Reliability Equivalence in Public Transport Contexts

This work provides initial investigation into whether equivalence between the mean-variance and scheduling approaches to transport reliability can be applied in the context high frequency public transport services. Each of these approaches is briefly outlined and the current work is framed by previous research attempting to demonstrate equivalence: both theoretically and empirically. The basic assumptions underpinning the theoretical approach to equivalence are explored and then re-formulated based upon which variables are likely to be known. The concept of headway is introduced to the theoretical approach using notation from previous research in order to represent public transport services. An empirical illustration of the method is undertaken using smart card data obtained from the London Underground metro system. The data are combined with timetable data and a previously developed method for estimating passenger preferred arrival times, which in turn allows the theoretical equivalence between mean-variance and scheduling approaches to be tested empirically. This is initially performed for a single origin-destination (OD) pair and then for 23 other ODs of varying headways. The example using a single OD demonstrates that even for a high frequency metro service, application of the theoretical equivalence is problematic, with variable parameters substantially affected. In the case of many ODs, a linear relationship is observed between the ratio of public transport to standard scheduling parameters and headway, suggesting the theoretical equivalence becomes less viable as headway increases. At the lowest values of headway, it is concluded that the equivalence remains problematic and further work is required before equivalence between the mean variance and scheduling approaches can be implemented in the public transport context

On the low energy end of the QCD spectrum

The energy gap of QCD is now understood very well. There is no doubt that the expansion in powers of the two lightest quark masses does represent a very useful tool for the analysis of the low energy structure. Concerning the expansion in powers of m_s, however, the current situation leaves much to be desired. While some of the lattice results indicate, for instance, that the violations of the Okubo-Iizuka-Zweig rule in the quark condensate and in the decay constants are rather modest, others point in the opposite direction. I am confident that the dust will settle soon, so that the effective coupling constants that govern the dependence of the various quantities of physical interest on m_s can be determined, to next-to-next-to-leading order of the chiral expansion. The range of validity of ChPT can be extended by means of dispersive methods. The properties of the physical states occurring in the spectrum of QCD below KKbar threshold can reliably be investigated on this basis. In particular, as shown only rather recently, general principles of quantum field theory lead to an exact formula that expresses the mass and width of resonances in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions of broad resonances.Comment: Talks given at QCD08 and Confinement

Multiscale Technicolor and the Zbb-bar Vertex

We estimate the correction to the Zbb-bar vertex arising from the exchanges of the sideways extended technicolor (ETC) boson and the flavor-diagonal ETC boson in the multiscale walking technicolor model. The obtained result is too large to explain the present data. However, if we introduce a new self- interaction for the top quark to induce the top quark condensate serving as the origin of the large top quark mass, the corrected R_b=Gamma_b/Gamma_h can be consistent with the recent LEP data. The corresponding correction to R_c=Gamma_c/Gamma_h is shown to be negligibly small.Comment: 9-page LaTex fil

The isospin symmetry breaking effects in Ke4K_{e4} decays

The Fermi-Watson theorem is generalized to the case of two coupled channels with different masses and applied to final state interaction in $K_{e4}$ decays. The impact of considered effect on the phase of the $\pi\pi$ scattering is estimated and shown that it can be crucial for scattering lengths extraction from experimental data on $K_{e4}$ decays

Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking

Dispersive representations of the pi-pi scattering amplitudes and pion form factors, valid at two-loop accuracy in the low-energy expansion, are constructed in the presence of isospin-breaking effects induced by the difference between the charged and neutral pion masses. Analytical expressions for the corresponding phases of the scalar and vector pion form factors are computed. It is shown that each of these phases consists of the sum of a "universal" part and a form-factor dependent contribution. The first one is entirely determined in terms of the pi-pi scattering amplitudes alone, and reduces to the phase satisfying Watson's theorem in the isospin limit. The second one can be sizeable, although it vanishes in the same limit. The dependence of these isospin corrections with respect to the parameters of the subthreshold expansion of the pi-pi amplitude is studied, and an equivalent representation in terms of the S-wave scattering lengths is also briefly presented and discussed. In addition, partially analytical expressions for the two-loop form factors and pi-pi scattering amplitudes in the presence of isospin breaking are provided.Comment: 57 pages, 12 figure

Empirical parameterization of the K+- -> pi+- pi0 pi0 decay Dalitz plot

As first observed by the NA48/2 experiment at the CERN SPS, the \p0p0 invariant mass (M00) distribution from \kcnn decay shows a cusp-like anomaly at M00=2m+, where m+ is the charged pion mass. An analysis to extract the pi pi scattering lengths in the isospin I=0 and I=2 states, a0 and a2, respectively, has been recently reported. In the present work the Dalitz plot of this decay is fitted to a new empirical parameterization suitable for practical purposes, such as Monte Carlo simulations of K+- -> pi+- pi0 pi0 decays.Comment: 9 pages, 3 figures

K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe

We study the decay K^+ -> pi^+ pi^0 e^+ e^-, currently under analysis by the NA62 Collaboration at CERN. In particular, we provide a detailed analysis of the Dalitz plot for the long-distance, gamma^*-mediated, contributions (Bremsstrahlung, direct emission and its interference). We also examine a set of asymmetries to isolate genuine short-distance effects. While we show that charge asymmetries are not required to test short distances, they provide the best environment for its detection. This constitutes by itself a strong motivation for NA62 to study K^- decays in the future. We therefore provide a detailed study of different charge asymmetries and the corresponding estimated signals. Whenever possible, we make contact with the related processes K^+ -> pi^+ pi^0 gamma and K_L -> pi^+ pi^- e^+ e^- and discuss the advantages of K^+ -> pi^+ pi^0 e^+ e^- over them.Comment: 25 pages, 6 figure

The electromagnetic effects in Ke4K_{e4} decay

The final state interaction of pions in $K_{e4}$ decay allows one to obtain the value of the isospin and angular momentum zero $\pi\pi$ scattering length $a_0^0$.We take into account the electromagnetic interaction of pions and isospin symmetry breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering length extraction from $K_{e4}$ decay.Comment: 8 pages,1 figur

Bremsstrahlung simulation in K to pi l^pm nu_l (gamma) decays

In physics simulation chains, the PHOTOS Monte Carlo program is often used to simulate QED effects in decays of intermediate particles and resonances. The program is based on an exact multiphoton phase space. In general, the matrix element is obtained from iterations of a universal kernel and approximations are involved. To evaluate the program precision, it is necessary to formulate and implement within the generator the exact matrix element, which depends on the decay channel. Then, all terms necessary for non-leading logarithms are taken into account. In the present letter we focus on the decay K to pi l^pm nu_l and tests of the PHOTOS Monte Carlo program. We conclude a 0.2% relative precision in the implementation of the hard photon matrix element into the emission kernel, including the case where approximations are used.Comment: 1+20 pages, 8 figure

On ordinal utility, cardinal utility, and random utility

Though the Random Utility Model (RUM) was conceived  entirely in terms of ordinal utility, the apparatus throughwhich it is widely practised exhibits properties of  cardinal utility.  The adoption of cardinal utility as a  working operation of ordinal is perfectly valid, provided  interpretations drawn from that operation remain faithful  to ordinal utility.  The paper considers whether the latterrequirement holds true for several measurements commonly  derived from RUM.  In particular it is found that  measurements of consumer surplus change may depart from  ordinal utility, and exploit the cardinality inherent in  the practical apparatus.