Power counting and Wilsonian renormalization in nuclear effective field theory

Valderrama, Manuel Pavón

doi:10.1142/s021830131641007x

Cited by 44 publications

(47 citation statements)

References 90 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent reviews and references addressing this problem can be found, e.g., in Refs. [2][3][4][5][6][7][8][9][10]. The Lagrangian of any consistent EFT includes all local interactions allowed by the underlying symmetries.…”

Section: Introductionmentioning

confidence: 99%

How (not) to renormalize integral equations with singular potentials in effective field theory

et al. 2018

View full text Add to dashboard Cite

We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of QCD. We also describe a particular subtractive renormalization scheme and consider a specific application to a toy-model with a singular potential serving as its effective field theoretical leading-order approximation.

show abstract

Section: Introductionmentioning

confidence: 99%

How (not) to renormalize integral equations with singular potentials in effective field theory

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Unlike its higher energy cousin chiral-EFT, the power counting of EFT(/ π) is well understood and unambiguous [15]. EFT(/ π) has had great success in describing PC (See Refs.…”

Section: Introductionmentioning

confidence: 99%

Parity-violating three-nucleon interactions at low energies and large NC

Vanasse

2019

Phys. Rev. C

View full text Add to dashboard Cite

The parity-violating (PV) nucleon-nucleon (NN ) interaction in the three-nucleon system is investigated using pionless effective field theory (EFT(/ π)). This work shows that a next-to-leading order (NLO) PV three-body force is necessary in contradiction with a previous claim [1]. Including three-body P to D-wave transitions PV three-nucleon observables are calculated to higher energies than previously considered. Using the recent large-N C analysis of the PV NN interaction in EFT(/ π) the current understanding of low energy PV few-body measurements is reassessed. The recent measurement of the asymmetry A γ in np → dγ from the NPDGamma collaboration [2] gives the value g (N −1 C ) 4 * jvanasse@stetson.edu arXiv:1809.10740v2 [nucl-th] 12 May 2019 PV PV PV PV PV PC PC PC PC PV FIG. 2. Coupled integral equations for the LO PV scattering amplitude. The green box represents an insertion of a two-body PV LEC and the yellow oval the LO PV scattering amplitude. Some diagrams only exist in certain channels with the LO three-body force only existing if the outgoing partial wave is 2 S1 /2 . the integral equation t PV J L S ,LS 1 2 1 −1 1 1 K PV J L S ,LS (k, p, E) t PV J LS,L S (k, q, E) T ⊗ D NLO (E, q) t PC J LS,LS (k, q, E) + t PC J L S ,L S (k, q, E) T ⊗ D NLO (E, q) t PV J L S ,LS (k, q, E)

show abstract

“…Daniel Phillips' evenhanded account at Chiral Dynamics 2012 [41] and van Kolck's more recent review [42]); some additional notable contributions include Refs. [15,24,29,30,32,[43][44][45][46]. This is not just stamp-collecting or a philosophical question which potentially exposes the soft underbelly of χEFT and the credibility of its error assessments, but which is "otherwise" of little practical consequence.…”

Section: Rationale: Consistency Issues In Efts With Shallow Bound Statesmentioning

confidence: 99%

A consistency test of EFT power countings from residual cutoff dependence

Grießhammer

2020

Eur. Phys. J. A

View full text Add to dashboard Cite

I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the breakdown scale of an Effective Field Theory (EFT), on the low-momentum scales, and on the order of the calculation. Passing this test is a necessary but not sufficient consistency criterion for a suggested power counting whose exact nature is disputed. For example, in Chiral Effective Field Theory (χEFT) with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the relation between convergence pattern and numerical results, and led to proposals which predict different numbers of Low Energy Coefficients (LECs) at the same chiral order, and at times even predicts a different ordering long-range contributions. The method may provide an independent check whether an observable is properly renormalised at a given order, and allows one to estimate both the breakdown scale and the momentum-dependent order-by-order convergence pattern of an EFT. Conversely, it may help identify those LECs (and long-range pieces) which produce renormalised observables at a given order. I also discuss its underlying assumptions and relation to the Wilsonian Renormalisation Group Equation; useful choices for observables and cutoffs; the momentum window in which the test likely provides best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting LECs to data in different or the same channel; and caveats as well as limitations. Since the test is designed to minimise the use of data, it allows one to quantitatively falsify if the EFT has been renormalised consistently. This complements other tests which quantify how an EFT compares to experiment. Its application in particular to the 3 P0 and 3 P2-3 F2 partial waves of NN scattering in χEFT may elucidate persistent power-counting issues.

show abstract

Power counting and Wilsonian renormalization in nuclear effective field theory

Cited by 44 publications

References 90 publications

How (not) to renormalize integral equations with singular potentials in effective field theory

How (not) to renormalize integral equations with singular potentials in effective field theory

Parity-violating three-nucleon interactions at low energies and large NC

A consistency test of EFT power countings from residual cutoff dependence

Contact Info

Product

Resources

About