ELSEVIER Nuclear Physics 13 (Proc. Suppl.) 55A (1997) 44-47

Two body weak hadronic decays o f charmed baryons and b- baryons

Mohinder. P. Khanna

Centre for Advanced Study in Physics, Department of Physics, Panjab University, Chandigarh - 160014 India

UCLEAR PHYSICS

P R O C E E D I N G S SUPPLEMENTS

The two body Cabibbo favored hadronic decays of charmed baryons into an octet baryon and a pseudoscalar meson are examined in the SU(3) symmetry scheme and those of b-baryons in pole model. The numerical estimates for decay widths and branching ratios of some of the modes are obtained and are in good agreement with experiment. We also study b- conserving strangeness changing mode of b- baryon decays.

1. I N T R O D U C T I O N

The nonleptonic weak decays of hyperons and K-mesons have been with us for forty years but have so far evaded their complete understanding mainly because of the lack of proper knowledge on confinement of quarks and gluons. As these strong interaction effects are smaller at higher energy scale, it is expected that the study of hadronic decays of the charmed and heavier hadrons would help in the understanding of the nonleptonic decay processes. Upto now, a greater part of theoretical effort to understand charm decays, has been devoted to charmed mesons. Only recently, the study of hadronic two body decays of the charmed baryons has gained serious attention [11 as some data [2, 3 ] on these decays has started coming. It is our hope that more and more data will become available in the near future and will provide a new arena in which to study the standard model. Some very recent data [3], prompts us to make a systematic analysis of the Cabibbo allowed decays of charmed baryons in the framework of flavor SU(3) symmetry generated by u, d, and s quarks.

Theoretical techniques used to study two body weak decays are current algebra with soft pion, pole model, flavor symmetry, factorization, specatator quark model and quark line diagrams. The symmetry approach does have a number of parameters, but has the advantage that it lumps the effects of all dynamical processes together. Further, the dynamical methods have uncertainities associated with them. Since s-u mass difference is much smaller than c - u mass difference, the

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SU(3) is a better symanetry than SU(4) for the charm hadrons [4]. Using 6* dominance, we have three parameters each for the s- and p-wave amplitudes. First, we use the available data on Ac + --~ An + / E+n 0 / E0K + decays to fix the parameters and then make predictions on the remaining branching ratios and asymmetries. Further, we attempt to relate p-wave charm baryon decays with those of the hyperons following the approach of Altarelli, Cabibbo and Maiani [41. The predictions obtained in the present analysis are consistent with the experimental values. Particularly, a small observed value of the ratio Br. ( Ac + -+ An + )/Br. (A c+-+ p ~0 ) is explained.

We also analyze two body hadronic decays of bottom baryons in the pole model.The pole model terms seem to be important only for the modes where a light pseudoscalar meson is emitted.

2. CHARMED BARYON DECAYS

Work done with R. C. Verma

The effective Hamiltonian transforms as an admixture of the 6* and 15 representations of flavor SU(3). There exist 7 parameters in each PV and PC modes, three corresponding to the 6* and four to the 15 representations, respectively. QCD perturbative corrections give rise to enhancement of coefficient of 6* over that of 15. Consequently, it is possible, in analogy with octet dominance in hyperon decays, that sextet dominance may give reasonable results.

M.P Khanna/NucIear Physics B (Proc. Suppl.) 55A (1997) 44-47 45

So, we assume 6* dominance which gives relations for all the decay amplitudes in terms of the amplitudes,

(E+rt 0 [ Ac + ) , (Art + [Ac +) and (EOK+IA c + ).

2.1 Results and Conclusions The following sets of the parity violating (PV)

amplitude, A and the parity conservin~ (PC) amplitue, B (in units o fG F Vud Vcs x 10 "z GeV) have been mentioned in a recent CLEO measurements [3],

+ 0 . 8 +0.8 A(A c + -+ Art + ) = -3.0 -1.2 or 4-3+0.9

B(A c + --~ Art+ ) = +12.7

+2.7 +3.4 or 8.9

-2.5 -2.4

+0.9 +0,9

A(A c + -+ E+rt 0 ) =+1.3 -1-1 or 5.4 4).7

+2.3 +3.4 B(A c + ~ E+rt 0 ) =-17"3_2. 9 or -4.1.3.0

With SU(3) symmetry and 6* dominance, we obtain

Br. (Ac + ~ E0x + ) = Br. (Ac + --~ Y.+n 0 )

Experimentally the L. H. S. is 0. 87 + 0.20 % and R. H. S. is 0.87 + 0.22% 12, 3]. We carry out numerical analysis for all the choices and obtain branching ratios and asymmetry parameters for various modes. The present data on Br.(Ac+-+ p~0) seems to prefer the following choice for the input.

A(Ac + ~ E+x0 ) = +5.4,

B(Ac + ~ ]~+rt0 ) =-4-1;

A(Ac + ~ Art + ) = -3 .0 ,

B(Ac + --~ Art + ) = +12.7.

To predict the remaining decays which are listed in Table 1., we use

A(Ac + ~ EOK+) ~0,

B (Ac + ~ E0K +) = :t:16.21.

as we expect the decay asymmetry for this mode to be close to zero.

3. b B A R Y O N DECAYS

Work done with Sonali Sinha

The two body weak decays of b- baryons have been studied in heavy quark effective theory with factorization approximation. Here, we analyze two body hadronic decays of bottom baryons in the framework of pole model. The pole term contribution to the amplitude is non-factorizable. In the pole model, one introduces a set of intermediate states in the decay process so that the weak and strong vertices get separated. The decay amplitudes are then given by the product of strong and weak coupling constants divided by the baryon mass sum and baryon mass difference for the PV and PC modes, respectively. The symmetric strong couplings are given in terms of gd and gf. gd(gf) is the d(f) type coupling constant. We take gd +gf = 14 and gd/gf =1-5 so that gd=8.4 and gf=5.6. The symmetry broken coupling constants are calculated from [4]

gifjSB=gifj(Mi+Mf) / 2 Mn

For D-meson emitting vertices, however, we use the symmetry value of the coupling constant. For the computation of the weak transition vertex, we may use flavor symmetry or quark model, and for calculational purposes we take the weak transition

amplitude az+p= 1.2× 10 -7 The calculated transi-

tion rates are listed in Table 2. For the decay modes Ab-+Ac+n', and Ab---~++rt" the pole contribution is not negligible as compared to the contribution from factorization [5]. In some of the decay modes, however, particularly the ones in which a D- meson is emitted, the pole contribution turns out to very small compared with that of factorization. It has been observed [6] that if the strong interaction BBP coupling constant is mass

46 M.P Khanna/Nuclear Physics B (Proc. Suppl.) 55A (1997) 44 47

Table 1. Branching ratios and decay asymmetries of charmed baryon decays.

Decay Modes Set I Set II Br. Frac. % Asymmetry ct Br. Frac. % Asymmetry ~t

Ac+.__~p~0 2.74 -0.99 2.74 -0.99

Ac+---~Ax + 0.79" -0.94* 0.79* -0.94*

Ac+---~E+Tt 0 0.87* -0.45* 0.87* -0.45*

Ac+---~E+rl 0.45 +0.99 0.67 +0.99

Ac+---~E0x + 0.87 -0.45 0.87 -0.45

Ac+---~EOK + 0.34* 0.00 0.34 0.00

Ec+--~E0rt + 4.05 +0.02 0.06 -0.19

"=c+---~E~ 0 4.23 +0.02 0.07 -0.17

Ec 0__.~=0x0 0.51 +0.71 0.77 -0.99

_=c0---~E0rl 0.20 4). 97 0.14 +0.65

Ec0--r'=-Tt + 1.31 -0.96 1.31 -0.96

Ec0---~E+K" 0.38 0.00 0.38 0.00

Ec0--~Y.0g. 0 0.11 +0.05 0.11 +0.05

Ec0---~AK0 0.69 -0.86 0.69 -0.86

* input

independent, the pole contribution for the b- baryon decays will be small. We find that the mass dependence of the BBP strong coupling constant is likely to play an imprtant role in deciding about the size of the contribution of the pole terms. The measurement on the decays of lambda b- baryon will certainly throw light on the mechanism of these decays.

3.1 b Conserving Decay Modes If the mass difference permits, a cascade b-

baryon will decay into lambda b- baryon and a pion. Such decays may be important as they are described by the weak Hamiltonian responsible for the hyperon decays. In such decays the center of mass momentum Iql will be very small, but the Cabibbo-Kobayashi-Maskawa factor is large, so that

M.t? Khanna/Nuclear Physics B (Proc. Suppl.) 55A (1997) 44 47

Table 2. Decay rates of b- baryons in units of 10 -15 GeV.

47

Decay Mode Decay Rate Decay rate (Pole model PC mode only) (Factorization* both PV & PC)

Ab0---~Ac+n - 0.22 2.55

Ab0--~Ec+n" 1.02

Ab0--~Ac + K" 0.07 0.20

Ab0---~Ac + D" 0.01 0.55

Ab0---~Ac+Ds" 1.7× 10 -6 12.8

Eb'--->Ec0~" 0.08

* T. Mannel et. al. Phys. Lett. B259, 485 (1991)

it is possible that this decay mode has a significant branching ratio. As a matter of fact, we find, that such decay mode has a branching ratio comparable to that of b changing modes. For the estimation of the decay rate for the b conserving but strangeness changing modes, we only take the parity violating part of the amplitude as the parity conserving part will not contribute to the decay rate due to its smallness because of p- wave suppression. For the computation of parity violating amplitude, we use flavor symmetry or the quark model and the factorization. The factorization term for the parity violating amplitude, being proportional to the mass difference of the initial and final baryon, introduces symmetry breaking. For the value 5.8 GeV of the mass of b- cascade, the decay rate turns out to be 17.5 ×10 "15 GeV.

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