Abstract
In the quark-diagram scheme, we study the charmed baryon decays of \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\), where \(\mathbf{B}_c\) is \(\Lambda _c^+\) or \(\Xi _c^{+(0)}\), together with \(\mathbf{B}^*\) (M) the decuplet baryon (pseudoscalar meson). It is found that only two W-exchange processes are allowed to contribute to \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\). Particularly, we predict \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*0(+)} \pi ^{+(0)})=(2.8\pm 0.4)\times 10^{-3}\), which respects the isospin symmetry. Besides, we take into account the SU(3) flavor symmetry breaking, in order to explain the observation of \({\mathcal {B}}(\Lambda _c^+\rightarrow \Sigma ^{*+}\eta )\). For the decays involving \(\Delta ^{++}(uuu)\), we predict \({\mathcal {B}}(\Lambda _c^+\rightarrow \Delta ^{++} \pi ^-,\Xi _c^+ \rightarrow \Delta ^{++} K^-) =(7.0\pm 1.4,13.5\pm 2.7)\times 10^{-4}\) as the largest branching fractions in the singly Cabibbo-suppressed \(\Lambda _c^+,\Xi _c^+\rightarrow \mathbf{B}^*M\) decay channels, respectively, which are accessible to the LHCb, BELLEII and BESIII experiments.
Similar content being viewed by others
Avoid common mistakes on your manuscript.
1 Introduction
To determine the mass and lifetime of the \(\Lambda _b\) baryon, \(\Lambda _c^+\) is often taken as the final state in the \(\Lambda _b\) decays [1], which involves the favored Cabibbo–Kobayashi–Maskawa (CKM) matrix elements for bigger branching fractions. With the higher precision in the recent years [2, 3], the subsequent \(\Lambda _c^+\rightarrow p K^-\pi ^+\) decay has helped to make more accurate observations for the \(\Lambda _b\) decays, which receives the significant contribution from \(\Lambda _c^+\rightarrow \Delta ^{++}K^-,\Delta ^{++}\rightarrow p \pi ^+\). Similarly, one uses \(\Xi _b^0\rightarrow \Xi _c^+\pi ^-\) to determine the \(\Xi _b^0\) lifetime, whereas we find that the subsequent process \(\Xi _c^+\rightarrow pK^-\pi ^+\) and its resonant contribution from \(\Xi _c^+\rightarrow \Delta ^{++}K^-,\Delta ^{++}\rightarrow p \pi ^+\) have not been well studied yet [1]. Therefore, \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\) plays the key role in the precision measurements for the multi-body decays of beauty and charm baryons, where \(\mathbf{B}_c=(\Lambda _c^+,\Xi _c^{+(0)})\), \(\mathbf{B}^*\) the decouplet baryon and M the meson state, such as \(\Lambda _c^+(\Xi _c^+)\rightarrow \Delta ^{++}K^-\).
The \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\) decays are not richly observed. Therefore, it is still unclear how the \(\mathbf{B}_c\rightarrow \mathbf{B}^* M,\mathbf{B}^*\rightarrow \mathbf{B}M'\) decays mix with the non-resonant contributions to \(\mathbf{B}_c\rightarrow \mathbf{B}MM'\). In addition, \(\mathbf{B}_c\rightarrow \mathbf{B}V,V\rightarrow MM'\) with V the vector meson causes more complicated mixtures [1]. The SU(3) flavor (\(SU(3)_f\)) symmetry has been widely applied to the charmed baryon decays [4,5,6,7,8,9,10,11,12,13,14,15,16]. By well explaining the data, the flavor symmetry does not appear to be severely broken in \(\mathbf{B}_c\rightarrow \mathbf{B}M\) [17], where \(\mathbf{B}\) denotes the octet baryon. By contrast, \({\mathcal {B}}(\Lambda _c^+\rightarrow \Sigma ^{*+} \eta )\) not well interpreted by the \(SU(3)_f\) symmetry might hint the broken effect in \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\) [7], which could be as large as that in the D meson decays [18,19,20,21].
For a better understanding of the hadronization in \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\), there have been some theoretical attempts, which are in terms of the pole model, quark model and irreducible SU(3) flavor (\(SU(3)_f\)) symmetry [4,5,6,7, 22,23,24]. Particularly, the quark-diagram scheme with the topological \(SU(3)_f\) symmetry provides a clear picture for the decay processes [17, 25,26,27]. Due to the fact that \(\mathbf{B}^*\) is a spin-3/2 baryon with totally symmetric quark contents, it can be shown that the topological diagrams involving the flavor anti-symmetric quark pair in \(\mathbf{B}^*\) are forbidden or suppressed. Therefore, we purpose to use the quark-diagram scheme to relate all possible \(\mathbf{B}_c\rightarrow \mathbf{B}^*M\) decay channels. With the existing data, we will perform the numerical analysis, and determine different topological contributions. We can hence test the validity of the topological scheme, which involves the \(SU(3)_f\) symmetry and its broken effect. Furthermore, we will give predictions for \({\mathcal {B}}(\mathbf{B}_c\rightarrow \mathbf{B}^* M)\) to be compared to the future measurements, which can help to clarify how \(\mathbf{B}_c\rightarrow \mathbf{B}^*M,\mathbf{B}^*\rightarrow \mathbf{B}M'\) mixes with \(\mathbf{B}_c\rightarrow \mathbf{B}V,V\rightarrow MM'\) and the non-resonant configuration in \(\mathbf{B}_c\rightarrow \mathbf{B}MM'\).
2 Formalism
2.1 Effective Hamiltonian in the flavor symmetry
To study the two-body charmed baryon decays, the corresponding quark-level effective Hamiltonian is given by [28]
with \(\lambda _{(a,p,c)}\equiv (V_{cs}^*V_{ud},V_{cp}^*V_{up},V_{cd}^*V_{us})\) and \(p=(d,s)\), where \(G_F\) is the Fermi constant, and \(c_i\) the Wilson coefficients. The current–current operators \(O_i^{(a,p,c)}\) are written as
where \((\bar{q}_1 q_2)=\bar{q}_1\gamma _\mu (1-\gamma _5)q_2\), and the subscripts \((\alpha ,\beta )\) denote the color indices. With \(s_c\equiv \sin \theta _c\simeq 0.22\), where \(\theta _c\) denotes the Cabibbo angle for the quark-mixing in the weak interaction, the decays with \(|\lambda _{(a,p,c)}|\simeq (1,s_c,s_c^2)\) are regarded as the Cabibbo-allowed (CA), singly Cabibbo-suppressed (SCS) and doubly Cabibbo-suppressed (DCS) processes, respectively.
For the lowest-lying anti-triplet charmed baryon states \(\Xi _c^0\), \(\Xi _c^+\) and \(\Lambda _c^+\) that consist of \((ds-sd)c\), \((su-us)c\) and \((ud-du)c\), respectively, we present them as
The pseudoscalar meson states are given by
where \((\eta ,\eta ')\) mix with \(\eta _q=\sqrt{1/2}(u\bar{u}+d\bar{d})\) and \(\eta _s=s\bar{s}\). The mixing angle \(\phi =(39.3\pm 1.0)^\circ \) in \((s\phi ,c\phi )\equiv (\sin \phi ,\cos \phi )\) comes from the mixing matrix, given by [29, 30]
The decuplet baryons are written as
By neglecting the Lorentz indices, \({\mathcal {H}}_{eff}\) for the \(c\rightarrow q_i\bar{q}_j q_k\) transition can be presented with the tensor notation, \(H^{ki}_j\), and the nonzero entries are given by [27]
2.2 The quark-diagram scheme
In the quark-diagram scheme, there exist six different topological diagrams for the \(\mathbf{B}_c\rightarrow \mathbf{B}^{(*)}M\) decays, as drawn in Fig. 1a–f, parameterized as the topological amplitudes \((T,C,C')\) and \((E',E_\mathbf{B},E_M)\), respectively [17]. More explicitly, T and \(C^{(\prime )}\) proceed with the W-boson emission (\(W_{\text {EM}}\)). By exchanging the W boson (\(W_{\text {EX}}\)), it gives rise to \(E'\) and \(E_{\mathbf{B}(M)}\). Since only (T, C) can be decomposed of two separate matrix elements based on the factorization, that is, \((T,C)\propto \langle M|\bar{q}_1 q_2|0\rangle \langle \mathbf{B}^{(*)}|\bar{q}_3 c|\mathbf{B}_c\rangle \) [31], one classifies (T, C) and \((C',E',E_{M,\mathbf{B}})\) as the factorizable and non-factorizable amplitudes, respectively.
Furthermore, it is found in Fig. 1a, b that \(\mathbf{B}_c\) with \((q_a q_b-q_b q_a)c\) cannot be turned into \(\mathbf{B}^*(q_a q_b q_{k(i)})\), where \(q_a q_b q_{k(i)}\) are totally symmetric, such that (T, C) give no contributions to \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\). Thus, the \(\mathbf{B}_c\rightarrow \mathbf{B}^*M\) decays are purely non-factorizable processes. In addition, \(C'\) and \(E'\) are suppressed in \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\) [25], which is in accordance with the K\(\ddot{\text {o}}\)rner–Pati–Woo theorem [32,33,34]. With the current–current structure of \((\bar{q}_i q_j)_{V-A}(\bar{q}_k c)_{V-A}\) in Eq. (2), \(q_i\) and \(q_k\) are color anti-symmetric. When combined as the constituents of the baryon, \(q_{i,k}\) are flavor anti-symmetric, such that the topological diagrams \((C',E')\) in Fig. 1c, d contribute to \(\mathbf{B}_c\rightarrow \mathbf{B}M\), instead of \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\). Consequently, we are left with the \(W_{\text {EX}}\) topological diagrams \((E_\mathbf{B},E_M)\) in Fig. 1e, f for \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\).
To proceed, we derive the amplitudes as \({\mathcal {A}}(\mathbf{B}_c\rightarrow \mathbf{B}^*M)=({G_F}/{\sqrt{2}}) T(\mathbf{B}_c\rightarrow \mathbf{B}^*M)\). Explicitly, the T amplitudes (T-amps) read [17, 25, 27]
where the parameters \(E_{\mathbf{B},M}^{(s)}\) correspond to the topological diagrams in Fig. 1e, f, respectively. The \(W_{\text {EX}}\) decay process needs an additional quark pair from \(g\rightarrow q\bar{q}\), where \(q\bar{q}\) could be \(u\bar{u}\), \(d\bar{d}\) or \(s\bar{s}\). To take into account the broken \(SU(3)_f\) symmetry, \(E_{\mathbf{B}(M)}\) with \(g\rightarrow s\bar{s}\) can be more specifically denoted by \(E_{\mathbf{B}(M)}^s\). Under the exact \(SU(3)_f\) symmetry, it leads to \(E_{\mathbf{B}(M)}^s=E_{\mathbf{B}(M)}\) [26]. In Tables 1, 2 and 3, we present the full expansions of \(T(\mathbf{B}_c\rightarrow \mathbf{B}^*M)\) for the CA, SCS and DCS decay modes, respectively. For the branching fractions, we use the equation for the two-body decays, given by [1]
with \(m_\pm =m_{\mathbf{B}^*}\pm m_M\), where \(\tau _{\mathbf{B}_c}\) stands for the \(\mathbf{B}_c\) baryon lifetime.
3 Numerical analysis and discussions
In the numerical analysis, we adopt the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements as [1]
with \(\lambda =s_c=0.22453\pm 0.00044\) in the Wolfenstein parameterization. Besides, the \(\mathbf{B}_c\) and \(\mathbf{B}^*\) masses, together with the lifetime for \(\mathbf{B}_c\), are adopted from the PDG [1]. We perform a minimum \(\chi ^2\)-fit with \(\chi ^2=\sum ({\mathcal {B}}_{th}-{\mathcal {B}}_{ex})^2/\sigma _{ex}^{2}\), where \({\mathcal {B}}_{th(ex)}\) represents the theoretical (experimental) input of the branching ratio, and \(\sigma _{ex}\) the experimental error. We calculate \({\mathcal {B}}_{th}\) with the equation in Eq. (9), together with \(({\mathcal {B}}_{ex},\sigma _{ex})\) from Table 1. Note that \({\mathcal {B}}(\Xi _c^+ \rightarrow \Sigma ^{*+} \bar{K}^0,\Xi ^{*0} \pi ^+)\) are not involved in the fit.
We use two scenarios for the global fit. In the first scenario (S1), we take \(E_{\mathbf{B}(M)}^s=E_{\mathbf{B}(M)}\) under the exact \(SU(3)_f\) symmetry. Since \(E_\mathbf{B}\) and \(E_{M}\) are complex numbers, it leads to three independent parameters, given by
where \(E_\mathbf{B}\) is set to be real, and \(\delta _{E_{M}}\) is a relative strong phase. Using the \(\chi ^2\)-fit, we extract that
with \(\chi ^2/n.d.f=4.5\), where \(n.d.f=1\) is the number of the degrees of freedom. For \(\delta _{E_M}\), its information is from \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta )\). Although \(\delta _{E_M}=180^\circ \) has induced the largest positive interference between \(E_\mathbf{B}\) and \(E_M\), our result of \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta )=(5.3\pm 0.7)\times 10^{-3}\) is still shown to be in tension with the observation of \((9.1\pm 2.0)\times 10^{-3}\). Sizeably, it adds 3.6 to the total \(\chi ^2\) value.
Since \(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta \) is in association with \(|E_M^s|\), the tension hints the broken \(SU(3)_f\) symmetry, where \(|E_M^s|\) is not equal to \(|E_M|\). On the other hand, \({\mathcal {B}}(\Xi _c^0 \rightarrow \Omega ^- K^+)\) is fitted to agree with the data, indicating that \(|E_\mathbf{B}^s|\) is not deviating from \(|E_\mathbf{B}|\). Currently, the data points are not sufficient for an independent extraction of \(|E_M^s|\). We hence adopt the numerical results from the two-body D meson decays, where the similar \(W_{\text {EX}}\) contributions have been found to induce the severe \(SU(3)_f\) symmetry breaking [18,19,20,21]. In the second scenario (S2), we take \(|E_M^s|=n_q\times |E_M|\) and \(|E_\mathbf{B}^s|\simeq |E_\mathbf{B}|\), with \(n_q=1.4\) adopted from [21]. Consequently, we obtain
where \(\chi ^2/n.d.f\) is reduced as 1.3. As the demonstration, we obtain \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta )=(7.3\pm 1.5)\times 10^{-3}\), which alleviates the deviation from the observation. With the fit values of \((|E_\mathbf{B}|,|E_{M}|,\delta _{E_M})\) in S1 and S2, we present the branching ratios of the \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\) decays in Tables 1, 2 and 3, along with the recent theoretical results for comparison.
We get some useful relations in the quark-diagram scheme. For example, we find out three triangle sum rules for \(\mathbf{B}_c\rightarrow \Delta \pi \), given by
Besides, we obtain
as the consequence of \(C'\) being set to give no contribution to \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\). Indeed, \(C'\) is the only topology that takes part in the decays in Eq. (15), but suppressed due to the K\(\ddot{\text {o}}\)rner–Pati–Woo theorem [32,33,34]. According to the other theoretical calculations [6, 7, 22,23,24], \({\mathcal {B}}(\Xi _c^+ \rightarrow \Sigma ^{*+} \bar{K}^0,\Xi ^{*0} \pi ^+)=0\) is also predicted, which supports that \(C'=0\). Experimentally, \({\mathcal {B}}_{ex}(\Xi _c^+ \rightarrow \Sigma ^{*+} \bar{K}^0,\Xi ^{*0} \pi ^+)\) in Table 2 can be used to test the suppression. With \({\mathcal {B}}(\Xi _c^+ \rightarrow \Xi ^{*0} \pi ^+)/{\mathcal {B}}(\Xi _c^+\rightarrow \Xi ^-\pi ^+\pi ^+)<0.1\) and \({\mathcal {B}}(\Xi _c^+\rightarrow \Xi ^-\pi ^+\pi ^+) =(2.86\pm 1.21\pm 0.38)\times 10^{-2}\) [1, 35], we determine \({\mathcal {B}}_{ex}(\Xi _c^+ \rightarrow \Xi ^{*0} \pi ^+)<4.0\times 10^{-3}\), which can be seen as the non-observation to agree with \(T(\Xi _c^+ \rightarrow \Xi ^{*0} \pi ^+)=0\). However, \({\mathcal {B}}_{ex}(\Xi _c^+ \rightarrow \Sigma ^{*+} \bar{K}^0)=(2.9\pm 1.7)\times 10^{-2}\) seems to disagree with the prediction of \({\mathcal {B}}(\Xi _c^+ \rightarrow \Sigma ^{*+} \bar{K}^0)=0\), despite of the large uncertainty. While the K\(\ddot{\text {o}}\)rner–Pati–Woo theorem is regarded as a tree-level approximation, allowing possible corrections to \(C'\) and \(E'\), we need more accurate observations to test if \(C'(E')=0\).
Uniquely, the decuplet baryon can contain three identical quarks, denoted by \(\mathbf{B}^*(qqq)\), which leads to an additional weight factor of \(\sqrt{3}\) among the decuplet baryons in Eq. (6). The factor can be considered as the main reason why \(\Lambda _c^+ \rightarrow \Delta ^{++} K^-\) and \(\Xi _c^0 \rightarrow \Omega ^- K^+\) are measured with the largest branching fractions in the CA decay channels of \(\Lambda _c^+,\Xi _c^0\rightarrow \mathbf{B}^*M\), respectively. Accordingly, the T-amps with \(\mathbf{B}^*(qqq)\) are listed as
While \({\mathcal {B}}(\Lambda _c^+\rightarrow \Delta ^{++} K^-)\) and \({\mathcal {B}}(\Xi _c^0 \rightarrow \Omega ^- K^+)\) have been observed, the other branching fractions are given by
which are predicted as the largest branching fractions in the SCS \(\Lambda _c^+(\Xi _c^+)\) and DCS \(\Xi _c^{+(0)}\) decay channels, respectively. Here, we present our predictions of S2, which is favored by the \(\chi ^2\)-fit. The equality of \(T(\Lambda _c^+ \rightarrow \Sigma ^{*0} \pi ^+)=T(\Lambda _c^+ \rightarrow \Sigma ^{*+} \pi ^0)\) corresponds to the isospin symmetry. The branching fraction, given by
can be used to test the broken effect. The decays \(\mathbf{B}_c\rightarrow \mathbf{B}^*\eta ^{(\prime )}\), \(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta \), \(\Xi _c^0 \rightarrow \Xi ^{*0} \eta \) and \(\Xi _c^+ \rightarrow \Sigma ^{*+}\eta \) have sizeable branching fractions, which is due to the constructive interferences between \(E_\mathbf{B}\) and \(E_M\). However, the other branching fractions of \(\mathbf{B}_c\rightarrow \mathbf{B}^*\eta ^{(\prime )}\) are typically small with the destructive interferences. Moreover, we find that \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta ^\prime )=0\) with \(m_{\Lambda _c^+}<m_{\Sigma ^{*+}}+m_{\eta ^\prime }\).
The approach of the irreducible \(SU(3)_f\) symmetry has been widely used in the hadron weak decays [4,5,6,7,8,9,10,11,12,13,14,15,16]. For \(\mathbf{B}_c\rightarrow \mathbf{B}^*M\), there exist four parameters \(a_8\) and \(a_{9,10,11}\) [4, 6], which correspond to the decomposition of \({\mathcal {H}}_{eff}=H(6)+H(\overline{15})\) in the \(SU(3)_f\) representation of 6 and \(\overline{15}\), respectively. By comparison, we derive that
such that \(a_i\) are found to correspond to the topologies. Since \((E',C')\) have been the vanishing topological parameters, one has \(a_9=-a_{10}\) and \(a_{11}=0\). Moreover, our global fits for \(E_{\mathbf{B},M}\) indicate that \(a_{9(10)}\) from \(H(\overline{15})\) has a non-zero value. By contrast, the numerical analysis performed with the irreducible \(SU(3)_f\) symmetry neglects the contributions from \(H(\overline{15})\) [7], whose results are given in the tables. In the physical mass scenario (\(S_{pm}\)) for the global fit in Ref. [7], where \(m_{\mathbf{B}_c}\), \(m_{\mathbf{B}^*}\) and \(m_M\) are taken from the physical values in Ref. [1], \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta ,\Xi ^{*0} K^+)\) and \({\mathcal {B}}(\Xi _c^0 \rightarrow \Omega ^- K^+)\) are fitted to be a few times smaller than the observations. Instead of considering the \(SU(3)_f\) symmetry breaking, one performs another fit in the equal mass scenario (\(S_{em}\)), where \(m_{\Lambda _c}=m_{\Xi _c}\), \(m_\Delta =m_{\Sigma ^*}=m_{\Omega }\) and \(m_\pi =m_\eta =m_K\), resulting in the raised values of the above branching fractions.
4 Conclusions
In summary, we have studied the \(\mathbf{B}_c\rightarrow \mathbf{B}^* M\) decays in the quark-diagram scheme. We have found that only two W-exchange diagrams, \(E_\mathbf{B}\) and \(E_M\), could give contributions to the observed branching fractions of \(\Lambda _c^+ \rightarrow (\Delta ^{++} K^-\), \(\Sigma ^{*+} \eta \), \(\Xi ^{*0} K^+)\) and \(\Xi _c^0 \rightarrow \Omega ^- K^+\). In addition, we have predicted \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*0(+)} \pi ^{+(0)})=(2.8\pm 0.4)\times 10^{-3}\), which respects the isospin symmetry. To interpret the observation of \({\mathcal {B}}(\Lambda _c^+ \rightarrow \Sigma ^{*+} \eta )\), we have taken into account the \(SU(3)_f\) symmetry breaking. In particular, \({\mathcal {B}}(\Lambda _c^+\rightarrow \Delta ^{++} \pi ^-,\Xi _c^+ \rightarrow \Delta ^{++} K^-) =(7.0\pm 1.4,13.5\pm 2.7)\times 10^{-4}\) and \({\mathcal {B}}(\Xi _c^+ \rightarrow \Delta ^{++} \pi ^-,\Xi _c^0 \rightarrow \Delta ^- \pi ^+) =(7.8\pm 1.6,2.5\pm 0.4)\times 10^{-5}\) have been predicted as the largest branching fractions in the SCS \(\Lambda _c^+(\Xi _c^+)\) and DSC \(\Xi _c^{+(0)}\) decay channels, respectively.
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data used in this paper are publicly available and they can be found in the corresponding references.]
References
M. Tanabashi et al., [Particle Data Group]. Phys. Rev. D 98, 030001 (2018)
A. Zupanc et al., [Belle Collaboration]. Phys. Rev. Lett. 113, 042002 (2014)
M. Ablikim et al., [BESIII Collaboration]. Phys. Rev. Lett. 116, 052001 (2016)
M.J. Savage, R.P. Springer, Phys. Rev. D 42, 1527 (1990)
M.J. Savage, Phys. Lett. B 257, 414 (1991)
C.Q. Geng, Y.K. Hsiao, C.W. Liu, T.H. Tsai, JHEP 1711, 147 (2017)
C.Q. Geng, C.W. Liu, T.H. Tsai, Y. Yu, Phys. Rev. D 99, 114022 (2019)
X.G. He, Y.K. Hsiao, J.Q. Shi, Y.L. Wu, Y.F. Zhou, Phys. Rev. D 64, 034002 (2001)
H.K. Fu, X.G. He, Y.K. Hsiao, Phys. Rev. D 69, 074002 (2004)
Y.K. Hsiao, C.F. Chang, X.G. He, Phys. Rev. D 93, 114002 (2016)
J. Pan, Y.K. Hsiao, J. Sun, X.G. He, Phys. Rev. D 102, 056005 (2020)
C.D. Lu, W. Wang, F.S. Yu, Phys. Rev. D 93, 056008 (2016)
C.Q. Geng, Y.K. Hsiao, Y.H. Lin, L.L. Liu, Phys. Lett. B 776, 265 (2017)
C.Q. Geng, Y.K. Hsiao, C.W. Liu, T.H. Tsai, Phys. Rev. D 97, 073006 (2018)
C.Q. Geng, Y.K. Hsiao, C.W. Liu, T.H. Tsai, Phys. Rev. D 99, 073003 (2019)
Y.K. Hsiao, Y. Yu, H.J. Zhao, Phys. Lett. B 792, 35 (2019)
H.J. Zhao, Y.L. Wang, Y.K. Hsiao, Y. Yu, JHEP 2002, 165 (2020)
H.Y. Cheng, C.W. Chiang, Phys. Rev. D 86, 014014 (2012)
Hn Li, C.D. Lu, F.S. Yu, Phys. Rev. D 86, 036012 (2012)
Hn Li, C.D. Lu, Q. Qin, F.S. Yu, Phys. Rev. D 89, 054006 (2014)
H.Y. Cheng, C.W. Chiang, Phys. Rev. D 100, 093002 (2019)
Q.P. Xu, A.N. Kamal, Phys. Rev. D 46, 3836 (1992)
J.G. Korner, M. Kramer, Z. Phys. C 55, 659 (1992)
K.K. Sharma, R.C. Verma, Phys. Rev. D 55, 7067 (1997)
Y. Kohara, Phys. Rev. D 44, 2799 (1991)
L.L. Chau, H.Y. Cheng, B. Tseng, Phys. Rev. D 54, 2132 (1996)
X.G. He, Y.J. Shi, W. Wang, Eur. Phys. J. C 80, 359 (2020)
A.J. Buras, arXiv:hep-ph/9806471
T. Feldmann, P. Kroll, B. Stech, Phys. Rev. D 58, 114006 (1998)
T. Feldmann, P. Kroll, B. Stech, Phys. Lett. B 449, 339 (1999)
Y.K. Hsiao, L. Yang, C.C. Lih, S.Y. Tsai, arXiv:2009.12752 [hep-ph]
K. Miura, T. Minamikawa, Prog. Theor. Phys. 38, 954 (1967)
J.G. Korner, Nucl. Phys. B 25, 282 (1971)
J.C. Pati, C.H. Woo, Phys. Rev. D 3, 2920 (1971)
Y.B. Li et al., [Belle Collaboration]. Phys. Rev. D 100, 031101 (2019)
Acknowledgements
We would like to thank Prof. X.G. He for useful discussions. This work was supported by National Science Foundation of China (11675030).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
About this article
Cite this article
Hsiao, Y.K., Yi, Q., Cai, ST. et al. Two-body charmed baryon decays involving decuplet baryon in the quark-diagram scheme. Eur. Phys. J. C 80, 1067 (2020). https://doi.org/10.1140/epjc/s10052-020-08659-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjc/s10052-020-08659-4