Model-independent predictions for low energy isoscalar heavy baryon observables in the combined heavy quark and large Nc expansion

Abstract

Model-independent predictions for excitation energies, semileptonic form factors and electromagnetic decay rates of isoscalar heavy baryons and their low energy excited states are discussed in terms of the combined heavy quark and large Nc expansion. At leading order, the observables are completely determined in terms of the known excitation energy of the first excited state of Λc. At next-to-leading order in the combined expansion all heavy baryon observables can be expressed in a model-independent way in terms of two experimentally measurable quantities. We list predictions at leading and next-to-leading order.A number of nonperturbative expansions have been used to study low-energy hadronic observables. The heavy quark expansion has been very successful in describing hadrons containing one heavy quark. In the heavy quark limit the heavy quark spin-flavor decouples from the dynamics and hadronic spectrum exhibits an approximate heavy quark spin-flavor symmetry. Heavy quark effective theory (HQET) is a consistent framework to study the 1/m Q corrections to the heavy quark limit [1][2][3][4][5][6]. Another useful limit is the large N c limit where the number of colors N c of the QCD gauge group is taken to be large [7,8]. In the large N c limit the baryon sector of QCD exhibits an approximate light quark spin-flavor symmetry; eg. as N c goes to infinity the nucleon and ∆ become degenerate [9-13]. For heavy baryons, i.e. baryons containing one (c or b) heavy quark it is useful to consider a double limit and a combined heavy quark and large N c expansion [14]. In Ref. [15][16][17] isoscalar heavy baryons have been considered near the combined limit.The combined heavy quark and large N c expansion is formulated in terms of the counting parameter λ ∼ Λ had /m Q , 1/N c with Λ had N c /m Q arbitrary (here Λ had is a typical hadronic scale). As λ approaches zero, the heavy baryon spectrum exhibits an approximate dynamical symmetry-a contracted O(8) symmetry-which connects orbitally excited states of the heavy baryons to the ground state [14,15]. An effective theory describing low-energy excitations of heavy baryons can be developed using the counting rules consistent with a contracted O(8) symmetry [16]. The purpose of the present paper is to use the formalism of Ref.[17] to derive model-independent relations among observables characterizing isoscalar heavy baryons and their decays. At present, experimental data is available only for the excitation energies of the doublet of the first excited state of Λ c . At leading order in the combined expansion this energy completely determines the excitation energy of the low-energy orbitally excited state of Λ b as well as the dominant semileptonic form factors and electromagnetic decay rates. Such predictions are necessarily rather crude as our expansion is in powers of λ 1/2 . At next-to-leading order an additional observable is required to make further model independent predictions. As data for more heavy baryon observables (such as the excitation energy of Λ b baryon, semil...

Observation of ExcitedΛb0Baryons

“…Calculation involving a combined heavy quark and large number of colors expansion [9,10] gives a value roughly in agreement, although only the spin-averaged prediction is available. The earlier prediction based on the relativized quark potential model [13] matches well the absolute mass values for both states, but the à 0 b mass prediction using this model is 35 MeV=c 2 lower than the measured value.…”

“…The properties of excited à 0 b baryons are discussed in Refs. [9][10][11][12][13][14][15]. Most predictions give masses above the à 0 b % þ % À threshold but below the AE b % threshold.…”

Evidence for a bottom baryon resonanceΛb*0in CDF data

“…− state to be approximately in the range 300-310 MeV/c 2 [6,8,9]. The mass splitting between the two states is predicted to be in the range 10-17 MeV/c 2 .…”

“…The spectroscopy of isoscalar heavy baryons and their excitations is studied in Ref. [9] within the framework of HQET at leading and next-toleading orders in the combined inverse heavy-quark mass, 1/m Q , and inverse number of colors, 1/N c , expansions. The nonperturbative formalism of QCD sum rules is applied within HQET to calculate the mass spectra of the bottom baryon states [10].…”

“…The 2 range of the Q-value spectrum motivated by the theoretical estimates [6,8,9] and the LHCb findings [20].…”