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M. Faber

Publications and source records attributed to M. Faber.

At least 37 records · Page 2Linked to original sources
arXiv2005

On the renormalization of the sine-Gordon model

We analyse the renormalizability of the sine-Gordon model by the example of the two-point Green function up to second order in alpha_r(M), the dimensional coupling constant defined at the normalization scale M, and to all orders in beta^2, the dimensionless coupling constant. We show that all divergences can be removed by the renormalization of the dimensional coupling constant using the renormalization constant Z_1, calculated in (J.Phys.A36,7839(2003)) within the path-integral approach. We show that after renormalization of the two-point Green function to first order in alpha_r(M) and to all orders in beta^2 all higher order corrections in alpha_r(M) and arbitrary orders in beta^2 can be expressed in terms of alpha_ph, the physical dimensional coupling constant independent on the normalization scale M. We solve the Callan-Symanzik equation for the two-point Green function. We analyse the renormalizability of Gaussian fluctuations around a soliton solution.We show that Gaussian fluctuations around a soliton solution are renormalized like quantum fluctuations around the trivial vacuum to first orders in alpha_r(M) and beta^2 and do not introduce any singularity to the sine-Gordon model at beta^2 = 8pi.

hep-th↗
arXiv2005

Recent Theoretical Studies on Hadronic Atoms

A report contains a review of recent theoretical investigations on kaonic atoms carried out at Stefan Meyer Institute of the Austrian Academy of Sciences. We discuss (1) a phenomenological quantum field theoretic model for bar-K N interactions at threshold of the reactions K^-p -> K^-p, K^-n -> K^-n and K^-d ->K^-d, and (2) the energy level displacements of the ground and nP excited states of kaonic hydrogen, (3) the contribution of the sigma-term to the shift of the energy level of the ground state of kaonic hydrogen, (4) the isospin-breaking and dispersive corrections to the energy level displacement of the ground state of kaonic hydrogen, (5) the radiative transitions nP -> 1S + γ, induced by strong low-energy interactions and enhanced by the Coulomb interaction, in kaonic hydrogen and kaonic deuterium, (6) Perspectives and (7) Comments on the approach, where we adduce our recent results obtained after the Workshop EXA05.

nucl-th↗
arXiv2005

Energy level displacement of excited np states of kaonic hydrogen

We compute the energy level displacement of the excited np states of kaonic hydrogen within the quantum field theoretic and relativistic covariant model of strong low-energy bar-KN interactions suggested in EPJA21, 11 (2004). For the width of the energy level of the excited 2p state of kaonic hydrogen, caused by strong low-energy interactions, we find Gamma_2p = 2 meV. This result is important for the theoretical analysis of the X-ray yields in kaonic hydrogen.

nucl-th↗
arXiv2005

On isospin-breaking corrections to the energy level displacement of the ground state of kaonic hydrogen

In the model of low-energy bar-K N interactions near threshold (EPJA 21, 11 (2004); 25, 79 (2005)) we calculate isospin-breaking corrections to the energy level displacement of the ground state of kaonic hydrogen, investigated by Meissner, Raha and Rusetsky (EPJC 35, 349 (2004)) within the non-relativistic effective Lagrangian approach based on ChPT by Gasser and Leutwyler. Our results agree well with those by Meißner et al.. In addition we calculate the dispersive corrections, caused by the transition K^-p -> bar-K^0n ->K^-p with the bar-K^0n pair on-mass shell. We show also how hypothesis on the dominant role of the bar-K^0n-cusp for the S-wave amplitude of low-energy K^-p scattering near threshold, used by Meissner et al., can be realized in our approach. The result agrees fully with that by Meissner et al..

nucl-th↗
arXiv2004

Are there Local Minima in the Magnetic Monopole Potential in Compact QED?

We investigate the influence of the granularity of the lattice on the potential between monopoles. Using the flux definition of monopoles we introduce their centers of mass and are able to realize continuous shifts of the monopole positions. We find periodic deviations from the $1/r$-behavior of the monopole-antimonopole potential leading to local extrema. We suppose that these meta-stabilities may influence the order of the phase transition in compact QED.

hep-lat↗
arXiv2004

Quantum field theoretic model of metastable resonant spin-singlet state of the np pair

The np pair in the spin-singlet state is treated as a Cooper np-pair within the extension of the Nambu-Jona-Lasinio model of light nuclei, describing the deuteron as a Cooper np-pair in the spin-triplet state. For the Cooper np-pair in the spin-singlet state we compute the binding energy and express the S-wave scattering length of np scattering in the spin-singlet state in terms of the binding energy. The theoretical value of the S-wave scattering length of np scattering agrees well with the experimental data.

nucl-th↗
arXiv2004

From Solar Proton Burning to Pionic Deuterium through the Nambu-Jona-Lasinio model of light nuclei

Within the Nambu-Jona-Lasinio model of light nuclei (the NNJL model), describing strong low-energy nuclear interactions, we compute the width of the energy level of the ground state of pionic deuterium. The theoretical value fits well the experimental data. Using the cross sections for the reactions nu_e + d -> p + p + e^- and nu_e + d -> p + n + nu_e, computed in the NNJL model, and the experimental values of the events of these reactions, detected by the SNO Collaboration, we compute the boron neutrino fluxes. The theoretical values agree well with the experimental data and the theoretical predictions within the Standard Solar Model by Bahcall. We argue the applicability of the constraints on the astrophysical factor for the solar proton burning, imposed by helioseismology, to the width of the energy level of the ground state of pionic deuterium. We show that the experimental data on the width satisfy these constraints. This testifies an indirect measurement of the recommended value of the astrophysical factor for the solar proton burning in terrestrial laboratories in terms of the width of the energy level of the ground state of pionic deuterium.

nucl-th↗
arXiv2004

Exotic Baryons from the Chiral Quark Soliton Model

From the interpretation of the $Θ^+(1540)$ and $Ξ_{3/2}(1862)$ baryons as an excitation of the ``skyrmion liquid'' with SU(3) flavour symmetry $\bar{10}$ we deduce a new series of baryons, $Θ_1^{++}$, $Θ_1^{+}$ and $Θ_1^0$, situated at the top of the 27-plet of SU(3) flavour, with hypercharge Y=2, isospin I=1 and spin $J=\frac32$. The $Θ_1$ mass and width are estimated from the chiral quark soliton model. We demonstrate that the predicted mass, $m_{Θ_1}=1599 \mathrm{MeV/c^2}$, and broad width are in qualitative conflict with experiment which shows no structure in the total $K^+p$ cross section near $P_\mathrm{lab}=585$ MeV/c. We also discuss properties of other exotic baryons from the 27- and 35-plets.

hep-ph↗
arXiv2003

On the vacua in the massless Thirring model

We calculate the most general effective potential for the massless Thirring model in dependence of the local fields of all fermion-antifermion collective excitations. We analyse the minima of this potential describing different vacua of the quantum system. We confirm the existence of the absolute minimum found in EPJC 20, 723 (2001) corresponding to the chirally broken phase of the massless Thirring model. As has been shown in EPJC 20, 723 (2001) this minimum is stable under quantum fluctuations.

hep-th↗
arXiv2003

On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach

We study kaonic hydrogen, the bound K^-p state A_(Kp). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K^-p scattering for arbitrary relative momenta. The amplitude of low-energy K^-p scattering near threshold is defined by the contributions of three resonances Lambda(1405), Lambda(1800) and Sigma^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K^-p scattering fit experimental data on near threshold behaviour of the cross sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculation of the partial width of the radiative decay of pionic hydrogen A_(pi p) -> n + gamma and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to the calculation of the partial widths of radiative decays of kaonic hydrogen A_(Kp) -> Lambda^0 + gamma and A_(Kp) -> Sigma^0 + gamma. We show that the contribution of these decays to the width of the energy level of the ground state of kaonic hydrogen is less than 1%.

nucl-th↗
arXiv2003

Energy level displacement of the excited nl state of pionic hydrogen

The energy level displacements of the excited nl states of pionic hydrogen and the contribution of the ns -> 1s transitions and the (pi^-p)_Coul -> 1s transitions of the pi^-p pair, coupled by the attractive Coulomb field in the S-wave state with a continuous energy spectrum, to the shift of the energy level of the ground state of pionic hydrogen, caused by strong low-energy interactions, are calculated within a quantum field theoretic, relativistic covariant and model-independent approach developed in nucl-th/0306047.

nucl-th↗
arXiv2003

On pionic hydrogen. Quantum field theoretic, relativistic covariant and model-independent approach

We consider pionic hydrogen A_(pi p), the bound pi^- p state. Within the quantum field theoretic and relativistic covariant approach we calculate the shift and width of the energy level of the ground state of pionic hydrogen caused by strong low-energy interactions treated perturbatively. The generalization of the Deser-Goldberger-Baumann-Thirring (DGBT) formulas (Phys. Rev. 96, 774 (1954)) is given. The generalized DGBT formulas for the energy level displacement of the ground state of pionic hydrogen contain the non-perturbative and model-independent correction about 1%, caused by the relativistic covariant smearing of the wave function of the ground state around origin. This non-perturbative correction is very important for the precise extraction of the S-wave scattering lengths of pion-nucleon scattering from the experimental data on the energy level displacements in pionic hydrogen by the PSI Collaboration. In addition the shift of the energy level of the ground state of pionic hydrogen is improved by the second order correction of strong low-energy interactions which is about 0.1%. This testifies the applicability of the perturbative treatment of strong low-energy interactions to the analysis of pionic hydrogen. We show that the width of the energy level of the ground state of pionic hydrogen is valid to all order of perturbation theory in strong low-energy interactions.

nucl-th↗
arXiv2003

On spontaneous breaking of continuous symmetry in 1+1-dimensional space-time

We analyse Coleman's theorem asserting the absence Goldstone bosons and spontaneously broken continuous symmetry in the quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-time (Comm. Math. Phys. 31, 259 (1973)). We confirm that Coleman's theorem reproduces well-known Wightman's statement about the non-existence of a quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-time in terms of Wightman's observables defined on the test functions from S(R^2). Referring to our results (Eur. Phys. J. C 24, 653 (2002)) we argue that a formulation of a quantum field theory of a free massless (pseudo)scalar field in terms of Wightman's observables defined on the test functions from S_0(R^2) is motivated well by the possibility to remove a collective zero-mode motion of the ``center of mass'' of a free massless (pseudo)scalar field (Eur. Phys. J. C 24, 653 (2002)) responsible for infrared divergences of the Wightman functions. We show that in the quantum field theory of a free massless (pseudo)scalar field with Wightman's observables defined on the test functions from S_0(R^2) a continuous symmetry is spontaneously broken. Coleman's theorem reformulated for the test functions from S_0(R^2) does not refute this result. We construct a most general version of a quantum field theory of a self-coupled massless (pseudo)scalar field with a conserved current. We show that this theory satisfies Wightman's axioms and Wightman's positive definiteness condition with Wightman's observables defined on the test functions from S(R^2) and possesses spontaneously broken continuous symmetry. Nevertheless, in this theory the generating functional of Green functions exists only when the collective zero-mode is not excited by the external source.

hep-th↗
arXiv2003

On the ground state of a free massless (pseudo)scalar field in two dimensions

We investigate the ground state of a free massless (pseudo)scalar field in 1+1-dimensional space-time. We argue that in the quantum field theory of a free massless (pseudo)scalar field without infrared divergences (Eur. Phys. J. C24, 653 (2002)) the ground state can be represented by a tensor product of wave functions of the fiducial vacuum and of the collective zero-mode, describing the motion of the ``center of mass'' of a free massless (pseudo)scalar field. We show that the bosonized version of the BCS wave function of the ground state of the massless Thirring model obtained in (Phys.Lett. B563, 231 (2003)) describes the ground state of the free massless (pseudo)scalar field.

hep-th↗
arXiv2003

Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.

hep-th↗
arXiv2003

Dynamical breaking of conformal symmetry in the massless Thirring model

We discuss conformal invariance of the massless Thirring model. We show that conformal symmetry of the massless Thirring model is dynamically broken due to the constant of motion caused by the equations of motion. This confirms the existence of the chirally broken phase in the massless Thirring model (Eur. Phys. J. C20, 723 (2001), which is accompanied by the appearance of massless (pseudo)scalar Goldstone bosons (Eur. Phys. J. C24, 653 (2002), hep-th/0210104 and hep-th/0305174).

hep-th↗
arXiv2003

Goldstone bosons in the massless Thirring model. Witten's criterion

We discuss the Ward identity and the low-energy theorem for the divergence of the axial-vector current in the massless Thirring model with fermion fields quantized in the chirally broken phase (Eur. Phys. J. C20, 723 (2001)). The Ward identity and the low-energy theorem are analysed in connection with Witten's criterion for Goldstone bosons (Nucl. Phys. B145, 110 (1978)). We show that the free massless (pseudo)scalar field bosonizing the massless Thirring model in the chirally broken phase satisfies Witten's criterion to interpret quanta of this field as Goldstone bosons. As has been shown in hep-th/0210104 and hep-th/0212226, Goldstone's criterion, the non-invariance of the wave function of the ground state, is also fulfilled.

hep-th↗