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M. Knecht

Publications and source records attributed to M. Knecht.

At least 37 records · Page 2Linked to original sources
arXiv2001

Electromagnetic corrections to gamma pi(+) -> pi(0) pi(+)

The amplitude for the anomalous transitions gamma pi(+) -> pi(0) pi(+) is analyzed within Chiral Perturbation Theory including electromagnetic interactions. The presence of a t-channel one-photon exchange contribution induces sizeable e^2 corrections which enhance the cross-section in the threshold region and bring the theoretical prediction into agreement with available data. In the case of the crossed reaction gamma pi(0) -> pi(+) pi(-), the same contribution appears in the s-channel and its effects are small.

hep-ph↗
arXiv2000

Contributions of order ${\cal O}(m_{\rm quark}^2)$ to $K_{\ell 3}$ form factors and unitarity of the CKM matrix

The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_π$, $K_{\ell 3}$ decay rates and the scalar form factor slope $λ_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $β$-decays.

hep-ph↗
arXiv1999

A New Approach to Weak Amplitudes in Large-Nc QCD

We report on some recent progress made in understanding weak matrix elements of mesons in the context of the next-to-leading order of the large-Nc approximation to QCD. Specifically, we first use the example of the weak contributions to the pi^+ - pi^0 mass difference to exhibit how a systematic matching can be achieved analytically between short distances and long distances within our large-Nc framework. We are then also able to compute matrix elements of the operator Q_7, as they turn out to depend on the same QCD correlator as the previous pion mass difference. As a final example we determine the chiral counterterms governing the pseudoscalar decay into a lepton pair, where we briefly comment also on the special case K_L -> mu^+ mu^-.

hep-ph↗
arXiv1999

Chiral Perturbation Theory with Virtual Photons and Leptons

We construct a low-energy effective field theory which allows the full treatment of isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays pi -> l nu_{l} and K -> l nu_{l}.

hep-ph↗
arXiv1999

Decay of pseudoscalars into lepton pairs and large-Nc QCD

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colours Nc. When further restricted to the lowest meson dominance approximation to large-Nc QCD, our results agree well with the available experimental data.

hep-ph↗
arXiv1999

Low-energy photon-photon fusion into three pions in Generalized Chiral Perturbation Theory

The processes $γγ\toπ^0π^0π^0$ and $γγ\to π^+ π^- π^0$ are considered in Generalized Chiral Perturbation theory, in view of their potential sensitivity to the mechanism of spontaneous breaking of chiral symmetry and to various counterterms. The amplitudes are computed up to order ${\cal O}(p^6)$. The event production rates are estimated for the Daphne $ϕ$-Factory and for a future $τ$-Charm Factory.

hep-ph↗
arXiv1999

Matrix Elements of Electroweak Penguin Operators in the 1/Nc Expansion

It is shown that the K -> pi pi matrix elements of the four-quark operator Q_7, generated by the electroweak penguin-like diagrams of the Standard Model, can be calculated to first non-trivial order in the chiral expansion and in the 1/Nc expansion. Although the resulting B factors B_7^(1/2) and B_7^(3/2) are found to depend only logarithmically on the matching scale, mu, their actual numerical values turn out to be rather sensitive to the precise choice of mu in the GeV region. We compare our results to recent numerical evaluations from lattice-QCD and to other model estimates.

hep-ph↗
arXiv1998

The electroweak pi^+ - pi^0 mass difference and weak matrix elements in the 1/Nc expansion

The pi^+ - pi^0 mass difference generated by the electroweak interactions of the Standard Model is expressed, to lowest order in the chiral expansion and to leading order in alpha, in terms of an integral involving the same correlation function Pi_{LR}(Q^2) which governs the well known electromagnetic pi^+ - pi^0 mass difference. We calculate this contribution within the framework of QCD in the limit of a large number of colours $N_c$. We show how this calculation, which requires non-trivial contributions from next-to-leading terms in the 1/Nc expansion, provides an excellent theoretical laboratory for studying issues of long- and short-distance matching in calculations of weak matrix elements of four-quark operators. The electroweak pi^+ - pi^0 mass difference turns out to be a physical observable which is under good analytical control and which should, therefore, be an excellent testground of numerical evaluations in lattice-QCD and of model calculations in general.

hep-ph↗
arXiv1997

Patterns of Spontaneous Chiral Symmetry Breaking in the Large-Nc Limit of QCD-Like Theories

It is shown that in vector-like gauge theories, such as QCD, and in the limit of a large number of colours Nc, the ordering pattern of narrow vector and axial-vector states at low energies is correlated with the size of the possible local order parameters of chiral symmetry breaking. This has implications on the underlying dynamics of spontaneous chiral symmetry breaking in QCD, and also on possible values of the parameter S for oblique electroweak corrections, the analogue of the QCD low energy constant L10.

hep-ph↗
arXiv1997

Working group on $ππ$ and $π$N interactions - Summary

This is the summary of the working group on $ππ$ and $π$N interactions of the Chiral Dynamics Workshop in Mainz, September 1-5, 1997. Each talk is represented by an extended one page abstract. Some additional remarks by the convenors are added

hep-ph↗
arXiv1997

Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering

Four of the six parameters defining the two-loop ππscattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard χPT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r, l_2^r$. The result $l_2^r ( M_ρ ) = ( 1.6 \pm 0.4 \pm 0.9 ) \times 10^{-3} ( {\bar l_2} = 4.17 \pm 0.19 \pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard χPT analyses of $K_{l4}$ form factors beyond one loop.

hep-ph↗
arXiv1996

Determination of Two-Loop $ππ$ Scattering Amplitude Parameters

The chiral expansion of the $ππ$ amplitude to the order of two loops was expressed in terms of six independent parameters in a previous paper: four of these are shown here to satisfy sum rules. Their derivation, where crossing symmetry plays a key role, is explained. Their convergence properties are studied and their practical evaluation, in terms of the available data on $ππ$ phase shifts above 0.5 GeV, is discussed. Below 0.5 GeV, the chiral amplitude itself is employed, such that the parameters are determined in a self-consistent way. Some care is devoted to the estimate of the errors.

hep-ph↗
arXiv1995

The Low Energy $π\,π$ Amplitude to One and Two Loops

The low-energy $ππ$ amplitude is computed explicitly to two-loop accuracy in the chiral expansion. It depends only on six independent (combinations of) low-energy constants which are not fixed by chiral symmetry. Four of these constants are determined {\it via} sum rules which are evaluated using $ππ$ scattering data at higher energies. Dependence of the low-energy phase shifts and of the threshold parameters on the remaining two constants (called $α$ and $β$) are discussed and compared to the existing data from $K_{l4}$ experiments. Using generalised $χ$PT, the constants $α$ and $β$ are related to fundamental QCD parameters such as the quark condensate $\langle 0|\bar{q}q|0\rangle$ and the quark mass ratio $m_s/\widehat{m}$. It is shown that forthcoming accurate low-energy $ππ$ data can be used to provide, for the first time, experimental evidence in favour of or against the existence of a large quark-antiquark condensate in the QCD vacuum.

hep-ph↗
arXiv1995

Painlevé analysis and integrability properties of a $2+1$ nonrelativistic field theory.

A model for planar phenomena introduced by Jackiw and Pi and described by a Lagrangian including a Chern-Simons term is considered. The associated equations of motion, among which a 2+1 gauged nonlinear Schrödinger equation, are rewritten into a gauge independent form involving the modulus of the matter field. Application of a Painlevé analysis, as adapted to partial differential equations by Weiss, Tabor and Carnevale, shows up resonance values that are all integer. However, compatibility conditions need be considered which cannot be satisfied consistently in general. Such a result suggests that the examined equations are not integrable, but provides tools for the investigation of the integrability of different reductions. This in particular puts forward the familiar integrable Liouville and 1+1 nonlinear Schrödinger equations.

hep-th↗
arXiv1994

Generalized Chiral Perturbation Theory

The Generalized Chiral Perturbation Theory enlarges the framework of the standard $χ$PT, relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard $χ$PT become possible. Emphasis is put on physical aspects rather than on formal developements of G$χ$PT.

hep-ph↗
arXiv1994

The Reaction $γγ\toπ^0π^0$ in Generalized Chiral Perturbation Theory

The cross section for $γγ\toπ^0π^0$ and the pion polarizabilities are computed, within generalized chiral perturbation theory, in the full one loop approximation, {\it i.e.} up to and including order $O({p^5})$. The result depends on the parameter $α_{ππ}$ defining the tree level $π- π$ scattering amplitude and on an additional low energy constant. The latter is shown to be related by an exact sum-rule to the $e^+ e^-$ data. The parameter $α_{ππ}$ is related to the quark mass ratio $r = m_s /{\hat m}$ via the expansion of pseudoscalar meson masses. The generalized one loop $γγ\toπ^0π^0$ amplitude agrees with the experimental data in the threshold region provided $r= {m_s}/{\hat m}\lapprox 10$. Higher order corrections are estimated comparing our calculation with the dispersive approach.

hep-ph↗