Baryonic mass formula in large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>QCD versus quark model

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one-and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proven to be a powerful technique in the case of two-body problems. A general procedure is given and applied to various Hamiltonians of interest, in atomic and hadronic physics in particular. A test of formulas is performed for baryons described as a three-quark system.

show abstract

“…This formula generalizes a result obtained for a small value of ␣ S in Ref. 33. Following the considerations of Sec.…”

Section: Application To Baryonssupporting

confidence: 52%

“…In order to allow a more realistic calculation of the correct baryon masses, this Hamiltonian must be completed with terms that can be computed in perturbation. 33 As these contributions represent no interest for the AFM, they are not considered in this study.…”

Section: Application To Baryonsmentioning

confidence: 99%

The Quantum N-Body Problem and the Auxiliary Field Method

2010

View full text Add to dashboard Cite

show abstract

“…Second, such a symmetry argument could point the way for the treatment of higher excitations with a more complicated spin-flavor structure. Finally, in several recent papers [11,12] the validity of the usual approach based on the core+excited decomposition has been questioned, and a symmetry argument should settle the objections raised in these works.…”

Section: Introductionmentioning

confidence: 99%

Permutation groupSNand largeNcexcited baryons

Pirjol¹,

Schat

2008

Phys. Rev. D

View full text Add to dashboard Cite

We study the excited baryon states for an arbitrary number of colors N c from the perspective of the permutation group S N of N objects. Classifying the transformation properties of states and quark-quark interaction operators under S N allows a general analysis of the spin-flavor structure of the mass operator of these states, in terms of a few unknown constants parameterizing the unknown spatial structure. We explain how to perform the matching calculation of a general twobody quark-quark interaction onto the operators of the 1/N c expansion. The inclusion of core and excited quark operators is shown to be necessary. Considering the case of the negative parity L = 1 states transforming in the M S of S N , we discuss the matching of the one-gluon and the Goldstone-boson exchange interactions.

show abstract

“…In the real world, the degeneracies are removed by spin-or isospin-dependent operators which can be computed as perturbations. 33 When an eigenstate of H B is computed for given values of S, T, and the total angular momentum L, we determine the band number of its dominant components. It can then be compared with the eigenstate of H AFB with the same spin-isospin quantum numbers and the same band number.…”

Section: Application To Baryonsmentioning

confidence: 99%