80,559 research outputs found

    Azimuthal angle dependence of di-jet production in unpolarized hadron scattering

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    We study the azimuthal angular dependence of back-to-back di-jet production in unpolarized hadron scattering HA+HBJ1+J2+XH_A+H_B \to J_1 + J_2 +X, arising from the product of two Boer-Mulders functions, which describe the transverse spin distribution of quarks inside an unpolarized hadron. We find that when the di-jet is of two identical quarks (Jq+JqJ_q+J_q) or a quark-antiquark pair (Jq+JqˉJ_q+J_{\bar{q}}), there is a cosδϕ\cos \delta \phi angular dependence of the di-jet, with δϕ=ϕ1ϕ2\delta \phi=\phi_1-\phi_2, and ϕ1\phi_1 and ϕ2\phi_2 are the azimuthal angles of the two individual jets. In the case of Jq+JqJ_q+J_q production, we find that there is a color factor enhancement in the gluonic cross-section, compared with the result from the standard generalized parton model. We estimate the cosδϕ\cos \delta \phi asymmetry of di-jet production at RHIC, showing that the color factor enhancement in the angular dependent of Jq+JqJ_q+J_q production will reverse the sign of the asymmetry.Comment: 10 pages, 7 figures, version accepted by Physical Review

    Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

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    The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, viz., nextRkn_{ext}\propto R^{-k}, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: t=R/4(4k)γ2ct_\oplus=R/4(4-k)\gamma^2c, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: tco=2R/(5k)γct_{co}=2R/(5-k)\gamma c. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p=2.5p=2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming k=2k=2.Comment: 17 pages, no figures, Latex file, MNRAS in pres

    Local linear spatial quantile regression

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    Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.Let {(Yi,Xi), i ∈ ZN} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x → qp(x), p ∈ (0, 1), x ∈ Rd , the spatial quantile regression function of order p, characterized by P{Yi ≤ qp(x)|Xi = x} = p. Assume that the process has been observed over an N-dimensional rectangular domain of the form In := {i = (i1, . . . , iN) ∈ ZN|1 ≤ ik ≤ nk, k = 1, . . . , N}, with n = (n1, . . . , nN) ∈ ZN. We propose a local linear estimator of qp. That estimator extends to random fields with unspecified and possibly highly complex spatial dependence structure, the quantile regression methods considered in the context of independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation for the estimators of qp and its first-order derivatives, from which we establish consistency and asymptotic normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time series mixing concepts. The size of the rectangular domain In is allowed to tend to infinity at different rates depending on the direction in ZN (non-isotropic asymptotics). The method provides muchAustralian Research Counci