New quantum number in the Nieh-Wu-Yang theory

P H Y S I C A L R E V I E W D V O L U M E 1 3 , N U M B E R 1 1 J A N U A R Y 1 9 7 6

New quantum number in the Nieh-Wu-Yang theory

S. Y. Lo*

School of Physics, University of Melbourne, Parkville, Victoria, 3052, Australia

(Received 17 March 1975)

The possibility of extending the new quantum number introduced by Nieh, Wu, and Yang to account for new experimental observation is discussed. A t-spin scheme as contrasted to an additive scheme is discussed

The discovery' of the new narrow-width resonances ~ (3 .105) and $(3.695) in ef e - annihilation immediately ra ises the crucial problem of fitting them into the traditional pattern of particles. All pre-J discovered particles a r e classified into the following classes:

(1) hadrons, (2) leptons, (3) mediator of the electromagnetic interaction y , (4) hypothetical

a . mediator of the weak interaction, e.g. W boson,

b. mediator of the gravitational interaction- graviton.

I t i s c lear that the new particles cannot be leptons because they have lepton number zero, and their interaction i s too strong for them to belong to the c lass of graviton. Therefore, al l theoretical at- t e m p t ~ ~ - ~ try to accommodate them into ( I ) , (3), and (4a).

In the case of classifying J, $ a s hadrons, there i s in general a need of a new quantum number so that their interactions with ordinary hadrons a r e suppressed in order that they have narrow widths. The new quantum number could be an implicit one a s in the charmonium (FC) model, o r i t could be an explicit one a s in the Nieh-Wu-Yang (NWY) theory .2 v 3

In the present paper we wish to investigate in some detail the nature of the new quantum number t a s proposed in the NWY theory. The new quantum number t may be one of the following three kinds:

(1) multiplicative, like parity, (2) additive, like strangeness, (3) vectorial ( t spin), like isospin.

All three kinds of quantum number can guarantee the stability of the f irst narrow-width resonance 43.105) against strong decays.

F o r the case of multiplicative quantum numbers,

i t i s easy to assign all previous hadrons with t = 1, and the new meson t = - 1. One then requires the strong interaction to conserve t parity. The ob- servations of the decay of the narrow-width resonances

$(3.695) -43.105)+ a n , (1)

which i s t -parity conserving, would deal a severe blow to this scheme unless i t can be shown to be a strong decay. Fo r the case of the additive quantum number i t i s possible to assign an additional additive quantum number S t = i 1 to the second narrow- width resonance $(3.695) in order to ensure i t s stability against strong decay. One may even be tempteds to identify the new quantum number S' to be the ordinary strangeness number in order to have an economy of new quantum numbers. The unfortunate fact i s that

Hence $(3.695) can decay via

The observation of (1) instead of (2) and (3) also damages severely the simple picture where S' i s identified with ordinary strangeness. However, there would be no contradiction with facts if one allowtki S' to be a new independent quantum number.7

In the las t case of a vectorial quantum number, i.e., t spin behaves like siospin, there a r e some very interesting consequences, which will be elaborated

13 - N E W Q U A N T U M N U M B E R IN T H E N I E H - W U - Y A N G T H E O R Y 185

in the following. (a) Quantum -number assignment. All previously

known particles a r e t singlet, and the new particles ~ (3 .105) and q(3.695) a r e ei ther t doublet o r t triplet. Strong interaction i s assumed to be t - conserving just a s isospin conservation. The usual additive-quantum-number rule may be extended to become

Utilizing (4) i t i s easy to l i s t the various quantum numbers of minimum number of t nonzero mesons and baryons. They a r e tabulated in Table I for definiteness to facilitate further discussion. I t i s c lear that without experimental confirmation of al l members of the multiplet no commitment can be made a t this stage for i t s correctness. Neverthe- less, i t i s interesting to note that the t doublet J has two neutral partners J O , p , while the t triplet +O has only one. This contrasts strongly with the additive scheme where there must be two neutral partners.' If future experiments prove that there i s no splitting in any one of the mesons J o r $, then i t definitely rules out the additive scheme, but not necessarily the t-spin scheme.

F o r the higher-mass mesons created in e'e- annihilation, e.g., the structure a t 4.2 GeV/c (see Ref. 8) can be classified into two types: the t = i type S, like J0 o r the t = 1 type like $. Then their strong decays can be

$*(4.2) -#(3.695) + hadrons,

but not

However, if i t s mass i s greater than 2M,, the decays

a r e allowed in the t-spin scheme, but not in the additive-quantum-number scheme.

(b) Associated production. F o r associated pro-

TABLE I. Possible quantum-number assignments for t * 0 hadrons.

(a) J(3.105) meson (c ) 0 baryon

1 3 1 -z +

t 3 t y O

1 - J O J+ B B(

1 J - YO 1 -z -Y 6"

03) q(3.695) meson (d) X baryon

IS3 O 1 3 + t -4

t3

+ 1 * + + 1 X + + X +

o q0 o x + x O -1 $ - -1 x x-

duction the t-spin case i s s imilar to the additive- number case where both the J and J, can be created in association with the t+O baryon,

P P - J + e + P , (8)

P P - $ + X + P ,

where 0 and X a r e the t = i and t = 1 baryons, re - spectively. In order to conserve t spin JB and $X must be produced together, but not JX and $8. Hence i t i s easy to explain the following two experimental facts:

(1) In the Brookhaven experimentg 5(3.105), but not $(3.695) i s produced in pp scattering a t P = 30 GeV/c.

(2) In photoprod~ction, '~ J and + a r e not produced for P, B 18.2 GeV.

These experimental facts can be explained provided that the t#O baryons have the following mass:

2.79 c Me 4 3.56 GeV , 2.92 c M, c4.64 GeV .

The lower l imits of M e and M x a r e estimated from the suppression of ~ (3 .105) in photoproduction and that of tj(3.698) in pp scattering. The upper limit for M e is se t s o that J(3.105) can be produced in pp scattering, and that of M, is se t so that i t is stable against strong decay to p$.

(c) Gene~al ized G parity. With the addition of the t spin which i s conserved in the strong interaction i t is possible to generalize the traditional G-conjugation operator to become

For the t-singlet hadron i t retains the same G

parity, e.g.

G I . > = - 1.) , and the t zO mesons J, $ become eigenstates of G,

The higher-mass resonances t-doublet J* and t - triplet t,b* a r e also eigenstates of G:

GIJ*)=* IJ*), (13)

GI$) =* I+ ) .

Hence the strong decays of J * and $* can be

with n being either even o r odd, but not both. The relative G parity between various t #O mesons can be determined if the $* a r e heavy enough to decay to multiple q. For example, if $* decays only into an odd number of $, one can conclude that the G pari t ies for both $* and $ a r e odd. If +* decays only into an even number of $, then the G parity for $* i s even. If +* decays into two J'S, then i t s G parity is even, and so on.

(d) Possible connection with quark model. From a symmetry point of view the existence of a new

quantum number t implies the possibility of extending the usual SU(3) group to la rger groups such as SU(3)xSU(2).

To incorporate the new quantum number in the quark model requires some more effort, and l e s s freedom. In the additive t-number scheme, if there i s only one new quantum number i t i s natural to identify i t with ~ h a r r n . ~ With two new quantum numbers t and st a more natural scheme, however, is to identify them with the color of the quarks.

In the t-spin scheme, i t is also possible to re - gard the SU(2) of the t spin to be a subgroup of the SU(3)' group of the colored quark. Since there a r e three colors, we expect one more quantum number to be identified with the third color in either schemes. A th i rd narrow-width resonance $' in e t e - annihilation should then become necessary. One should have three resonances J O , $, $I

in the SU(3)' group similar to the p, w, @ in the ordinary SU(3) group.

The color of quarks would take on different prop- e r t ies from those normally discussed in the litera- tureS4 F o r example, one kind of color quark can decay into another kind of color quark via the medium-weak interaction:

TABLE 11. Comparison of t-spin and additivequantum-number schemes.

t spin Two additive quantum

numbers t and S'

(1) Further splitting of one only J(3.105), q(3.695) into two narrow width resonances.

(2) l b o species J * and $* J*- J +hadrons J*- $ +hadrons

(3) Vector addition J*-J+ $*- JJ

(4) Associated production PP -JJxP

allowed forbidden

allowed allowed

both necessary

allowed forbidden

forbidden forbidden

allowed forbidden

(5) Generalized G conjugation (a) J * - J + (odd number n) mutually both possible

-J + (even number n) exclusive

mutually forbidden exclusively if allowed GI#) =-I#)

(6) Consistency with color Yes Yes quark model

13 - N E W Q U A N T U M N U M B E R I N T H E N I E H - W U - Y A N G T H E O R Y 187

Various selection ru les governing the medium- In summary we presen t Table 11, where the vari- weak interaction can then be derived in a s i m i l a r ous predictions of the additive-quantum-number fashion, as discussed i n Ref. 3. scheme and the t -spin scheme are listed f o r com-

I t is amusing to note that a t f i r s t sight the scheme parison. discussed h e r e may appear f a r too complicated to be t rue whether it i s a two-additive-quantum-num- b e r scheme o r a t -spin scheme. However, the traditional color-quark model is already complicated enough to accommodate the NWY theory easily ."

The author wishes to thank D r . G. Josh i and P r o f e s s o r G. Opat f o r many stimulating discus- s ions. He a l so wishes to thank P r o f e s s o r C. N. Yang f o r h i s kind hospitality a t Stony Brook, where the ideas were originally conceived.

*Work supported in part by the Australian Research Grant Committee.

'J. J . Aubert e t a l . , Phys. Rev. Lett. 33, 1404 (1974); J . E. Augustin et a l . , ibid. 33, 1406 (1974); C. Bacci et al ., ibid. g, 1408 (1974);~. Abrams et a1 ., ibid. 3, 1453 (1974).

2 ~ . T . Nieh, T . T. Wu, and Chen Ning Yang, Phys. Rev. Lett. 34, 49 (1975).

3 ~ . Y. Lo, Phys. Rev. D 2, 2628 (1975). 4 ~ . G. Callan et a1 ., Phys. Rev. Lett. 34, 52 (1975);

A. S. Goldhaber and M. Goldhaber, ibid. 34, 36 (1975); J. Schwinger, ibid. 34, 37 (1975); S. Borchardt et al. , a d . 34, 38 (1975); R. M. Barnett, ibid. 34, 41 (1975); A. De RGjula and S. L. Glashow, ibid. 4, 46 (1975); G . Joshi, University of Melbourne report (unpublished) .

5 ~ . D. Jackson, University of California, Berkeley, notes (unpublished) .

6 ~ . T . Nieh, T . T . Wu, and Chen Ning Yang, Stony

Brook Report No. 1TP74/46 (u~ublished) . 'S. Pakvasa and S. F . Tuan, Phys. Rev. Lett. 34, 552

(1975); L. Pilachowski and S. F. Tuan, Phys. Rev. D 11, 3148 (1975).

' J ~ E . Augustin et a1 ., SLAC-Berkeley collaboration, Phys. Rev. Lett. 34, 764 (1975).

$J. J. Aubert et a1 ., Phys. Rev. Lett. 33, 1624 (1974). 'OD. E . Andrews et a l . , Phys. Rev. Lett. 34, 233 (1975);

J . F . Martin et a1 ., ibid. 34, 288 (1975). "1t is realized, however, that this runs contrary to the

current assumption in the standard quark picture where quark and color gluons have to be confined. The author wishes to thank Professor M. Gell-Mann for a discussion on this point. The colored scheme here is also different from the Han-Nambu scheme, where color transition goes through electromagnetic interaction instead of medium-weak interaction proposed here.

Documents

New quantum number in the Nieh-Wu-Yang theory