)(12

dtdφ

dσ2π TTLT


Q2 dependence of σL and σT

• 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

T. Horn et al., arXiv:0707.1794 (2007)

Hall C data at 6 GeV

Q2=1.4-2.2 GeV2

Q2=2.7-3.9 GeV2

σL

σT

G. Huber, H. Blok, T. Horn et al., arXiv:0809.3052 (2008). Accepted by PRC


• 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

T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

T. Horn et al., arXiv:0707.1794 (2007).

A.P. Bakulev et al, Phys. Rev. D70 (2004)]

FFππ - a factorization puzzle? - a factorization puzzle?

• Studying the kaon could provide additional information

• New experiment needed


• How can we solve the factorization puzzle presented by the current data?

We are on a quest!We are on a quest!


The road to a hard place…The road to a hard place…

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 (E12-07-105)

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

• Need to understand if we are already scattering from clusters of point-like objects (current data are ambiguous), and if not, when this occurs


SHMSSHMS

The 12 GeV JLab and Hall CThe 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)

HMSHMS

• 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 Q2 meson production experiments, the large momentum (and small angle) capability is essential


• 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

Q-n scaling after the Jlab Upgrade

Fit: 1/Qn

• Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

x Q2

(GeV2)

W

(GeV)

-t

(GeV/c)2

0.31 1.5-4.0 2.0-3.1 0.1

0.40 2.1-5.5 2.0-3.0 0.2

0.55 4.0-9.1 2.0-2.9 0.5


FFππ,K,K after the JLab Upgrade after the JLab Upgrade

The Q2 dependence of the kaon form factor gives the spatial quark distribution

Normalization of the pion form factor


GPD studies beyond JLabGPD 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….


Nucleon with some momentumNucleon with some momentum

• May expect:

x

1xd(x)xu(x)

• Might expect the 3 valence quarks to carry all of the momentum of the nucleon

• Actually, one gets:

5.0xd(x)xu(x)x

• There is something else in the nucleon, which carries at least half of the nucleon’s momentum

p1

2 3


GluonsGluons

• 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


Sea quarksSea 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


Quark Momentum DistributionsQuark Momentum Distributions

Fraction x of Overall Proton Momentum Carried by Proton

Mom

entu

m F

ract

ion

Tim

es P

arto

n D

ensi

ty

• Where do we look for gluons in the nucleon? – at low x!!

• This is also the place to look for strange sea quarks


GPD studies beyond JLabGPD 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


Exclusive Processes at Collider Exclusive Processes at Collider EnergiesEnergies


SummarySummary

• 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


Backup SlidesBackup Slides


S.J. Brodsky, G.P. Lepage “Perturbative QCD”,A.H. Mueller, ed., 1989.

An early pQCD Prediction: An early pQCD Prediction: ScalingScaling

• 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:

1n2

2

)(Q

1)F(Q


Details of my pion production Details of my pion production program (E12-07-105)program (E12-07-105)

x Q2

(GeV2)

W

(GeV)

-t

(GeV/c)2

0.31 1.5-4.0 2.0-3.1 0.1

0.40 2.1-5.5 2.0-3.0 0.2

0.55 4.0-9.1 2.0-2.9 0.5

Phase space for L/T separations with SHMS+HMS

• Provides a Q2 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


Details of my kaon production Details of my kaon production programprogram

• 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 1.6-3.5 2.4-3.4 0.2

0.40 3.0-6.0 2.0-3.0 0.5


• 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)

)~~

(~ dd

uup

HeHeA o

)~~

(~ dd

uup

EeEeB o

))(~~

(~ dudu

peeHHA

))(~~

(~ dudu

peeEEB

0+

VGG GPD-based calculation

pole

non-pole

Details of my Details of my π°π° experiment experiment

• Measurement of σL for 0 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.)


The other kinematic other kinematic dependencies of the cross dependencies of the cross

sectionsection

• Cross section W-dependence given by: (W2-M2)n

– Earlier data suggest: n~2

Fit: n=1.8Fit: n=1.8

Fπ1

Fπ2

VGL σLVGL σT

• 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?


• 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

Extraction of FExtraction of Fππ from p(e,e’ from p(e,e’ππ++)n )n datadata


• 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.

Check of the pion Check of the pion electroproduction techniqueelectroproduction technique


Documents

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