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N. H. Fuchs

Publications and source records attributed to N. H. Fuchs.

8 recordsLinked to original sources
arXiv2003

Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory

Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline how additional information may be incorporated to further constrain the pattern of ChSB in the N_f=3 chiral limit.

hep-ph↗
arXiv2002

Analysis and interpretation of new low-energy Pi-Pi scattering data

The recently published E865 data on charged K_e4 decays and Pi-Pi phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters alpha and beta, of the low-energy constants l3-bar and l4-bar as well as of the main two-flavour order parameters: and F_pi in the limit m_u = m_d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on Pi-Pi phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2 a_0^0 - 5 a_0^2 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1-sigma level is found and commented upon.

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↗
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↗
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.

hep-ph↗