Chiral dynamics and B to 3 pi decay
I discuss our knowledge of the scalar sector of QCD and how it impacts the determination of the CKM angle αfrom the isospin analysis of B\to ρπdecay.
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arXiv subjects
Ulf-G. Meißner
Publications and source records attributed to Ulf-G. Meißner.
Analysis of the pion-kaon sigma-term and related topics
We calculate the one-loop contributions to the difference Δ_{πK} between the isoscalar on-shell pion-kaon scattering amplitude at the Cheng-Dashen point and the scalar form factor Γ_K (2M_π^2) in the framework of three flavor chiral perturbation theory. These corrections turn out to be small. This is further sharpened by treating the kaons as heavy fields (two flavor chiral perturbation theory). We also analyze the two-loop corrections to the kaon scalar form factor based on a dispersive technique. We find that these corrections are smaller than in the comparable case of the scalar form factor of the pion. This is related to the weaker final state interactions in the pion-kaon channel.
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In-medium chiral perturbation theory beyond the mean-field approximation
An explicit expression of the generating functional of two-flavor low-energy QCD with external sources in the presence of non-vanishing nucleon densities has been derived recently [1]. Within this approach we derive power counting rules for the calculation of in-medium pion properties. We develop the so-called standard rules for residual nucleon energies of the order of the pion mass and a modified scheme (non-standard counting) for vanishing residual nucleon energies. We also establish the different scales for the range of applicability of this perturbative expansion, which are \sqrt{6}πf_π\simeq 0.7 GeV for the standard and 6π^2 f_π^2/2m_N\simeq 0.27 GeV for non-standard counting, respectively. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions. In particular, we find a mass shift for negatively charged pions in heavy nuclei that agrees with recent determinations from deeply bound pionic Pb-207. We have also established the absence of in-medium renormalization in the π^0 \to γγdecay amplitude up to the same order. The study of ππscattering requires the use of the non-standard counting and the calculation is done at leading order. Even at that order we establish new contributions not considered so far. We also point towards further possible improvements of this scheme and touch upon its relation to more conventional many-body approaches.
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Rescattering and chiral dynamics in B\to ρπdecay
We examine the role of B^0(\bar B^0) \to σπ^0 \to π^+π^- π^0 decay in the Dalitz plot analysis of B^0 (\bar B^0) \to ρπ\to π^+π^-π^0 decays, employed to extract the CKM parameter α. The σπchannel is significant because it can break the relationship between the penguin contributions in B\toρ^0π^0, B\toρ^+π^-, and B\toρ^-π^+ decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The σπ^0 state is of definite CP, however; we demonstrate that the B\toρπanalysis can be generalized to include this channel without difficulty. The σor f_0(400-1200) ``meson'' is a broad I=J=0 enhancement driven by strong ππrescattering; a suitable scalar form factor is constrained by the chiral dynamics of low-energy hadron-hadron interactions - it is rather different from the relativistic Breit-Wigner form adopted in earlier B\toσπand D\toσπanalyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br(\bar B^0 \to ρ^\mp π^\pm) / Br(B^-\to ρ^0 π^-).
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Chiral dynamics with strange quarks: Mysteries and opportunities
Recent developments and open issues in chiral dynamics with strange quarks are reviewed. Topics include: Order parameters of chiral symmetry breaking, the flavor dependence of these order parameters, speculations about the phase structure of QCD with varying number of flavors, OZI violation and its natural emergence in case of a small strange quark condensate, heavy kaon chiral perturbation theory, an update on pion-pion, pion-kaon and pion-nucleon sigma terms, the dynamics and nature of scalar mesons, the role of the scalar pion and kaon form factors, attempts to describe some strange baryons employing coupled channel dynamics tied to unitarity and chiral perturbation theory, and the role of final state interactions in Goldstone boson pair production in proton-proton collisions.
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Effective Field Theories of QCD
These are the proceedings of the workshop on ``Effective Field Theories of QCD'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from November 26 to 30, 2001. The workshop concentrated on Chiral Perturbation Theory in its various settings, its relations with lattice QCD and dispersion theory and the use of effective field theories in systems with one, two or more nucleons as well as at high baryon densities. Included are a short contribution per talk and a listing of some review papers on the subject.
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Isospin violation in pion-kaon scattering
We consider strong and electromagnetic isospin violation in near-threshold pion-kaon scattering. At tree level, such effects are small for all physical channels. We work out the complete one-loop corrections to the process pi^- K^+ -> pi^0 K^0. They come out rather small. We also show that the corresponding radiative cross section is highly suppressed at threshold.
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Isospin violation in low-energy charged pion-kaon scattering
We evaluate the isospin breaking corrections to the scattering amplitude π^- K^+ -> π^- K^+ at threshold in the framework of chiral perturbation theory. This channel is of particular interest for the strong 2S-2P energy level shift in pion-kaon bound states. While a prediction of this level shift is hampered by a large uncertainty in the isoscalar scattering length, we find only a moderate uncertainty of about 3% in the electromagnetic corrections which are relevant for the extraction of the scattering lengths from experiment
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Progress in Meson-Nucleon Physics: Status and Perspectives
In this opening talk I will address some issues that exemplify the theoretical progress that has been made and is to be expected in the field of meson-nucleon physics. My emphasis will be on performing precision calculations to test aspects of QCD, including also electroweak probes. In addition, I discuss the problems and opportunities related to the strange quark sector.
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Chiral dynamics in few-nucleon systems
We report on recent progress achieved in calculating various few-nucleon low-energy observables from effective field theory. Our discussion includes scattering and bound states in the 2N, 3N and 4N systems and isospin violating effects in the 2N system. We also establish a link between the nucleon-nucleon potential derived in chiral effective field theory and various modern high-precision potentials.
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Nucleon deformation in finite nuclei
The deformation of a nucleon embedded in various finite nuclei is considered by taking into account the distortion of the chiral profile functions under the action of an external field representing the nuclear density. The baryon charge distribution of the nucleon inside light, medium-heavy and heavy nuclei is discussed. The mass of the nucleon decreases as it is placed deeper inside the nucleus and reaches its minimum at the center of the nucleus. We discuss the quantization of non-spherical solitons and its consequences for the mass splitting of the delta states. We show that bound nucleons acquire an intrinsic quadrupole moment due to the deformation effects. These effects are maximal for densities of nuclei about ρ(R)\sim 0.3...0.35 ρ(0). We also point out that scale changes of the electromagnetic radii can not simply be described by an overall swelling factor.
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Chiral dynamics and the reactions pp \to d K^+ \bar{K}^0 and pp \to d π^+ η
We perform a study of the final state interactions of the K^+ \bar{K^0} and the \bar{K^0}d systems in the reactions pp \to d K^+ \bar{K^0} and pp \to d π^+ η. Since the two-meson system couples strongly to the a_0(980) resonance, these reactions are expected to be an additional source of information about the controversial scalar sector. We also show that these reactions present peculiar features which can shed additional light on the much debated meson-baryon scalar sector with strangeness -1. We deduce the general structure of the amplitudes close to the d K^+\bar{K}^0 threshold, allowing for primary K^+ \bar{K^0} as well as π^+ηproduction with the two mesons in relative S- or P-wave. The interactions of the mesons are accounted for by using chiral unitary techniques, which generate dynamically the a_0(980) resonance, and the \bar{K^0}d interaction is also taken into account. General formulae are derived that allow to incorporate the final state interactions in these systems for any model of the production mechanism. We illustrate this approach by considering two specific production mechanisms based on three flavor meson-baryon chiral perturbation theory. It is demonstrated that in this scenario the \bar{K^0}d interactions are very important and can change the cross section by as much as one order of magnitude. The amount of π^+ηversus K^+ \bar{K^0} production is shown to depend critically on the primary mixture of the two mechanisms, with large interference effects due to final state interactions. These effects are also shown to occur in the event distributions of invariant masses which are drastically modified by the final state interactions of the two-meson or the \bar{K}d system.
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Axial structure of the nucleon
We review the current status of experimental and theoretical understanding of the axial nucleon structure at low and moderate energies. Topics considered include (quasi)elastic (anti)neutrino-nucleon scattering, charged pion electroproduction off nucleons and ordinary as well as radiative muon capture on the proton.
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Resonance saturation for four-nucleon operators
In the modern description of nuclear forces based on chiral effective field theory, four-nucleon operators with unknown coupling constants appear. These couplings can be fixed by a fit to the low partial waves of neutron-proton scattering. We show that the so determined numerical values can be understood on the basis of phenomenological one-boson-exchange models. We also extract these values from various modern high accuracy nucleon-nucleon potentials and demonstrate their consistency and remarkable agreement with the values in the chiral effective field theory approach. This paves the way for estimating the low-energy constants of operators with more nucleon fields and/or external probes.
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Aspects of near threshold neutral pion photoproduction off protons
We investigate near threshold neutral pion photoproduction off protons to fourth order in heavy baryon chiral perturbation theory in the light of the new data from MAMI. We show that the unitarity cusp at the secondary π^+ n threshold is in agreement with expectations from the final state theorem. We also analyze the fourth order corrections to the P-wave low-energy theorems and show that potentially large Delta-isobar contributions are cancelled by sizeable pion loop effects. This solidifies the parameter free third order predictions, which are in excellent agreement with the data.
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Elastic electron-deuteron scattering in chiral effective field theory
We calculate elastic electron-deuteron scattering in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct the current operators and the deuteron wave function at next-to-leading (NLO) and next-to-next-to-leading (NNLO) order simultaneously within a projection formalism. The leading order comprises the impulse approximation of photons coupling to point-like nucleons with an anomalous magnetic moment. At NLO, we include renormalizations of the single nucleon operators. To this order, no unknown parameters enter. At NNLO, one four-nucleon-photon operator appears. Its strength can be determined from the deuteron magnetic moment. We obtain not only a satisfactory description of the deuteron structure functions and form factors measured in electron-deuteron scattering but also find a good convergence for these observables.
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Virtual photons in the pion form factors and the energy-momentum tensor
We evaluate the vector and scalar form factor of the pion in the presence of virtual photons at next-to-leading order in two-flavor chiral perturbation theory. We also consider the scalar and tensor pion form factors of the energy-momentum tensor. We find that the intrinsic electromagnetic corrections are of the expected size for the vector form factor and very small for the charged pion scalar form factor. Detector resolution independent photon corrections reduce the vector radius by about one percent. The scalar radius of the neutral pion is reduced by two percent by isospin-breaking contributions. We perform infrared regularization by considering electron-positron annihilation into pions and the decay of a light Higgs boson into a pion pair. We discuss the detector resolution dependent contributions to the various form factors and pion radii.
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Watson's theorem and electromagnetism in K -> pi pi decay
We consider what constraints unitarity and CPT invariance yield on the strong and electromagnetic phases entering K -> pi pi decay. In particular, we show that the relative size of the electromagnetically-induced changes in the I=0 and I=2 phase shifts in the two--pion final state do not depend on the explicit coupling to the pi^+ pi^- gamma channel. This demonstrates that Watson's theorem can be extended to include the presence of electromagnetism. We point out the consequences for the general structure of the K -> pi pi decay amplitudes in the presence of isospin violation.
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