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Sep 19, 2013
09/13

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S. Scherer

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We discuss the most general form of the electromagnetic vertex of an off-shell pion. The framework of chiral perturbation theory is used to illustrate the representation dependence of the electromagnetic three-point Green's function. For that purpose we discuss the concept of field transformations which, in comparison with the standard Gasser and Leutwyler Lagrangian, generate equivalent Lagrangians containing additional terms at order p^4 proportional to the lowest-order equation of motion. We...

Source: http://arxiv.org/abs/nucl-th/9506028v1

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Sep 20, 2013
09/13

by
S. Scherer

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We address the issue of a consistent power counting scheme in manifestly Lorentz-invariant baryon chiral perturbation theory. We discuss the inclusion of vector mesons in the calculation of the nucleon electromagnetic form factors. We comment on the chiral expansion of the nucleon mass to order O(q**6).

Source: http://arxiv.org/abs/0802.2461v1

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Sep 18, 2013
09/13

by
S. Scherer

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This article provides a pedagogical introduction to the basic concepts of chiral perturbation theory and is designed as a text for a two-semester course on that topic. Chapter 1 serves as a general introduction to the empirical and theoretical foundations which led to the development of chiral perturbation theory. Chapter 2 deals with QCD and its global symmetries in the chiral limit; the concept of Green functions and Ward identities reflecting the underlying chiral symmetry is elaborated. In...

Source: http://arxiv.org/abs/hep-ph/0210398v1

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Sep 22, 2013
09/13

by
S. Scherer

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Two different topics relevant for DA$\Phi$NE and CEBAF, respectively, are covered. First we analyze the rare radiative eta decay mode $\eta\to\pi\pi\gamma\gamma$ within the framework of chiral perturbation theory at ${\cal O}(p^4)$. We then discuss virtual Compton scattering off the nucleon at low energies. Predictions for the two spin-independent generalized polarizabilities are shown.

Source: http://arxiv.org/abs/hep-ph/9612228v1

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Sep 21, 2013
09/13

by
S. Scherer

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We discuss the virtual Compton scattering amplitude $\gamma^\ast+\pi\to \gamma+\pi$ which enters the reaction $\pi^-+e^-\to\pi^-+e^-+\gamma$. The low-energy scattering amplitude is divided into a model-independent part, involving only the electromagnetic form factor, and a residual part which contains structure information related specifically to (virtual) Compton scattering. In the limit of vanishing final-photon energy, the residual amplitude can be expressed in terms of three generalized...

Source: http://arxiv.org/abs/hep-ph/9907416v1

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Sep 18, 2013
09/13

by
S. Scherer

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These lectures give a pedagogical introduction to real and virtual Compton scattering at low energies. We will first discuss real Compton scattering off a point particle as well as a composite system in the framework of nonrelativistic quantum mechanics. The concept of electromagnetic polarizabilities is introduced. We then address a description of the Compton-scattering tensor within quantum field theory with particular emphasis on the derivation of low-energy theorems. The importance of a...

Source: http://arxiv.org/abs/nucl-th/9901056v1

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Sep 22, 2013
09/13

by
S. Scherer

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Virtual Compton scattering off nucleons and pions at low energies is discussed. Predictions for the generalized polarizabilities of the nucleon are presented within the framework of heavy-baryon chiral perturbation theory and the linear sigma model. First results for the generalized polarizabilities of the charged pion in chiral perturbation theory at ${\cal O}(p^4)$ are shown.

Source: http://arxiv.org/abs/hep-ph/9807562v1

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Sep 17, 2013
09/13

by
J. Gegelia; S. Scherer

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By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are equivalent at the classical level, differences appear due to the quantum corrections.

Source: http://arxiv.org/abs/1003.4409v1

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Sep 19, 2013
09/13

by
J. Gegelia; S. Scherer

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In the framework of effective quantum field theory we address the definition of physical quantities characterizing unstable particles. With the aid of a one-loop calculation, we study this issue in terms of the charge and the magnetic moment of a spin-1/2 resonance. By appealing to the invariance of physical observables under field redefinitions we demonstrate that physical properties of unstable particles should be extracted from the residues at complex (double) poles of the corresponding...

Source: http://arxiv.org/abs/0910.4280v1

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Sep 19, 2013
09/13

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T. Fuchs; S. Scherer

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We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we...

Source: http://arxiv.org/abs/nucl-th/0303002v1

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Sep 22, 2013
09/13

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J. Gegelia; S. Scherer

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It is argued that Weinberg's approach to the nucleon-nucleon (NN) interaction problem within effective field theory provides a consistent power counting for renormalized diagrams. Within this scheme the NN potential is organized as an expansion in terms of small quantities like small external momenta and the pion mass (divided by the characteristic large scale of the effective theory). Physical observables to any given order in these small quantities are calculated from the solutions of the...

Source: http://arxiv.org/abs/nucl-th/0403052v1

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Sep 18, 2013
09/13

by
S. Scherer; H. W. Fearing

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We consider a simple model and make use of field transformations in Lagrangian field theories to illustrate the impossibility of measuring off-shell effects in nucleon-nucleon bremsstrahlung and related processes.

Source: http://arxiv.org/abs/nucl-th/0006076v1

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Sep 24, 2013
09/13

by
S. Scherer; H. W. Fearing

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We consider Compton scattering by a pion in the framework of chiral perturbation theory. We investigate off--shell effects in the s-- and u--channel pole diagrams. For that purpose we perform a field transformation which, in comparison with the standard Gasser and Leutwyler Lagrangian, generates additional terms at order $p^4$ proportional to the lowest--order equation of motion. As a result of the equivalence theorem the two Lagrangians predict the same Compton scattering S--matrix even though...

Source: http://arxiv.org/abs/hep-ph/9408312v1

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Sep 23, 2013
09/13

by
H. W. Fearing; S. Scherer

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In the context of simple models illustrating field transformations in Lagrangian field theories we discuss the impossibility of measuring off-shell effects in nucleon-nucleon bremsstrahlung, Compton scattering, and related processes. To that end we introduce a simple phenomenological Lagrangian describing nucleon-nucleon bremsstrahlung and perform an appropriate change of variables leading to different off-shell behavior in the nucleon-nucleon amplitude as well as the photon-nucleon vertex. As...

Source: http://arxiv.org/abs/nucl-th/9909076v1

14 pages ; 23 x 10 cm

Topics: Nursery stock Prices New York (State) Northport, Water lilies Prices, Aquatic plants Prices, Bog...

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Sep 20, 2013
09/13

by
M. R. Schindler; S. Scherer

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The theoretical and experimental status of the isovector axial-vector current form factors G_A(q^2) and G_P(q^2) of the nucleon is reviewed. We also describe a new calculation of these form factors in manifestly Lorentz-invariant chiral perturbation theory (ChPT) with the inclusion of axial-vector mesons as explicit degrees of freedom.

Source: http://arxiv.org/abs/hep-ph/0608325v1

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Sep 24, 2013
09/13

by
S. Scherer; H. W. Fearing

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The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory. The use of the 'classical equation of motion' is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number...

Source: http://arxiv.org/abs/hep-ph/9408298v1

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Sep 24, 2013
09/13

by
H. W. Fearing; S. Scherer

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We have derived the most general chirally invariant Lagrangian ${\cal L}_6$ for the meson sector at order $p^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\cal L}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion'...

Source: http://arxiv.org/abs/hep-ph/9408346v1

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Sep 23, 2013
09/13

by
H. W. Fearing; S. Scherer

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We discuss the low-energy behavior of the virtual Compton scattering amplitude off a spin-zero target. We first compare various methods of obtaining a low-energy expression based either on the soft-photon approximation or the use of Ward-Takahashi identities. We point out that structure-dependent terms are defined with respect to a low-energy approximation of the pole terms which commonly is separated from the full amplitude. We derive a general expression for the structure-dependent terms in...

Source: http://arxiv.org/abs/nucl-th/9607056v1

14 pages ; 23 x 11 cm

Topics: Nursery stock Prices New York (State) Northport, Water lilies Prices, Aquatic plants Prices, Bog...

1 folded sheet (4 unnumbered pages) : 11 x 23 cm folded, 31 x 46 cm unfolded

Topics: Nursery stock Prices New York (State) Northport, Water lilies Prices, Aquatic plants Prices, Bog...

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Jun 30, 2018
06/18

by
Y. Unal; A. Kucukarslan; S. Scherer

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We describe a constraint analysis for the interaction of the vector-meson octet with the baryon octet. Applying Dirac's Hamiltonian method, we verify that the standard interaction in terms of two independent SU(3) structures is consistent at the classical level. We argue how the requirement of self consistency with respect to perturbative renormalizability may lead to relations among the renormalized coupling constants of the system.

Topics: High Energy Physics - Phenomenology, Nuclear Theory

Source: http://arxiv.org/abs/1409.5014

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Sep 21, 2013
09/13

by
N. Wies; J. Gegelia; S. Scherer

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We analyze the constraint structure of a spin-3/2 particle interacting with a pseudoscalar. Requiring the self consistency of the considered effective field theory imposes restrictions on the possible interaction terms. In the present case we derive two constraints among the three lowest-order $\pi\Delta$ interaction terms. From these constraints we find that the total Lagrangian is invariant under the so-called point transformation. On the other hand, demanding the invariance under the point...

Source: http://arxiv.org/abs/hep-ph/0602073v1

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Jun 29, 2018
06/18

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P. Bickert; P. Masjuan; S. Scherer

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We present a calculation of the $\eta$-$\eta'$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $\eta$-$\eta'$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $\eta$-$\eta'$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and...

Topics: High Energy Physics - Phenomenology, High Energy Physics - Lattice, Nuclear Theory

Source: http://arxiv.org/abs/1612.05473

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Sep 22, 2013
09/13

by
S. Haussler; S. Scherer; M. Bleicher

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Within a dynamical quark recombination model we explore various proposed event-by-event observables sensitive to the microscopic structure of the QCD-matter created at RHIC energies. Charge fluctuations, charge transfer fluctuations and baryon-strangeness correlations are computed from a sample of central Au+Au events at the highest RHIC energy available ($\sqrt{s_{NN}}$=200 GeV). We find that for all explored observables, the calculations yield the values predicted for a quark-gluon plasma...

Source: http://arxiv.org/abs/hep-ph/0702188v1

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Sep 22, 2013
09/13

by
B. Pasquini; D. Drechsel; S. Scherer

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Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into...

Source: http://arxiv.org/abs/0805.0213v1

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Sep 22, 2013
09/13

by
B. Pasquini; D. Drechsel; S. Scherer

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We reply to the Comment by Fil'kov and Kashevarov, arXiv:0805.4486 [hep-ph]. We show that the discrepancies between ChPT and dispersion theory, reported for the polarizability of the pion, result from applying dispersion theory to non-analytic functions.

Source: http://arxiv.org/abs/0908.4291v1

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Sep 18, 2013
09/13

by
G. Knoechlein; S. Scherer; D. Drechsel

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We investigate the rare radiative eta decay modes eta -> pi+ pi- gamma gamma and eta -> pi0 pi0 gamma gamma within the framework of chiral lagrangians at o(p^4) and present photon spectra for both processes.

Source: http://arxiv.org/abs/hep-ph/9510374v1

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Jun 28, 2018
06/18

by
Y. Unal; A. Kucukarslan; S. Scherer

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We analyze the constraint structure of the interaction of vector mesons with baryons using the classical Dirac constraint analysis. We show that the standard interaction in terms of two independent SU(3) structures is consistent at the classical level. We then require the self-consistency condition of the interacting system in terms of perturbative renormalizability to obtain relations for the renormalized coupling constants at the one-loop level. As a result we find a universal interaction...

Topics: Nuclear Theory, High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1510.02205

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Sep 22, 2013
09/13

by
B. Pasquini; D. Drechsel; S. Scherer

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Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected to non-analytic structures

Source: http://arxiv.org/abs/0908.4260v1

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Sep 23, 2013
09/13

by
D. Djukanovic; J. Gegelia; S. Scherer

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The pole mass and the width of the Roper resonance are calculated as functions of the pion mass in the framework of low-energy effective field theory of the strong interactions. We implement a systematic power-counting procedure by applying the complex-mass renormalization scheme.

Source: http://arxiv.org/abs/0903.0736v1

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Sep 18, 2013
09/13

by
B. Pasquini; S. Scherer; D. Drechsel

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We study low-energy virtual Compton scattering off the proton within the framework of a nonrelativistic constituent quark model. The Compton tensor is divided into two separately gauge-invariant contributions. The first consists of the groundstate propagation in the direct and crossed channels together with an appropriately chosen term to satisfy gauge invariance. The residual part contains the relevant structure information characterized by the so-called generalized polarizabilities. We...

Source: http://arxiv.org/abs/nucl-th/0008046v1

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Jul 20, 2013
07/13

by
D. Djukanovic; J. Gegelia; S. Scherer

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Using the examples of pion-nucleon scattering and the nucleon mass we analyze the convergence of perturbative series in the framework of baryon chiral perturbation theory. For both cases we sum up sets of an infinite number of diagrams by solving equations exactly and compare the solutions with the perturbative contributions.

Source: http://arxiv.org/abs/hep-ph/0604164v2

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Sep 22, 2013
09/13

by
D. Djukanovic; J. Gegelia; S. Scherer

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A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang-Mills theory with an additional mass term.

Source: http://arxiv.org/abs/1001.1077v1

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Jun 30, 2018
06/18

by
T. Bauer; S. Scherer; L. Tiator

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We analyze the form factors of the electromagnetic nucleon-to-Roper-resonance transition in the framework of low-energy effective field theory. A systematic power-counting procedure is generated by applying the complex-mass scheme. Within this power counting we calculate the form factors to next-to-next-to-leading order and fit the results to empirical data.

Topics: High Energy Physics - Phenomenology, Nuclear Experiment, Nuclear Theory

Source: http://arxiv.org/abs/1402.0741

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Sep 18, 2013
09/13

by
B. Pasquini; S. Scherer; D. Drechsel

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We discuss low-energy virtual Compton scattering off the proton within the framework of a nonrelativistic constituent quark model. A simple interpretation of the spin-averaged generalized polarizabilities is given in terms of the induced electric polarization (and magnetization). Explicit predictions for the generalized polarizabilities obtained from a multipole expansion are presented for the Isgur-Karl model and are compared with results of various models.

Source: http://arxiv.org/abs/nucl-th/0105074v1

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Sep 18, 2013
09/13

by
D. Djukanovic; J. Gegelia; S. Scherer

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In the framework of effective field theory we show that, at two-loop order, the mass and width of the \Delta resonance defined via the (relativistic) Breit-Wigner parametrization both depend on the choice of field variables. In contrast, the complex-valued position of the pole of the propagator is independent of this choice.

Source: http://arxiv.org/abs/0707.2030v1

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Sep 17, 2013
09/13

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J. H. Koch; V. Pascalutsa; S. Scherer

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The description of electromagnetic reactions at intermediate energies, such as pion electroproduction or (virtual) Compton scattering, traditionally starts from covariant tree-level Feynman diagrams (Born or pole terms). Internal hadron structure is included by means of (on-shell) form factors in the vertices while free propagators are used. To overcome problems with gauge invariance, simple prescriptions such as choosing $F_1^V (q^2) = F_{\pi} (q^2)$ in pion electroproduction or the ``minimal...

Source: http://arxiv.org/abs/nucl-th/0108044v1

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Sep 18, 2013
09/13

by
T. Bauer; J. C. Bernauer; S. Scherer

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We calculate the electromagnetic form factors of the nucleon to third chiral order in manifestly Lorentz-invariant effective field theory. The rho and omega mesons as well as the Delta(1232) resonance are included as explicit dynamical degrees of freedom. To obtain a self-consistent theory with respect to constraints we consider the proper relations among the couplings of the effective Lagrangian. For the purpose of generating a systematic power counting, the extended on-mass-shell...

Source: http://arxiv.org/abs/1209.3872v1

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Sep 18, 2013
09/13

by
G. Kn"ochlein; S. Scherer; D. Drechsel

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We investigate the rare radiative eta decay modes $\eta\to\pi^+\pi^-\gamma\gamma$ and $\eta\to\pi^0\pi^0\gamma\gamma$ within the framework of chiral perturbation theory at $O(p^4)$. We present photon spectra and partial decay rates for both processes as well as a Dalitz contour plot for the charged decay.

Source: http://arxiv.org/abs/hep-ph/9601252v1

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Sep 24, 2013
09/13

by
B. C. Lehnhart; J. Gegelia; S. Scherer

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We discuss the masses of the ground state baryon octet and the nucleon sigma terms in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. In order to obtain a consistent power counting for renormalized diagrams the extended on-mass-shell renormalization scheme is applied.

Source: http://arxiv.org/abs/hep-ph/0412092v1

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Sep 22, 2013
09/13

by
M. R. Schindler; J. Gegelia; S. Scherer

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We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied straightforwardly to multi-loop diagrams with an arbitrary number of particles with arbitrary masses.

Source: http://arxiv.org/abs/hep-ph/0309005v1

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Sep 22, 2013
09/13

by
M. R. Schindler; J. Gegelia; S. Scherer

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Using a toy model Lagrangian we demonstrate the application of both infrared and extended on-mass-shell renormalization schemes to multiloop diagrams by considering as an example a two-loop self-energy diagram. We show that in both cases the renormalized diagrams satisfy a straightforward power counting.

Source: http://arxiv.org/abs/hep-ph/0310207v1

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Sep 18, 2013
09/13

by
T. Ebertshäuser; H. W. Fearing; S. Scherer

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We present a revised and extended construction of the mesonic Lagrangian density in chiral perturbation theory (ChPT) at order $p^6$ in the anomalous (or epsilon) sector, ${\cal{L}}_{6,\epsilon}$. After improving several aspects of the strategy we used originally, i.e., a more efficient application of partial integration, the implementation of so-called Bianchi identities, and additional trace relations, we find the new monomial sets to include 24 $SU(N_f)$, 23 SU(3), and 5 SU(2) elements....

Source: http://arxiv.org/abs/hep-ph/0110261v1

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Sep 22, 2013
09/13

by
D. Djukanovic; J. Gegelia; A. Keller; S. Scherer

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We consider an effective field theory of unstable particles (resonances) using the complex-mass renormalization. As an application we calculate the masses and the widths of the $\rho$ meson and the Roper resonance.

Source: http://arxiv.org/abs/1001.1772v1

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Sep 19, 2013
09/13

by
T. Fuchs; J. Gegelia; G. Japaridze; S. Scherer

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We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized diagrams beyond the standard $\bar{\rm MS}$ scheme of chiral perturbation theory to remove contributions violating the power counting. This is achieved by a suitable renormalization of the parameters of the most general effective Lagrangian. In addition to...

Source: http://arxiv.org/abs/hep-ph/0302117v2

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Sep 22, 2013
09/13

by
C. Hacker; N. Wies; J. Gegelia; S. Scherer

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The magnetic dipole moment of the $\Delta (1232)$ is calculated in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop...

Source: http://arxiv.org/abs/hep-ph/0603267v1

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Sep 18, 2013
09/13

by
T. Bauer; J. Gegelia; G. Japaridze; S. Scherer

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We derive cutting rules for loop integrals containing propagators with complex masses. Using a field-theoretical model of a heavy vector boson interacting with a light fermion, we demonstrate that the complex-mass scheme respects unitarity order by order in a perturbative expansion provided that the renormalized coupling constant remains real.

Source: http://arxiv.org/abs/1211.1684v1

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Sep 22, 2013
09/13

by
H. W. Fearing; G. I. Poulis; S. Scherer

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Two different methods of obtaining ``effective $2\times 2$ Hamiltonians'' which include relativistic corrections to nonrelativistic calculations are discussed, the standard Foldy--Wouthuysen transformation and what we call the ``direct Pauli reduction''. We wish to investigate under which circumstances the two approaches yield the same result. Using a generic interaction with harmonic time dependence we show that differences in the corresponding effective S--matrices do arise beyond...

Source: http://arxiv.org/abs/nucl-th/9302014v1

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Sep 23, 2013
09/13

by
D. Drechsel; G. Knoechlein; A. Metz; S. Scherer

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We discuss the low-energy behavior of the spin-averaged amplitude of virtual Compton scattering (VCS) off a nucleon. Based on gauge invariance, Lorentz invariance and the discrete symmetries, it is shown that to first order in the frequency of the final real photon only two generalized polarizabilities appear. Different low-energy expansion schemes are discussed and put into perspective.

Source: http://arxiv.org/abs/nucl-th/9608061v1