Deep inelastic scattering near the endpoint in soft-collinear effective theory

We apply the soft-collinear effective theory (SCET) to deep inelastic scattering near the endpoint region. The forward scattering amplitude, and the structure functions are shown to factorize as a convolution of the Wilson coefficients, the jet functions, the parton distribution functions. The behavior of the parton distribution functions near the endpoint region is considered. It turns out that it evolves with the Altarelli-Parisi kernel even in the endpoint region, and the parton distribution function can be factorized further into a collinear part and the soft Wilson line. The factorized form for the structure functions is obtained by the two-step matching, and the radiative corrections or the evolution for each factorized part can be computed in perturbation theory. We present the radiative corrections of each factorized part to leading order in alpha_s, including the zero-bin subtraction for the collinear part.Comment: 40 pages, 12 figures. Two major changes: (1) The zero-bin subtraction is included in the radiative corrections for the collinear part. (2) The parton distribution function near the endpoint region is considered including the soft part. Figures and references are added accordingl

Structure of divergences in Drell-Yan process with small transverse momentum

We consider the structure of divergences in Drell-Yan process with small transverse momentum. The factorization proof is not trivial because various kinds of divergences are intertwined in the collinear and soft parts at high orders. We prescribe a method to disentangle the divergences in the framework of the soft-collinear effective theory. The rapidity divergence is handled by introducing the $\delta$ regulator in the collinear Wilson lines. The collinear part, which consists of the transverse-momentum-dependent parton distribution function (TMDPDF), is free of the rapidity divergence after the soft zero-bin subtraction. There still remains the problem of mixing between the ultraviolet and infrared divergences, which forbids the renormalization group description. We show that the mixing is cancelled by the soft function. This suggests that the collinear and soft parts should be treated as a whole in constructing a consistent factorization theorem. The renormalization group behavior of the combined collinear and soft parts is presented explicitly at one loop. We also show that the integrated PDF can be obtained by integrating the TMDPDF over the transverse momentum.Comment: 26 pages, 2 figures. Version published in PR

Contribution of b→sggb \to sgg through the QCD anomaly in exclusive decays B±→(η′,η)(K±,K∗±)B^{\pm}\to (\eta^{\prime},\eta)(K^{\pm}, K^{*\pm}) and B0→(η′,η)(K0,K∗0)B^{0}\to (\eta^{\prime},\eta)(K^{0},K^{*0})

We compute the decay rates for the exclusive decays $B^{\pm} \to (\eta^{\prime},\eta) (K^{\pm}, K^{*\pm})$ and $B^{0}\to (\eta^{\prime},\eta) (K^{0}, K^{*0})$ in a QCD-improved factorization framework by including the contribution from the process $b\to sgg \to s (\eta^{\prime}, \eta)$ through the QCD anomaly. This method provides an alternative estimate of the contribution $b \to s c\bar{c} \to s(\eta,\eta^\prime)$ to these decays as compared to the one using the intrinsic charm content of the $\eta^{\prime}$ and $\eta$ mesons determined through the decays $J/\psi \to (\eta,\eta^\prime ,\eta_c) \gamma$. The resulting branching ratios are compared with the CLEO data on $B^{\pm} \to \eta^{\prime} K^{\pm}$ and $B^{0} \to \eta^{\prime} K^{0}$ and predictions are made for the rest.Comment: 16 pages including 4 postscript figures; uses epsfig. The most recent branching ratios from CLEO, ref. [5], are taken into account. The theory part is unchange

The Central Role of Noise in Evaluating Interventions that Use Test Scores to Rank Schools

Several countries have implemented programs that use test scores to rank schools, and to reward or penalize them based on their students' average performance. Recently, Kane and Staiger (2002) have warned that imprecision in the measurement of school-level test scores could impede these efforts. There is little evidence, however, on how seriously noise hinders the evaluation of the impact of these interventions. We examine these issues in the context of Chile's P-900 program a country-wide intervention in which resources were allocated based on cutoffs in schools' mean test scores. We show that transitory noise in average scores and mean reversion lead conventional estimation approaches to greatly overstate the impacts of such programs. We then show how a regression discontinuity design that utilizes the discrete nature of the selection rule can be used to control for reversion biases. While the RD analysis provides convincing evidence that the P-900 program had significant effects on test score gains, these effects are much smaller than is widely believed.

Azimuthal Correlation in Lepton-Hadron Scattering via Charged Weak-Current Processes

We consider the azimuthal correlation of the final-state particles in charged weak-current processes. This correlation provides a test of perturbative quantum chromodynamics. The azimuthal asymmetry is large in the semi-inclusive processes in which we identify a final-state hadron, say, a charged pion compared to that in the inclusive processes in which we do not identify final-state particles and use only the calorimetric information. In semi-inclusive processes the azimuthal asymmetry is more conspicuous when the incident lepton is an antineutrino or a positron than when the incident lepton is a neutrino or an electron. We analyze all the possible charged weak-current processes and study the quantitative aspects of each process. We also compare this result to the ep scattering with a photon exchange.Comment: 25 pages, 2 Postscript figures, uses RevTeX, fixes.st

On measuring alpha in B(t)-> rho^\pm pi^\mp

Defining a most economical parametrization of time-dependent B-> rho^\pm pi^\mp decays, including a measurable phase alpha_{eff} which equals the weak phase alpha in the limit of vanishing penguin amplitudes, we propose two ways for determining alpha in this processes. We explain the limitation of one method, assuming only that two relevant tree amplitudes factorize and that their relative strong phase, delta_t, is negligible. The other method, based on broken flavor SU(3), permits a determination of alpha in B^0-> rho^\pm pi^\mp in an overconstrained system using also rate measurements of B^{0,+}-> K^* pi and B^{0,+}->rho K. Current data are shown to restrict two ratios of penguin and tree amplitudes, r_\pm, to a narrow range around 0.2, and to imply an upper bound |alpha_{eff} - alpha| < 15 degrees. Assuming that delta_t is much smaller than 90 degrees, we find alpha =(93\pm 16) degrees and (102 \pm 20) degrees using BABAR and BELLE results for B(t)-> rho^\pm pi^mp. Avoiding this assumption for completeness, we demonstrate the reduction of discrete ambiguities in alpha with increased statistics, and show that SU(3) breaking effects are effectively second order in r_\pm.Comment: 23 pages, 2 figures, data and references updated, to be published in Phys. Rev.

Nonfactorizable B→χc0KB\to\chi_{c0}K decay and QCD factorization

We study the unexpectedly large rate for the factorization-forbidden decay $B\to \chi_{c0}K$ within the QCD factorization approach. We use a non-zero gluon mass to regularize the infrared divergences in vertex corrections. The end-point singularities arising from spectator corrections are regularized and carefully estimated by the off-shellness of quarks. We find that the contributions arising from the vertex and leading-twist spectator corrections are numerically small, and the twist-3 spectator contribution with chiral enhancement and linear end-point singularity becomes dominant. With reasonable choices for the parameters, the branching ratio for $B\to\chi_{c0}K$ decay is estimated to be in the range $(2-4)\times 10^{-4}$, which is compatible with the Belle and BaBar data.Comment: Appendix added; it is emphasized that in the dominant twist-3 spectator corrections the end-point singularity contributions may be estimated by the off-shellness of the charm quark (by the binding energy in charmonium) and the gluon (by the transverse momentum of the light quark in the kaon

Soft-Collinear Messengers: A New Mode in Soft-Collinear Effective Theory

It is argued that soft-collinear effective theory for processes involving both soft and collinear partons, such as exclusive B-meson decays, should include a new mode in addition to soft and collinear fields. These "soft-collinear messengers" can interact with both soft and collinear particles without taking them far off-shell. They thus can communicate between the soft and collinear sectors of the theory. The relevance of the new mode is demonstrated with an explicit example, and the formalism incorporating the corresponding quark and gluon fields into the effective Lagrangian is developed.Comment: 22 pages, 5 figures. Extended Section 6, clarifying the relevance of different types of soft-collinear interaction

Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure

The central role of noise in evaluating interventions that use test scores to rank schools

Several countries have implemented programs that use test scores to rank schools, and to reward or penalize them based on their students' average performance. Recently, Kane and Staiger (2002) have warned that imprecision in the measurement of school-level test scores could impede these efforts. There is little evidence, however, on how seriously noise hinders the evaluation of the impact of these interventions. We examine these issues in the context of Chile's P-900 program-a country-wide intervention in which resources were allocated based on cutoffs in schools' mean test scores. We show that transitory noise in average scores and mean reversion lead conventional estimation approaches to greatly overstate the impacts of such programs. We then show how a regression discontinuity design that utilizes the discrete nature of the selection rule can be used to control for reversion biases. While the RD analysis provides convincing evidence that the P-900 program had significant effects on test score gains, these effects are much smaller than is widely believed