Two Body Hadronic Decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2}^{+})+P$ in a quark model

TL;DR

This paper analyzes specific baryonic decay processes involving $ ext{Lambda}_b$ into excited baryons and mesons using a non-relativistic quark model, predicting decay rates and asymmetry parameters.

Contribution

It introduces a novel analysis of $ ext{Lambda}_b$ decays to $B^*$ and $P$ via baryon pole contributions, extending the theoretical framework beyond previous models.

Findings

Branching ratios for specific decay channels are estimated.

The asymmetry parameter $ ext{alpha}$ is predicted to be zero.

The model's predictions can be tested against future experimental data.

Abstract

The framework under which decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B(\frac{1}{2}^{+})+M$ are analyzed is not applicable for the decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2} ^{+})+M$. These decays occur through a baryon pole $\Sigma^{0}_{c}$ which is generated by the W-exchange diagram in the process $b+u \xrightarrow {W} c+d$. The effective Hamiltonian which arises from the W-exchange diagram is expressed in the non relativistic limit. Since $% \Sigma^{0}_{c}$ belongs to representation $6$ of SU(3), it contributes to two sets of decays: $\Lambda_{b}\rightarrow\Delta^{0}D^{0},\Delta^{-}D^{+},% \Sigma^{*-}D_s^{+}$ and $\Lambda_{b}\rightarrow\Sigma^{\ast-}_{c}\pi^{+},% \Sigma^{\ast 0}_{c}\pi^{0}\;, \Xi^{\ast 0}_{c}K^{0}$. The branching ratios for these decays are evaluated which can be compared with their experimental values when the data become available. Other prediction of the model is that asymmetry parameter $\alpha = 0$, since baryon pole contributes to parity conserving (p-wave) amplitude and does not contribute to parity violating (d-wave) amplitude.

Equations

$$H_{eff}\equiv V_{cb}{V}_{q{q}^{\prime }}^{\ast }[(C_1+\frac{1}{3}{C}_2)({\bar{q}}^{\prime \beta }{q}_{\beta }{)}_{V-A}({\bar{c}}^{\alpha }{b}_{\alpha }{)}_{V-A}+(C_2+\frac{1}{3}{C}_1)({\bar{c}}^{\beta }{q}_{\beta }{)}_{V-A}({\bar{q}}^{\prime \alpha }{b}_{\alpha }{)}_{V-A}]$$

$$H_{eff}=V_{cb}{V}_{cs}^{\ast }[a_1(\bar{s}c{)}_{V-A}(\bar{c}b{)}_{V-A}+a_2(\bar{c}c{)}_{V-A}(\bar{s}b{)}_{V-A}]$$

$$H_{eff}=V_{cb}{V}_{ud}^{\ast }[a_1(\bar{d}u{)}_{V-A}(\bar{c}b{)}_{V-A}+a_2(\bar{c}u{)}_{V-A}(\bar{d}b{)}_{V-A}]$$

$$a_1=C_1+\frac{1}{3}{C}_2:\text{ Tree diagram}$$

$$a_2=C_2+\frac{1}{3}{C}_1:\text{color suppressed tree diagram}$$

$$T=\frac{1}{(2\pi {)}^{\frac{9}{2}}}\sqrt{\frac{m{m}^{\ast }}{2p_0{p}_0^{\prime }{q}_0}}\frac{q^{\lambda }}{f_P}{\bar{u}}_{\lambda }(p^{\prime })[C-D{\gamma }_5]u(p)$$

$$\sum _{spin}{u}_{\lambda }(p^{\prime }){\bar{u}}_{\mu }(p^{\prime })$$

$$\overline{\sum _{spin}}u(p)\bar{u}(p)$$

$$\Gamma =\frac{1}{6\pi }\frac{m|q{|}^3}{m^{\prime 2}{f}_P^2}[(E^{\prime }+m^{\prime })|C{|}^2+(E^{\prime }-m^{\prime })|D{|}^2]$$

$$\alpha =\frac{2|\mathbf{q}|ReC{D}^{\ast }}{(E^{\prime }+m^{\prime })|C{|}^2+(E^{\prime }-m^{\prime })|D{|}^2}$$

$$H_{eff}=V_{cb}{V}_{ud}^{\ast }[(C_1+\frac{1}{3}{C}_2)({\bar{d}}^{\beta }{\gamma }^{\mu }(1-{\gamma }^5)u_{\beta })({\bar{c}}^{\alpha }{\gamma }_{\mu }(1-{\gamma }^5)b_{\alpha })+(C_2+\frac{1}{3}{C}_1)({\bar{c}}^{\alpha }{\gamma }^{\mu }(1-{\gamma }^5)u_d)({\bar{d}}^{\beta }{\gamma }_{\mu }(1-{\gamma }^5)b_{\beta })]$$

$$M\approx V_{cb}{V}_{ud}^{\ast }\frac{G_F}{\sqrt{2}}(C_1+\frac{1}{3}{C}_2)[\bar{u}(p_i^{\prime }){\gamma }^{\mu }(1-{\gamma }_5){\alpha }_i^{+}u(p_i)][[\bar{u}(p_j^{\prime }){\gamma }_{\mu }(1-{\gamma }_5){\gamma }_j^{+}u(p_j)]$$

$$\bar{u}{\gamma }^{0}u\approx u_A^{†}{u}_A+O(v^2/c^2)$$

$$\bar{u}{\gamma }^i{\gamma }_{5}u\approx u_A^{†}{\sigma }^i{u}_A+O(v^2/c^2)$$

$$H_W^{pc}$$

$$H_W^{pv}$$

$${\alpha }_i^{+}|b⟩=|c⟩$$

$${\gamma }_j^{-}|u⟩=|d⟩.$$

$$|{\Lambda }_{b,c}^0⟩=\frac{1}{\sqrt{2}}|(ud-du)b,c>{\chi }_{MA}$$

$$S_{ij}(S_{ij}^{\ast })=\frac{1}{2}|(q_i{q}_j+q_j{q}_i)c>{\chi }_{MS}({\chi }_S)$$

$${\chi }_{MA}=\frac{1}{\sqrt{2}}|(\uparrow \downarrow -\downarrow \uparrow )\uparrow >$$

$${\chi }_{MS}=\frac{1}{\sqrt{6}}|-(\uparrow \downarrow +\downarrow \uparrow )\uparrow +2\uparrow \uparrow \downarrow >$$

$${\chi }_S=\frac{1}{\sqrt{3}}|\uparrow \uparrow \downarrow +(\uparrow \downarrow +\downarrow \uparrow )\uparrow >$$

$$S_{22}=\sqrt{2}ddc{\chi }_{MS}=\sqrt{2}{\Sigma }_c^0$$

$${\alpha }_3^{+}{\gamma }_1^{-}(1-{\sigma }_1.{\sigma }_3)+{\alpha }_3^{+}{\gamma }_2^{-}(1-{\sigma }_2.{\sigma }_3)$$

$$\sum _{i\ne j}{\alpha }_i^{+}{\gamma }_j^{-}(1-{\sigma }_i.{\sigma }_j)|{\Lambda }_b>=\sqrt{6}|{\Sigma }_c^0>$$

$$\bar{3}\times 10=6+24,8\times 6=\bar{3}+6+15+24$$

$${\Lambda }_b\to {\Sigma }_c^0\to {\Delta }^0{D}^0,{\Delta }^{-}{D}^{+},{\Sigma }^{\ast -}{D}_s^{+}({\Sigma }_c^{\ast -}{\pi }^{+},{\Sigma }_c^{\ast 0}{\pi }^0,{\Xi }_c^{\ast }{K}^0)$$

$$C=F(C_1+\frac{1}{3}{C}_2)\frac{<{\Sigma }_c^0|H_W^{pc}|{\Lambda }_b>}{m_{{\Lambda }_b}-m_{{\Sigma }_c}}$$

$$<{\Sigma }_c^0|H_W^{pc}|{\Lambda }_b>=[\frac{G_F}{\sqrt{2}}{V}_{cb}{V}_{ud}^{\ast }]\sqrt{6}{d}^{\prime }$$

$$d^{\prime }=<{\psi }_0|{\delta }^3(x)|{\psi }_0>=\frac{3(m_{\Delta }-m_{{\Sigma }_c})}{8\pi {\alpha }_s}{\bar{m}}^2$$

$$d^{\prime }=\frac{3(m_{{\Sigma }_c^{\ast }-m_{{\sum }_c}})}{8\pi {\alpha }_s}{\bar{m}}_c^2$$

Full text

**Two Body Hadronic Decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2}^{+})+P$ in a quark model

**

Fayyazuddin

*National Centre for Physics, Quaid-i-Azam University Campus, Islamabad, Pakistan.

**Abstract

**

The framework under which decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B(\frac{1}{2}^{+})+M$ are analyzed is not applicable for the decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2}^{+})+M$. These decays occur through a baryon pole $\Sigma^{0}_{c}$ which is generated by the W-exchange diagram in the process $b+u\xrightarrow{W}c+d$. The effective Hamiltonian which arises from the W-exchange diagram is expressed in the non relativistic limit. Since $\Sigma^{0}_{c}$ belongs to representation $6$ of SU(3), it contributes to two sets of decays: $\Lambda_{b}\rightarrow\Delta^{0}D^{0},\Delta^{-}D^{+},\Sigma^{*-}D_{s}^{+}$ and $\Lambda_{b}\rightarrow\Sigma^{\ast-}_{c}\pi^{+},\Sigma^{\ast 0}_{c}\pi^{0}\;,\Xi^{\ast 0}_{c}K^{0}$. The branching ratios for these decays are evaluated which can be compared with their experimental values when the data become available. Other prediction of the model is that asymmetry parameter $\alpha=0$, since baryon pole contributes to parity conserving (p-wave) amplitude and does not contribute to parity violating (d-wave) amplitude.

I INTRODUCTION

In the standard model two body hadronic decays of heavy flavor mesons and baryons are analyzed in terms of effective Lagrangian or Hamiltonian [1,2,3];

[TABLE]

where $q=c,q^{\prime}=s$ or $q=u,q^{\prime}=d$. Above Hamiltonian corresponds to decays which are not Cabbibo suppressed.

The effective Hamiltonian arises from the transition $b\rightarrow c+s+\bar{c}$ or $b\rightarrow c+d+\bar{u}$. The short distance QCD effects are incorporated in the Wilson coefficient $C_{1}$ and $C_{2}$. In the factorization ansatz long distance strong interaction effects are shifted to the evaluation of the baryon form factors in some model.

Finally, effective Hamiltonian is written in the form,

[TABLE]

[TABLE]

where

[TABLE]

[TABLE]

In ref. [4], these decays were analyzed. The form factors which are functions of $s=q^{2}=(p-p^{\prime})^{2}$, where $p=p^{\prime}+q$ were evaluated at the $s=(\text{mass of}\;M)^{2}$ in quark model, using heavy quark spin symmetry. In particular using $a_{2}\approx 0.10,$ for $C_{1}(m_{b})\approx 1.121$ and $C_{2}(m_{b})\approx-0.275$ [3] and recent experimental values of other parameters, one finds $BR(\Lambda_{b}\rightarrow\Lambda J/\psi)\simeq 1.21\times 10^{-4}$ and asymmetry $\alpha\simeq-0.18$ to be compared with the experimental values [3]: $((6.3\pm 0.8)\times 10^{-4})$, $\alpha=0.05\pm 0.18$. However, replacing $C_{2}+\frac{1}{3}C_{1}$, with more general value $C_{2}+\zeta C_{1}$ and taking $\zeta=0.46$ we get $BR=6.0\times 10^{-4}$ [4].

It is clear that $(\bar{c}b)_{V-A}$ and $(\bar{s}b)_{V-A}$ in Eq. (2) belong to singlet and triplet representation of $SU(3)$, respectively. Thus in the factorization ansatz, only possible decay modes for $B_{b}$ belonging to representation $\bar{3}$ are $\Lambda_{b}\to\Lambda_{c}^{+}D_{s}^{-}$, $\Xi_{b}^{0}\to\Xi_{c}^{+}D_{s}^{-}$, $\Xi_{b}^{-}\to\Xi_{c}^{0}D_{s}^{-}$ for the first term. For the second term, since $\bar{3}\times 3=8+1$, possible decay modes are $\Lambda_{b}\to\Lambda J/\psi$, $\Xi_{b}^{0}\to\Xi^{0}J/\psi$, $\Xi_{b}^{-}\to\Xi^{-}J/\psi$, where $\Lambda$, $\Xi^{0}$ and $\Xi^{-}$ are members of octet representation of $SU(3)$.

Hence for the decays $B_{b}(\frac{1}{2}^{+})\to B^{*}_{b}(\frac{3}{2}^{+})P$, where $B_{b}$ belong to representation $\bar{3}$ of $SU(3)$, above framework is not applicable as $B^{*}_{b}(\frac{3}{2}^{+})$ either belong to decuplet or sextet representation of $SU(3)$. In this paper, the framework needed for the above decays is formulated.

II Effective Hamiltonian for decays $\Lambda_{b}(p)\rightarrow B^{\ast}(p^{\prime})+P(q)$

For the decays of type $\Lambda_{b}(p)\rightarrow B^{\ast}(p^{\prime})+P(q)$, the Lorentz structure of $T-$matrix is given by [5]

[TABLE]

where $u_{\lambda}$ is the Raita-Schwinger spinor, $u$ is the Dirac spinor, and $q=p-p^{\prime}$. It is clear that $C$ is the parity conserving ($p-$ wave) amplitude and $D$ is the parity-violating ($d-$ wave) amplitude. $f_{P}$ is the pseudo scalar meson decay constant, which is introduced here to make the amplitudes $C$ and $D$ dimensionless. For the Rarita-Schwinger spinor $u_{\lambda}(p^{\prime})$

[TABLE]

Using above equations and taking traces, we get the decay rate [5]

[TABLE]

and for asymmetry $\alpha$ is given by

[TABLE]

In order to determine the amplitudes $C$ and $D$, one needs basic $H_{eff}$. In the non-leptonic decays of hyperons, there is important contribution viz the baryon-pole contribution (Born term) to the parity conserving (p-wave) decay amplitude for which $W$-exchange is relevant [6]. Such a contribution for $\Lambda_{b}$ decays arises from the W-exchange $b+u\xrightarrow{W}c+d$.

The effective Hamiltonian for $W-$exchange diagram $b+u\rightarrow c+d$, is given by

[TABLE]

after taking into account the QCD correction. For the case considered in this paper the first term is relevant. Corresponding to first term, the $M-$ matrix for the $W-$exchange diagram is given by

[TABLE]

where $q=p_{i}-p_{i}^{\prime}=p_{j}^{\prime}-p_{j}$ and $q^{2}<<m^{2}_{W}$. In the Pauli representation of $\gamma$ matrices, the four component Dirac Spinor can be written as $u=\begin{pmatrix}u_{A}\\ u_{B}\end{pmatrix}$, where each $u_{A}$ and $u_{B}$ has two components. In the non-relativistic limit $u_{B}$ is of order $v/c$ compared to $u_{A}$. Thus only the bilinears

[TABLE]

are large (see for example [7]). Using above results, after writing $M$ in terms of two component spinors and then taking the Fourier transform, one gets the effective Hamiltonian in the leading non-relativistic limit for the $W-$exchange [5,6].

[TABLE]

where $\alpha_{i}^{+}$ and $\gamma^{-}_{j}$ are operators which convert $b-$quark to $c-$quark and $u-$quark to $d-$quark.

[TABLE]

Following comments are in order. $H_{W}^{pc}$ in the leading non-relativistic limit was first derived in ref. [6] for the parity conserving non-leptonic decays of baryons. The result obtained insure $\Delta I=1/2$ rule (or octet dominance) in agreement with experiment. Other results obtained were also in agreement with the experimental values.

In ref. [5], the decays $\Lambda_{c}\to\Delta^{++}K^{-}\;,\Sigma^{*\;0}\pi^{+}\;,\Xi^{*\;0}K^{+}$, were analysed in the same framework. The branching ratio: $BR(\Lambda_{c}\to\Delta^{++}K^{-})=9.0\times 10^{-3}$ obtained is in good agreement with the experimental value $(8.6\pm 1.0)\times 10^{-3}$. For the case, analyzed in this paper, the $W$-exchange diagram $b+u\to c+d$, involves two heavy quarks, hence the leading non-relativistic approximation valid upto $O(v^{2}/c^{2})$ is viable to apply. We note that our approach has some analogy with that considered in ref. [8]: Finally, QCD correction has also been incorporated, it gives a factor $C_{1}+\frac{1}{3}C_{2})^{2}\approx 1.06$

Before we proceed further we note that [9]

[TABLE]

Thus $\Lambda_{b}$ and $\Lambda_{c}$ belong to triplet rep. $\bar{3}$ of SU(3). The spin ${\frac{1}{2}}^{+}$ and spin ${\frac{3}{2}}^{+}$ baryons which belong to representation 6 of SU(3), are

[TABLE]

where $q=u,d,s$. The spin wave function $\chi_{MA},\chi_{MS}$ and $\chi_{S}$ are [9].

[TABLE]

[TABLE]

[TABLE]

In particular, we note that

[TABLE]

It is clear that relevant operators are

[TABLE]

Hence we get

[TABLE]

We note

[TABLE]

Thus only possible decays through $\Sigma^{0}_{c}$ pole are

Set I (II)

[TABLE]

Hence in SU(3) limit, the p-wave (parity conserving) amplitude $C$ for the two sets of decays is given by:

[TABLE]

where $F$ is $(2,2\sqrt{3},2)g$ and $(\sqrt{2},-\sqrt{2},\sqrt{2})g_{c}$ for Set I and II, respectively. The weak matrix elements $<\Sigma^{0}_{c}|H^{pc}_{w}|\Lambda_{b}>$ on using Eq. (12) and Eq. (20) is given by:

[TABLE]

where [8],

[TABLE]

for Set I and for Set II:

[TABLE]

Since $H_{W}^{p.v.}=0$, it follows that baryon pole can not generate $d-$wave amplitude, hence $D=0$ and thus asymmetry $\alpha=0$. This is in accordance with two particle non-leptonic decay of $\Omega^{-}$ for which the experimental value of $\alpha=0$. This is the first prediction of framework used without detailed analysis.

III Detailed analysis of $\Lambda_{b}\rightarrow\Delta D$ and $\Lambda_{b}\rightarrow\Sigma^{*}_{c}\pi$

We first discuss the decay $\Lambda_{b}\rightarrow\Delta D$ decay. In the rest frame of $\Lambda_{b},|\mathbf{q}|=2.327$ Gev for the final state $\Delta^{0}D^{0},\Delta^{-}D^{+}$ and $|\mathbf{q}|=2.242$ Gev for $\Sigma^{\ast-}D_{s}^{+}$. Using experimental values for $m=m_{\Lambda_{b}}$ and $m^{\ast}=m_{\Delta}$ or $m_{\Sigma^{\ast}}$ $f_{D}$ = 207 MeV and $f_{D_{s}}$ = 257 MeV [10], we get from Eq. (8)

[TABLE]

[TABLE]

for $\Delta^{0}D^{0},\Delta^{-}D^{+}$ and $\Sigma^{\ast-}D_{s}^{+}$ First we note that constant $g$ in Eq. (24) can be estimated by using PCAC (partial conservation of axial vector current) and NQM (non-relativistic quark model):

[TABLE]

Now in NQM [11], $g_{A}=-\frac{2\sqrt{2}}{3\sqrt{3}}$. Thus

[TABLE]

and

[TABLE]

In Eq. (24) in order to take into account large momentum transfer in heavy flavor baryon decays, we take

[TABLE]

Using constituent quark masses, $m_{d}\approx 0.334GeV\;,m_{c}\approx 1.4GeV\;,m_{b}\approx 4.85GeV\;,\alpha_{s}\approx 0.32$ and experimental values

[TABLE]

we get from Eqs. (22, 23) and Eqs. (28-30)

[TABLE]

Hence from Eqs. (25, 26):

[TABLE]

[TABLE]

[TABLE]

Using $\tau_{\Lambda_{b}}\approx 1.451\times 10^{-12}s,$ we get

[TABLE]

[TABLE]

Set II

[TABLE]

[TABLE]

From Eq. (8), using $f_{\pi}\approx 131MeV$ and $f_{K}\approx 160MeV$, we get

[TABLE]

[TABLE]

Now PCAC gives

[TABLE]

on using NQM value $g_{Ac}=2/3$. Hence from Eqs. (22, 24), using

[TABLE]

and

[TABLE]

we get

[TABLE]

for $\Sigma_{c}^{\ast-}\pi^{+}$ and $\Xi_{c}^{\ast 0}K^{0}.$

Hence for the decay rates and the branching ratios, we get from Eqs. (37) and (38)

[TABLE]

[TABLE]

[TABLE]

[TABLE]

To conclude: No experimental data for the branching ratios of two set of decay channels:

[TABLE]

and

[TABLE]

are available to test the branching ratios given in Eq. (35, 36) and Eqs. (43, 44). One notes that relative branching ratios viz

[TABLE]

and

[TABLE]

are independent of the parameters $\bar{m}^{2},\bar{m}_{c}^{2}$ and the axial vector coupling constants $g_{A}$ and $g_{Ac}$. Thus Eqs. (45, 46) together with prediction that asymmetry parameter $\alpha=0$ will test the general frame work used in the analysis of decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2}^{+})+P$.

Finally decays with three particles in the final state through resonances:

[TABLE]

are of considerable interest. For the decuplet $\Delta,m_{\Delta}=1232$ MeV, $\Gamma_{\Delta}\approx 117$MeV, $m_{\Sigma^{\ast}}=1385$MeV, SU(3) gives [1]:

[TABLE]

Using physical masses and phase space factor:

[TABLE]

Thus $\Gamma_{\Sigma^{\ast-}}\simeq 38.3MeV,$ to be compared with the experimental value $\Gamma_{\Sigma^{\ast-}}\approx(39.1\pm 2.1)MeV$ [3]. Finally, we get

[TABLE]

[TABLE]

For the second set of decays, we note that $\Xi_{c}^{0},\Xi_{c}^{+},\Lambda_{c}$ belong to representation $\bar{3}$: and $\Sigma_{c}^{\ast 0},\Xi_{c}^{\ast 0},\Xi_{c}^{*\;+}$ belong to representation 6 of SU(3). Now $\bar{3}\times 8\rightarrow 6+\bar{3}+15$, thus SU(3) gives

[TABLE]

[TABLE]

First prediction of the above analysis taking into account phase space is that total decay width of $\Xi^{*0}_{c}$:

[TABLE]

on using the experimental value

[TABLE]

The experimental limits on decay width $\Gamma_{\Xi_{c}^{\ast 0}}<5.5$MeV, $\Gamma_{\Xi_{c}^{\ast+}}<3.1$MeV, [3].

Finally the branching ratios for three particle states $\Lambda_{c}^{+}\pi^{-}\pi^{0}$ and $\Xi_{c}^{+}\pi^{-}K^{0}$ through resonances $\Sigma_{c}^{\ast 0}$ and $\Xi_{c}^{\ast 0}$ is given by

[TABLE]

To summarize, we have analyzed two sets of decays of $\Lambda_{b}$:

[TABLE]

[TABLE]

We note that the other two members of triplet $\bar{3}$ are $\Xi_{b}^{0}=\frac{1}{\sqrt{2}}(us-su)b\chi_{MA}$ and $\Xi_{b}^{-}=\frac{1}{\sqrt{2}}(ds-sd)b\chi_{MA}$. The $W-$exchange can not generate a baryon pole for $\Xi_{b}^{-}$, thus the decays $\Xi_{b}^{-}\rightarrow B^{*}(\frac{3}{2}^{+})+P$ are not possible. This is another prediction of our formalism. However, for $\Xi_{b}^{0}$, $W-$exchange give:

[TABLE]

Thus $\langle\Xi^{\prime 0}_{c}|H_{W}^{p.c.}|\Xi_{b}^{0}\rangle=\sqrt{6}$.

Hence the pole diagram gives two set of decays:

[TABLE]

[TABLE]

Hence in SU(3) limit, for two sets of decays, $p-$wave (parity conserving) amplitude $C$ is given by Set I:

[TABLE]

Set II:

[TABLE]

Following exactly the same procedure as for the $\Lambda_{b}$ decays, one can calculate the branching ratios $\Xi^{0}_{b}\to B(\frac{3^{+}}{2})+P$ decays. At present no experimental data for $\Lambda_{b}\to B^{*}(\frac{3^{+}}{2})+P$ and $\Xi^{0}_{b}\to B^{*}(\frac{3^{+}}{2})+P$ are available to test the prediction of our model. In future, it is expected that more data for heavy flavor hadron decays will be coming from LHCb including the decays considered in this paper.

Acknowlegement

The author would like to thank Dr. Muhammad Jamil Aslam for discussions.