Threshold Resummation for the Top Quark Charge Asymmetry

We study the QCD charge asymmetry in t\bar{t} production at the Tevatron. We investigate the role of higher orders in perturbation theory by considering the resummation of potentially large logarithmic corrections that arise near partonic threshold. This requires us to employ the rapidity-dependent anomalous dimension matrices that describe color mixing due to soft gluon emission in both quark- and gluon-initiated processes. The charge asymmetry appears directly in the resummed cross section at next-to-leading logarithm (NLL), and we find that the first-order expansion of the NLL resummed charge asymmetry reproduces the known fixed-order result for the asymmetry well. Beyond its lowest order, the asymmetric component of the cross section is enhanced by the same leading-logarithmic threshold corrections as the total cross section. As a result, the charge asymmetry is robust with respect to the higher-order perturbative corrections generated by threshold resummation. We observe that the asymmetry increases with pair mass and with scattering angle.Comment: 14 pages, 4 figures. One reference added, version to appear in Phys. Rev.

Drell-Yan forward-backward and spin asymmetries for arbitrary vector boson production at next-to-leading order

Longitudinally polarized, unpolarized and forward-backward mass differential cross sections for Drell-Yan lepton-pair production by arbitrary vector bosons are calculated in next-to-leading order (NLO) QCD. Analytical results are presented in a form valid for all consistent $n$-dimensional regularization schemes, with the mass factorization scheme kept general. NLO predictions for all Drell-Yan type processes ($W^\pm$, $Z$ and $\gamma^*$) at BNL's relativistic heavy ion collider (RHIC) are made using polarized parton distributions which fit the recent deep-inelastic scattering data. These are examined as tools in the determination of the polarized parton distributions and the unpolarized $\bar{u}/\bar{d}$ ratio. NLO predictions for the forward-backward lepton asymmetry at Fermilab are made and the precision determination of $\sin^2 \theta_W$ from future runs is studied. In all the above, the QCD corrections are found to be significant. An introductory discussion is given of various theoretical issues, such as allowable factorization and regularization schemes, and scale dependences.Comment: 34 pages, figures included, revtex. Some discussions and references added/modified. In more compact form. To appear in Phys. Rev.

The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions

According to a rederivation - due to Collins and Qiu - the DGLAP equation can be reinterpreted (in leading order) in a probabilistic way. This form of the equation has been used indirectly to prove the bound $|\Delta f(x,Q)| < f(x,Q)$ between polarized and unpolarized distributions, or positivity of the helicity distributions, for any $Q$. We reanalize this issue by performing a detailed numerical study of the positivity bounds of the helicity distributions. To obtain the numerical solution we implement an x-space based algorithm for polarized and unpolarized distributions to next-to-leading order in $\alpha_s$, which we illustrate. We also elaborate on some of the formal properties of the Collins-Qiu form and comment on the underlying regularization, introduce a Kramers-Moyal expansion of the equation and briefly analize its Fokker-Planck approximation. These follow quite naturally once the master version is given. We illustrate this expansion both for the valence quark distribution $q_V$ and for the transverse spin distribution $h_1$.Comment: 38 pages, 27 figures, Dedicated to Prof. Pierre Ramond for his 60th birthda

The light-cone gauge and the calculation of the two-loop splitting functions

We present calculations of next-to-leading order QCD splitting functions, employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP). In contrast to the `principal-value' prescription used in the original CFP paper for dealing with the poles of the light-cone gauge gluon propagator, we adopt the Mandelstam-Leibbrandt prescription which is known to have a solid field-theoretical foundation. We find that indeed the calculation using this prescription is conceptionally clear and avoids the somewhat dubious manipulations of the spurious poles required when the principal-value method is applied. We reproduce the well-known results for the flavour non-singlet splitting function and the N_C^2 part of the gluon-to-gluon singlet splitting function, which are the most complicated ones, and which provide an exhaustive test of the ML prescription. We also discuss in some detail the x=1 endpoint contributions to the splitting functions.Comment: 41 Pages, LaTeX, 8 figures and tables as eps file

Scale Dependence of Polarized DIS Asymmetries

We compare the $Q^{2}$ dependence of the polarized deep inelastic scattering proton asymmetry, driven by the leading order Altarelli Parisi evolution equations, to those arising from fixed order $\alpha_{s}$ and $\alpha_{s}^{2}$ approximations. It is shown that the evolution effects associated with gluons, which are not properly taken into account by the leading order approximation, cannot be neglected in the analysis of the most recent experimental data.Comment: Latex file, (9 figures in postcript available from [email protected]

Next-to-leading order Q^2-evolution of the transversity distribution h_1(x, Q^2)

We present a calculation of the two-loop anomalous dimension for the transversity distribution h_1(x,Q^2), $\gamma^{h(1)}_n$, in the MS scheme of the dimensional regularization. Due to the chiral-odd nature, h_1 does not mix with the gluon distributions, and thus our result is the same for the flavor-singlet and nonsinglet distributions. At small n (moment of h_1), $\gamma^{h(1)}_n$ is significantly larger than $\gamma^{f(1)}_n$ (the anomalous dimension for the nonsinglet f_1), but approaches $\gamma^{f(1)}_n$ very quickly at large n, keeping the relation $\gamma^{h(1)}_n > \gamma^{f(1)}_n$. This feature is in parallel to the relation between the one-loop anomalous dimension for f_1 and h_1.Comment: 28 pages, Latex. 10 figures. Submitted for publication some time ag

Scheme Independence of g1p(x,Q2)g_1^p (x, Q^2)

We work with two general factorization schemes in order to explore the consequences of imposing scheme independence on $g_1^p (x, Q^2)$. We see that although the light quark sector is indifferent to the choice of a particular scheme, the extension of the calculations to the heavy quark sector indicates that a scheme like the $\bar{MS}$ is preferable.Comment: 11 pages, 2 figures. To appear in the Brief Reports of Phys. Rev.

Spin Structure Function of the Virtual Photon Beyond the Leading Order in QCD

Polarized photon structure can be studied in the future polarized $e^{+}e^{-}$ colliding-beam experiments. We investigate the spin-dependent structure function of the virtual photon $g_1^{\gamma}(x,Q^2,P^2)$, in perturbative QCD for $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon. The analysis is performed to next-to-leading order in QCD. We particularly emphasize the renormalization scheme independence of the result.The non-leading corrections significantly modify the leading log result, in particular, at large $x$ as well as at small $x$. We also discuss the non-vanishing first moment sum rule of $g_1^\gamma$, where ${\cal O}(\alpha_s)$ corrections are computed.Comment: 39 pages, LaTeX, 6 Postscript Figures, eqsection.sty file include

A Simple Regulatory Incentive Mechanism Applied to Electricity Transmission Pricing and Investment

The informationally simple approach to incentive regulation applies mechanisms that translate the regulator's objective function into the firm's profit-maximizing objective. These mechanisms come in two forms, one based on subsidies/taxes,the other based on constraints/ price caps. In spite of a number of improvements and a good empirical track record simple approaches so far remain imperfect. The current paper comes up with a new proposal, called H-R-G-V, which blends the two traditions and is shown to apply well to electricity transmission pricing and investment. In particular, it induces immediately optimal pricing/investment but is not based on subsidies. In the transmission application, the H-RG- V approach is based on a bilevel optimization with the transmission company (Transco) at the top and the independent system operator (ISO) at the bottom level. We show that HR- G-V, while not perfect, marks an improvement over the other simple mechanisms and a convergence of the two traditions. We suggest ways to deal with remaining practical issues of demand and cost functions changing over time

Summary: Working Group on QCD and Strong Interactions

In this summary of the considerations of the QCD working group at Snowmass 2001, the roles of quantum chromodynamics in the Standard Model and in the search for new physics are reviewed, with empahsis on frontier areas in the field. We discuss the importance of, and prospects for, precision QCD in perturbative and lattice calculations. We describe new ideas in the analysis of parton distribution functions and jet structure, and review progress in small-$x$ and in polarization.Comment: Snowmass 2001. Revtex4, 34 pages, 4 figures, revised to include additional references on jets and lattice QC