Improving the ultraviolet behavior in baryon chiral perturbation theory

Djukanovic, Dalibor; Schindler, Matthias R.; Gegelia, J.; Scherer, Stefan

doi:10.1103/physrevd.72.045002

Cited by 37 publications

(47 citation statements)

References 60 publications

(82 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Starting with the above given "canonical" effective Lagrangian one encounters ultraviolet divergences in the equations for the few-nucleon scattering amplitudes. This problem can be handled by considering a nucleon propagator with improved ultraviolet behavior [24]. To that end we employ a "non-canonical" form of the effective Lagrangian generated by using suitable field transformations.…”

Section: The Effective Lagrangianmentioning

confidence: 99%

See 1 more Smart Citation

NN scattering in higher-derivative formulation of baryon chiral perturbation theory

et al. 2007

Self Cite

View full text Add to dashboard Cite

We consider a new approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Starting with a Lorentzinvariant form of the effective Lagrangian we work out a new symmetry-preserving framework where the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively. Analogously to the KSW approach, the (leading) renormalization scale dependence to any finite order is absorbed in the redefinition of a finite number of parameters of the effective potential at given order. On the other hand, analogously to Weinberg's power counting, the one-pion-exchange potential is of leading order and is treated non-perturbatively.

show abstract

Section: The Effective Lagrangianmentioning

confidence: 99%

“…We start with the higher-derivative formulation of the manifestly Lorentz-invariant Lagrangian of Ref. [24] and perform the non-relativistic reduction at the level of Feynman diagrams.…”

Section: Introductionmentioning

confidence: 99%

NN scattering in higher-derivative formulation of baryon chiral perturbation theory

et al. 2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…The resummation of the chiral series through the introduction of a regulator (or similar variant) has been studied in various instances [5,[10][11][12][13][14][15][16][17][18]. The method consists of inserting a regulator function uðk 2 Þ into the integrand of the meson-loop integrals.…”

Section: A Renormalization In Frr Eftmentioning

confidence: 99%

Power counting regime of chiral effective field theory and beyond

2010

View full text Add to dashboard Cite

Chiral effective field theory (χEFT) complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of χEFT, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may be used in a nonperturbative manner to describe lattice simulation results outside of the PCR. Positive results that improve on the current optimistic application of chiral perturbation theory (χPT) beyond the PCR are reported.

show abstract

“…Different renormalization methods leading to a consistent PC have been developed within dimensional [11,12] and cutoff [18] regularization schemes. In the following we focus on the former ones.…”

mentioning

confidence: 99%

Leading SU(3)-Breaking Corrections to the Baryon Magnetic Moments in Chiral Perturbation Theory

et al. 2008

View full text Add to dashboard Cite

We calculate the baryon magnetic moments using covariant Chiral Perturbation Theory (χPT) within the Extended-on-mass-shell (EOMS) renormalization scheme. By fitting the two available low-energy constants (LECs), we improve the Coleman-Glashow description of the data when we include the leading SU(3) breaking effects coming from the lowest-order loops. This success is in dramatic contrast with previous attempts at the same order using Heavy Baryon (HB) χPT and covariant Infrared (IR) χPT. We also analyze the source of this improvement with particular attention on the comparison between the covariant results. PACS numbers: 12.39.Fe, 14.20.Dh, 14.20.Jn,13.40.Em In the limit that SU(3) is an exact flavour symmetry it is possible to relate the magnetic moments of the baryon-octet and the ΛΣ 0 transition to those of the proton and the neutron. These are the celebrated Coleman-Glashow formulas [1]. The improvement of this description requires the inclusion of a realistic SU(3)-breaking mechanism. Chiral Perturbation Theory (χPT), as the realization of non-perturbative QCD at lowenergies [2,3,4], should be an appropriate framework to tackle this problem in a systematic fashion. However, it was soon noticed that the leading-order chiral corrections are large and tend to worsen the results [5,6]. This problem has often been used to question the validity of SU(3)-χPT in the baryon sector.In the last decade several calculations in HBχPT up to nextto-next-to-leading order (NNLO) have been performed both with [6,7,8] and without [9] the inclusion of the baryon decuplet. The large number of LECs appearing at this order reduces the predictive power of the theory. Besides that, it is also known that there are substantial relativistic corrections [10].The development of covariant χPT has been troubled by the complications in the power counting introduced by the baryon mass as a new large scale [3]. Different ways of solving this problem, such as the IR [11] and, more recently, the EOMS [12] renormalization schemes, have been explored. In SU(3) BχPT only the self-energies have been studied with both schemes [13,14]. The baryon-octet magnetic moments have been calculated using the IR method [15] and, at NLO, the SU(3)-breaking corrections are still large. Moreover, the agreement with the data is even worse than in HBχPT. The size of NLO terms raises the question about the convergence of the chiral series [7,9,16].In this letter we present a covariant calculation of the baryon-octet magnetic moments at O(p 3 ) (NLO) using the EOMS renormalization technique. In contrast to the previous works, we find small loop-corrections leading to a considerable improvement over the SU(3)-symmetric description. We also show the results in HB and covariant IR χPT, and investigate the origin of the differences.In χPT, the power counting (PC) provides a systematic organization of amplitudes as a perturbative expansion in powers of (p/Λ χSB ) nχP T , where p is a small momentum or scale and Λ χSB , the chiral symmetry breaking scale. In the onebar...

show abstract

Improving the ultraviolet behavior in baryon chiral perturbation theory

Cited by 37 publications

References 60 publications

NN scattering in higher-derivative formulation of baryon chiral perturbation theory

NN scattering in higher-derivative formulation of baryon chiral perturbation theory

Power counting regime of chiral effective field theory and beyond

Leading SU(3)-Breaking Corrections to the Baryon Magnetic Moments in Chiral Perturbation Theory

Contact Info

Product

Resources

About