“Complete” Measurements for Meson Photoproduction

An Experimentalist’s Point of View with Theoretical Help

William J. BriscoeMark Paris

Igor StrakovskyRon Workman

The George Washington UniversityInstitute for Nuclear Studies

*also borrowed/revised some ideas from Lothar’s talk at PWA 2011

Motivation• The goal of performing “complete experiments” for

photoproduction is now being realized at three international laboratories – JLab, ELSA, MAMI.

• Realizing this goal may be cut short by a lack of understanding as to what is involved in obtaining a “complete” set of measurements for what should be more properly referred to as the “complete nucleon experiment”. – After all, we are studying the properties of the nucleon!

• For measurements to be truly “complete” they must be extensive and include all possible initial and final isospin states .

Current Experimental Situation

• MAMI, ELSA and JLab:– “complete experiments” for e.g. g,p g,h g,K – Some measurements for e.g. pp, ph– linearly and circularly polarized photons– longitudinal and transverse polarized targets– recoil polarization of outgoing nucleon

• recoil polarimeter - only at MAMI• Magnet - one can rotate to measure both polarizations

– Last done for pN measurement at LAMPF• Looking for new pion beam lines for more precise πN data.

Current Phenomenology • Coupled-channel (multi-channel) analyses

– Database still limited • High-precision analyses of π, η, KY

photoproduction are in progress – SAID (GW – Institute for Nuclear Studies)– MAID (JGU – KPH)– BoGa (UB – HISKP)– EBAC (JLab – Theory Center)

Complete Experimentsin the Traditional Sense

• For Meson Photoproduction:– 16 possible observables for each individual channel– 8 are needed for complete experiment for each channel

• for amplitude analysis

– Recoil Polarization must be included• Difficult but not impossible and sometimes get it free – e.g. KY

– These need to be for each isospin state of the meson and target to determine phases in multipole approach.

– Some channels have charged products – some neutral.– Production off the neutron lags behind

» No free neutron target – Problem with final state interactions

» GW/ITEP/Duke code development

Polarization Observables• Assuming we wish to make the

theorist and phenomenologist happy, we should provide measurements of a good fraction of the above over an energy range, say, from threshold through third resonance region.

• For amplitude analysis of a single channel this is eight carefully selected observables.

• No agreement as to what is needed for multipole analysis, which is what we do now.

• Measurements should include all combinations of isospin.– possible only if measurements

off the proton and neutron.

set observablessingle(none) S d/d

T P

beam-target BT G H E F

beam-recoil BR Ox´ Oz´ Cx´ Cz´

target-

recoilTR Tx´ Tz´ Lx´ Lz´

set observablessingle(none) S d/d

T P

beam-target BT G H E F

beam-recoil BR Ox´ Oz´ Cx´ Cz´

target-

recoilTR Tx´ Tz´ Lx´ Lz´

Polarization Observables• Ignoring the controversy over signs and frames of reference.

– Dick Arndt: “There ought to be a law requiring ALL measurements be done in the cm frame.”

• The traditional convention is of Barker, Donnachie, and Storrow (1975) wrt signs and number of measurements.– “In order to determine the amplitudes uniquely (up to an overall phase of

course) one must make five double polarization measurements in all, provided that no four of them come from the same set.”

• Keaton, Workman (1996) and Chiang,Tabakin (1997):– “a carefully chosen set of 8 observables is sufficient.”– This takes into account that the same information may be obtained in more

than one of the above measurements. • Some feel we can do with fewer double-polarization

measurements – mostly in multipole analysis.

Double-Polarization Observables(From Lothar’s talk at PWA Workshop)

• BT: polarized photons and polarized target

(red signs change in different conventions.)

• BR: polarized photons and recoil polarization

• TR: polarized target and recoil polarization

Complete Experiment for Pion Photoproduction

• Assuming the experimenter wishes to make the theorists and phenomenologists happy most feel that they should at least provide the measurements as prescribed above by Barker, Donnachie, and Storrow (or the others) over as wide an energy range as possible, but especially including threshold through the third resonance region.– N.B. only MAMI boost a recoil polarimeter – with a magnet can

obtain both recoil polarizations. • Measurements should include all combinations of

isospin.– This is only possible if measurements of production off the

proton and neutron are made.

The “Complete” Nucleon Experiment

Why do we need photoproduction off the neutron?

Why do we need to make measurements over a wide range of

energies?

Why do we need to include measurements for other production

channels?

Phases and isospin

For π-N scattering3 charge channels 2 isospin states (triangle equality)

For gN production4 charge channels3 isospin states(quadrilateral relation)(ambiguity)

π-p + √2 π0n = π+p

√2 π0n + π+n + π-p = √2 π0p

From Ron Workman’s talk at NSTAR 2011

π+n

π0p

I=3/2

Fixing overall phases

π +n phase fixed

[ by ‘known’ high-L part (real) ]

From Ron Workman

I=3/2

π+ n

π0 p

π0 n

π- p

π+ n and π- p phases fixed

[ by measure proton and neutron ]

From Ron Workman

Isospin Symmetry in the Photoproduction of Pions• The nucleon current is given by• eN is the nucleon charge ( ep = +1 , en = 0 ) in units of

proton charge, -e. • Operator in isospin space:

– eN = ½ ( + ) where• Decompose nuclear current into isoscalar and isovector

components.

• Where: with

• We note that

)()()( xexxj NNNN g

N3

10

013N

)()()( xjxjxj vsN

g )()( 21 xxj Ns )(xN

)()()( )(32

1 xxxj NN

Nv g

)()(

)(xx

xn

pN

.)()()()()(

)()()()()(

21

21

xxxxxj

xxxxxj

nnppv

nnpps

gg

gg

Photoproduction Transition Amplitude

• NB: Isospin symmetry does not constrain the three independent amplitudes: V(3/2) ; Vp

(1/2) ; Vn(1/2).

channelshadronicallNNNN

VVVTGVT

NWqqTNT

N

o

jiijNN

,.....,,,,

);,'(

,

,

php

gp

g

gp

)(32)(

31

)1(31)(

320

)()(32

)1(31)(

320

21

23

23

21

23

23

2

n

n

p

p

np

nn

pn

pp

ΤΤΤ

ΤΤΤ

ΤΤΤ

ΤΤΤ

gp

gp

gp

gp

Photoproduction Dynamics• Our objective is not just to collect some of the

individual amplitudes, but to learn something about the dynamics, i.e. V, of the pion photoproduction process.

• The interaction, V is composed of many interaction mechanisms – e.g. a multichannel model for the gNpN transition amplitude can have a V with 50100 terms. Some simple tree-level diagrams are shown here.

• The photoproduction amplitude from proton and neutron are distinguished by linearly independent combinations of these mechanisms yielding independent observables and permitting detailed analysis of the relative contribution of such mechanisms

From Igor StrakovskyFrom Igor Strakovsky

From Igor Strakovsky

Conclusion

• Since the object is to study the properties of the nucleon and learn about the photoproduction dynamics, the complete nucleon experiment includes more than just performing a “complete experiment” on a single channel.– To obtain independent information on hadronic couplings (both

resonant and non resonant) one must make a “complete” set of measurements for meson photoproduction off both the proton and the neutron.

– Measurements must made over a wide range of energies.– Measurements need to include different production products.

i.e. complete here does not means a complete measurement of a single photoproduction channel, but rather multiple channels.