PHYSICAL REVIEW D VOLUME 43, NUMBER 7 1 APRIL 1991

Quark-diagram analysis of B-meson decays to charmed baryons

Yoji Kohara iVihon University at Fujisawa, Kameino, Fujisawa, Kartagawa 252, Japan

(Received 15 June 1990)

Two-body decay amplitudes of B mesons to a charm antibaryon and a tloncharm baryon are ex- amined on the basis of the quark-diagram scheme.

Recently baryonic two-body decays of R mesons to a charm antibaryon and a noncharm baryon have been ex- amined from the point of view of SU(3) symmetry1 and SU(6) symmetry. * Chau and ~hen-nal~zed pseudoscalar-pseudoscalar and pseudoscalar-vector two- body decays of the charmed mesons in the quark-diagram scheme. It provided a useful model-independent way of analysis. Though the relation between the SU(6)- symmetry amplitudes and the quark-diagram calculation was argued in Ref. 2, it was not clear. So in this Brief Report we shall investigate AC = - 1 and A S = O two- body baryonic decay amplitudes of B mesons based on the quark-diagram scheme and compare them with SU(3)-symmetry results. There are two groups of charm baryons: SU(3) sextet ( B:+,+.', sS,+.O, 0: ) and triplet

+ - A +,0 A , i . We consider not only ground-state non- charm octet baryons, but also decuplet baryons.

These baryonic decays of B,,, B d , and B, mesons occur through (a) spectator diagrams or (b) W-boson-exchange diagrams. The ( V - A i X ( V - A i structure of weak Hamiltonian is invariant under Fierz transformations,

and the antiquarks in antibaryons are color antisym- metric. Then the produced diantiquark in spectator dia- grams is flavor antisymmetric.

Two constituent quarks in an SU(3)-octet baryon are antisymmetric, and octet baryons are represented in terms of B,,,,,. The following equation is satisfied by

B, [ ] k ] :

The relation between the usual notation B,' and B , [ J k l is B,'=E'J~B, [,k1/2. The above equation corresponds to the traceless condition of B,'. Because of this constraint two spectator diagrams and two W-boson-exchang: diagrams are independent in B - 8 + 6 and B -8 + 3 * decays. They are depicted in Fig. 1; the bracket in the diagrams denotes an antisymmetric pair of constituents. The am- plitudes of B + 8 + 6 and B + 8 + 3 * decays are given in Tables I and 11, respectively. There a , arid a* terms are from spectator diagrams, and b , and b, terms are from W-exchange diagrams.

TABLE I. Amplitudes of B + 8 + 6 decays. Here a, terms are from spectator diagrams; b, terms are from W-exchange diagrams. -- --

SUi3)-symmetric Decay modes

-- amplitudes

- --- Amplitudes with FSI's

.\-L B,++p%p ( a l + a 2 ) ( a , + a 2 ) e ~ p ( i S ~ , ~ ~ )

1;: ~,++x+g $ 0 ( 1 / d 2 ) ( - a ~ - a 2 ) (1/d?)(-a,-a,)exp(i~?,~ .v L

B : - - ~ E , ( l / d ? ) ( - ~ z + b I ) - ( 1 / 3 d 2 ) [ 2 ( a l +a,)exp(iS,,,') - (2a , -a ,+3b l )exp(i6~,4')]

z: B;-z+=: - ( l / d ? ) b , ( 1 / 3 d ? ) [ ( a l +a,)exp(iS,,, 1

X E - ( a , + a 2 + 3 b , )exp(iS,,,')]

,v 1 B:+~IE: 0 1 + b , ( 1/3) [ i a , +a , )exp(iS,,,')

R P + ( 2 a , - a 2 + 3 b l )exp(iSl,2C)]

AE; B: + A E :" ( 1 / 2 d ? ) ( - a , +a2-3b , (1/2\ /3)( - a l +a, -36, ) e ~ p ( i S , , ~

2' 7 B; + cog i0 ( 1 / 2 ) ( a l + a 2 + b l ) (1 /6 ) [2 (u l + ~ ~ ) e r p ( i S ~ , ~ ' )

+ ( a l +a ,+3bI )exp(i6f,;")]

Bj+Eofi! -b , - b I e x p ( i S ~ ~ ~ ) -

B , O + ~ + X ; ( I / d 2 ) a , ( 1/d2)u,exp(i~:") -

B:-AE: 1 / 3 2 , -a, ( 1 / ~ 6 ) ( -2a, - ~ , ) ~ x p ( i ~ : ~ '

B ; - ~ ( ' E : - ( 1/ /2 )a2 - ( 1 / d 3 ) a , e x p ( i ~ f L c ) - -

B;+ ~ ( ) z - ( l / d 2 ) 0 ~ - ( l / \ / ~ ) a , e x ~ ( i ~ f " . ) --

43 2429 @ 1991 The American Physical Society

2430 BRIEF REPORTS

FIG. 1. Quark diagrams of B-meson decays including an oc- FIG. 2. Quark diagrams of B-meson decays including a dec- tet baryon. uplet baryon.

TABLE 11. Amplitudes of B - 8 + 5 * decays.

SU(3)-symmetric Decay modes amplitudes Amplitudes with FSI's

TABLE 111. Amplitudes of B + 1 0 + 6 decays. Here the a term is from the spectator diagram and the b term is from the W-boson-exchange diagram.

SU(3)-symmetric Decay modes amplitudes Amplitudes with FSI's

A % B,++A++E; ( 1 / d 2 ) a ( 1 / d 2 ) a e ~ p ( i 6 , ~ ' )

A X B,+-A+E: ( 1 /d3 )a ( 1 / d j ) a exp(i6,,;

Z*ES B,++z*f f sO - C ( l / d % ) a ( l / d % ) a exp(i6,,,_ A X )

B;+A++E ;- -b - ( 1 /3 )[a exp( i6, - - ( a -3b)e_xp(i~f;; ) ]

B,O-A+H; ( l / y % ) ( a -2b) (1 /3d%)[a exp(i6f,:') aP

+2(a -3b)gxp(i6,,;)]

B,O-AOH; ( l / d j ) ( a -b) (1 /3d3) [2a exp(i6:X) A I

+ ( a - 3 b ) e ~ p ( i 6 ~ , ; ) ] * f s ~ j + z * + E ; - ( l / d % ) ( - 2 b ) - ( 1/3d%)[a e x p ( i ~ : , ~ - ~ )

Z*FS - ( a -6b)exp(i6,,,

=*zs B ~ L , ~ * O E ;O ( 1 / 2 d j ) ( a -2b) (1 /6d3) [2a e ~ p ( i 6 ~ / ,

= * = I

+ ( a -6b)exp(i6,,, 'I] -*- ~ j - ~ * o f i o - ( l / d j ) b - ( 1 /dj )b exp( i6fjznc

BP-x*+E; ( l / d % ) a ( 1 / d 6 ) a e ~ ~ ( i 6 : * ' ~ ) *- B:+L*OE; ( 1 /d% )a ( 1 /d% )a exp( i6: )

- * m s BP-E*OE S,O ( l / d % ) a ( l / d % ) a e x p ( i 6 f

43 - BRIEF REPORTS 243 1

TABLE IV. Amplitudes of B - lo+ 5 * decays.

SU(3)-symmetric Decav modes am~litudes Am~litudes with FSI's

The rescattering effects by strong interaction modify the amplitudes. We have also shown the decay ampli- tudes with final-state interactiogs (FSI's) in the third column of these tables. Here SfB represents an isospin-I phase shift of 'so ( 3 ~ o ) BB scattering for parity- conserving (parity-violating) amplitudes. These phase shifts are complex in general.

The constituent quarks in decuplet baryons are totally symmetric. So in ~ - 1 0 + g and B - 1 0 + 3 * decays there is only one kind of spectator diagram and one kind of W-exchange diagram. Their contributions are denoted in terms of a and b, respectively. The decay amplitudes are given in Tables I11 and IV. In the decay amplitudes with FSI's, 6's are 5 ~ 0 ( 3 ~ 0 ) phase shifts for parity- conserving (parity-violating) amplitudes.

Both B : - z + ~ to and B P - Z + X ; decays contain the same quark products. We can see from the tables that the former have a , and a2 amplitudes, but the latter

do not have a , amplitudes. So the decay amplitudes of the two are not equal. This result is consistent with SU(3)- or SU(6)-symmetry analysis.

We can compare the obtained SU(3)-symmetric ampli- tudes with the amplitudes in Ref. 1. Our amplitudes give the same results as the amplitudes obtained from SU(3)- symmetry arguments. There are no experimental data of exclusive decay modes of B mesons to a noncharm baryon and a charm antibaryon at present. In the future it will become possible to obtain the magnitude of each diagram by comparison with experimental data, and to determine whether or not the spectator diagrams dom- inate the amplitudes.

The author wishes to thank Professor Ling-Lie Chau for suggesting the addition of the final-state-interaction formulation.

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Phys. Rev. D 36, 137 (1987). 4K. Miura and T. Minamikawa, Prog. Theor. Phys. 38, 954

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