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J. Stern

Publications and source records attributed to J. Stern.

29 records · Page 2Linked to original sources
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↗
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

Chiral Symmetry Aspects of the Scalars

Electromagnetic decays of the scalar mesons are shown to be constrained by chiral symmetry as a consequence of the fact that, in the chiral limit, the two and three-point functions $ $ and $ $ satisfy super-convergent dispersion relations. The QCD asymptotic behavior of the latter is canonical and it can be saturated by a finite number of resonances. The corresponding chiral lagrangian for vector and scalar resonances is constructed. Matching to the correct asymptotic structure generates non-minimal terms which have so far been ignored. It is found that the width $a_0(980)\to2γ$ can be naturally reproduced suggesting that the $a_0(980)$ is not an exotic particle.

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↗
arXiv1993

Light Quark Masses from Exclusive Tau Decays: An Experimental Proposal

A method of indirect measurement of the light quark running mass $\hat{m} = (m_d + m_u)/2$ is elaborated in detail. It is based on measuring 1\%-level azimuthal angular asymmetries in the decay $τ\rightarrow ν_τ+ 3π$. The latter are then used in QCD sum rules to obtain experimental lower bounds for $\hat{m}$. For a sample of $2.5 \times 10^5$ $τ\rightarrow ν_τ+ 3π$ decays free of background, the resulting statistical error in the bound for $\hat{m}$ is estimated to be 1 MeV, i.e., comparable to the systematic error due to the use of QCD sum rules. Contribution to the Third Workshop on the $τ$ Charm Factory 1-6 June 1993, Marbella, Spain.

hep-ph↗
arXiv1993

What $π-π$ Scattering Tells Us About Chiral Perturbation Theory

We describe a rearrangement of the standard expansion of the symmetry breaking part of the QCD effective Lagrangian that includes into each order additional terms which in the standard chiral perturbation theory ($χ$PT) are relegated to higher orders. The new expansion represents a systematic and unambiguous generalization of the standard $χ$PT, and is more likely to converge rapidly. It provides a consistent framework for a measurement of the importance of additional ``higher order'' terms whose smallness is usually assumed but has never been checked. A method of measuring, among other quantities, the QCD parameters $\hat{m}\langle\bar{q}q\rangle$ and the quark mass ratio $m_s/\hat{m}$ is elaborated in detail. The method is illustrated using various sets of available data. Both of these parameters might be considerably smaller than their respective leading order standard $χ$PT values. The importance of new, more accurate, experimental information on low-energy $π-π$ scattering is stressed.

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