Extension of the chiral perturbation theory meson Lagrangian to order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Fearing, Harold W.; Scherer, Stefan

doi:10.1103/physrevd.53.315

Cited by 207 publications

(275 citation statements)

References 44 publications

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“…In appendix C we list the resulting divergent parts for the relevant L (6) -constants β j . The fact that they are independent of the masses, is a consistency check between our calculation and the Lagrangian L (6) from [5].…”

Section: Divergent Two-loop Contributions To F ±supporting

confidence: 67%

“…The series of calculations on form factors taken up by us begun before this paper was published. In order to preserve the continuity with our previous papers on order p 6 chiral perturbation theory, we stick to the convention of [5]. There is no harm in keeping more than the minimal number of operators, as it is, for all practical purposes, impossible to determine by the necessary independent experiments such a large number of counterterms (including their finite parts), be it 143 or 90.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Kl3 form factors at order p of chiral perturbation theory

Post

Schilcher

2002

Eur. Phys. J. C

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This paper describes the calculation of the semileptonic K l3 decay form factors at order p 6 of chiral perturbation theory which is the nextto-leading order correction to the well-known p 4 result achieved by Gasser and Leutwyler. At order p 6 the chiral expansion contains 1-and 2-loop diagrams which are discussed in detail. The irreducible 2-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian L (6) produces direct couplings with the W -bosons. Due to these unknown couplings, one can always add linear terms in q 2 to the predictions of the form factor f − (q 2 ). For the form factor f + (q 2 ), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q 4 counter term, the q 4 -ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q 2 our calculation shows that chiral perturbation theory converges very well in this application, as the O(p 6 )-corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f + (q 2 ) is well described by a linear fit, but that the slope λ + is smaller by about 2 standard deviations than the O(p 4 ) prediction. The unavoidable q 2 counter term of the O(p 6 ) corrections allows to bring the predictions of chiral perturbation theory into perfect agreement with experiment.

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Section: Divergent Two-loop Contributions To F ±supporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Kl3 form factors at order p of chiral perturbation theory

Post

Schilcher

2002

Eur. Phys. J. C

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“…The first category contains vertices of the same structure as those occurring in the general SU(3) Lagrangian of order p 6 , which are listed in ref. [30]. For a complete set of terms of order p 4 , we refer to [14].…”

Section: Higher Orders and Loopsmentioning

confidence: 99%

Large $N_ c$ in chiral perturbation theory

2000

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The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large N c counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan-Manohar transformation is in conflict with these rules and is suppressed to all orders in 1/N c . The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten term, which accounts for the U(3) R ×U(3) L anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in 1/N c , but requires specific unnatural parity contributions in the effective Lagrangian that restore renormalization group invariance.

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“…For strong and electromagnetic processes involving an odd number of Goldstone bosons, the Wess-Zumino-Witten term provides the leadingorder contribution. At O(p 6 ) the effective Lagrangian involves 111 terms of even and 32 terms of odd intrinsic parity [4]. Ever since the sixties the interactions of Goldstone bosons with baryons have been described in terms of tree-level diagrams derived from effective chiral Lagrangians.…”

Section: Introductionmentioning

confidence: 99%