Dimensional Power Counting in Nuclei

Abstract. We use the framework of effective field theories to discuss the determination of the S-wave πN scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length a πd is extracted from the data. Next, a πd is related to the S-wave πN scattering lengths a+ and a−. We discuss the use of this information for constraining the values of these scattering lengths in the full analysis, which also includes the input from the pionic hydrogen energy shift and width measurements, and throughly investigate the accuracy limits for this procedure. In this paper, we also give a detailed comparison to other effective field theory approaches, as well as with the earlier work on the subject, carried out within the potential model and multiple scattering framework.

show abstract

“…Performing now a standard dimensional analysis of the LECs in ChPT (see e.g. [39]), we get the estimate of the uncertainty in the quantity f 0…”

Section: Initial-and Final-state Interactionsmentioning

confidence: 99%

The pion-nucleon scattering lengths from pionic deuterium

2005

View full text Add to dashboard Cite

show abstract

“…The integrals diverge at some order, signaling this with "non-analytic" terms in z 2 (e.g., z 3 = (z 2 ) 3/2 ). Such terms play an important role in modern effective field theories [42]. In small terms that we will only estimate, z 4 charge terms and z 2 seagull terms, we will replace log(z) and log(ω N ) by average (constant) values, log(z) and log(Ē), respectively, in order to obtain tractable expressions for estimation.…”

Section: Appendix Amentioning

confidence: 99%

Higher-order nuclear-polarizability corrections in atomic hydrogen

Friar

Payne

1997

Phys. Rev. C

Self Cite

View full text Add to dashboard Cite

Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only three primary nuclear observables contribute: the electric polarizability, α E , the paramagnetic susceptibility, β M , and the third Zemach moment, r 3 (2) . Cartesian multipole decomposition of the virtual Compton amplitude and its concomitant gauge sum rules are used in the analysis.

show abstract

“…In the present context of Weinberg power counting, dimensional scaling arguments allow one to express any term of the effective Lagrangian with nucleon and pion fields as well as derivative and pion mass insertions (for a derivation and further discussion, see e.g. [19]) as…”

Section: Naturalness Of the Lecs And Wigner Symmetrymentioning

confidence: 99%

“…Before elaborating on the details, we mention that in studies of pion production in proton-proton collisions or charge symmetry breaking in the NN interaction, ideas of resonance saturation have already been used [17,18]. Also, Friar [19] has discussed aspects of integrating out heavy meson fields to generate local four-nucleon operators with given LECs but did not attempt a detailed comparison with existing models of the nuclear forces as done here.…”

mentioning

confidence: 99%

Resonance saturation for four-nucleon operators

et al. 2002

View full text Add to dashboard Cite

In the modern description of nuclear forces based on chiral effective field theory, four-nucleon operators with unknown coupling constants appear. These couplings can be fixed by a fit to the low partial waves of neutron-proton scattering. We show that the so determined numerical values can be understood on the basis of phenomenological one-boson-exchange models. We also extract these values from various modern high accuracy nucleon-nucleon potentials and demonstrate their consistency and remarkable agreement with the values in the chiral effective field theory approach. This paves the way for estimating the low-energy constants of operators with more nucleon fields and/or external probes.

show abstract

Dimensional Power Counting in Nuclei

Cited by 65 publications

References 29 publications

The pion-nucleon scattering lengths from pionic deuterium

The pion-nucleon scattering lengths from pionic deuterium

Higher-order nuclear-polarizability corrections in atomic hydrogen

Resonance saturation for four-nucleon operators

Contact Info

Product

Resources

About