arXiv subjects

Tran N. Truong

Publications and source records attributed to Tran N. Truong.

13 recordsLinked to original sources

arXiv2010

Bethe-Schwinger Effective Range Theory and Lehmann and Weinberg Chiral Perturbation Theories

This paper is a brief review of low energy soft hadronic physics, starting from the invention of the low energy effective range theory in the late 40's due to Bethe and Schwinger for nucleon-nucleon scattering, and its generalization to the static Chew-Low model for pion nucleon scattering, to the present development of the Lehmann and Weinberg Chiral Perturbation Theories. It is pointed out that a consistent low energy calculation can be achieved with the incorporation of the unitarity relation in the Chiral Perturbation Theory.

hep-ph↗

arXiv2001

Study of $γπ\to ππ$ below 1 GeV using Integral Equation Approach

The scattering of $γπ\to ππ$ is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. Using the technique to derive the Roy's equation, an integral equation for the P-wave amplitude is obtained in terms of the strong P-wave pion pion phase shifts. Its solution is obtained numerically by an iteration procedure using the starting point as the solution of the integral equation of the Muskelshsvilli-Omnes type. It is, however, ambiguous and depends sensitively on the second derivative of the P-wave amplitude at $s=m_π^2$ which cannot directly be measured.

hep-ph↗

arXiv2001

Dispersion Relations and Sum Rules for the pi ->gamma gamma* and gamma* ->gamma pi form factor

Sum rules for the off-shell isovector form factor pi -> gamma gamma* are given in terms of the pion form factor and the gamma pi ->pi pi experimental data. Similarly the corresponding sum rules for the isoscalar form factor are given in terms of the experimental photon-3 pi form factor and the gamma pi -> 3 pi amplitude. For some set of parameters, e.g. rho -> pi gamma width = 90 KeV, the pi -> gamma gamma rate and the slope parameter of the decay pi -> gamma e plus e minus are in good agreement with the experimental data.

hep-ph↗

arXiv2001

On the Ambiguity of the Solution of the Muskhelishvili-Omnes Integral Equation

The solution of the Muskhelishvili-Omnes Integral Equation is ambiguous by a real polynomial. The coefficients of this polynomial can be fixed either by the knowledge of the low energy parameters or by the asymptotic behavior of the form factor. The role of the contact terms of the low energy effective Lagrangian is explicitly analysed.

hep-ph↗

arXiv2000

Remarks on the Calculation of the Enhancement Factor in the K -> 2 pion Decay

The problem of calculation of the enhancement factor due to the strong pion final state interaction is reexamined in the light of recent interest in understanding of the origine of the $ΔI=1/2$ rule and calculations of the CP violation parameter $ε^{\prime}/ε$. It is shown that the traditional method of calculating the \emph{absolute} enhancement factor is model dependent, while the method of relating $K \to 2π$ amplitude to the $K-π$ matrix element using Current Algebra is on a safer ground.

hep-ph↗

arXiv2000

When is it possible to use perturbation technique in field theory ?

The vector pion form factor is used as an example to analyze this question. Given the experimental radius of the pion, the crucial question is whether perturbative methods could be used for the effective chiral lagrangian to calculate the pion form factor. Our analysis shows that the pion rms radius is far too large (or the related rho resonance mass is too low) for the perturbation theory to be valid.

hep-ph↗

arXiv2000

Dispersion Relation Analyses of Pion Form Factor, Chiral Perturbation Theory and Unitarized Calculations

The Vector Pion form factor below 1 GeV is analyzed using experimental data on its modulus, the P-wave pion pion phase shifts and dispersion relation. It is found that causality is satisfied. Using dispersion relation, terms proportional to s squared and s cubed are calculated using the experimental data, where s is the momentum transfer. They are much larger than the one-loop and two-loop Chiral Perturbation Theory calculations. Unitarized model calculations agree very well with dispersion relation results.

hep-ph↗

arXiv2000

Reinterpretation of Effective Chiral Lagrangian

Effective tree Chiral Lagrangian is interpreted as a power series expansion of the kinematical variables. In the presence of the strong interaction this expansion is valid below the unitarity cut, hence in the unphysical region. Consequences of this reinterpretation of the Chiral Lagrangian are analysed for the relation between K-pi and K-pipi transitions.

hep-ph↗

arXiv1999

Study of Gamma + Pi --> Pi + Pi

The problem of Gamma + Pi --> Pi + Pi is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. Single variable dispersion relation is assumed. Using elastic unitarity relation, an integral equation equation for the lowest partial wave amplitude is obtained. The solution for this integral equation is obtained by an iteration procedure corresponding to that obtained from the vector meson dominance model but with multiple scattering effects taken into account.

hep-ph↗

arXiv1998

Taylor's Series and Dispersion Relation Analyses of the Vector Pion Form Factor and their Comparison with Perturbative and Non Perturbative Calculations

The first three coefficients of the Taylor's series expansion of the vector pion form factor as a function of the momentum transfer are evaluated using experimental data on the pion form factor and the P-wave pi pi phase shifts. The real part of the form factor as a function of energy is also calculated by dispersion relation. Comparisons these results with Chiral Perturbation Theory and unitarized models are given.

hep-ph↗

arXiv1997

Calculation of gamma plus pion to two pions

The problem of $γπ\to ππ$ is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. The solution of the integral equation for this amplitude is given by an iteration procedure.The final solution disagrees with vector meson dominance models.

hep-ph↗

arXiv1994

Application of Current Algebra in Three Pseudoscalar Meson Decays of $τ$ Lepton

The decays of $τ\to 3πν$ and $τ\to πK^{*} ν, Kρν$ are calculated using the hard pion and kaon current algebra and assuming the Axial-Vector meson dominance of the hadronic axial currents. Using the experimental data on their masses and widths, the $τ$ decay branching ratios into these channels are calculated and found to be in a reasonable agreement with the experimental data. In particular, using the available Aleph data on the $3π$ spectrum, we determine the $A_1$ parameters, $m_A=1.24\pm 0.02 GeV$, $Γ_A=0.43\pm 0.02$ GeV; the hard current algebra calculation yields a $3π$ branching ratio of $19 \pm 3 \%$.

hep-ph↗

arXiv1994

$τ\to πK ν$ Decay and $πK$ Scattering

Using chiral low energy theorems and elastic unitarity assumption, the $τ\toπK ν$ decay is investigated. The vector and scalar $πK$ form factors are calculated. It is found that the $πK$ spectrum is dominated by the $K^*$ resonance. By measuring the forward-backward asymmetry, it is shown that the S wave $πK$ phase shift can be determined near the $K^{*}$ resonance region. The calculated branching ratio and resonance parameters are in good agreement with experiments.

hep-ph↗