Analyticity as a Robust Constraint on the LHC Cross Section

It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of $pp$ and $\bar pp$ cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor of cross sections that grow asymptotically as $\ln^2s$. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results and yield essentially identical tightly constrained values for the LHC cross section. The agreement can be understood as a new analyticity constraint derived as an extension of a Finite Energy Sum Rule.Comment: 8 pages, Latex2e, 2 postscript figures; major changes made; accepted for publication in Phys Rev

The Elusive p-air Cross Section

For the \pbar p and $pp$ systems, we have used all of the extensive data of the Particle Data Group[K. Hagiwara {\em et al.} (Particle Data Group), Phys. Rev. D 66, 010001 (2002).]. We then subject these data to a screening process, the ``Sieve'' algorithm[M. M. Block, physics/0506010.], in order to eliminate ``outliers'' that can skew a $\chi^2$ fit. With the ``Sieve'' algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high \delchi, the individual i$^{\rm th}$ point's contribution to the total $\chi^2$. The $\chi^2$ fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of total hadronic cross sections when we require that these amplitudes {\em also} describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the ``sieved'' high energy measurements of $\bar p p$ and $pp$ total cross sections and $\rho$-values for $\sqrt s\ge 6$ GeV, while requiring that their asymptotic fits smoothly join the the $\sigma_{\bar p p}$ and $\sigma_{pp}$ total cross sections at $\sqrt s=$4.0 GeV--again {\em both} in magnitude and slope. Our results strongly favor a high energy $\ln^2s$ fit, basically excluding a $\ln s$ fit. Finally, we make a screened Glauber fit for the p-air cross section, using as input our precisely-determined $pp$ cross sections at cosmic ray energies.Comment: 15 pages, 6 figures, 2 table,Paper delivered at c2cr2005 Conference, Prague, September 7-13, 2005. Fig. 2 was missing from V1. V3 fixes all figure

Predicting Proton-Air Cross Sections at sqrt s ~30 TeV, using Accelerator and Cosmic Ray Data

We use the high energy predictions of a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton-air cross sections at energies near \sqrt s \approx 30 TeV. The parameterization of the proton-proton cross section incorporates analyticity and unitarity, and demands that the asymptotic proton is a black disk of soft partons. By comparing with the p-air cosmic ray measurements, our analysis results in a constraint on the inclusive particle production cross section.Comment: 9 pages, Revtex, uses epsfig.sty, 5 postscript figures. Minor text revisions. Systematic errors in k included, procedure for extracting k clarified. Previously undefined symbols now define

The supply of legal and illegal activity: A choice theoretic analysis

We will show below that failure to fully specify the choice problem and therefore the transformation between what is inherently a multi-attribute decision problem and the wealth only problem has led Becker, Ehrlich, and Sjoquist to conclusions which are valid only in very special cases. In general, we show that plausible preference restrictions are not sufficient to generate unambiguous supply results, a result that should come as no surprise since it is the same situation that confronts the investigator in most household allocation problems. Therefore, policy prescriptions in this area, as in the tax incentive area do not follow from theory but rather require empirical determination of relative magnitudes

A Labor Theoretic Analysis of the Criminal Choice

Although many criminal choice problems may be viewed within an expanded labor choice framework, care must be exercised if these problems are to be interpreted in terms of strictly monetary costs and benefits. We show below that by not fully specifying their choice problems, and therefore the transformation between what is inherently a multiattribute decision problem and the wealth-only problem, Becker, Ehrlich, and Sjoquist are led to conclusions which are valid only in very special cases. In general, we show that plausible preference restrictions are not sufficient to generate unambiguous supply results, a result that should come as no surprise since it is the same situation that confronts the investigator in most household allocation problems. Therefore, policy prescriptions in this area, as in the tax incentive area, do not follow from theory but rather require empirical determination of relative magnitudes

A theory of household behavior under uncertainty

In this paper we are concerned with the effects of uncertainty on household decisions. In particular we are interested in the response of a single economic agent\u27s factor allocations to changes in the amount of uncertainty with which the agent\u27s beliefs regarding his income are held. For problems of choice under uncertainty the recent work of Arrow [1], Sandmo [9, 10, 11], Leland [5, 6], Stiglitz [12], and others clearly testifies to the power of the expected utility hypothesis as an analytical framework. In what follows two models are examined in which the agent is assumed to be confronting a two period planning horizon and making a joint labor-saving supply decision in the expected utility sense. Although Sandmo [10] and Leland [5] have investigated the effects of uncertainty on the savings decision and Block and Heineke [4] have investigated the effects of uncertainty on the labor decision, to our knowledge no general treatment of the effects of uncertainty on the joint labor-savings decision has been done. It will be shown that the assumptions underlying the Sandmo-Leland analysis are not sufficient to generate their savings results in the more general household model. Additional assumptions are presented that are sufficient not only for the Sandmo-Leland savings results, but which also provide the requisite preference information for an analysis of the labor decision

The Allocation of Effort Under Uncertainty: The Case of Risk Averse Behavior

This paper analyzes the labor supply decision of a single economic agent within the expected utility framework. Two formulations of the problem are considered: pure income uncertainty and wage rate uncertainty. In each case, the effects on the labor supply decision of changes in both expected returns and the dispersion of returns (about a constant mean) are investigated. Arguments concerning the disincentive effects of uncertainty are shown not to be unambiguously supported by theory