Threshold Factorization Redux

We reanalyze the factorization theorems for Drell-Yan process and for deep inelastic scattering near threshold, as constructed in the framework of the soft-collinear effective theory (SCET), from a new, consistent perspective. In order to formulate the factorization near threshold in SCET, we should include an additional degree of freedom with small energy, collinear to the beam direction. The corresponding collinear-soft mode is included to describe the parton distribution function (PDF) near threshold. The soft function is modified by subtracting the contribution of the collinear-soft modes in order to avoid double counting on the overlap region. As a result, the proper soft function becomes infrared finite, and all the factorized parts are free of rapidity divergence. Furthermore, the separation of the relevant scales in each factorized part becomes manifest. We apply the same idea to the dihadron production in $e^+ e^-$ annihilation near threshold, and show that the resultant soft function is also free of infrared and rapidity divergences.Comment: 20 pages, 2 figures; matches published versio

Small and Large Scale Granular Statics

Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are elliptic in nature). Propagating (hyperbolic) or diffusive (parabolic) models have been proposed to replace the `old' models. Since several recent experiments were performed on small systems, one should not really be surprised that (continuum) elasticity, a macroscopic theory, is not directly applicable, and should be replaced by a grain-scale (``microscopic'') description. Such a description concerns the interparticle forces, while a macroscopic description is given in terms of the stress field. These descriptions are related, but not equivalent, and the distinction is important in interpreting the experimental results. There are indications that at least some large scale properties of granular assemblies can be described by elasticity, although not necessarily its isotropic version. The purely repulsive interparticle forces (in non-cohesive materials) may lead to modifications of the contact network upon the application of external forces, which may strongly affect the anisotropy of the system. This effect is expected to be small (in non-isostatic systems) for small applied forces and for pre-stressed systems (in particular for disordered systems). Otherwise, it may be accounted for using a nonlinear, incrementally elastic model, with stress-history dependent elastic moduli. Although many features of the experiments may be reproduced using models of frictionless particles, results demonstrating the importance of accounting for friction are presented.Comment: 10 pages, 9 figures. Accepted for publication in "Granular Matter" (special issue: 4th Int. Conf. on Conveying and Handling of Particulate Solids, Budapest, Hungary, May 2003). v2: Minor revisions to text and figure

Factorization theorem for high-energy scattering near the endpoint

A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the infrared divergences appear only in the parton distribution functions by carefully reorganizing collinear and soft parts. The central idea is extracting the soft contributions from the collinear part to avoid double counting. Combining it with the original soft part, an infrared-finite kernel is obtained. This factorization procedure can be applied to various high-energy scattering processes.Comment: 4 pages, version published in PR

Cone Algorithm Jets in e+e- Collisions

The structure of hadronic jets depends not only on the dynamics of QCD but also on the details of the jet finding algorithm and the physical process in which the jet is produced. To study these effects in more detail we calculate the jet cross section and the internal jet structure in e+e- annihilations and compare them to the results found in hadronic collisions using the same jet definition, the cone algorithm. The different structures of the overall events in the two cases are evident in the comparison. For a given cone size and jet energy, the distribution of energy inside the cone is more concentrated near the center for jets from e+e- collisions than for jets from hadronic collisions.Comment: 22 pages, 5 Postscript epsf-embedded figures, uses fixes.st

Endpoint behavior of high-energy scattering cross sections

In high-energy processes near the endpoint, there emerge new contributions associated with spectator interactions. Away from the endpoint region, these new contributions are suppressed compared to the leading contribution, but the leading contribution becomes suppressed as we approach the endpoint and the new contributions become comparable. We present how the new contributions scale as we reach the endpoint and show that they are comparable to the suppressed leading contributions in deep-inelastic scattering by employing a power counting analysis. The hadronic tensor in deep-inelastic scattering is shown to factorize including the spectator interactions, and it can be expressed in terms of the lightcone distribution amplitudes of initial hadrons. We also consider the contribution of the spectator contributions in Drell-Yan processes. Here the spectator interactions are suppressed compared to double parton annihilation according to the power counting.Comment: 21 pages, 5 figures, published versio

1/mb1/m_b Corrections in the ACCMM Model for Inclusive Semileptonic B Decay

We re-examine the model of Altarelli, Cabibbo, Corb\`{o}, Maiani and Martinelli for inclusive semileptonic B decay, in the light of recent calculations in heavy quark effective theory. The model can be shown to have no~$1/m_b$ corrections, with a suitable definition of the b quark mass~$m_b$. However, we find that the structure of the $1/m_b^2$~terms is incompatible with the predictions of heavy quark effective theory. The numerical significance of this discrepancy is discussed.Comment: 10 pages (uses revtex), UCLA/93/TEP/4

Does Air Quality Matter? Evidence from the Housing Market

This study exploits the quasi-random assignment of air pollution changes across counties induced by federally mandated air pollution regulations to identify the impact of particulate matter on property values. Two striking empirical regularities emerge from the analysis. First particulate matter declined substantially more in regulated than in unregulated counties during the 1970s and 1980s. At the same time, housing prices rose more in regulated counties. The evidence suggests that this approach identifies two causal effects: 1) the impact of regulation on air quality improvements, and 2) the impact of regulation on economic gains for home-owners. In addition, the results highlight the importance of choosing regulatory instruments that are orthogonal to unobserved housing price shocks that vary by county over long time horizons. It appears that using regulation-induced changes in particulate matter leads to more reliable estimates of the capitalization of air quality into property values. Whereas the conventional cross-sectional and unstable and indeterminate across specifications, the instrumental variables estimates are much larger, insensitive to specification of the model, and appear to purge the biases in the conventional estimates. The estimates imply that a one-unit reduction in suspended particulates results in a 0.7-1.5 percent increase in home values. In addition, it appears that air pollution regulations resulted in real economic benefits to home-owners in regulated counties.