Masses and Magnetic Moments of Charmed Baryons Using Hyper Central Model
Bhavin Patel, Ajay Kumar Rai, P. C. Vinodkumar
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8 Pages, 2 figures Paper submitted to Frascati Physics Series Vol. XLVI (2007) HADRON07: Presented in XII Int. Conf. on Hadrons Spectroscopy- Frascati, October 8-13,2007
Heavy flavour baryons containing one or two charm quarks with light flavour combinations are studied using the hyper central description of the three-body system. The confinement potential is assumed as hyper central coulomb plus power potential with power index $ν$. The ground state masses and the magnetic moments of charmed, $J^P={1/2}^+$ and ${3/2}^+$ baryons are computed for different power index, $ ν$ starting from 0.5 to 2.0.
It is proved that the nonleptonic decay amplitudes of antitriplet charmed baryons to octet baryons do not depend on the representation of the octet baryons in the quark diagram scheme. Relations among various representations are derived, and correct decay amplitudes of the charmed baryons are given.
Electric form factors of $S$-wave charmed baryons are calculated within the relativistic quark model in the region of low and intermediate momentum transfers, $Q^2 \le 1 GeV^2$. The charge radii of low-lying charmed baryons are determined.
The measured masses of the three charge states of the charmed $Σ_c$ baryon are found to be in disagreement with a sum rule based on the quark model, but relying on no detailed assumptions about the form of the interaction. This poses a significant problem for the charmed baryon sector of the quark model. Other relations among charmed baryon masses are also discussed.
We speculate on a possible interpretation of events selected by the SELEX collaboration and stress an insufficient evidence for the observation of doubly charmed baryon.
Flavor $SU(3)$ symmetry is a powerful tool to analyze charmed baryon decays. In this work, we propose an approach to generate $SU(3)$ sum rules for the singly and doubly charmed baryon decays without writing the Wigner-Eckhart invariants explicitly. The $SU(3)$ sum rules are computed routinely in several master formulas. Hundreds of $SU(3)$ sum rules are found to serve as test of the flavor symmetry in the charmed baryon decays.
The masses of negative parity $(70,1^-)$ charmed nonstrange baryons are calculated in the relativistic quark model. The relativistic three-quark equations of the $(70,1^-)$ charmed baryon multiplet are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitude are obtained. The calculated mass values of the $(70,1^-)$ charmed baryons are in good agreement with the experimental data.
We study the vector and axial vector form factors in the heavy to light transitions in charmed baryon decays using HQET. We calculate the 1/m_c corrections to the form factors and show that these corrections can be significant. We also consider applications to semi-leptonic and hadronic decays of charmed baryons.
We study two-body weak decays of charmed baryons Λ_c and Ξ_c into an octet or decuplet baryon and a pseudoscalar meson employing the SU(3) flavor symmetry. Using certain measured Cabibbo-favored modes, we fix the reduced amplitudes and predict the branching ratios of various decays of charmed baryons in the Cabibbo-enhanced, -suppressed and -doubly suppressed modes.
The weak decay of charmed baryons multiplets into ground state and mesons are investigated using current algebra technique. Some of the interesting results on the partial decays rates and the asymmetry parameters for $Δ$C=$Δ$S=-1 the mode are calculated and consequences discussed
The total and differential cross sections for the production of triply charmed $Ω_{ccc}$ baryons in $e^{+}e^{-}$ annihilation are calculated at the $Z$-boson pole.
The analysis of singly charmed hadrons has been extended to the case of doubly charmed baryons, $Ξ_{cc}^{++}$, $Ξ_{cc}^{+}$ and $Ω_{cc}^{+}$. Doubly charmed baryons are described as a system containing a heavy $cc$-diquark and a light quark, similarly as in a heavy-light meson. This leads to preasymptotic effects in semileptonic and nonleptonic decays which are essentially proportional to the meson wave function. Interplay between preasymptotic effects in semileptonic and/or nonleptonic decay rates leads to very clear predictions for semileptonic branching ratios and lifetimes of doubly charme…
This is an extension of the prediction of strange baryon decays to the decays of charmed baryons using QCD Sum Rules. Using QCD Sum Rules we estimate the decay $Λ^+_c (udc) \rightarrow Λ^o_s(uds)+ π^+$. Although some weak decays of the $Λ^+_c$ have been measured, since it is difficult to measure $Λ^+_c \rightarrow Λ^o_s+ π^+$ our estimates should be useful for future experiments
Sum rules for the low-energy constants of the chiral SU(3) Lagrangian with charmed baryons of spin J^P=1/2^+ and J^P=3/2^+ baryons are derived from large-N_c QCD. We consider the large-$N_c$ operator expansion at subleading orders for current-current correlation functions in the charmed baryon-ground states for two scalar and two axial-vector currents.
In the framework of dispersion relation technique the relativistic three-quark equations including heavy quarks are found. The approximate solutions of the relativistic three-particles equations based on the extraction of leading singularities of amplitudes are obtained. The mass values of S-wave multiplets of charmed baryons are calculated.
The cross-section for the double charmed baryon production at a $B$-factory is estimated on the basis of the perturbative QCD calculations for the $c c$-diquark production as well as of the quark-hadron duality.
The yield of doubly charmed baryons with excited heavy diquark in $S$ wave and $P$ wave states has been estimated at LHC energies. The observation possibility of such baryons is discussed.
The mass of the $Ω^0_c$ baryon with quark content (ssc) is computed in a potential model whose parameters have been determined in 1981 by fitting the spectrum of heavy mesons. It is found in perfect agreement with a recent measurement at the CERN hyperon-beam experiment. The spectroscopy of other charmed baryons in potential models is briefly reviewed.
The two body Cabibbo favored hadronic decays of charmed baryons $Λ^{+}_{c}$, $Ξ^{+}_{c}$ and $Ξ_{c}^{0}$ into an octet or decuplet baryon and a pseudoscalar meson are examined in the SU(3) symmetry scheme. The numerical estimates for decay widths and branching ratios of some of the modes are obtained and are in good agreement with experiment.
We extend the analysis of weak decays of heavy hadrons to the case of doubly charmed baryons, Ξ_{cc}^{++}, Ξ_{cc}^{+} and Ω_{cc}^{+}. Doubly charmed baryons are modeled as a heavy-light system containing a heavy cc-diquark and a light quark. Such a model leads to preasymptotic effects in semileptonic and nonleptonic decays which are essentially proportional to the meson wave function. Very clear predictions for semileptonic branching ratios and lifetimes of doubly charmed baryons are obtained.
The high production rate and $\langle x_{F} \rangle > 0.33$ of the doubly charmed baryons measured by the SELEX experiment is not amenable to perturbative QCD analysis. In this paper we calculate the production of the doubly heavy baryons with the double intrinsic charm Fock states whose existence is rigorously predicted by QCD. The production rate and the longitudinal momentum distribution are both reproduced. We also show that the production rates of the doubly charmed baryons and double $J/ψ$ production observed by NA3 collaboration are comparable. Recent experimental results are reviewed. …
We derive a Bjorken sum rule for semileptonic $Ω_b$ decays to ground and low-lying negative-parity excited charmed baryon states, in the heavy quark limit. We discuss the restriction from this sum rule on form factors and compare it with some models.
The radiative decays of the p-wave charmed heavy baryons to the ground state baryon states are studied in the framework of the light cone QCD sum rules method. Firstly, the transition form factors that describe these transitions are estimated, and then using these form factors the corresponding decay widths are calculated. A comparison of our results on the decay widths with those predicted by the other approaches existing in literature is performed.
A diquark model is used to investigate single charmed baryons. In this model, baryon is composed of two diquarks and an antiquark. Masses of lowest lying states with $J^P= 1/2 ^ \pm$ are obtained. Some masses are smaller than other theoretic predictions which indicates that these baryons of pentaquark structure could be relatively stable. The results also show that $Λ(2882)$ may be a pentaquark with $J^P=1/2^-$ and $Ξ(3125)$ may be a pentaquark with $J^P=1/2^+$.
We study pion induced reactions for charmed baryons $B$, $π$ + N $\rightarrow$ $D^*$ + $B$. First we estimate charm production rates in comparison with strangeness production using a Regge model which is dominated by vector ($D^*$ or $K^*$ ) Reggeon exchange. Then we examine the production rates of various charmed baryons $B$ in a quark-diquark model. We find that the production of excited states are not necessarily suppressed, a sharp contrast to strangeness production, which is a unique feature of the charm production with a large momentum transfer.
The chiral effective meson-baryon Lagrangian for the description of interactions between the doubly charmed baryons and Goldstone bosons is constructed up to the order of $q^{4}$. The numbers of linearly independent invariant monomials of $\mathcal{O}(q^2)$, $\mathcal{O}(q^3)$ and $\mathcal{O}(q^4)$ are 8, 32 and 218, in order. The obtained Lagrangian can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at complete one-loop level in future. For completeness, the non-relativistic reduction of the Lagrangian is also discussed.
The magnetic moments, transition magnetic moments and the radiative decay widths of singly charmed baryons are calculated with $ {J^P = \frac{1}{2}}^+$ and $ {J^P = \frac{3}{2}}^+$ in the constitute quark model. Further, the strong decay rates for $ S $, $ P $ and $ D $ wave transitions are also presented. The singly charmed baryon masses used in the calculations were obtained from the hypercentral Constitute Quark Model (hCQM) without and with first order relativistic correction. Obtained results are compared with experimental observation as well as with the other theoretical predictions.
In the framework of quark-hadron duality, the cross section values of charmonium and doubly charmed baryon production in $e^+e^-$-annihilations have been estimated at interaction energy $\sqrt{s}=10.6$ GeV. It has been shown that the approach under discussion allows to resolve some contradictions between the experimental data and pQCD predictions.
Charm spectroscopy has studied under a string model. Charmed baryons are composed of diquark and charm quark which are connected by a constant tension. In a diquark picture, the quantum numbers $J^P$ of confirmed baryons are well assigned. We give energy predictions for the first and second orbital excitations. We see some correspondences with the experimental data. Meanwhile, we have obtained diquark masses in the background of charm quark which satisfy a splitting relation based on spin-spin interaction.
The width of a recently discovered excited charmed-strange baryon, a candidate for a state $Ξ_c^*$ with spin 3/2, is calculated. In the absence of configuration mixing between the ground-state (spin-1/2) charmed-strange baryon $Ξ_c^{(a)}$ and the spin-1/2 state $Ξ_c^{(s)}$ lying about 95 MeV above it, one finds $\tilde Γ(Ξ^*_c \to Ξ_c^{(a)} π) = (3/4) \tilde Γ(Ξ^* \to Ξπ)$ and $\tilde Γ(Ξ^*_c \to Ξ_c^{(s)} π) = (1/4) \tilde Γ(Ξ^* \to Ξπ)$, where the tilde denotes the partial width with kinematic factors removed. Assuming a kinematic factor for P-wave decay of $p_{\rm cm}^3$, one predicts $Γ(Ξ^…
We calculate mass spectra of charmed baryons within a relativistically covariant quark model based on the Bethe-Salpeter-equation in instantaneous approximation. Interactions are given by a linearly rising three-body confinement potential and a flavor dependent two-body force derived from QCD instanton effects. This model has already been successfully applied to the calculation of light flavor baryon spectra and is now extended to heavy baryons. Within the same framework we compare the results to those obtained with the more conventional one-gluon-exchange potential.
The total decay widths of the charmed baryons are calculated by means of the $^3P_0$ model. Our calculations consider in the final states: the charmed baryon-(vector/pseudoscalar) meson pairs and the (octet/ decuplet) baryon-(pseudoscalar/vector) charmed meson pairs, within a constituent quark model. Furthermore, we calculate the masses of the charmed baryon ground states and their excitations up to the $D$-wave in a constituent quark model both in the three-quark and in the quark-diquark schemes, utilizing a Hamiltonian model based on a harmonic oscillator potential plus a mass splitting term…
Quark and pole models of nonleptonic decays of charmed baryons are analysed from the point of view of their symmetry properties. The symmetry structure of the parity conserving amplitudes that corresponds to the contribution of the ground-state intermediate baryons is shown to differ from the one hitherto employed in the symmetry approach. It is pointed out that the "subtraction" of sea quark effects in hyperon decays leads to an estimate of $W$-exchange contributions in charmed baryon decays that is significantly smaller than naively expected on the basis of $SU(4)$. An $SU(2)_{W}$ constraint…
The nonleptonic decays of $Ξ_c^0$ and $Λ_c^+$ that are dominated by $W$-exchange are studied. In particular, we anlayse the decay modes $Ξ_c^0 \rightarrow Ξ^{*-} π^+, Σ^{*+}K^-, Ω^-K^+$ and $Λ_c^+\rightarrow Σ^0π^+, Ξ^0 K^+$, $Ξ^0_c\rightarrow Σ^+K^-$.
The masses of the charmed baryons in the ${\bf 6}$ representation of $SU(3)$ obey an equal spacing rule at lowest order in $SU(3)$ breaking, ${\cal O}(m_s)$. We compute the corrections to this relation at order ${\cal O}(m_s^{3/2})$ arising from meson loops using chiral perturbation theory combined with heavy quark symmetry and find them to be small. We also examine the hyperfine interaction responsible for the splitting between the $J^π={3\over 2}^+$ and $J^π={1\over 2}^+$ baryons in the ß representation. The results also hold in the b-baryon sector.
The calculation of muon spectra from the decay of Lambda_c baryons was carried out on the basis of the description of recent data on charmed-baryon production in hadronic interactions. Data are described in the framework of Quark--Gluon String Model that allowes us to consider primary proton interactions of arbitrary high energy. MC code was built for charmed-baryon semileptonic decay in order to obtain the kinematical characteristics of resulting particles. It is predicted that the charge asymmetry between energy spectra of mu+ and mu- in laboratory system is clearly seen as the consequence o…
In the recent years, fruitful results on charmed baryons are obtained by BESIII, Belle and LHCb. We investigate the two-body non-leptonic decays of charmed baryons in the flavor $SU(3)$ symmetry. Hundreds of amplitude relations are clearly provided, and are classified according to the $I$-, $U$- and $V$-spin symmetries. Among them, some amplitude relations are tested by the experimental data, or used to predict the branching fractions based on the exact flavor symmetry without any other approximation. Some relations of $K^0_S-K^0_L$ asymmetries and $CP$ asymmetries are obtained under the $U$-s…
The finite size of doubly heavy diquark gives a positive correction to the masses of baryons calculated in the local diquark approximation. We evaluate this correction for the basic states of doubly charmed baryons to give quite accurate predictions actual for current searches of those baryons at LHCb: $m[{Ξ_{cc}^{1/2}}^{+}]\approx m[{Ξ_{cc}^{1/2}}^{++}]=3615\pm 55$ MeV and $m[{Ξ_{cc}^{3/2}}^{+}]\approx m[{Ξ_{cc}^{3/2}}^{++}]=3747\pm 55$ MeV.
The interaction of the low lying pseudo-scalar mesons with the ground state baryons in the charm sector is studied within a coupled channel approach using a t-channel vector-exchange driving force. The amplitudes describing the scattering of the pseudo-scalar mesons off the ground-state baryons are obtained by solving the Lippmann--Schwinger equation. We analyze in detail the effects of going beyond the $t=0$ approximation. Our model predicts the dynamical generation of several open charmed baryon resonances in different isospin and strangeness channels, some of which can be clearly identified…
The results of a recent quenched lattice QCD simulation for charmed baryons are presented. In contrast to a previous calculation, it is found that hyperfine splittings are in agreement with quark model expectations and comparable to experimental values. Preliminary calculations using lattice NRQCD yield results which are compatible with those obtained using a Dirac-Wilson action of the D234 type for the charm quark.
The magnetic moments of spin ${1/2}{^+}$ and spin ${3/2}{^+}$ charmed baryons have been calculated in chiral constituent quark model ($χ$CQM). The effects of configuration mixing and quark masses have also been investigated. The results are not only in good agreement with existing experimental data but also show improvement over other phenomenological models.
Motivated by the recent LHCb observation of $CP$ violation in charm, we study $CP$ violation in the charmed baryon decays. A simple method to search for the $CP$ violation relations in the flavor $SU(3)$ limit, which is associated with a complete interchange of $d$ and $s$ quarks, is proposed. With this method, hundreds of $CP$ violation sum rules in the doubly and singly charmed baryon decays can be found. As examples, the $CP$ violation sum rules in two-body charmed baryon decays are presented. Some of the $CP$ violation sum rules could help the experiment to find better observables. As bypr…
We have performed a detailed investigation of total lifetimes for the $Ξ_{cc}^{++}$ and $Ξ_{cc}^{+}$ baryons in the framework of operator product expansion over the inverse mass of charmed quark, whereas, to estimate matrix elements of operators obtained in OPE, some approximations of nonrelativistic QCD are used. This approach allows one to take into account the corrections to the spectator decays of $c$-quarks, which reflect the fact, that these quarks are bound, as well as the contributions, connected to the effects of both the Pauli interference for the $Ξ_{cc}^{++}$-baryon and the weak sc…
The production of the excited charmed baryon doublet $Λ_c^*$ via fragmentation is studied. An analysis of the subsequent hadronic decays of the doublet within the framework of heavy hadron chiral perturbation theory produces expressions for both the angular distribution of the decay products and the polarization of the final state heavy baryon in terms of various nonperturbative fragmentation parameters. Future experimental investigation of this system will determine these parameters. In addition, recent experimental results are shown to fix one of the parameters in the heavy hadron chiral Lag…
Using the quark-diquark approximation in the framework of Buchm\" uller-Tye potential model, we investigate the spectroscopy of doubly charmed baryons: $Ξ_{cc}^{++}$ and $Ξ_{cc}^{+}$. Our results include the masses, parameters of radial wave functions of states with the different excitations of both diquark and light quark-diquark system. We calculate the values of fine and hyperfine splittings of these levels and discuss some new features, connected to the identity of heavy quarks, in the dynamics of hadronic and radiative transitions between the states of these baryons.
The production of baryons containing two charmed quarks Xi_cc in hadronic interactions at high energies and large transverse momenta is considered. It is supposed, that Xi_cc-baryon is formed during a non-perturbative fragmentation of the (cc)-diquark, which was produced in the hard process of $c$-quark scattering from the colliding protons: c+c -> (cc) +g. It is shown that such mechanism enhances the expected doubly charmed baryon production cross section on Tevatron and LHC colliders approximately 2 times in contrast to predictions, obtained in the model of gluon - gluon production of (cc)-d…
The existence of doubly heavy flavor baryons has not been well established experimentally so far. In this Letter we systematically investigate the weak decays of the doubly charmed baryons, $Ξ_{cc}^{++}$ and $Ξ_{cc}^{+}$, which would be helpful for experimental searches for these particles. The branching fractions are studied under the factorization hypothesis for the short-distance contributions and considering the rescattering effect for the long-distance contributions which are significantly enhanced. Comparing all the decay modes, we recommend the processes of $Ξ_{cc}^{++}\to Λ_c^+K^-π^+π^…
I review the recent proposal that there are new isotriplet heavy baryons with masses approximately 2380 MeV and 5760 MeV. This prediction follows from the application of heavy spin-flavor and light $SU(3)$ symmetries to the observed charmed and bottom baryon states. It also entails assumptions about the spin and parity quantum numbers of the observed states which are different than is commonly supposed. The discovery of such states would imply that the nonrelativistic constituent quark model is a poor predictor of heavy baryon spectroscopy. I update the analysis in light of new data which have…
The isotriplet Sigmac(2800) baryon with possible quantum numbers J(P) = 1/2(+), 1/2(-) or 3/2(+), 3/2(-) is considered as a hadronic molecule composed of a nucleon and a D meson. We determine the strong two-body decay widths Sigmac to Lambdac + pi which are shown to be consistent with current data for the J(P) = 1/2(+) and J(P) = 3/2(-) assignments.
The significantly screened heavy-quark potential in hot medium provides the possibility to study exotic quantum states of three-heavy-quark systems. By solving the Schrödinger equation for a three-charm-quark system at finite temperature, we found that, there exist Borromean states which might be realized in high energy nuclear collisions, and the binding energies of the system satisfy precisely the scaling law for Efimov states in the resonance limit.
Up to now, the excited charmed and bottom baryon states are still not well studied both experimentally and theoretically. In the present paper, we predict the mass of $Ω_b^*$, the only $L = 0$ baryon state which has not been observed, to be 6069.2 MeV. The spectra of charmed and bottom baryons with the orbital angular momentum $L = 1$ are studied in two popular constituent quark models, the Goldstone boson exchange (GBE) and the one gluon exchange (OGE) hyperfine interaction models, respectively. Inserting the latest experimental data from the "Review of Particle Physics", we find that in the …
We propose to measure the decay asymmetry parameters in the hadronic weak decays of singly charmed baryons, such as $\ldc\to\ldπ^+,Σ^0π^+,p \bar K_0$, $Ξ_c^0\toΞ^-π^+$ and $Ω_c^0\toΩ^-π^+$. The joint angular formulae for these processes are presented, and are used to extract the asymmetry parameters in $\ee$ annihilation data. Base on the current $\ldc$ data set collected at BESIII, we estimate the experimental sensitivities to measure the parameters $α_{\ldπ^+}$ for $\ldc\to\ldπ^+$, $α_{Σ^+π^0}$ for $\ldc\toΣ^+π^0$ and $α_{\usigπ^+}$ for $\ldc\to\usigπ^+$.
The semileptonic $Ω_c^0 \rightarrow Ω^- l ν$ and non-leptonic $Ω_c^0 \to Ω^- π^+$, $Ω_c^0 \to Ω^- ρ^+$ decays of charmed $Ω_c$ baryon are studied within the light cone sum rules. The form factors responsible for $Ω_c \to Ω$ transitions are calculated using the distribution amplitudes of $Ω_c$ baryon. With the obtained form factors, the branching ratios of $Ω_c^0 \to Ω^- l^+ ν_l$, $Ω_c^0 \rightarrow Ω^- π^+$, and $Ω_c^0 \rightarrow Ω^- ρ^+$ decays are estimated. The results are compared with Belle data as well as the findings of the other approaches.
We study the masses of radial and orbital excited states of nonstrange singly charmed baryons in the framework of hypercentral Constituent Quark Model (hCQM). To obtain the mass spectra, the Coulomb plus screened potential is employed with the first order correction, which gives a relativistic effect of order $\cal{O}$$(1/m)$. The spin-spin, spin-orbit and tensor interactions are included (perturbatively as a spin dependent potential) in order to generate the splitting in mass spectra. We compare our computed mass spectra of nonstrange singly charmed baryons with the other theoretical predicti…
The doubly charmed baryon $Ξ^{++}_{cc}$ was observed by LHCb cooperation in 2017. The branching fractions of two-body doubly charmed baryon decays were predicted in the framework of rescattering mechanism, and some $SU(3)_F$ relations were investigated in the topological amplitudes. In this work, we study the correlation between topological diagram at quark level and rescattering triangle diagram at hadron level in the doubly charmed baryon decay. The completeness of our framework is confirmed from the fact that all the twelve possible structures of meson-baryon scattering appear once each in …
Light-Front quark model spin wave functions are employed to calculate the three independent couplings g_{Σ_c Λ_c π}, f_{Λ_{c1} Σ_c π} and f_{Λ^{*}_{c1} Σ_c π} of S-wave to S-wave and P-wave to S-wave one-pion transitions. It is found that g_{Σ_c Λ_c π}=6.81 MeV^{-1}, f_{Λ_{c1} Σ_c π}=1.16 and f_{Λ^{*}_{c1} Σ_c π}=0.96 . 10^{-4} MeV^{-2}. We also predict decay rates for specific strong transitions of charmed baryons.
