The ratio of the nucleon F2 structure functions, F n 2 /F p 2 , is determined by the MARATHON experiment from measurements of deep inelastic scattering of electrons from 3 H and 3 He nuclei. The experiment was performed in the Hall A Facility of Jefferson Lab and used two high resolution spectrometers for electron detection, and a cryogenic target system which included a low-activity tritium cell. The data analysis used a novel technique exploiting the mirror symmetry of the two nuclei, which essentially eliminates many theoretical uncertainties in the extraction of the ratio. The results, which cover the Bjorken scaling variable range 0.19 < x < 0.83, represent a significant improvement compared to previous SLAC and Jefferson Lab measurements for the ratio. They are compared to recent theoretical calculations and empirical determinations of the F n 2 /F p 2 ratio.
High precision data of dilepton angular distributions in γ * /Z production were reported recently by the CMS Collaboration covering a broad range of the dilepton transverse momentum, qT , up to ∼ 300 GeV. Pronounced qT dependencies of the λ and ν parameters, characterizing the cos 2 θ and cos 2φ angular distributions, were found. Violation of the Lam-Tung relation was also clearly observed. We show that the qT dependence of λ allows a determination of the relative contributions of the qq annihilation versus the qG Compton process. The violation of the Lam-Tung relation is attributed to the presence of a non-zero component of the q −q axis in the direction normal to the "hadron plane" formed by the colliding hadrons. The magnitude of the violation of the Lam-Tung relation is shown to reflect the amount of this 'non-coplanarity". The observed qT dependencies of λ and ν from the CMS and the earlier CDF data can be well described using this approach.
High precision data of lepton angular distributions for γ * /Z production in pp collisions at the LHC, covering broad ranges of dilepton transverse momenta (qT ) and rapidity (y), were recently reported. Strong qT dependencies were observed for several angular distribution coefficients, Ai, including A0 − A4. Significant y dependencies were also found for the coefficients A1, A3 and A4, while A0 and A2 exhibit very weak rapidity dependence. Using an intuitive geometric picture, we show that the qT and y dependencies of the angular distributions coefficients can be well described.
Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam-Tung relation. While the violation of the Lam-Tung relation is often expressed by frame-dependent quantities, we note that alternative frame-independent quantities are preferred.
Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. To illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound nonlinear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis to avoid confirmation bias.
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