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Charmed Baryon Weak Decays with Vector Mesons

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 Added by C. Q. Geng
 Publication date 2020
  fields
and research's language is English




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We give a systematic study of ${bf B}_cto {bf B}_n V$ decays, where ${bf B}_c$ and $ {bf B}_n$ correspond to the anti-triplet charmed and octet baryons, respectively, while $V$ stand for the vector mesons. We calculate the color-symmetric contributions to the decays from the effective Hamiltonian with the factorization approach and extract the anti-symmetric ones based on the experimental measurements and $SU(3)_F$ flavor symmetry. We find that most of the existing experimental data for ${bf B}_cto {bf B}_n V$ are consistent with our fitting results. We present all the branching ratios of the Cabbibo allowed, singly Cabbibo suppressed and doubly Cabbibo suppressed decays of ${bf B}_cto {bf B}_n V$. The decay parameters for the daughter baryons and mesons in ${bf B}_cto {bf B}_n V$ are also evaluated. In particular, we point out that the Cabbibo allowed decays of $Lambda_c^+ to Lambda^0 rho^+$ and $ Xi_c^0 to Xi^- rho^+$ as well as the singly Cabbibo suppressed ones of $Lambda_c^+ to Lambda^0 K^{*+}$, $Xi_c^+ to Sigma^+ phi$ and $Xi_c^0to Xi^- K^{*+}$ have large branching ratios and decay parameters with small uncertainties, which can be tested by the experimental searches at the charm facilities.



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A previous analysis of two-body Cabibbo allowed nonleptonic decays of $D^0$ mesons and of Cabibbo allowed and first-forbidden decays of $D^+$ and $D_s^+$ has been adjourned using more recent experimental data and extended to the Cabibbo forbidden decays of $D^0$. Annihilation and W-exchange contributions as well as final state interaction effects (assumed to be dominated by nearby resonances) have been included and are in fact crucial to obtain a reasonable agreement with the experimental data, which show large flavour SU(3) violations. New fitting parameters are necessary to describe rescattering effects for Cabibbo forbidden $D^0$ decays, given the lack of experimental informations on isoscalar resonances. We keep their number to a minimum - three - using phenomenologically based considerations. We also discuss CP violating asymmetries.
The BaBar Collaboration has recently reported branching fractions for semileptonic decays of the $B$ meson into final states with charged and neutral $D_{1}(2420)$ and $D_{2}^{ast}(2460)$, two narrow orbitally excited charmed mesons. We evaluate these branching fractions within the framework of a constituent quark model in two steps, one which involves a semileptonic decay and the other one mediated by a strong process. Our results are in agreement with the experimental data.
We analyze the decay processes of ${bf B}_c to {bf B}_n M$ with the $SU(3)_F$ flavor symmetry and spin-dependent amplitudes, where ${bf B}_c({bf B}_n)$ and $M$ are the anti-triplet charmed (octet) baryon and nonet meson states, respectively. In the $SU(3)_F$ approach, it is the first time that the decay rates and up-down asymmetries are fully and systematically studied without neglecting the ${cal O}(overline{15})$ contributions of the color anti-symmetric parts in the effective Hamiltonian. Our results of the up-down asymmetries based on $SU(3)_F$ are quite different from the previous theoretical values in the literature. In particular, we find that the up-down symmetry of $ alpha(Lambda_c^+to Xi^0 K^+)_{SU(3)} = 0.94^{+0.06}_{-0.11}$, which is consistent with the recent experimental data of $0.77pm0.78$ by the BESIII Collaboration, but predicted to be zero in the literature. We also examine the $K_S^0-K_L^0$ asymmetries between the decays of ${bf B}_c to {bf B}_n K_S^0$ and ${bf B}_c to {bf B}_n K_L^0$ with both Cabibbo-allowed and doubly Cabibbo-suppressed transitions.
We study the three-body anti-triplet ${bf B_c}to {bf B_n}MM$ decays with the $SU(3)$ flavor ($SU(3)_f$) symmetry, where ${bf B_c}$ denotes the charmed baryon anti-triplet of $(Xi_c^0,-Xi_c^+,Lambda_c^+)$, and ${bf B_n}$ and $M(M)$ represent baryon and meson octets, respectively. By considering only the S-wave $MM$-pair contributions without resonance effects, the decays of ${bf B_c}to {bf B_n}MM$ can be decomposed into irreducible forms with 11 parameters under $SU(3)_f$, which are fitted by the 14 existing data, resulting in a reasonable value of $chi^2/d.o.f=2.8$ for the fit. Consequently, we find that the triangle sum rule of ${cal A}(Lambda_c^+to nbar K^0 pi^+)-{cal A}(Lambda_c^+to pK^- pi^+)-sqrt 2 {cal A}(Lambda_c^+to pbar K^0 pi^0)=0$ given by the isospin symmetry holds under $SU(3)_f$, where ${cal A}$ stands for the decay amplitude. In addition, we predict that ${cal B}(Lambda_c^+to n pi^{+} bar{K}^{0})=(0.9pm 0.8)times 10^{-2}$, which is $3-4$ times smaller than the BESIII observation, indicating the existence of the resonant states. For the to-be-observed ${bf B_c}to {bf B_n}MM$ decays, we compute the branching fractions with the $SU(3)_f$ amplitudes to be compared to the BESIII and LHCb measurements in the future.
The hadronic two-body weak decays of the doubly charmed baryons $Xi_{cc}^{++}, Xi_{cc}^+$ and $Omega_{cc}^+$ are studied in this work. To estimate the nonfactorizable contributions, we work in the pole model for the $P$-wave amplitudes and current algebra for $S$-wave ones. For the $Xi_{cc}^{++}to Xi_c^+pi^+$ mode, we find a large destructive interference between factorizable and nonfactorizable contributions for both $S$- and $P$-wave amplitudes. Our prediction of $sim 0.70%$ for its branching fraction is smaller than the earlier estimates in which nonfactorizable effects were not considered, but agrees nicely with the result based on an entirely different approach, namely, the covariant confined quark model. On the contrary, a large constructive interference was found in the $P$-wave amplitude by Dhir and Sharma, leading to a branching fraction of order $(7-16)%$. Using the current results for the absolute branching fractions of $(Lambda_c^+,Xi_c^+)to p K^-pi^+$ and the LHCb measurement of $Xi_{cc}^{++}toXi_c^+pi^+$ relative to $Xi_{cc}^{++}toLambda_c^+ K^- pi^+pi^+$, we obtain $B(Xi_{cc}^{++}toXi_c^+pi^+)_{rm expt}approx (1.83pm1.01)%$ after employing the latest prediction of $B(Xi_{cc}^{++}toSigma_c^{++}overline{K}^{*0})$. Our prediction of $mathcal{B}(Xi_{cc}^{++}toXi_c^+pi^+)approx 0.7%$ is thus consistent with the experimental value but in the lower end. It is important to pin down the branching fraction of this mode in future study. Factorizable and nonfactorizable $S$-wave amplitudes interfere constructively in $Xi_{cc}^+toXi_c^0pi^+$. Its large branching fraction of order 4% may enable experimentalists to search for the $Xi_{cc}^+$ through this mode. That is, the $Xi_{cc}^+$ is reconstructed through the $Xi_{cc}^+toXi_c^0pi^+$ followed by the decay chain $Xi_c^0to Xi^-pi^+to ppi^-pi^-pi^+$.
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