The bound state corrections to the semileptonic decays of the heavy baryons
I. D'Souza, C. S. Kalman, P. Yu. Kulikov, I. M. Narodetskii
备注：
Latex, 5 pages, 3 figures. Talk presented by Calvin Kalman at the 5th International Conference on Hyperon, Charm and Beauty Hadrons, Vancouver, June 2002
We present an investigation of the lepton energy distributions in the inclusive semileptonic weak decays of heavy baryons performed within a relativistic quark model formulated on the light front (LF). Using the heavy-quark LF distribution functions related to the equal time momentum wave functions taken from the Kalman--Tran--D'Souza model we compute the electron energy spectra and the total semileptonic widths of the Lambda_Q and Xi_Q (Q=c,b) baryons and confront the results with existing data.
We complement the results for the radiative corrections to the s2.l angular correlation of baryon semileptonic decays of Ref. [1] with the final results in the rest frame of the decaying baryon.
This paper studies the leading chiral corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon semileptonic decay form factors. We derive the coupling between heavy diquarks and weak current in the limit of heavy quark-diquark symmetry, and construct the chiral Lagrangian for doubly heavy baryons coupled to weak current. We evaluate chiral corrections to doubly heavy baryon zero-recoil semileptonic decay for both unquenched and partially quenched QCD. This theory is used to derive chiral extrapolation expressions for measurements of form factors of doubly heavy baryon ze…
The semileptonic transition of $Λ_b$ baryon is studied using the Hypercentral constituent quark model. The six-dimensional hyperradial $Schr\ddot{o}dinger$ equation is solved in the variational approach to get masses and wavefunctions of heavy baryons. The matrix elements of weak decay are written in terms of the overlap integrals of the baryon wave function. The Isgur-Wise function is determined to calculate exclusive semileptonic decay $Λ_b$ $\rightarrow$ $Λ_c$ $\ell$ $\barν$. The calculated decay rate and the branching ratio of $Λ_b$ baryon are consistent with other theoretical predictions …
We study the semileptonic decays of the lowest lying double heavy baryons using the relativistic three-quark model. We do not employ a heavy quark mass expansion but keep the masses of the heavy quarks and baryons finite. We calculate all relevant form factors and decay rates.
We calculate semileptonic decays of light and heavy baryons in a relativistically covariant constituent quark model. The model is based on the Bethe-Salpeter-equation in instantaneous approximation. It generates satisfactory mass spectra for mesons and baryons up to the highest observable energies. Without introducing additional free parameters we compute on this basis helicity amplitudes of electronic and muonic semileptonic decays of baryons. We thus obtain form factor ratios and decay rates in good agreement with experiment.
We give a detailed account of the techniques to compute radiative corrections in baryon semileptonic decays developed over the years by Mexican collaborations. We explain how the method works by obtaining an expression for the Dalitz plot of semileptonic decays of polarized baryons including radiative corrections to order ${\mathcal O}(αq/πM_1)$, where $q$ is the four-momentum transfer and $M_1$ is the mass of the decaying baryon. From here we compute the totally integrated spin angular asymmetry coefficient of the emitted baryon and compare its value with other results.
It is shown that the absolute rate of the semileptonic decays of the $Ξ_c$ baryons can be as much as two times higher than the semileptonic decay rate of $Λ_c$ due to the Pauli interference of the strange quark. This interference effect is still larger in the semileptonic decay rate of $Ω_c$. An experimental measurement of the difference of these rates would thus provide an important piece of information on the spectator effects in decays of hadrons containing a heavy quark.
In the heavy quark limit a heavy baryon which contains two heavy quarks is believed to be composed of a heavy diquark and a light quark. Based on this picture, we evaluate the weak semileptonic decay rates of such baryons. The transition form factors between two heavy baryons are associated with those between two heavy mesons by applying the superflavor symmetry. The effective vertices of the W-boson and two heavy diquarks are obtained in terms of the Bethe-Salpeter equation. Numerical predictions on these semileptonic decay widths are presented and they will be tested in the future experiment…
We extend the approach based on the light-cone expansion and the heavy quark effective theory to the inclusive semileptonic decay of an unpolarized $b$-flavored hadron. It is applied to calculate the semileptonic decay width of the $Λ_b$ baryon and its ratio to that of the B meson. We obtain $Γ_{SL}(Λ_b)= 51\pm 9 |V_{cb}|^2{ps}^{-1}$ and $Γ_{SL}(Λ_b)/Γ_{SL}(B)= 1.052\pm 0.006$. From the latter, the semileptonic branching fraction for $Λ_b$ is predicted to be $(8.7\pm 0.7)%$.
We calculate the semileptonic baryon octet-octet transition form factors using a manifestly Lorentz covariant quark model approach based on the factorization of the contribution of valence quarks and chiral effects. We perform a detailed analysis of SU(3) breaking corrections to the hyperon semileptonic decay form factors. We present complete results on decay rates and asymmetry parameters including lepton mass effects for the rates.
The static properties and semileptonic decays of ground-state doubly heavy baryons are studied working in the framework of a non-relativistic quark model. Using a phenomenological potential model, we calculate the ground-state masses and magnetic moments of doubly heavy $ Ω$ and $ Ξ$ baryons. In the heavy quark limit, we introduce a simple form of the universal Isgur-Wise function used as the transition form factor and then investigate the exclusive $ b \rightarrow c $ semileptonic decay widths and branching ratios for $ \frac{1}{2}\rightarrow \frac{1}{2} $ baryon transitions. Our obtained res…
We study the semileptonic decays of double heavy baryons using a manifestly Lorentz covariant constituent three-quark model. We present complete results on transition form factors between double-heavy baryons for finite values of the heavy quark/baryon masses and in the heavy quark symmetry limit which is valid at and close to zero recoil. Decay rates are calculated and compared to each other in the full theory, keeping masses finite, and also in the heavy quark limit.
In semileptonic decays of spin-1/2 baryons containing heavy quarks up to six charge assignments for the baryons and lepton are possible. We show that the radiative corrections to four of these possibilities can be directly obtained from the final results of the two possibilities previously studied. There is no need to recalculate integrals over virtual or real photon momentum or any traces.
Semileptonic decays of heavy baryons consisting of one heavy (Q=b,c) and two light (q=u,d,s) quarks are considered in the heavy-quark--light-diquark approximation. The relativistic quasipotential equation is used for obtaining masses and wave functions of both diquarks and baryons within the constituent quark model. The weak transition matrix elements are expressed through the overlap integrals of the baryon wave functions. The Isgur-Wise functions are determined in the whole accessible kinematic range. The exclusive semileptonic decay rates and different asymmetries are calculated with applyi…
Semileptonic decays of heavy baryons consisting of one heavy (Q=b,c) and two light (q=u,d,s) quarks are considered in the heavy-quark--light-diquark approximation. The relativistic quasipotential equation is used for obtaining masses and wave functions of both diquarks and baryons within the constituent quark model. The weak transition matrix elements are expressed through the overlap integrals of the baryon wave functions. The Isgur-Wise functions are determined in the whole accessible kinematic range. The exclusive semileptonic decay rates are calculated with applying the heavy quark 1/m_Q e…
The semileptonic decays of heavy spin--1/2, $Ξ_{b(c)}$ and $Ξ'_{b(c)}$ baryons to the light spin-- 1/2, $Ξ$ and $Σ$ baryons are investigated in the framework of the light cone QCD sum rules. In particular, using the most general form of the interpolating currents for the heavy baryons as well as the distribution amplitudes of the $Ξ$ and $Σ$ baryons, we calculate all form factors entering the matrix elements of the corresponding effective Hamiltonians in full QCD. Having calculated the responsible form factors, we evaluate the decay rates and branching fractions of the related transitions.
We present a detailed analysis of the heavy-to-light semileptonic decays of the Lambda_b and Lambda_c baryons Lambda_b -> p l- bar(nu)_l and Lambda_c -> n l+ nu_l in the covariant confined quark model. We calculate the invariant and helicity amplitudes of the two processes which are then used to analyze their angular decay distributions, their rates and asymmetry parameters.
Semileptonic decays of doubly heavy baryons are studied in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The transition amplitudes of heavy diquarks bb and bc going respectively to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the transition matrix elements, the Isgur-Wise function and decay rates in the heavy quark limit.
We show that the radiative corrections containing terms up to order $αq / πM_1$ for unpolarized semileptonic decays of baryons with positron emission can be obtained by simply reversing the sign of the axial-vector form factors in the corresponding final expressions of such decays with electron emission. This rule is valid regardless of the final kinematical variables chosen and of the particular Lorentz frame in which the final results are required.
Charm and bottom baryons and mesons are studied within the framework of a relativistically covariant 3D reduction of the Bethe-Salpeter equation. We carry out an analysis of semileptonic decays of heavy hadrons within this framework using explicit oscillator-type wave functions where we calculate Isgur-Wise functions, decay rates and asymmetry parameters. Within this model we also study the effect of interactions between the light quarks inside the heavy baryon and how they affect the values of the computed heavy baryon observables. We also elaborate on the role of relativistic effects in the …
We have calculated the radiative corrections to the Dalitz plot of baryon semileptonic decays with angular correlation between polarized emitted baryons and charged leptons. This work covers both charged and neutral decaying baryons and is restricted to the so-called three-body region of the Dalitz plot. Also it is specialized at the center-of-mass frame of the emitted baryon. We have considered terms up to order (alpha/pi)(q/M_1)^0, where q is the momentum-transfer and M_1 is the mass of the decaying baryon, and neglected terms of order (alpha/pi)(q/M_1)^n$ for n >= 1. The expressions display…
We study the weak vector and axial-vector form factors of first- and second-class currents for the semileptonic octet baryon decays in the spirit of the chiral quark model. Our results for the weak magnetism form factors are consistent with the conserved vector current (CVC) results. The induced pseudotensor form factors, which are highly model dependent, are small. The overall performance of the chiral quark model is quite good and in general agreement with existing experimental data.
We study the semileptonic decays of the lowest-lying bc baryons to the lowest-lying cc baryons (Xi_{bc}^{(\prime*)}--> Xi_{cc}^{(*)} and Omega_{bc}^{(\prime*)}--> Omega_{cc}^{(*)}), in the limit m_b, m_c >> Lambda_{QCD} and close to the zero recoil point. The separate heavy quark spin symmetries make it possible to describe all these decays using a single form factor. We recover results derived previously by White and Savage in a manner which we think is more straightforward and parallels the method applied later to study Bc semileptonic decays. We further discuss the resemblance between the b…
In the framework of a non-relativistic quark model, the mass spectra of the ground and excited states of doubly heavy $Ξ$ and $Ω$ baryons are calculated. We estimate the mass difference between the $ Ω$ and corresponding $ Ξ$ baryons as $M_Ω-M_Ξ\simeq178 $ MeV for all the states containing $ cc,~bc $, or $ bb $ quarks. A simple form of the universal Isgur-Wise function, as the transition form factor between the doubly heavy baryons, is introduced. Working in the close-to-zero recoil limit, we investigate the $ b \rightarrow c $ semileptonic decay widths and branching fractions of the doubly he…
We study the semileptonic decays of the lowest-lying $bc$ baryons to the lowest-lying $cc$ baryons ($Ξ_{bc}^{(\prime*)}\to Ξ_{cc}^{(*)}$ and $Ω_{bc}^{(\prime*)}\to Ω_{cc}^{(*)}$), in the limit $m_b, m_c \gg Λ_\mathrm{QCD}$ and close to the zero recoil point. The separate heavy quark spin symmetries make it possible to describe all these decays using a single form factor. We also show how these constraints can be used to test the validity of different quark model calculations. $bb$ to $bc$ baryon decays are also discussed.
Analytical radiative corrections of order (α/π)(q/M_1) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s_1 \cdot p_2 correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter. We cover two cases, a charged and a neutral polarized decaying baryon.
Analytical radiative corrections of order (alpha/pi)(q/M) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s1.l correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter, except for a few exceptions. We cover two cases, a charged and a neutral polarized decaying baryon.
We analyze the effects of hyperfine mixing in $b \to c$ semileptonic decays of doubly heavy baryons. We qualitatively confirm the results by W. Roberts and M. Pervin in Int. J. Mod. Phys. A, 2009, {\bf 24}: 2401-2413, finding that mixing has a great impact on those transitions. However, predictions without mixing differ by a factor of 2 and this discrepancy translates to the mixed case where large differences in decay widths are observed between the two calculations.
The electromagnetic form factors of the Xi baryons and the semileptonic decay process Xi_c->Xi e^+nu_e are investigated in the frame work of the light-cone QCD sum rule method with Ioffe-type interpolating currents. Our estimates on the magnetic moments are $mu_{Xi^0}=-(1.75\pm0.21) mu_N and mu_{Xi^-}=-(1.01\pm0.11)mu_N. The decay width of the semileptonic process is expected to be Gamma(Ξ_c\to Ξe^+ν_e)=(6.17^{+2.24}_{-2.48})\times10^{-14}GeV. The results make sure that the adoption of this type interpolating current improve the calculations of the magnetic form factors and give more reliable …
The semileptonic decays of $Λ_{b}\toΛ_{c}^{(*)}\ellν_\ell$ and $Λ_{c}\toΛ^{(*)}\ellν_\ell$ are studied in the light-front quark model in this work. Instead of the quark-diquark approximation, we use the three-body wave functions obtained by baryon spectroscopy. The ground states $(1/2^{+})$, the $λ$-mode orbital excited states $(1/2^{-})$, and the first radial excited states $(1/2^{+})$ of $Λ_{(c)}^{(*)}$ are considered. The discussions are given for the form factors, partial widths, branching fractions, leptonic forward-backward asymmetries, hadron polarizations, lepton polarizations, and the…
We study the effect of the FCNC mediated $Z$ boson in the rare semileptonic baryonic decays $Λ_b \to Λl^+ l^-$. We consider the model where the standard model fermion sector is extended by an extra vector like down quark, as a consequence of which it allows CP violating Z mediated flavor changing neutral current at the tree level. We find that due to this non-universal $Zbs $ coupling, branching ratios of the rare semileptonic $Λ_b$ decays are enhanced reasonably from their corresponding standard model values and the zero point of the forward backward asymmetry for $Λ_b \to Λμ^+ μ^-$ is shifte…
Spin-1/2 baryons are considered as a composite system made out of a "core" of three quarks surrounded by a "sea" (of gluons and $q\bar{q}$-pairs) which is specified by its total quantum numbers. Specifically, we assume this sea to be a flavor octet with spin-0 or 1 but no color. We show our model can provide very goods fits to magnetic moments and semileptonic decay data using experimental errors. The predictions for spin distributions are in reasonable agreement with experiment.
We qualitatively corroborate the results of W. Roberts and M. Pervin in Int. J. Mod. Phys. A 24, 2401 (2009) according to which hyperfine mixing greatly affects the decay widths of $b\to c$ semileptonic decays involving doubly heavy $bc$ baryons. However, our predictions for the decay widths of the unmixed states differ from those reported in the work of Roberts and Pervin by a factor of 2, and this discrepancy translates to the mixed case. We further show that the predictions of heavy quark spin symmetry, might be used in the future to experimentally extract information on the admixtures in t…
We evaluate exclusive semileptonic decays of ground-state spin-1/2 and spin-3/2 doubly heavy $cb$ baryons driven by a $c\to s,d$ transition at the quark level. We check our results for the form factors against heavy quark spin symmetry constraints obtained in the limit of very large heavy quark masses and near zero recoil. Based on those constraints we make model independent, though approximate, predictions for ratios of decay widths.
We propose and discuss a numerical use of our previous precision results for the radiative corrections to unpolarized spin one-half baryon semileptonic decays, which is not compromised to fixing the form factors at prescribed values. We present various crosschecks and comparisons with other results available in the literature of such analytical radiative corrections. Our analysis, however, is general and applies to all charge assignments to the baryons allowed by heavy quarks. The procedure is exemplified with the processes Ξ^0 \to Σ^+ e\barν and Λ_c^+ \to Λe^+ ν.
The spin 1/2 baryons are pictured as a composite system made out of a "core" of three valence quarks (as in the simple quark model) surrounded by a "sea" (of gluon and $q\bar{q}$ pairs) which is specified by its total quantum numbers. We assume the sea is a SU(3) flavor octet with spin 0 or 1 but no color. This model, considered earlier, is used to obtain simultaneous fits for masses, magnetic moments and $G_A/G_V$ for semileptonic decays. These fits give predictions for nucleon spin distributions in reasonable agreement with experiment.
We consider spin-momentum correlations between the spin of the bottom baryon $Λ_{\mathrm{b}}$ and the momenta of its decay products in its inclusive semileptonic decay. We define several polar and azimuthal spin-momentum correlation measures in different event coordinate systems. The values of the spin-momentum correlation measures are calculated up to ${\cal O}(1/m_b^2)$ using the standard OPE und HQET methods. Some of the measures turn out to be sufficiently large to make them good candidates for a determination of the polarization of the $Λ_{\mathrm{b}}$ in e.g. $\mathrm{Z}$ decays.
We set up sum rules for heavy lambda decays in a full QCD calculation which in the heavy quark mass limit incorporates the symmetries of heavy quark effective theory. For the semileptonic $\La_c$ decay we obtain a reasonable agreement with experiment. For the $\La_b$ semileptonic decay we find at the zero recoil point a violation of the heavy quark symmetry of about 20%.
Form factors of the weak $Ξ_c \to Ξ(Λ)$ transitions are calculated within the light cone QCD sum rules. The pollutions coming from the contribution of the negative parity $Ξ_c^*$ baryon is eliminated by considering the combinations of sum rules corresponding to the different Lorentz structures. Having obtained the form factors, the branching ratios of the $Ξ_c \to Ξ(Λ) \ell ν$ decays are also calculated, and our predictions are compared with the results of other approaches as well as the measurements done by BELLE and ALICE Collaborations.
Working in the framework of a nonrelativistic quark model we evaluate the spectra and semileptonic decay widths for the ground state of doubly heavy $Ξ$ and $Ω$ baryons. We solve the three-body problem using a variational ansatz made possible by the constraints imposed by heavy quark spin symmetry. In order to check the dependence of our resultson the inter-quark interaction we have used five different quarkquark potentials which include Coulomb and hyperfine terms coming fromone-gluon exchange, plus a confining term. Our results for the spectra are in good agreement with a previous calculatio…
We present results for exclusive $b\to c$ semileptonic decays of ground state triply-heavy baryons and for semileptonic $c\to s,d$ decays of doubly heavy ground state $cb$ baryons. In both cases, we have derived for the first time heavy quark spin symmetry relations for the hadronic amplitudes near zero recoil. Though strictly valid in the limit of very large heavy quark masses and near zero recoil, they turn out to be reasonable accurate for the whole available phase space in these decays and for the actual heavy quark masses we use. With these relations we have made approximate, but model in…
The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited. We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes. We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.
We employ the flavor SU(3) symmetry to analyze semileptonic decays of anti-triplet charmed baryons ($Λ^{+}_{c},Ξ_{c}^{+,0}$) and find that the experimental data on ${\cal B}(Λ_c\toΛ\ell^+ν_{\ell})$ implies $\mathcal{B}(Ξ_c^0\toΞ^-e^+ν_{e})=(4.10\pm0.46)\%$ and $\mathcal{B}(Ξ_c^0\toΞ^-μ^+ν_μ)= (3.98\pm0.57)\%$. When this prediction is confronted with recent experimental results from Belle collaboration $\mathcal{B}(Ξ_c^0\toΞ^-e^+ν_e)=1.31(04\pm07\pm38)\%$ and $\mathcal{B}(Ξ_c^0\toΞ^-μ^+ν_μ)=1.27(06\pm10\pm 37)\%$, it is found that the SU(3) symmetry is severely broken. We then consider the gene…
We calculate the radiative corrections to the angular correlation between the polarization of the decaying baryon and the direction of the emitted charged lepton in the semileptonic decays of spin one-half baryons to order (α/π)(q/M_1). The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied on the quadratic products of form factors is discussed. This latter may be the most practical o…
We consider the role played by hyperfine mixing in electromagnetic and semileptonic decays of doubly heavy baryons, which give rise to large corrections to the decay widths in both cases.
We have quantitatively reanalyzed the inclusive charmed-baryon decays. New ingredients are the Voloshin preasymptotic effects in semileptonic decays and the Cabibbo-subleading contributions to both semileptonic and nonleptonic decays. It has been found that the Cabbibo-subleading Voloshin contribution essentially improves the theoretical semileptonic branching ratio of $Λ_c^{+}$, in agreement with experiment. The semileptonic branching ratios for $Ξ_c^{+}$ and $Ω_c^{0}$ are found to be large, i.e., of the order of 20%. The lifetimes hierarchy is in a good qualitative and even quantitative agre…
We calculate the semileptonic and a subclass of sixteen nonleptonic two-body decays of the double charm baryon ground states $Ξ_{cc}^{++},\,Ξ_{cc}^{+}$ and $Ω_{cc}^+$ where we concentrate on the nonleptonic decay modes. We identify those nonleptonic decay channels in which the decay proceeds solely via the factorizing contribution precluding a contamination from $W$-exchange. We use the covariant confined quark model previously developed by us to calculate the various helicity amplitudes which describe the dynamics of the $1/2^+ \to 1/2^+$ and $1/2^+ \to 3/2^+$ transitions induced by the Cabib…
We calculate the radiative corrections to the angular correlation between the polarization of the decaying and the direction of the emitted spin one-half baryons in the semileptonic decay mode. The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied by the quadratic products of form factors is discussed. This latter may be the most practical one to use in Monte Carlo simulations. A ser…
