Improved treatment of loop diagrams in SU(3) baryon chiral perturbation theory

Donoghue, John F.; Holstein, Barry R.

doi:10.1016/s0370-2693(98)00859-4

Cited by 35 publications

(64 citation statements)

References 15 publications

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“…(See, for example, Ref. [5].) However, the spacetime lattice is a particularly convenient implementation, due in part to its explicit preservation of chiral symmetry.…”

Section: Discussionmentioning

confidence: 99%

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Lattice regularization for chiral perturbation theory

Lewis

Ouimet

2001

Phys. Rev. D

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The SU(3) chiral Lagrangian for the lightest octets of mesons and baryons is constructed on a spacetime lattice. The lattice spacing acts as an ultraviolet momentum cutoff which appears directly in the Lagrangian so chiral symmetry remains explicit. As the lattice spacing vanishes, Feynman loop diagrams typically become divergent due to inverse powers of the lattice spacing, and these divergences get absorbed into counterterms such that the standard results of dimensional regularization are obtained. One advantage of lattice regularization is that power divergences are seen explicitly. In the present work, the octet meson masses, the octet baryon masses and the πN sigma term are all computed explicitly to one loop order.

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“…(See, for example, Ref. [5].) However, the spacetime lattice is a particularly convenient implementation, due in part to its explicit preservation of chiral symmetry.…”

Section: Discussionmentioning

confidence: 99%

“…One example of research that relies upon information about power divergences is found in Ref. [5], where a nonlattice cutoff was used to discuss the convergence of HBChPT and the scale of baryon substructure.…”

Section: Introductionmentioning

confidence: 99%

Lattice regularization for chiral perturbation theory

Lewis

Ouimet

2001

Phys. Rev. D

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“…[9,10] therefore favored the use of a cutoff regularization scheme in their recent analysis of the nucleon mass, which in their eyes is more suitable for such a scenario. While the use of cutoff methods in CHPT already has a long history [11,12,7] and constitutes a well-defined regularization procedure, from the viewpoint of field theory it is not acceptable that one scheme should provide superior results over the other (for a general discussion of regularization schemes in CHPT, see e.g. [13]).…”

Section: Introductionmentioning

confidence: 99%

“…In that regime an effective field theory of QCD, usually called chiral perturbation theory (CHPT), can be set up, which is written in terms of the very Goldstone degrees of freedom, with their couplings to matter fields dictated by chiral dynamics [4,5,6]. Recently doubts have been issued in the literature [7,8,9,10] whether such an effective field theory, in particular when it is utilized in connection with dimensional regularization, is "effective" enough to be applied to extended objects with complicated internal structure like baryons. The authors of Refs.…”

Section: Introductionmentioning

confidence: 99%

Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass

2004

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We discuss the use of cutoff methods in chiral perturbation theory. We develop a cutoff scheme based on the operator structure of the effective field theory that allows to suppress high momentum contributions in Goldstone boson loop integrals and by construction is free of the problems traditional cutoff schemes have with gauge invariance or chiral symmetries. As an example, we discuss the chiral expansion of the nucleon mass. Contrary to other claims in the literature we show that the mass of a nucleon in heavy baryon chiral perturbation theory has a well behaved chiral expansion up to effective Goldstone boson masses of 400 MeV when one utilizes standard dimensional regularization techniques. With the help of the here developed cutoff scheme we can demonstrate a well-behaved chiral expansion for the nucleon mass up to 600 MeV of effective Goldstone Boson masses. We also discuss in detail the prize, in numbers of additional short distance operators involved, that has to be paid for this extended range of applicability of chiral perturbation theory with cutoff regularization, which is usually not paid attention to. We also compare the fourth order result for the chiral expansion of the nucleon mass with lattice results and draw some conclusions about chiral extrapolations based on such type of representation.

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“…The first four terms in the chiral expansion of the nucleon mass were given in eq. (34). The corresponding expansion for σ ≡ σ(0) is of the form…”

Section: The σ-Termmentioning

confidence: 99%

Baryon chiral perturbation theory in manifestly Lorentz invariant form

Becher

Leutwyler

1999

Eur. Phys. J. C

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We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar form factor σ(t), for instance, breaks down in the vicinity of t = 4M 2 π . In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order p 4 .

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Improved treatment of loop diagrams in SU(3) baryon chiral perturbation theory

Cited by 35 publications

References 15 publications

Lattice regularization for chiral perturbation theory

Lattice regularization for chiral perturbation theory

Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass

Baryon chiral perturbation theory in manifestly Lorentz invariant form

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