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Meson production with CLAS

Volker D. Burkert Jefferson Lab

24th Student’s Workshop on Electromagnetic Interactions September 9–14, 2007, Bosen,

Germany

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Overview

• Introduction, N*’s and Δ’s, Multiplets, SU(6)xO(3)

• Meson production as a tool to study excited baryons

• Analysis Tools, CLAS

• Electromagnetic Excitation of resonances - the Δ(1232) and the shape of the nucleon

• The “Roper” resonance and other lower mass resonances, S11(1535), D13(1520), in single π and η production.

• Search for “Missing Resonances” in – Double pion production– Strangeness production.

I

II

III

IV

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Additional Reading Material

V.D. Burkert and T.-S. H. Lee, Electromagnetic Meson Production in the Nucleon Resonance Region, International Journal of Modern Physics E, Vol. 13, Nummer 6, (2004)

F.E. Close, A. Donnachie, D. Shaw (editors)Electromagnetic Interactions of Hadrons (2007)

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Why N*’s are important?

Nucleons represent the real world, they must be at the center of any discussion on “why the world is the way it is”

Nucleons represent the simplest system where “the non-abelian character of QCD is manifest”.

N*’s can teach us a lot about quark confinement in the basic building blocks of matter which make up 99.9% of the mass of the visible part of the universe.

Nucleons are complex enough to “reveal physics hidden from us in mesons”. Gell-Mann & Zweig - Quark Model: 3 x 3 x 3 = 10 + 8 + 8 + 1

O. Greenberg - The problem and “color”

Gluon flux of system of 3 heavy quarks.

3-gluon vertex

(Nathan Isgur at N*2000, JLab)

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(1232)

Phys. Rev. 85, 936 (1952)

p X

p X

Evidence for the first excited state of the proton and a hint for more.

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p(GeV/c)

Total cross section p X

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Δ++

π+ p → Δ++

is the largest πN cross section, butthe Δ++ state is not allowed in CQM without “color”.

O. Greenberg introduces a new quantum number to get asymmetric w.f.

u u u

sflavorspin

++

as flavorspincolor

u u u++

The Δ++(1232) leads to “color”

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Baryon multiplets

Y=B+S

I3

+1/2 1-1/2-1

1

2

18810333

Symmetry of Baryons made from u, d, s quarks:

N

─

++-

The symmetry underlying the QM predicts the existence of a new particle made from (sss).

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Production and decay of Ω- → Ξoπ-

V.E. Barnes et. al., Phys. Rev. Lett. 8, 204 (1964)

e-

e+

e-

e+

K0

–

K+ – p

K–

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Baryon Resonances and SU(6)xO(3)

3 Flavors: {u,d,s} SU(3)

{qqq}: 3 3 3 = 10 8 8 1 + + ++ +

SU(6) multiplets decompose into flavor multiplets:

56 = 410 28

+++70 = 210 48 28 21++20 = 28 41

|Baryon> : |qqq> + |qqq(qq)| + |qqqG> + ..

Quark spin sq = ½ SU(2)

+ + ++ +{qqq }: 6 6 6 = 56 70 70 20

Baryon spin: J = L + siparity: P = (-1)L

O(3)

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D13(1520)S11(1535)

P11(1440)

F15(1680)

P33(1232)

D33(1700)

SU(6)xO(3) Classification of Baryons

Missing States?

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Configuration Mixing in [70,1-]

States with same I, Jp quantum numbers and different total quark spins Sq = 1/2 or Sq = 3/2, mix with mixing angle M.

The pure quark states |N2, 1/2- > and |N4, 1/2- > in [70,1-] project onto physical states S11(1535) and S11(1650).

Sq = 1/2 Sq = 3/2

|S11(1535)> = cos1|N2,1/2-> - sin1|N4, 1/2-> |S11(1650)> = sin1 |N2,1/2-> + cos1|N4, 1/2-> 1 = 31o (measured in hadronic decays).

|D13(1520)> = cos2|N2,3/2-> - sin2|N4, 3/2->

|D13(1700)> = sin2 |N2,3/2-> +cos2|N4, 3/2-> 2 ~10o

Similarly for |N2,3/2- > and |N4,3/2- >

The |N4,5/2- > quark state has no N2 partner, and cannot mix.

|D15(1675) > = |N4,5/2- >

Notation: L2I,2J

p

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Analysis Tools

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Simple searches for resonances

For a 2-body decay one can search for resonance structures in the invariant mass distribution.

P, M

p1, m1

p2, m2

proton

pion

M2 = (pp + p)2

4-vectors

M

Rarely are resonances observed just in mass distributions, e.g. if the state is narrow, or if strongly excited. It also gives no information on quantum numbers other than isospin if one sees the “peak” in two channels.

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A resonance at m12 = 1.8 GeV will not appear like a resonance in m23

A narrow resonance at m23 will not appear as a narrow structure in m12

A known narrow resonance at m12 = 2.0 GeV may appear like an enhancement in m23 at a different mass (kinematical reflection).

P, M

p1, m1

p2, m2

p3, m3

Dalitz Plot for 3-body decay (e.g. pπ+K0)

3-body decay

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γp pK+K- Dalitz Plot:

E = 1.6-3.5 GeV

(1020)

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Argand Diagram

f(k,) = 1/k (2l+1)alPl(cos)l

Elastic scattering amplitude of spinless particle with momentum k in cms:

For purely elastic scattering: l = 1, (e.g. N → N)

d/d = |f(k,)|2

Optical theorem:

tot = 4/k[Im f(k,0)]

Cross section for l th partial wave is bounded:

l = 4/k2(2l+1)2|al|2 < 4(2l+1)2/k2

al = (l e2il – 1)/2i ,

0 < l < 1 , l : phase shift of lth partial wave

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Im a1

Re a-1/2 +1/2

1/2

al

/2

Argand Diagram, cont’d

inelasticity sets in

al : partial wave amplitude evolving with energy.

The amplitude leaves the unitary circle where inelasticity sets in.

al = (l e2il – 1)/2i resonance mass

increasing energy

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Breit-Wigner Form

B-W (non-relativistic) form for an elastic amplitude al with a resonance at cm energy ER and elastic width Γel and total width Γtot is

al =el/2

ER – E – itot/2

Relativistic form:

al =mel

s – m2 – imtot

Many other B-W forms exist,dependent on process dynamics.

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Argand Diagrams for some P–waves

P33 - the elastic wave

Crosses indicate every 50 MeV step in W Dots correspond to Breit-Wigner, WR = MR

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Some resonances in →

(1920)***(1600)***

N(1710)***

N(2100)*

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A comment

• Nearly all known nucleon resonances have been observed in elastic πN→πN scattering.

• If ε is branching ratio of resonance R into πN, then the cross section for πN→R→Nπ is σ ~ ε2 .

• If ε is small (e.g. ε = 0.05) then may be a very small number, and many resonances may not be seen in the elastic channel.

• We need to look for other decay channels as well!

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Hadron Structure with e.m. Probes?

resolution of probe

low

high

N

πAllows to address central question: What are the relevant degrees-of-freedom at varying distance scale?

LQCD/DSE/Instantons

e.m. probe

q

Constituent quark model with fixed quark masses only justified at photon point and low q.

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Reach of Current Accelerators

JLAB

Spring-8

Neutrals

Charged & some neutrals

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Emax ~ 6 GeV

Imax ~ 200 ADuty Factor ~ 100% E/E ~ 2.5 10-5

Beam P ~ 85%E(tagged) ~ 0.8-5.5GeV

CLAS

JLab Site: The 6 GeV CW Electron Accelerator

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CEBAF Large Acceptance Spectrometer

Liquid D2 (H2)target + start counter; e mini-torus;shielding solenoid

Drift chambersargon/CO2 gas, 35,000 cells

Electromagnetic calorimetersLead/scintillator, 1296 PMTs

Torus magnet6 superconducting coils

Gas Cherenkov counterse/p separation, 216 PMTs

Time-of-flight countersplastic scintillators, 684 PMTs

Large angle calorimetersLead/scintillator, 512 PMTs

In addition, polarized targets for electron and photon beams are in use.

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CLASCLAS during maintenanceduring maintenance

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CLAS Torus Magnet

Lines of constant absolute total field. The high field is concentrated at forward angles.

Note that the field in the inner part drops very rapidly to zero.

large ∫Bdl

small ∫Bdl

Target

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CLAS Momentum and angle resolution

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Neutron Detection in the EC

The EC is a scintillator-lead sandwich calorimeter with 40 layers of 1 cm thick plastic scintillators.

This provides excellent neutron detection efficiency of up to 60% at high momentum.

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`

Particle Identification by Time-of-Flight

An important aspect in any production experiment is particle identification. Charged particles are often identified through either time-of-flight or/and through energy loss measurements. In CLAS the main tool is precise timing information of 150psec(σ).

In electron scattering the start time at the target can be measured precisely since β=1 for identified electrons. With known path length from the target, the start time and the RF beam bucket can be determined. As the RF time is given with pico-second accuracy, the uncertainty of the electron timing can be eliminated.

e-

e-

Beam time structure

i

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Particle Identification by Time-of-Flight

β

P(GeV/c) Mass by TOF

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The Hall B Photon Energy Tagger

Energy resolution ΔE/E = 10-3

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PID with over-determined kinematics

γp → pX

P1

p2

pX

p3

pX = (p1 + p2 –p3)

pX2

= MX2 =(p1 + p2 –p3)2

2-body process with one unmeasured particle

pγ

pp

pX

pp

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Example of Single Event γd → p K+K─X

K- K+

p

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Electromagnetic Excitationof Baryon Resonances

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Electromagnetic Excitation of N*’s

Primary Goals:

Extract electro-coupling amplitudes for known △,N* resonances in Nπ, Nη, Nππ

– Partial wave and isospin decomposition of hadronic decay– Assume em and strong interaction vertices factorize– Helicity amplitudes A3/2 A1/2 S1/2 and their Q2 dependence

Study 3-quark wave function and underlying symmetries Quark models: relativity, gluons vs. mesons.

Search for “missing” resonances predicted in SU(6) x O(3) symmetry group

e

e’

γv

N N’,Λ

N*,△

A3/2, A1/2,S1/2

p

p

p

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Inclusive Electron Scattering ep→e’X

Resonances cannot be uniquely separated in inclusive scattering → exclusive processes

Q2=-(e-e’)2; W2 = MX2=(e-e’+p)2

(GE, GM)

(12

32)

N(1

440)

N(1

520)

N(1

535)

(16

20)

N(1

680)

ep→ep

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W-Dependence of selected channels at 4 GeV

e’Measurement of various final states needed to probe different resonances, and to determine isospin.

From panels 2 and 3 we can find immediately the isospins of the first and second resonances.

The big broad strength near 1.35 GeV in panel 3, and not seen in panel 2 hints at another I=1/2 state.

From panels 3 and 4 we see that there are 5 resonances.

Panel 5 indicates there might be a 6th resonance.

1

2

3

4

5

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End of 1st part

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γNΔ(1232) Transition

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N-Δ(1232) Quadrupole Transition

SU(6): E1+=S1+=0

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NΔ - in Single Quark Transition

M1

N(938) Δ(1232)

Magnetic single quark transition.

Δ(1232)N(938)

C2

C2

Coulomb single quark transition.

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Multipole Ratios REM, RSM before 1999

Sign?

Q2 dependence?

Data could not determine sign or Q2 dependence

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N ∆ electroproduction experiments in the JLAB era

Reaction Observable W Q2 Author, Conference, Publication LAB

p(e,e’p)π0 σ0 σTT σLT σLTP 1.221 0.060 S. Stave, EPJA, 30, 471 (2006) MAMI

p(e,e’p)π0 1.232 0.121 H. Schmieden, EPJA, 28, 91 (2006) MAMI

p(e,e’p)π0 1.232 0.121 Th. Pospischil, PRL 86, 2959 (2001) MAMI

p(e,e’p)π0 σ0 σTT σLT σLTP 1.232 0.127 C. Mertz, PRL 86, 2963 (2001)

C. Kunz, PLB 564, 21 (2003)

N. Sparveris, PRL 94, 22003 (2005)

BATES

p(e,e’p)π0 σ0 σTT σLT σLTP 1.232

1.221

0.127

0.200

N. Sparveris, SOH Workshop (2006)

N. Sparveris, nucl-ex/611033MAMI

p(e,e’p)π0 ALT ALTP 1.232 0.200 P. Bartsch, PRL 88, 142001 (2002)

D. Elsner, EPJA, 27, 91 (2006)MAMI

p(e,e’p)π0

p(e,e’π+)n

σ0 σTT σLT σLTP 1.10-1.40 0.16-0.35 C. Smith, SOH Workshop (2006)JLAB / CLAS

p(e,e’p)π0 σ0 σTT σLT 1.11-1.70 0.4-1.8 K. Joo, PRL 88, 122001 (2001) JLAB / CLAS

p(e,e’p)π0

p(e,e’π+)n

σLTP 1.11-1.70 0.40,0.65 K. Joo, PRC 68, 32201 (2003)

K. Joo, PRC 70, 42201 (2004)

K. Joo, PRC 72, 58202 (2005)

JLAB / CLAS

p(e,e’π+)n σ0 σTT σLT 1.11-1.60 0.3-0.6 H. Egiyan, PRC 73, 25204 (2006) JLAB / CLAS

p(e,e’p)π0 16 response functions 1.17-1.35 1.0 J. Kelly, PRL 95, 102001 (2005) JLAB / Hall A

p(e,e’π+)n σ0 σTT σLT σLTP 1.1-1.7 1.7-4.5 K. Park, Collaboration review JLAB / CLAS

p(e,e’p)π0 σ0 σTT σLT 1.10-1.40 3.0-6.0 M. Ungaro, PRL 97, 112003 (2006) JLAB / CLAS

p(e,e’p)π0 σ0 σTT σLT 1.10-1.35 2.8, 4.0 V. Frolov, PRL 82 , 45 (1999) JLAB / Hall C

p(e,e’p)π0 σ0 σTT σLT 1.10-1.40 6.5, 7.5 A. Villano, ongoing analysis JLAB / Hall C

lLT

nLT

tLT RRR '

lLT

nLT

tLT RRR '

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Pion Electroproduction Structure Functions

• Structure functions extracted from fits to * distributions for each (Q2 ,W, cosθ*) point.

• LT and TT interference sensitive to weak quadrupole and longitudinal multipoles.

21M

*1 1Re( )E M

*1 1Re( )S M

*22 * * * *

* * 2 ( 1)( sin cos2 sin cos )L LT L TT LTpd

d k

+ : J = l + ½ - : J = l - ½

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• Unpolarized structure function

– Amplify small resonant longitudinal multipole by interfering with a large resonance transverse multipole

The Power of Interference I

LT ~ Re(L*T)= Re(L)Re(T) + Im(L)Im(T)

Large

Small

P33(1232)

Im(S1+) Im(M1+)

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Typical Cross Sections vs cos * and*Q2 = 0.2 GeV2 W=1.22 GeV

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NΔ(1232) - Small Q2 Behavior

Structure Functions

→ Legendre expansion

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Structure Functions - Invariant Mass W

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Legendre Expansion of Structure Functions

0 1 1 2 2

0

0 1 1

LT L

TT

LT

A A P A P

C

D D P

2

1

*1 1 2 0

*1 1 1

/ 2

Re( ) 2 / 3 / 8

Re( ) / 6

oM A

E M A C

S M D

Resonant Multipoles

*0 1 1

*0 1 0

*1 1 2 0 0

Re( ) / 2

Re( )

Re( ) 2 / 8

E M A

S M D

M M A A C

Non-Resonant Multipoles

(M1+ dominance)