Organizer: J. L. Rosner Scientific Secretaries: F. Halzen

C.E.W.Ward A. B. Wicklund Resonances IV: Systematics __

RESONANCES IV - SYSTEMATICS

Topic

1. 8U(3) Classification of Baryon Resonances

2. The Quark Model and Resonance Couplings

3. Helicity Structure of Resonance Electro­production and the Quark Model

4. Symmetries Beyond SU(3)

5. Duality for Baryons: Quark Model Results Without Quarks

6. Duality in KN - TrA

7. General Zero-Width Dual Four-Point FUnctions

8. Conclusive Experiments to Search for BB Exotics and a New FESR

9. Quark Model Predictions for Reactions with Hyperon Beams

10. Quartet Models of Hadrons

if. Deep Binding in Composite Models of Hadrons

Speaker

A. Barbaro-Galtieri (LBL)

R. G. Moorhouse (Glasgow)

F. J. Gilman (SLAC)

J. L. Rosner (Minnesota)

C. Schmid (ETH, Zurich)

B. C. Shen (California, Riverside)

S. Gasiorowicz (Minnes ota)

H. J. Lipkin (Weizmann)

H. J. Lipkin (Weizmann)

P. G. O. Freund (Chicago)

H. Joos (DESY)

SU(3) CLASSIFICATION OF BARYON RESONANCES*

Presented by Angela Barbaro-Galtieri

Lawrence Berkeley Laboratory University of California

Berkeley, California 94720

Since the discovery of 5U(3) sym.metry, 1, 2 it has become cus­

tornary at every conference to combine the new data with the old ones

and che ck the validity of this symmetry scheme. The last co:mplete fits

of baryon resonances I know of were made in 1970: Plane et aL 3

presented their fits at the Duke Conference on Baryon Resonances,

and Samios reported at the Kiev Conference the results of fits that he

and his collaborators had made. 4 A more recent review, which does

not include any new fits, is the one by Meshkov. 5

In this review I will first sum:marize the new data presented at

this Conference; then I will discuss the individual multiplets for which

the am.ount of data available is sufficient to perform constrained fits;

finally, I will mention some other possible multiplets. Large discrep­

ancies for unbroken SU(3) fits to the couplings seem to persist in the

3+ 3'2 decuplet and the 2" octet and singlet states.

I. New and Old Data Used in the Fits

New data and analyses of data have been presented at this Con­

ference for various resonant states. For discussion of the individual

papers, I refer the reader to the reviews presented in the Baryon

Resonances Parallel Session. I will report here only the data relevant

to the SU(3) fits I will discuss.

The old data us ed in the fits are all listed in the Particle Data

Group compilation, 6 unless otherwise specified.

A. New Data on S =0 Baryons

For the elastic channel a new partial wave analysis has been

presented at the Conference by the Saclay group. 7 The recently pub­8

lished analysis of Al:mehed and Lovelace was already included in the

PDG compilation. Table I shows the masses, widths, and elasticities

of the Saclay analysis for the states used in the SU(3) fits discussed

-159 ­

in this paper. These values haye been averaged with the values from

other experiments compiled by PDG, and the mean values obtained

are shown in the table. The errors are" external errors" of the in­

dividual values and were obtained as discussed at the end of this sec­

tion.

For the inelastic channels. new partial wave analyses for de­

cays into .6.11' and pN have been reported at this Conference. Fung iOet ale 9 reported results on the reaction n+p -. A°tr+; Bunyatov et al.

and Herndon et al. it reported complete partial wave analyses of the

reaction 11'N -+ tr1TN. The three papers essentially agree on the gen­

eral features of the partial waves; however. since Ref. 11 is more

complete and covers a wider energy interval, I have used their re­

sults. The values of the amplitudes at resonance, t = ~, have been

read from their amplitude plots; the errors have been estimated by

looking at the dispersion of points in the amplitude plots. The values

of t:l:dt from this paper for the D13(1520), D15(1672). and F15(1687)

are shown in Tables VI-Vill.

B. New Data on S = - 1. Baryons

Three new partial wave analyses have been presented at this

Conference. The results relevant to the SU(3) fits discussed in this

review are shown in Tables II and ill. The three analyses follow. i2

(a) Langbein and Wagner have performed an energy-inde­

pendent multichannel analysis including data on R.N, ~11', An channels

in the 436- to 1216-MeV/c region. The solutions at different energies

were linked by shortest-path technique.

(b) Lea et ale 13 have reported preliminary results on an energy­

dependent multichannel analysis for KN, ~n, and Atr data in the 440­

to 1190-MeV/c region. The energy dependence was introduced in the

K-matrix elements. parametrized as a combinatIon of resonance poles

and linear background.

(c) Levi-Setti et al. 14 have reported preliminary results on an

energy-dependent partial wave analysis on the individual channels R.N,

An, and ~11'. This analysis was done in the 780- to 12Z0-MeV/c region

and included 90 000 new events from the authors' new experiment in the

860- to tOOO-MeV/e region. Tables II and III include more than one

line from this experiment because the individual channels occasionally

yielded different M and r.

-f60­

The results from the old partial wave analyses are listed in the

PDG com.pilation. ~ They were individually included in obtaining the

average values used in this review, but they are not individually

quoted in Tables II and ill for reasons of space.

The largest discrepancy am.ong the various analyses is the elas­

ticity of the 511 state I;(1760). Values ranging from 0.08 to 0.80 have

been reported for this elasticity, too large an interval to be accepted

as an uncertainty in the analysis. So for r:: i-, I did three dif­

ferent fits which will be discussed in Sec. III-i.

C. New Data on S :: - 2 Baryon States

New experimental results on the mass and width of =:(1532) have

been reported by Baltay et ale 1.5 at this Conference. They are:

Baltay et al. 15 PDG values 6

M(g*)- :: 1534.7:1.1. MeV

rcg*)­ = 7.8:~:~ MeV

M =1536.1.:1.4 MeV

M(E:*)O = 1.532.0±0.4 MeV

r(:s*)o :: 9.0:1:0.7 MeV

M

r :: 1531.3±0.6 MeV

:: 9.2±0 .. 8 MeV.

The m.ost relevant re suIt for this review is the width for:;: (1532)° ,

which, averaged with the old data, gives the weighted average:

r =9.1 :1:0.5 MeV.

Errors on input data. In order to perform a chi-squared fit to

determine the coupling constants for each m.ultiplet, errors should be

assigned to each experimentally measured quantity. Whenever pos­

sible I have used values and errors given in the PDG compilation, 6

which are the result of the weighted average of various experiments.

Often a weighted average cannot be done either because the experi­

menters did not quote errors or-as for am.plitudes obtained in partial

wave analyses -because the errors are difficult to evaluate and are

often underestimated. Plane et ale 3 have arbitrarily assigned an er­

ror of 0.05 to each am.plitude from. partial wave analysis. However,

I think that this error is som.etimes too large, giving a good fit where

there probably is not a good fit, and sometimes too small, therefore

showing a worse situation than the data really indicate.

-161 ­

For both the average and errors I have adopted one of the fol­

lowing methods:

(a) Used weighted averages and their errors whenever possible.

(b) Evaluated the m.ean value of the m.easured quantities, x, and

an II independent external error" of the individual values

_jE(X(oxi ) -

iN-X)2

and then used x and (ox.) as error. 6 The error on the m.ean is, of 1

course, smaller by 1/~ , but I used the error on the individual

measurements because I feel it best represents the real situation.

(c) Estim.ated an error whenever either (a) or (b) above could

not be used or provided an II unreasonable answer." Each entry used

in the fits will be shown in a table, and for each the method used will

be specified.

3+ ll. 2: Decuplet

Table IV shows the data used for the SU(3) fits. The relation

among r and the coupling constant g is

2 M N 2 r (cg) B 1 (p) ~ P =(cg) F b' (1) R

where c is the 5U(3) coefficient from. de Swart, 16 with the sign con­

vention discussed in Ref. 6; ~ is the nucleon mass; M is theR mas s of the state for which r is calculated; p is the cente r-of-mass

rnornentutn for the channel being considered; and B (p) is a barrier13factor. In the past, two different form.s , 4,17 have been used for the

barrier factor:

2(pr)

(2) 1 + (pr)

2

where B 1 is the form taken from Blatt-Weisskoft18 for 1. = 1, and

r is a radius of interaction taken to be 1 fermi. The results of the

fits with these two forms of B1 are shown in Table IV, in the columns

g1. and gz- With the new precise value for the width of E(1532), neither

of the two forms give s ~ good fit. Schmid19 has sugge sted a new rela­

tion between rand g:

3 r = (cg)2 P (3)

-162­

where Mn is the mass of the decay baryon (N, A, 1: or~). The re­

sults of this fit are shown in the g3 column; the X 2 is only 0.09 for

3 degrees of freedom. However, a derivation of this formula has not

been published yet. In addition, the values of M and r used in these

fits were derived by fitting the data with Breit-Wigner resonance

forms which included barrier factors of the form. B 1 ; therefore, it

seems carre ct to be consistent and use the s arne barrier factor here

too.

In view of the above considerations, fits using broken SU(3) have

also been done. The relation among the individual widths derived with

broken SU(3) is20 , 21

2 ( A +:e) =3 ( E *-+ A1T ) '+ (:E*.... :ETr) • (4)

This formula gives for the three cases;

21) 8.13±0.15 7.98±0.69 X = 0.04, Z2) 18.4:t:O.3 = 18.2±1.6 X = 0.02, 2

3) 549:1:11 = 595%52 X = 0.00,

2where the X is a measure of the consistency of the equivalence. Note,

however, that the goodness of fit is directly related to the fact that the

best-measured quantities (A and :.;:) are both on the same side of the

equation.

In conclusion, unbroken SU(3) gives a bad fit to the data, unless

a new form for the decay rates is used; broken SU(3) seems to fit the

data very well.

III. Octets and Singlets 3 - 5 - 5+

I will dis cus s aniy the fits formultiplets with JP = i ' '2 ' "2' '2 which have enough measured rates to make a fit worthwhile. Experi­

mental results are available for decays into {8} X {8}; that is, into a -P i+

baryon member of the .r = 2" octet and a mes-on mem.ber of the

r = 0- nonet. Some results have also been recently reported on

{10} X {8} decays; that is, decays into baryon members of the ~+ decuplet and meson m.embers of the 0 - nonet.

{8} X {8} decays. There are two couplings for members of an

octet, gn and gF- However. since there can be mixing between the

isospin-zero member of the octet and the singlet, we have to include

the singlet coupling in the fits. We have

-163­

Singlet (5)

2 MNOctet r =(cngn + cFgF ) B1 (p) M p, (6)

R

where c. are the 5U(3) coefficients 6, 16 and the other sym.bols are the 1

same as for Eq.. (1). H we define

(Sa)

(Sb)

the mixing between the two physical states A mostly octet, and AI II

mostly singlet, in terms of a mixing angle fJ is

A =G S cos 6 + G sin 6,i (9) A' =-G8 sin B + 01 cos e .

Since the experimentally measured quantities are not r butt

t = ..JXXf (see Tables II and ill), I will follow the suggestion of Plane

et al. 3 and use as input data t. instead of r... In this case we have 1 1

(10)

where x is the incoming channel (always the elastic channel); x' is

the outgoing channel, either elastic or inelastic; r T is the total width

of the resonant state; G and G' are (8a) or (Bb) depending upon whether

we are considering a singlet or an octet state; F b is a kinematical

factor defined in (10); and the other symbols are the same as in Eq.. (1).

Since only products of couplings are measured, as seen in Eq.. (10),

there are sign ambiguities inherent to the above definitions, so I

assum.e, by convention, that g1 and gF are always positive. The sign

convention for t = "'XXi adopted here (Tables II and ill) is the one 22

advocated by Levi-Setti and discussed in Ref. 6. The relations

among gn' gF and Fin and a are as follows:

F ,.;s gF (1 f)D =3" gn I

(i2)a=

-f64­

The expected values of a from the quark model, taken from� 5�

Meshkov. are shown on the tables reporting all the relevant data for

each m.ultiplet.

{to} X{ 81 decays. For these decays there is only one coupling

constant. The experimentally measured quantities are t ="'xx' , where x is the elasticity related to couplings in the {8} X{8} con­

figuration. With some algebra from Eq. (1), we get

g = '" xx' Jr. (13)c xFbM

where F = B1 M N p is the usual kinematical factor and c is theb R

usual 5U(3) coefficient. 6,16 Not many results are available for these

types of decay; the N ~ a(i233)-rr decays are from Herndon et ala , 11

the y * ~ ~ (1385)1T decays are from Prevost et ala 23

-P i­i. J = '2 States

For these states. Eqs. (5) and (6) have to be multiplied by the

extra factor

where M is the dec~y bary~n, and MR - M = 564 MeV is the dif­n n ference of the m.ean i and i baryon octet masses. This kinematic

factor comes from PCAC arguments, and it was advocated by

Graham et al. 24 For the i-states it has been used in this form first 25

by Gell-Mann et al.

The new data for r = '2i-

states are shown on Tables I-III; all the

data used in the 5U(3) fits are shown. on Table V and require some com­

m.ents:

a. For the A(1405) all the previous fits have used only the 1: 1T de­

cay mode (assum.ed to be the only channel), because it is the only de­

cay detectable in production experiments. However, by doing the

appropriate analysis of low-energy KN data. one finds that the

coupling to the KN channel is very large. The value used here is from.

the analyses of Kim.26 and Galtieri.. 27

b. For the decays A(1673) ... ATl and N(1530) ... NTl. the signs of

~ are not known. If fact, whenever a partial wave analysis is per­

form.ed there is an overall sign ambiguity; therefore, only relative

-165­

signs can be measured. For the decays of ~ and A states into

En and An,as mentioned in Sec. m. the convention adopted is the one 22chosen by Levi-Setti and discussed in Ref. 6. For decays into

AT} and NTI this convention has to be picked up from SU(3). Three fits

were made with the different sign combinations for these two decays.

and the minus-minus combination for fit 1. in Table V was found to

give X 2 =15 compared with X 2 =27 and X 2 = 31 for the other two

combinations. Therefore this combination was also used for fits 2

and 3.

c. The elasticity of ~(1760) has been found to be 0.08 in one ex­

periment, 0.45 in another, and 0.8 in others (see Table ill); therefore,

three fits have been done, as shown in Table V, using two pos sible

values for x or no value at all. The value of x = O._6±O.1 gives a better

fit than the other value.

Table V shows that none of the three fits is very good. The

major contribution to X Z =15 com.es from N(1.530) ~ NT}, which gives

a contribution of X 2 =5, the measured value being too large. The

value of a = 1.2 is somewhat lower than the quark-model prediction of

a = 1.5; on the other hand, a = 1.2 is too large to interpret this octet 3 2 as the 8 / member of the 70(L =1-) quark-model configuration.

2. r = '23-

States

Table VI shows all the relevant input data, taken from Tables

I-Ill and from. Refs. 11 and 23.

The {8} X {8} de cays give an acceptable over all fit (X 2 =9.1

for 4 degrees of freedom). The A(1518) and A(1688) mix. the latter

being the mostly octet m.ernber. The mixing angle (J = (-23:1:4)° is

consistent with the value obtained from the m.ass formula using

M(g*) = 1830 MeV. The value of a is very close to the value expected 1 2for the 8 / octet in the 70 (L = 1 -) configuration (for 83/ 2 , a = 1.5 is

expected) .

For the {10} X{ 8} decays the results are not very consistent:

g~ is considerably larger than g~ and (gAla; the X 2 is very bad

(X =16/2DF). A pure singlet state is not allowed to decay into

{10} X {8} • and this fact allows calculation of the mixing angle

through the relation

-1.66­

2 _ re15i8) F b (1688) r(1518)� tg 8 - r(1688) X F b (1518) = 9. 52X r(1688) .�

The value 8 = (75 _t~ )0 obtained is in large dis agreem.ent with the

one obtained above, as pointed out by Mast et at. 28 However, since

all the g's for Y * .... ~(1385) 'IT seem to be too small and the analysis. of Prevost et at. 23 is preliminary, we should probably await more

partial wave analysis results before drawing any conclusion of SU(3)

violation. H the analysis of Prevost et all 23 is confirmed. a plausible

explanation of this discrepancy is that mixing occurs among two -P 3- -P 3­r = '2 octets and a T =2" singlet and not between one octet and a

singlet. The quark m.odel, in fact, predicts two octets and a singlet

to all be part of the 70(L = 1-) configuration. Faiman and Plane29

have recently written a paper on this subject. However, as noted

earlier, a for the {8} X {8} decays is close to the 81/ 2 prediction,

which would indicate no mixing between 8-1/Z and 83/ 2 .

P 5­3. J = '2 States

Table VII shows all the relevant input data taken from Tables

I-III and from Refs. 11 and 23. The fitted values of gn and gF as

well as the value of a are given in the table. The fits look very good,

although for {10} X{S} g.L\. and g~ are, again, on the low side, or g~

is somewhat large. Notice that a is very close to the value expected ....P S-

by the quark model, which expects only one r =2" octet and no

singlets in the 70 (L = 1 -) configuration.

-P 5+ 4. oJ =2 States

Data and results of the fit are shown on Table VIne The fit is

good for {S} X {S} decays; the value of a is very close to the expected

one if this octet is part of the 56(L = 2) configuration of the quark model.

For {10} X {8} decays we notice the usual effect: the coupling for

N -+ ~TI' decay, g~, is larger than the one for A .... ~(13S5)'IT decay.

5.. Conclusions on Octet and Singlet States�

-P 5+ S­IS} X_f8} decays. The J = 2" and '2 octets fit SU(3) very welL

The? = ~ states do not fit very well, the chi- squared being 15 (for

6 degrees of freedom), and an octet-singlet m.i.xing angle 8 =(8.3::1:4.3>­1J> 3- 2

is required. The J = 2" states fit reasonably well (X :: 9/4DF) and

require a mixing angle 8 = (-23:4) 0 • 3 {10} X {8} decays. These rates do not fit SU(3) very well

where data are available. In particular, the mixing angle 8 cal­3 culated from these decays is 6 3 = (75±1~)O, in bad disagreement with

(-23:4)°. However, the partial wave analysis for y*~ ~(1385)1f used 23in these fits is preliminary, and new results should be obtained be­

fore a violation of unbroken SU(3) is claimed, or a three-way mixing of

two octets and a singlet is advocated. 29

IV. Candidates for Other r = 4-- and ~- "Multiplets

30The 70(L = t -) configuration of the quark model predicts: two

r = t- octets (one discussed in Sec. ill), two r = ~- octets (of ~ich 5

one is discussed in Sec. IT), two singlets (also in Sec. II), a r = -21- 3­

octet (Sec. II), and two decuplets, with JP = '2 ' 2". So there are

four mu1tiplets to be completed before we have all the states for this

configuration.

Tables IX and X show all the candidates for these states. Two

a and one N state are confirmed by many different analyses. The

N(t 730), r = ~-, is not seen by all the analyses of the elastic chan­

nel, but the an channel has a reasonable signal, therefore is very

likely to be 11 good. It As for the A and ~ states, the situation is

very confusing; there is little agreement among the various analyses -­

however J the new data of Levi-Setti et al. 14 will certainly help to

clarify the situation.

Acknowledgments

I wish to thank Dr. Nortnan Gelfand for m.aking his computer available

to me during the Conference. This paper was com.pleted while I was a

Visiting Professor at the University of Hawaii and I wiah to thank Prof.

Vince Peterson and the High Energy Physics Group for their support

and encouragement.

-168­

Footnote and References

*Work done under the auspices of the U. S. Atomic Energy

Conunission.

f.� M. Gell-Mann, "The Eightfold Way: A Theory of Strong Inter­

action Symmetry, II California Institute of Te chnology, Re port

CTSL-20 (1961), printed in The Eightfold Way, by M. Gell-Mann

and Y. Ne'eman (Frontier in Physics, Benjamin, New York, f964);

M.� Gell-Mann, Phys. Rev. 1.25, 1.067 (t962).

2.� Y. Nefeman, Nucl. Phys. 26, 222 (1961).

3.� D. E. Plane et al., Nucl. Phys. B22, 93 (i970).

4.� N. P. Samios, BNL report 15284, to be published in Proceedings

of the 15th International Conference on High-Energy Physics,

Kiev, 1970.

5.� S. Meshkov, Review of Hadron Spectroscopy, invited talk at the�

International Conference on Duality and Symmetry in Hadron�

Physics, Tel-Aviv, Israel (1971).�

6.� Review of Particle Properties, Particle Data Group, Phys.�

Le tte r s, 39B, 1 (i972) •�

7.� R. Ayed. P. Bareyre, and Y. Lemoigne, in "Zero Strangeness

Baryon States below 2.5 GeV Mass," CEN-SACLAY preprint

(1972).

8.� S. Alm.ehed and C. Lovelace, Nucl. Phys. B40, i57 (1.972).

9.� s. Y. Fungetal., IIPartial Wave Analysisof1T+p-+1ToA++ at

1820-2090 MeV." Presented to the XVI International Conference

on High-Energy Physics, Chicago- Batavia, Paper 666 (1.972).

to.� S. A. Bunyatov et al., "Partial Wave Analysis of 'll'N'" 1I'1TN

Reaction Near the Threshold of ~(tZ36) Resonance Production. It

Presented at the XVI International ,Conference on High-Energy

Physics. Chicago-Batavia, Paper 87t (1972).

if.� D. J. Herndon et al., itA Partial Wave Analysis of the Reaction

wN ... 'n'",N in the C. M. Energy Range t300-2000 MeV, 11 Lawrence

Berkeley Laboratory Report LBL-i065 and SLAC report SLAC­

PUB-1iOS (1972).

-169­

12.� W. Langbein and F. Wagner, "An Energy Independent Coupled

Channel Phase Shift Analysis for the KN System," Max Plank

Institute Report (Munich, Feb. 1972).

13.� A. T. Lea, G. C. Oades, B. R. Martin, and R. G. Moorhouse,

presented at the XVI International Conference on High-Energy

Physics, Chicago-Batavia, Paper 627 (1972).

14.� R. Levi-Setti et al., Chicago-LBL Collaboration, "Hyperon

Formation in the 1700-1900 MeV Region: New Data and Partial

Wave Analysis of the KN, ~11', ATr Channels, II presented at the

XVI International Conference on High-Energy Physics,

Paper 938 (1972).

15.� C. Baltay et al., Columbia-SUNY Collaboration, "Mass and

Width of ~(1530),rt presented at the XVI International Conference

on High-Energy Physics, Chicago-Batavia, Paper 418 (1972).

16.� J. J. de Swart, Rev. Mod. Phys.2..?, 916 (1963).

17.� R. D. Tripp etal., Nucl. Phys. B3, 10 (1967).

18.� J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics

(Wiley, New York, 1952).

19.� C. Schmid, private comm.unication, August 1972.

20.� C. Becchi, E .. Eberle, and G. Morpurgo, Phys. Rev. i36B,

808 (1964).

2i. V. Gupta and V•. Singh, Phys. Rev. 135B, i442 (1964).

22.� R.. Levi-Setti, in Proceedings of the Lund International Con­

ference on Elementary Particle s (1969) ..

23..� J. Prevost et al., "Partial Wave Analysis of KN .... ~(1.385)1T

Between 0.6 and 1.2 GeV/c, 11 paper presented at the Amsterdam

International Conference on Elementary Particles, 1971.

24.� R. Graham, S. Pakvasa, and K. Raman, Phys. Rev. 163, 1.774

( 1967).

25.� M. Gell-Mann, R. Oakes, and B. Renner, Phys. Rev .. ill, 2195

( 1968).

26.� J. K. Kim and F .. von Hippel, Phys. Rev. 1.84, 1961 (1969).

27.� A. Barbaro-Galtieri, in IISe lected Topics in Baryon Resonances,"

lectures delivered at the 1971. Erice Summer School on Subnuclear

Physics, Lawrence Berkeley Laboratory Report LBL-555 (to be

published by Academic Press, 1972).

-i 70­

28.� T. S. Mast et al., Phys. Rev. Letters 28, 1220 (f972).

29.� D. Faiman and D. E. Plane~ Phys. Letters 39B, 358 (1972).

30.� Some of the late st reviews of this model are: R. H. Dalitz in

Symmetries and Quark Models, edited by Chand (Gordon and

Breach, New York, 1970), p. 355. Also R. P. Feymnan in

Phenomenology in Particle Physics 1971, edited by E. B. Chiu,

G. C. Fox, and A. J. G. Hey (California Institute of Tech­

nology, Pasadena, California, 1971), p. 224. Also D. Faiman,

Nucl. Phys. 32B, 573 (1971).

31.� J. K. Kim, Phys. Re v. Lette r s 27, 356 (i9 7 f) .

32.� A. Barbaro-Galtieri, Hyperon Re sonances-70, edited by

E. C. Fowler (Moore Publishing Co., Durham, North Carolina,

f970), p. 173.

-i 71.­

7Table I. New param.eters of Ayed et al. for the non-strange baryon states used in SU(3) fits. The last three colwnns show the mean values and "External Errors, "6discussed in the text, obtained from the new as well as old results.

x

(MeV) (MeV) (MeV) (MeYl

State M r x M r

Sff fS23 78 0.33 1530 *27 104:1:38 0.32 :l:O.OSa

D13 1528 t19 0.57 1520:1: 9 121:l: 12 0.54 :1:0.04

D15 1655 141 0.40 1.672:i: 9 143:i: 26 0.42 ::1::0.04

F15 1679 133 0.60 1687:: 5 128 ::1::22 0.62 *0.05

aError increased from 0.04.

-t72­

Table II. Old and new parameters for isospin zero. 5 =1 baryon states included in the SU(3) fits. Values in square brackets [ ] have been kept constant in the fits. Values in parentheses ( ) have been constrained to be near the PDG values.

~.". A"M r KN Authors Ref.

(MeV) (MeV) .JXXI .JX'Xf 501 1640 :1:40 45 ±lO 0.35 ±0.05 Langbein + 1l

(1668) (l9) (0.16) (-0.l7) Lea + 13

[ 1676] [26] 0.38:1:0.05 [-0.30] Levi-Setti + 14

1670 15 to 38 0.20 -0.30 0.26 PDG 6 a1673:1: 7a 30:1: lOa 0.25 :l:0.08a -0.30 ±0.04 0.25±0.04b This review

D03 1680:1: lO 40:1: 10 0.t5:1:0.05 -0.26±0.07 Langbein + 12

(1689) (54) (0.24) (-0.32) Lea + 13

[ 1690] 63:1:5 0.35:1:0.05 Levi- Setti + 14

[1690 ] 90:t: 10 -0.4l:l:0.05 Levi-SetH + 14

1690 31- 85 0.20 -0.35 PDG 6 a

168B:I: Sa 53 ± 17 0.2B±0.05c -0.35 ±0.05c This review

DOS 1BI0 ± 10 60 ± 20 0.10 :1:0.03 -0.27:1:0.07 Langbein + 12

(1830) (80) (0.08) (-0.16) Lea + 13

[ 1831] 128:1: 20 0.07:1:0.02 Levi-Setti + 14

1831:l: fO 113:1: 10 -0.12 :1:0.02 Levi-Setti + 14

1835 74 - 150 0.07 -0.16 PDG 6 a

1B27 ± 1t 89 ± 32 a 0.07 ±0.03a -0.16±0.04a This review

FOS 1818±3 70 ± 5 0.47:1:0.02 -0.25 :1:0.03 Langbein + 12

( lB17) (79) (0.6t) ( -0.26) Lea. + 13

[ 1818] 86:1: 5 0.65 :1:0.02 Levi-Setti + 14

[ IB18) 95:1: 10 -0.29 :1:0.03 Levi-5etti + 14

1820 ± 5 64 - 104 0.62 -0.26 PDG 6

1819 ± 6c 80 ± 15c 0.58:l:0.0Bc - 0 . 2 6 ±O .0 3c This review

a Mean values and "External Errors" (see text).

bError increased.

CAverage and errors estimated from the dispersion of reported values.

-i73­

Table III. Old and new parameters for isospin-1. S; -1 baryon states included in the SU(3) fits. Values in square brackets [ ] have been kept constant in the partial wave analysis fit. Values in parentheses ( ) have been constrained to be near the PDG values.

M r KN Authors Ref. (MeV) (MeV) x

S11 1790 ± 15 100 ± 20 0.45±0.05 0.13::1::0.02 -0.30%0.05 Langbein + L.:.

(1750) (60) (0.79) (0.1S) -0 Lea + 13

1730:t:10 50±20 0.08±0.03 Levi-Setti +a 14

1719± 10 90±20 0.1.1:t:0.02 Levi-Setti + 14

1727±10 65 ± 10 - 0.12 ± 0.03 Levi-SetH + 14

1750 50 - 80 0.1 -0.8 - 0.25 to -0.10 PDG 6 d1756::1::24c 65 ± 20 c 0.08 or 0.6 -0.18 :t:O.OSe This review

Di3 1675:t: 15 65::1::20 0:10 ::1::0.03 0.23 ± 0.05 0.13 % 0.03 Langbein + 12

(1670) (51) (0.08) (0.19) (0.09) Lea + 13

1670 50 0.08 -0.18 0.08 to 0.16 PDG 6

1669±8c 50 ± 9c 0.08±0.03 c 0.19:1::0.04 c 0.t1±0.03 c This review

DiS 1770 ± 5 123 ::l: 10 0.39 :1::0.01 ~0.09 -0.15::1=0.04 Langbein + 12

(1766) ( 105) (0.18) (0.06) (-0.25) Lea + 13

[ 1765] [ 110] 0.35±0.03 0.09:1:: 0.02 Levi-Setti 14

1768 % 5 119 ± 10 -0.28±0.03 Levi-Setti 14

1765::1:: 5 60 to 146 0.42 0.07 -0.25 PDG 6 e1765 ± 8 108 ± 28 OAO±O.OSe 0.07±0.03e -0.22±0.04e This review

F15 (1915) (80) (0.15) (-0.10) (-0.10) Lea + 13

[ 1915] [ 651 -0.05 Levi-Setti + 14

1910 70 0.11 to 0.t8 -0.06to -0.14 -0.07to-0.11 PDG 6 e1910 ± fOe 70 ± 20e 0.15 ::I::O.OSe -0.10±0.04 -O.09±0.03e This review

a For another very close state see Table IX.

bValue from J. K. KIM, Ref. 31­

c Mean values and tlExternal Errors tl (see text).

dThree fits were performed (see Table V): one with x = 0.08±0.06. another with x=O.6±0.1, and one without thi s information at all.

eAverage and errors estim.ated from the dispersion of reported values.

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Table IV. Unbroken SU(3) fits lo the 3/2+ decuplet. The data used are listed in the PDa compilation; new data are discussed in Sec. I. The three values of g corre-spond to different form.s for the kinematicalfac­tor, as discussed in the text. .

Decay r Partial mode g1 g2 g3(MeV) ( %)

A( 1233)-+ N1I' 115 ± 5 99.4±0.6 2.29 :to.05 5.02 ±0.11 149 ±3

E:( 1532)-+ ~1r 9.1 :J:0.5 100 1.78:1:0.05 4.21 :1:0.12 148:J:4

1:( 1385)-+ A 11' 36:1:6 88:1:5 2.02 :1:0.18 4.53 ±0.40 147: 13

:E( 1385)-+ ~11' 36± 6 12 ±5 1.91 ±0.43 4.6 ::t: 1.0 155 ± 35

(g ) 2.04 ±0.04 4.65 :0.08 149 ±3

2 50.0/3DF 24.0/3DF O.09/3DFX

-i75­

Table V. Mass and width are listed for each state, as well as the values of the amplitude,~, at the

resonance mass for each decay mode. For a discussion of how average values were obtained, see

Sec. I. F b are kinematical factors, F b = B£(p) ~ p. where B£ is the Blatt-Weisskopf barrier fac­

tor. 18 The g., ~, and (J are defined in the text. R 1

State M r Mode ...r;;xr Fb

(MeV/c)~ ~

A(1405) 1402 ±4 38%8� NK 0.80 z 0.06a 65

~1f 0.20 ±0.06a 29

N(t530) 1530 ±27 104 ± 38� NIT' 0.32::1::0.05 312

N" b(_)0.42 ±0.05 :19:1

1\( 1670) 1.673 ± 7 30 ± 10 NK 0.25 ±0.08 394

1:1T -0.30 ::1::0.04 249

b(_)0.25 ::1::0.04 t31A"

~(1760) 1756:1:24 65:1:20� NK 0.08 or O.bc

550

~1T 0.14::1::0.04 364

A'TT' -0.18:1:0.08 440

2Fits� ~ egF gn g1� X

~

i- No KN for 1::(1760) 0.41 :1::0.05 -0.08 ±0.04 1.t±O.f 1.2 :l:O.t 8±4 15

2. x[~(1760)]= 0.08±0.05 0.28±0.04 0.05 ± 0.06 1.1 ±O.t 0.88:1:0.04 -3 ± 6 26

3. x[I:(1760)]= 0.6±0.1 0.41:1:0.04 -0.09::1::0.04 1.1 :1:0.1 1.2 :1:0.:1 8±3 15

aValues obtained in low-energy KN partial wave analyses (Refs. 26 and 27).

b The signs of these two amplitudes were not measured. they both have been chosen - because this choice gave better fits.

cniffere nt partial wave analyse s give different re suIts; see Table In and Sec. 1.

-176­

Table VI. JP=3/2- state s . The mas s (in pare nthe se s with the s yInboll and total width are Hste d for

each state, as well as the values of the amplitude ~ at the resonance mass for each decay mode.

~or a discussion of how M~h value has been obtained, see :ables I -III and Sec. 1. F bare kinemat­

lcal factors. F b =B t(p) ""MR""" p. where for B t the Blatt-We18skopf form was used. t8

The results of

the fits are shown in the lower part of the table (for both {8}X{8} and {fO}X {8} decays).

{8 }X {s} {fO}X{8}F FState r b b

(MeV) Mode ~ (MeV/c) Mode ~ (MeV/c)

A(t518) 16±2� KN 0.45 ±0.03 19.8 ~(1385)1!' 0.20 ±0.02a t4.2

~1f 0.43 ±0.03 23.7

N(f520) t21 ± 12� N'II' 0.54±O.O4 t50 ~(1233)'II' 0.32 :l::0".05b 135

A(t688) 53 ± 17� KN 0.28±0.05 117 1;(1385)'11' -0.06±0.03a :135

~'II' -0.35 ±O.OS 109

~(1669) 50 :1:9� KN 0.08 :1:0.03 106 ~(1385)'II' -O.Of ±0.03a 125

~1l' 0.19 :1:0.04 99 Atr 0.11±0.03 tiB

2{8}X{8} X =9.1/4DF gF =0.30 ±0.04 g~ =0.47±0.08�

gD =0.80 ± 0.04 g~ =0.O6±0.18�

2�{f0}X{8} X =16/2DF = 0.87:1:0.07 (gA)8=0. 12 :1:0.04gt

For 70, 81/ 2� a = 0.34:1:0.09 = 0.i9±0.04gay

a exp =0.375� (] =-(23 ±4) (] = (75 ~~O)

aprevost et al. 23�

bHerndon et aLI 11 see Sec. 1.�

-t 77­

Table VII. JP = 5/2- states. The mass (in parentheses with the symbol) and total width are listed

for each state, as we 11 as the value s of the amplitude ,JXXl at the re S onance ma s s for each de cay

mode. For a discussion of how each value has been obtained, see Sec. I. F b are kinematical factors.

F b = Bi p) ~N p, whe re for B..e the Blatt- We is skopf form was used. i8 The re suIts of the fits are

shown in the rower part of the table (for the two types of decays {8}X{8} and {10}X{8}).

{8}X {8} {iO}X{8} F FState r Mode ..[XXi b Mode ~ b

(MeV) (MeV/c) (MeV/c)

N(1672) 143::1: 26 N'rr 0.42::1: 0.04 209 .6(1233)'" 0.50 ::I:O.iSa 74

A(t827) 89::1: 32 KN 0.07::1:0.03 183 ~( 1385}rr 0.11 ±0.03b 76

~1T -0.16 ± 0.04 170

E( 1765) 108::t:: 28� KN 0.40±0.05 156 ~( i38S)1I' -0.12 ±0.03b 47

~1T 0.07::1:0.03 146

ATr -0.2l::l:0.04 162

{8}X {8}� gF = 0.82 ::1:0.05

{10}X{8} Xl := l.O/lDF gn =-0.12::1:: 0.04 gA = 0.6::1::0.2

For� F/n = -0.11::1:: 0.04 g~ = 0.8::1::0.2

a = 1.5 a� = 1.13::1::0.05 g = 0.76.::1::0.13 exp� av

aHerndon et al. ,11 see Sec. I.

bprevost et ale 23

-178­

Table VIII. JP =5/2+ states. The mass (in parentheses with the symbol) and total width are listed

for each decay mode. For a discussion of how each value has been obtained see Table s I - III andJ

.. F ( ) MN� .Se c. 1. F b are klnem.ahcal factor s. b:::: B£ p ~ p. where for B £ the Blatt- Welsskopf form. was

used. 18 The results of the fits are shown in the lo:er part of the table (for both {8}X {8} and

{fO}X {8} decays).

{8}X{8}� {10}X{8}F� F

b� bState� Mode ~ Mode ~ (:tkV)� (MeV/c) (MeV/c)

N( 1687) 128±22� NTT 0.62±0.OS 116 ~1236)TT 0.2S±0.OSa 160

A(1819) 80 ± 15� KN 0.58 ±0.05 90 L( 1385)TT 0.11 ± 0.03b 142

LTT -0.26±0.03 78

L(1910) 70 ±20� KN 0.15±0.05 128

LTT -0.10 ±0.04 114

ATf -0.09±0.03 130

2{8}X{8} X 6.S/4DF� g F = 0.7 i ± 0.05 g6. :::: 0.32:1::0.07

2{10}X{8} 5.0/1DF� gD = 0.58:1:: 0.08 gA =0.14:1::0.04X

For 56. 8 1/ 2� F/D:::: 0.61±0.09 g :::: O. 19 :!:: 0.0-4 av

ex = 0.6� ex :::: 0.62±0.04 exp

aHerndon et al.,i1 see Sec. I.

bprevost et al. 23

-179­

Table IX. Candidates for other JP = 1/2- multiplets. Old results are listed in the PDG compi­lation. 6 States listed with a status of "good" are established; the ones listed as "possible" are still in doubt. essentially because the different partial wave analyses do not agree.

State M r Mode ~ Reference Status Multiplet (MeV) (MeV)

A( 1650) 1615 ­ i695 130 ­ 200 N'Ir 0.28 PDG6 Good {iO}

N(f700) 1665-1765 100 - 400 N1T 0.60 PDG6

Good {8}

A(i800) 1780 ­ i872 40 ­ 100 NK 0.i8 - 0.80 PDG6 Possible {8}

1830 ± 20 70 ± 15 NK 0.35 :f:0.15 Langbein12 Possible

~TI' 0.24 Kim31 Possible

~( 1620) 1620 40 NK 0.05 Kim3f Possible {S}, {iO}

L'lf 0.08 Kim31 Possible

A1T 0.15 Kim31 Possible

1620 65 ± 20 NK 0.22:1: 0.02 Langbein12 Possible

1:11' 0040 %0.06 Langbein t2 Possible

~(t 725) 1730 ± to 50 ±20 NK 0.08:1:0.03 Levi-SetH 14 Possible {8}, {to}

1.719*10 90:t 20 1:'Ir 0.11.:i:0.02 Levi-Setti t4 Possible

1727 ± 10 65:i: to An -0.12:i:0.03 Levi-Setti 14 Possible

6Table X. Candidates for other JP .; 3/2- multiplets. Older results are listed in the PDG com­pilation. States 1iste d with a status of IIgood II are established; the others are still in doubt.

State M r Mode ~ Reference Status Multiplet (MeV) (MeV)

6.0(1670) 1650-1720 175 - 300 Nil' 0.15 PDG Good {10 }

7N(1730) 1730 130 Nn 0.10 Ayed Likely {8}

11 ~n Herndon

32A(2010) 2010 130 ~n -0.20 Galtieri Possible {8}

~( 1710) 1719±10 50 ± to ~n -0.06±0.03 Levi-Setti14 Possible {a}. {to}

f41700 ± 20 48± 10 Afr -0.04 ±0.02 Levi-Setti Possible

~( 1740) 173 t ::I: 10 56::1: 10 ~fr 0.05 ±0.03 Levi_Settii4 Possible {a}. {10 } i4

1752 ± 20 80::1:30 An 0.06::1:0.02 Levi_Setti

~(1860) 1863 95 NK 0.22 Lea13 Possible {8 }. {to} 13

An -0.12 Lea

6 ~(t940) 1940 220 ~n -0.13 PDG Possible {8}, {fO}

Afr -0.09

-181­