Chiral perturbation theory: Introduction and recent results in the one-nucleon sector

Scherer, Stefan

doi:10.1016/j.ppnp.2009.08.002

Cited by 43 publications

(18 citation statements)

References 169 publications

(258 reference statements)

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“…Another general problem is that the LEC does not necessarily have to be of natural size anymore, as it contains a power-counting-violating part. In our specific case this is true for loop diagrams at fourth order that are renormalized in terms ofd 9 . Nevertheless, in the present case, it turns out that this part is either small or has the opposite sign and same magnitude of the numerical contribution of the renormalized coupling, because even thoughd 9 contains a power-counting-violating part it is of natural size.…”

Section: Appendix B: Renormalization Of Power-counting-violating Contmentioning

confidence: 90%

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Thresholdπ0photoproduction in relativistic chiral perturbation theory

2013

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We present a calculation of π 0 photoproduction on the proton in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including chiral order q 4 . With the results we analyze the latest π 0 photoproduction data in the threshold region obtained at the Mainz Microtron. In the calculation of observables and the fit of the low-energy constants, we take S, P , and D waves into account. We compare the results for the multipoles with the corresponding single-energy analysis. Furthermore, we also fit the O(q 4 ) heavy-baryon chiral perturbation theory calculation and compare both results. We provide predictions for several polarization observables for future experiments. Finally, we discuss the β parameter of the unitarity cusp which is related to the breaking of isospin symmetry.

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Section: Appendix B: Renormalization Of Power-counting-violating Contmentioning

confidence: 90%

“…[7,8], the discrepancy between experiment and theory was addressed with the aid of chiral perturbation theory (ChPT) which is an effective field theory of QCD at low energies based on chiral symmetry (see, e.g., Refs. [9,10] for an introduction). In particular, it was shown that E 0+ gets modified by certain nonanalytic loop contributions.…”

Section: Introductionmentioning

confidence: 99%

Thresholdπ0photoproduction in relativistic chiral perturbation theory

2013

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“…Such a success has not been fully understood. In some cases, e.g., for the scalar form factor of the nucleon at t = 4m 2 π [51], it can be attributed to the fact that EOMS is covariant and satisfies analyticity in the loop amplitudes. For other quantities such as the octet baryon masses [27], the good phenomenological description is somehow unexpected from a power-counting perspective.…”

Section: Introductionmentioning

confidence: 99%

Consistency between SU(3) and SU(2) covariant baryon chiral perturbation theory for the nucleon mass

et al. 2017

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Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the 19 low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-toleading order [1] is supported by comparing the effective parameters (the combinations of the 19 couplings) with the corresponding low-energy constants in the SU(2) sector [2]. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.[2] that the SU(2) baryon chiral perturbation theory can be applied to study n f = 2 + 1 lattice QCD simulations as long as the strange quark mass is close to its physical value.

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“…Standard chiral-EFT calculations fail to describe the proton and nucleon form factors for momentum transfers beyond Q 2 ∼ 0.1 GeV 2 [43]. The inclusion of vector mesons sensibly improve the agreement with data [22]. Within our explicit-pion QMC framework, we plan to assess whether the resummation of important higher-order contributions can mimic their inclusion.…”

Section: Discussionmentioning

confidence: 99%

“…The first term is the axial-vector pion-nucleon coupling, and the second (referred to as the Weinberg-Tomozawa term) is the contact interaction with two factors of the pion field interacting with the nucleon at a single point [22]. Finally, the nucleon Hamiltonian is given by…”

Section: A Chiral Lagrangianmentioning

confidence: 99%

Quantum Monte Carlo formalism for dynamical pions and nucleons

Madeira¹,

Lovato²,

Pederiva³

et al. 2018

Phys. Rev. C

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In most simulations of nonrelativistic nuclear systems, the wave functions found solving the manybody Schrödinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.

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Chiral perturbation theory: Introduction and recent results in the one-nucleon sector

Abstract: We provide an introduction to the basic concepts of chiral perturbation theory and discuss some recent developments in the manifestly Lorentz-invariant formulation of the one-nucleon sector.

Cited by 43 publications

References 169 publications

Thresholdπ0photoproduction in relativistic chiral perturbation theory

Thresholdπ0photoproduction in relativistic chiral perturbation theory

Consistency between SU(3) and SU(2) covariant baryon chiral perturbation theory for the nucleon mass

Quantum Monte Carlo formalism for dynamical pions and nucleons

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