Stella, Nicoletta
(1996)
Heavy baryon phenomenology from lattice QCD.
*University of Southampton, Doctoral Thesis*.

## Abstract

The results of an exploratory lattice study of heavy baryon spectroscopy are presented. We have computed the full spectrum of the eight baryons containing a single heavy quark, on a 24^{3} x 48 lattice at *β* = 6.2, using an *O*(*a*)-improved fermion action. We discuss the lattice baryon operators and give a method for isolating the contributions of the spin doublets (∑,∑^{*}), (Ξ>',Ξ^{*}) and (Ω,Ω^{*}) to the correlation function of the relevant operator. We compare our results with the available experimental data and find good agreement in both the charm and the beauty sectors, despite the long extrapolation in the heavy quark mass needed in the latter case. We also predict the masses of several undiscovered baryons. We compute the Λ-pseudoscalar meson and ∑-Λ mass splittings. Our results, which have errors in the range 10-30%, are in good agreement with the experimental numbers. For the ∑^{*}-∑ mass splitting, we find results considerably smaller than the experimental values for both the charm and the beauty baryons, although in the latter case, the experimental results are still preliminary. This is also the case for the lattice results for the hyperfine splitting for the heavy mesons.

Then we study the hadronic matrix elements of the weak current between Λ* _{b}*,Λ

*and Ξ*

_{c}*,Ξ*

_{b}*baryon states, which enter in the corresponding semi-leptonic decay. These matrix elements can be written in terms of six form factors, which, using the tool of the Heavy Quark Effective Theory, can be related to the baryonic Isgur and Wise function. This is studied in detail, as a function of the quark masses as well as of the velocity transfer ω for the first time. We find that for our range of masses (around and above the charm), the Isgur and Wise function does not show any statistically significant dependence on the heavy quark mass. In the kinematical region ω ϵ [1,1.2] it can be succesfully described by a linear function, normalized to the identity at ω = 1 and with a slope ranging from 1.2*

_{c}^{+8}

_{-11}for the Λ

*to 1.5*

_{b}^{+7}

_{-9}for the Ξ

*. The six form factors contain also information on the corrections proportional to the inverse heavy quark masses, which can be parametrized in terms of Λ̅;: the heavy quark binding energy inside the baryon. We find Λ̅; = 0.37*

_{b}^{+11}

_{-12}GeV for the Λ and Λ̅; = 0.50

^{+11}

_{-13}GeV for the Ξ baryon. The measure of the Isgur and Wise function along with the estimate of Λ̅; are enough to predict the value of the semi-leptonic decay rate of the processes Λ

*→ Λ*

_{b}*+*

_{c}*lv*and Ξ

*→ Ξ*

_{b}*+*

_{c}*lv*near zero recoil and up to next to leading order in the inverse heavy quark mass expansion. Model-independent predications for the decay rates, partially integrated with respect to the velocity trasfer ω, near zero recoil, are given in chapter 5, and will provide an independent estimate of the Kobayashi-Maskawa matrix element |V

*|, as soon as experimental data become available.*

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