Double Counting Problem Research Articles

Motorists' Use of Sirens: An Informal Look

The motor vehicle code of New York State permits driven of fire engines, ambulances, pol~ce can and other emergency vehicles, when responding to emergencies, to sound a siren. When hearing a suen nearby, other motorists are mandated to pull over to the right edge of the road and stop. This must be done even when it is not known exactly where the emergency vehicle is (2). To achieve some insight as to whether or not other driven might well be using sirens, which may be part of their vehicle's antitheft device, to expedite their passage through congested traffic, an informal inquiry was conducted during the Fall-Winter of 1984-85 and 198788. On both occasions observations were made at the same road intersection in a large city in New York State: a three-lane north-bound street having a peak traffic volume of approximately 1900 commercial and private vehicles per hour and a two-lane west-bound street handling about 1200 vehicles per hour. Flow of traffic through the intersection was controlled by a signal light. During both periods a total of 43 'A-hr. convenience citings were conducted, on Monday through Friday, between the hours of 0800-0930 and 1700-1830. Note was made of the number of times a siren was sounded in the immediate vicinity of the intersection. While the problem of double counting was recognized, it was felt that the changing situation, the large number of vehicles involved, and the dispersion of the observation times, would minimize the probability of that happening. Two siren-sounding occurrences were noted in Fall-Winter of 1984-85 and seven in 198788. In none of these nine instances was an emergency vehicle on call, identifiable by a flashing whlte and red light, seen. The number of discrete soundings per occurrence was one, with a duration of about two to three seconds. In no case was it possible to identify the vehicle from which the sound was coming. However, in the rwo occurrences observed in 1984-85, a private vehicle was noted to use the opening in the traffic which resulted. In the other seven instances, drivers did not respond to the siren, and there was no alteration in the pattern of the vehicle flow. The results of this inquiry suggest, as the work of others such as McKelvie (1) and Trinkaus (3) have implied, that drivers' compliance with motor vehicle regulations may well be declining. First, there is what appears to be an increase in the use of sirens by drivers of nonemergency vehicles. And, second, there is seemingly a lessening of the rate of assent by drivers in yielding the right-of-way when they hear a siren. While this implies that there is some decay in adherence to motor vehicle regulations, with its explicit implication for motorists' safety, perhaps of more importance is the suggested implicit increase in the demise of overall concern for the well being of othen

Improved parton showers in ep interactions

A scheme for including the first-order matrix element in ep parton showers is presented. This is an important improvement since it applies to hard emission where the leading-log approximation is less reliable. The contributions from the initial-and final-state showers are treated on an equal footing, solving the potential problem of double-counting of emission. Kinematical constraints, relating the dynamics of the two separate showers, are also solved in this context. The choice of splitting variable in initial-state showers is furthermore discussed.

Semi-empirical description of low energy nuclear collective states

The low-lying collective quadrupole and octupole states in spherical nuclei are described as superpositions of quasi-particle excitations coupled to the isoscalar L = 2 or L = 3 giant resonance states, identified as the coherent states of the nucleus with angular momenta L = 2 and 3, respectively. The scheme can also be interpreted as an economical way of performing RPA calculations. The energy density method provides all the necessary ingredients so that the model is in principle free of adjustable parameters. The double counting problem is handled by requiring the energy weighted sum rule to be fullfilled “after diagonalization.” The calculations have been made for closed shell nuclei, as well as for the Samarium-isotopes. The bulk properties of low-lying levels are reproduced. The model predicts interesting features for the proton and neutron transition densities.

Gluon-exchange currents: The nucleon axial-vector coupling constant and magnetic moments in bag models

Possible numerical importance of the two-body currents arising from exchange of one hard gluon between two constituent quarks is investigated by studying the evaluation of the nucleon axial-vector coupling constantg A and magnetic moments μ tot , μ tot in the context of the MIT bag model. The double counting problem is resolved only to the extent that, in accord with the standard wisdom, hard gluons have nothing to do with the formation of bags (quark confinement) and so are not included in bag-model wave functions. For reasonable choices of the parameters, we find that (1) the contribution tog A arising from one-gluon-exchange currents (OGEC) could account for the discrepancy between the observed value and the one-body bag-model prediction, and that (2) whereas the OGEC contribution to μ tot is negligible, the contribution to μ tot could be important but does not allow further understanding of the observed μ p /μ n ratio.

γγscattering and extended vector dominance

We show that the extended vector-dominance model (EVDM) provides a reasonable fit to the presently available data, both for the photon-photon cross section ${\ensuremath{\sigma}}_{\ensuremath{\gamma}\ensuremath{\gamma}}$ and for the photon structure function ${F}_{2}^{\ensuremath{\gamma}}$ for values of ${Q}^{2}\ensuremath{\lesssim}25$ Ge${\mathrm{V}}^{2}$. The EVDM approach allows us to circumvent the problem of double counting concerning the hadronic and pointlike pieces of the photon, and yields a value of ${b}_{2}\ensuremath{\simeq}\ensuremath{-}0.04$, for the undetermined coefficient of the second moment of ${F}_{2}^{\ensuremath{\gamma}}$.

Landau-Migdal theory made consistent for even- and odd-particle nuclei

It is shown that a problem non-existent in infinite matter-the completely different low-energy structure of even- and odd-particle nuclei-can be handled in the spirit of Landau's theory, at least for magic nuclei and their neighbours, by using the Hamiltonian and the particle-number operator as external fields in response equations for even-odd nuclei. Thereby it is proved that the many-body T matrix, which governs the properties of even-particle nuclei, also determines completely the structure of even-odd nuclei, without the appearance of irreducible three-body interactions. The role played by Landau's amplitude in infinite matter is taken over by the completely irreducible kernel K in a set of Bethe-Salpeter equations for the many-body T matrix. The non-existence of double-counting problems is demonstrated by considering results in second-order perturbation theory.

The problem of double counting and international trade flows

The problem of double counting and international trade flows

Double counting and the collective coordinate method

The double counting problem of the collective coordinate resolution of identity 1 = ∫ d T δ(∫ d t( φ( t)− φ cl( t− T)) f( t− T)) · J( φ, T) is discussed. Since for a particular φ the argument of the δ-function can be zero for several values of T, the above equation is not an unreserved identity. Its self-consistency is tested by computing the vacuum expectation values of both sides in a one-kink background. With J = −∫ φ( t) f′( t− T) d t (no absolute magnitudes) the error is found to be non-perturbative and its dependence on the constraints function ƒ; is exposed. Further tests and remedies are suggested.

On the α2(Zα)2-vacuum polarisation contribution to the muonic atom energy levels

A derivation of the relativistic, quantum electrodynamical expression for the alpha 2(Z alpha )2-vacuum polarisation correction to muonic energy levels is presented. Using this derivation based on the bound-state interaction picture, the expression for the other radiative corrections such as the Lamb shift alpha (Z alpha )3-vacuum polarisation, etc are obtained. This shows that the resulting expression for the alpha 2(Z alpha )2-vacuum polarisation contribution is consistent with those used in other calculations which are rigorously based on quantum electrodynamics. Furthermore, this approach avoids the problem of double counting.

Effect ofN*resonances and the effective channel approach to nucleon-nucleus scattering

Recent experimental reesults for p-/sup 4/He elastic scattering at 1 GeV are in fair agreement with the previous Saclay data, and also with the effective channel approach calculation, while a recent multiple diffraction analysis has found the N* effect important near the first diffraction minimum. In view of these, we comment on the role of the N* and other rearrangement channels within the effective channel approach, and show that the effective channel approach contains these effects collectively. The nonorthogonality and double-counting problems are discussed.

The πN scattering in nuclear matter

The effect of a nuclear medium on the πN scattering amplitude is discussed in a general formalism. A double-counting problem coming from the usual definition of the density-dependent πN scattering amplitude is resolved in this framework. We study the corrections to the fourth-order Chew-Low amplitude. It is shown that the leading terms of the Pauli correction cancel to this order, when one includes the Pauli effect in all intermediate states. The effect of a nuclear medium at nuclear matter density is found to be a 12 % quenching of the amplitude at threshold.

Veneziano Duality inSU(3)-Symmetric Meson-Baryon Scattering

An SU(3) symmetric Veneziano model for pseudoscalar meson-baryon scattering is con­ structed. The model incorporates the full content of the exchange degeneracy pattern of baryon spectrum. A hypothesis is made that the leading trajectories bootstrap themselves as long as it is consistent with the crossing relation, no ghosts on the leading trajectories and certain physical requirements. If we further adopt a subsidiary hypothesis on the SU (3) structures of the daughter states, the A amplitude (we use CGLN's notation) is completely determined to within a scale factor. Possible SU (3) splitting of the trajectories is considered. Theoretical prediction for threshold values of A amplitudes agrees quantitatively with ex­ perimental values (which are given in terms of the s-wave and p-wave scattering lengths) for rrN and KN scattering. It is shown that in the limit of quantized intercepts, the present model satisfies Adler's condition approximately. When applied to high-energy forward scat­ tering, the model predicts the t-dependence of the F/ D ratios of vector and tensor meson couplings. The theoretical value of the A amplitude associated with the nonstrange vector and tensor Regge pole exchange agrees with the empirical value within a factor of two. § I. Introduction In vanous dynamical schemes ever proposed to describe hadron scattering processes, exchanges play a primary role. In the early days, particle exchanges in the s-, t- and u-channels were treated separately and added up to give the whole amplitude. The results, however, are sensitive to the choice of types of couplings and the way of extrapolating resonance formula to the off-mass shell region. Even if the particle exchange is Reggeized, the t-dependence of residue functions remains undetermined. Furthermore, it has become evident from the study of finite energy sum rules applied to pion-nucleon scattering that the extrapolation of Regge pole terms down to the intermediate energy region gives the average of the contributions of the direct channel resonances. 1 ),Z) The problem of double counting would occur m general if one simply sums resonance terms in all three channels. Veneziano has proposed a new model as a solution to this problem. 3 ) The

Particle Exchange, Regge-Pole Exchange and the Veneziano Amplitude forKNScattering

Based on the observation that the (t, u) -Veneziano terms can be expressed as an infinite sum of one-particle exchange contributions in the physical region, contrary to the (s, t) and (s, u) terms where the particle exchange picture is divergent, the validity of the particle exchange picture and the transcendental mechanism to the Regge pole exchange picture is examined in a KN Veneziano amplitude consisting of (t, u) terms only. At threshold, the contribution of meson exchanges with the lowest mass almost saturates the KN Veneziano amplitude. The hyperon exchange contributions should be discarded there, because of the duality between meson exchange contributions and hyperon exchange contributions. As energy increases, the meson towers with various spin states and degenerate mass begin to contribute one by one. Regge behaviour is obtained as a result of a detailed cancellation among the contributions of meson exchanges with various masses and spins. Here, Regge behaviour in a limited energy region is given by a finite sum of one-meson exchange terms. On the other hand, the hyperon exchange picture with finite terms does not approximate well the amplitude in the low energy region, even at threshold. These situations are understood through the study of the condition for an approximate truncation of infinite series of poles in the (t, u) -terms. The low energy interpolations of Regge asymptotic forms are studied, and the meson Regge pole exchange is also confirmed to give the gross features of the amplitude down to the threshold. The problem of double counting between the t- and u-Regge poles in low energy is noted.

Generalized Interference Model

A crossing-symmetric Regge-pole model of the generalized interference type is discussed. The model consists of a sum of infinitely many Regge poles in each channel, corresponding to a leading Regge trajectory and its parallel daughters. All the usual requirements are satisfied by the Regge residues, and nonlinear trajections can be introduced without difficulty. At the expense of a loss of physical interpretation, the double-counting problem can be eliminated by identifying the Schmid loops with the direct-channel resonances.