Pulsar Velocity with Three-Neutrino Oscillations in Non-adiabatic Processes

We have studied the position dependence of neutrino energy on the Kusenko-Segr\`{e} mechanism as an explanation of the proper motion of pulsars. The mechanism is also examined in three-generation mixing of neutrinos and in a non-adiabatic case. The position dependence of neutrino energy requires the higher value of magnetic field such as $B\sim 3\times 10^{15}$ Gauss in order to explain the observed proper motion of pulsars. It is shown that possible non-adiabatic processes decrease the neutrino momentum asymmetry, whereas an excess of electron neutrino flux over other flavor neutrino fluxes increases the neutrino momentum asymmetry. It is also shown that a general treatment with all three neutrinos does not modify the result of the two generation treatment if the standard neutrino mass hierarchy is assumed.Comment: 8 pages, REVTEX, no figure

Axial Anomaly and the Nucleon Spin

In this letter, we have taken a particular Lagrangian, which was introduced to resolve U(1) problem, as an effective QCD Lagrangian, and have derived a formula of the quark content of the nucleon spin. The difference between quark content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n) is evaluated by this formula. Neglecting the higher-order isospin corrections, this formula can reduce to Efremov's results in the large N_c limit.Comment: (1) A few changes and corrections made following Referee. (2) The difference between quark content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n) is evaluated. Neglecting the higher-order isospin corrections, this formula can reduce to Efremov's results in the large N_c limi

Monitoring Frequency of Intra‐Fraction Patient Motion Using the ExacTrac System for LINAC‐based SRS Treatments

Purpose: The aim of this study was to investigate the intra‐fractional patient motion using the ExacTrac system in LINAC‐based stereotactic radiosurgery (SRS). Method: A retrospective analysis of 104 SRS patients with kilovoltage image‐guided setup (Brainlab ExacTrac) data was performed. Each patient was imaged pre‐treatment, and at two time points during treatment (1st and 2nd mid‐treatment), and bony anatomy of the skull was used to establish setup error at each time point. The datasets included the translational and rotational setup error, as well as the time period between image acquisitions. After each image acquisition, the patient was repositioned using the calculated shift to correct the setup error. Only translational errors were corrected due to the absence of a 6D treatment table. Setup time and directional shift values were analyzed to determine correlation between shift magnitudes as well as time between acquisitions. Results: The average magnitude translation was 0.64 ± 0.59 mm, 0.79 ± 0.45 mm, and 0.65 ± 0.35 mm for the pre‐treatment, 1st mid‐treatment, and 2nd mid‐treatment imaging time points. The average time from pre‐treatment image acquisition to 1st mid‐treatment image acquisition was 7.98 ± 0.45 min, from 1st to 2nd mid‐treatment image was 4.87 ± 1.96 min. The greatest translation was 3.64 mm, occurring in the pre‐treatment image. No patient had a 1st or 2nd mid‐treatment image with greater than 2 mm magnitude shifts. Conclusion: There was no correlation between patient motion over time, in direction or magnitude, and duration of treatment. The imaging frequency could be reduced to decrease imaging dose and treatment time without significant changes in patient position

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