Baryon chiral perturbation theory in manifestly Lorentz invariant form

Becher, Thomas; Leutwyler, H.

doi:10.1007/pl00021673

Cited by 543 publications

(1,093 citation statements)

References 41 publications

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“…The dominant k-independent component of f g 1 is larger by a factor of 5π, roughly an order of magnitude, than the power-counting estimate. The enhancement by a numerical factor of π is a common feature of triangular diagrams [26,[30][31][32][33], while the factor 5 can be traced back to a coherent sum over isospin. The three-pion ∆ vertex also gives rise to the leading irreducible CP-violating 3N potential relevant for the considered 3N systems [8,18], The CP-conserving interactions are here treated non-perturbatively in all orders.…”

Section: Jhep03(2015)104mentioning

confidence: 99%

Nuclear electric dipole moments in chiral effective field theory

Bsaisou

Vries

Hanhart

et al. 2015

J. High Energ. Phys.

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We provide a consistent and complete calculation of the electric dipole moments of the deuteron, helion, and triton in the framework of chiral effective field theory. The CP-conserving and CP-violating interactions are treated on equal footing and we consider CP-violating one-, two-, and three-nucleon operators up to next-to-leading-order in the chiral power counting. In particular, we calculate for the first time EDM contributions induced by the CP-violating three-pion operator. We find that effects of CP-violating nucleon-nucleon contact interactions are larger than those found in previous studies based on phenomenological models for the CP-conserving nucleon-nucleon interactions. Our results which apply to any model of CP violation in the hadronic sector can be used to test various scenarios of CP violation. As examples, we study the implications of our results on the QCD θ-term and the minimal left-right symmetric model.

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Section: Jhep03(2015)104mentioning

confidence: 99%

Nuclear electric dipole moments in chiral effective field theory

Bsaisou

Vries

Hanhart

et al. 2015

J. High Energ. Phys.

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“…Vertices in these familes involve only g A and F π , and all dependence on other LECs is concentrated in family III, which begins at O(q 3 ). These LECs can be extracted from subthreshold πN amplitudes [8] and one finds that the components V − C and V + C are very strongly dominated by families I and III, respectively. …”

Section: Nuclear Interactionsmentioning

confidence: 99%

“…and has already been expanded to O(q 4 ) [11,8]. The leading O(q 2 ) contribution comes from a tree diagram proportional to c 1 , whereas corrections at O(q 3 ) and O(q 4 ) are due to loops involving nucleon intermediate states and LECs.…”

Section: Nucleon Sigma-termmentioning

confidence: 99%

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Nuclear interactions and the space-like structure of the pion

Robilotta¹

2010

Proceedings of 6th International Workshop on Chiral Dynamics — PoS(CD09)

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Three instances are discussed in which results produced by chiral perturbation theory can be reliably pushed to high space-like values of transferred momenta. 1. nuclear interactions: At present, expansions are available for about 20 components of both two-and three-nucleon forces, and the vast majority of them follows the patterns predicted by chiral symmetry. The outstanding exception is V + C , the isospin independent central potential. Standard calculations show that this O(q 3 ) contribution is about 10 times larger than the leading O(q 2 ) isospin dependent term V − C . In spite of defying counting rules, these results are quite well supported by phenomenology up to distances smaller than 1 fm (→ |t| ∼ 20 M 2 π ). nucleon sigma-term:The configuration space nucleon scalar form factorF s (r) is an important substructure of V + C , and its integration over the entire volume yields σ N , the nucleon σ -term. Perturbative results based on diagrams involving N and ∆ intermediate states vanish at large distances, and increase monotonically as one approaches the nucleon center, where they can become arbitrarily large. Assuming that the pion cloud of the nucleon is constructed at the expenses of the surrounding condensate, an upper limit forF S (r) can be set at a critical radius R ≃ 0.6 fm (→ |t| ∼ 40 M 2 π ), where a phase transition takes place. This mechanism excludes the problematic region and yields 43 MeV< σ N < 49 MeV, in agreement with the empirical value 45±8 MeV. 3. space-like structure of the pion: The extension of the model for σ N to the pion describes it as a Goldstone boson at large distances, surrounded by a quark-antiquark condensate. As one moves towards its center, the condensate is gradually destroyed and a phase transition occurs at a distance R ≃ 0.6 fm (→ |t| ∼ 40 M 2 π ). When only pion loops are considered, the model depends on just M π and F π , and yields r 2 π S = 0.50 fm 2 andl 4 = 3.9. The inclusion of a scalar resonance of mass 980 MeV, with two known coupling constants, improves these values to r 2 π S = 0.59 fm 2 andl 4 = 4.3, well within the error bars of the precise estimates r 2 π S = 0.61 ± 0.04 fm 2 and l 4 = 4.4 ± 0.2, produced in 2001 by Colangelo, Gasser and Leutwyler. In both cases, results are given in terms of simple analytic expressions.

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“…In the works of Becher and Leutwyler [1] it was shown that the convergence of the chiral expansion of the nucleon scalar form factor, driven by the triangle diagram of Fig. 1, is a delicate issue for values of the momentum transfer t near (2m π ) 2 due to the presence of an anomalous threshold, i.e.…”

Section: Motivation: the Problem In The Heavy Baryon Formalismmentioning

confidence: 99%

Two-pion exchange NN potential from Lorentz-invariant χEFT

2007

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We outline the progress made in the past five years by the São Paulo group in the development of a two-pion exchange nucleon-nucleon potential within a Lorentz-invariant framework of (baryon) chiral perturbation theory. Motivation: the problem in the heavy baryon formalismIn the works of Becher and Leutwyler [1] it was shown that the convergence of the chiral expansion of the nucleon scalar form factor, driven by the triangle diagram of Fig. 1, is a delicate issue for values of the momentum transfer t near (2m π ) 2 due to the presence of an anomalous threshold, i.e. a branch point in the second Riemann sheet right below the two-pion threshold. Such a singularity is completely neglected in heavy baryon chiral perturbation theory (HBχPT), and can only be recovered by resumming the heavy baryon series to all orders. In order to understand this problem one can start from the spectral representation of the triangle integral, Figure 1. The triangle diagram that contributes to the nucleon scalar form factor. The solid, dashed, and wiggly lines represent, respectively, the nucleon, the pions, and an external scalar-isoscalar source.

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Baryon chiral perturbation theory in manifestly Lorentz invariant form

Cited by 543 publications

References 41 publications

Nuclear electric dipole moments in chiral effective field theory

Nuclear electric dipole moments in chiral effective field theory

Nuclear interactions and the space-like structure of the pion

Two-pion exchange NN potential from Lorentz-invariant χEFT

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