80,559 research outputs found

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

We study the azimuthal angular dependence of back-to-back di-jet production
in unpolarized hadron scattering $H_A+H_B \to J_1 + J_2 +X$, 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 ($J_q+J_q$) or a quark-antiquark pair
($J_q+J_{\bar{q}}$), there is a $\cos \delta \phi$ angular dependence of the
di-jet, with $\delta \phi=\phi_1-\phi_2$, and $\phi_1$ and $\phi_2$ are the
azimuthal angles of the two individual jets. In the case of $J_q+J_q$
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 $\cos \delta \phi$ asymmetry of di-jet production at
RHIC, showing that the color factor enhancement in the angular dependent of
$J_q+J_q$ 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

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., $n_{ext}\propto R^{-k}$, 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: $t_\oplus=R/4(4-k)\gamma^2c$, and
also derive a new relation among the comoving time, the shock radius and the
fireball's Lorentz factor: $t_{co}=2R/(5-k)\gamma c$. 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 $p=2.5$, implied from the
spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming
$k=2$.Comment: 17 pages, no figures, Latex file, MNRAS in pres

### Local linear spatial quantile regression

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

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