We study the non-relativistic behavior of a particle with electric dipole moment and interacting with external electromagnetic fields on a noncommutative space (NCS). For a special configuration of the field, the phase of an electric dipole is derived as an application of the Aharonov-Bohm effect to a system composed of two charges. We find that the quantum phase for an electric dipole obtains some corrections, and these corrections depend on the noncommutative parameter explicitly.
As part of a recent analysis of exclusive two-photon production of W + W − pairs at the LHC, the CMS experiment used di-lepton data to obtain an "effective" photon-photon luminosity. We show how the CMS analysis on their 8 TeV data, along with some assumptions about the likelihood for events in which the proton breaks up to pass the selection criteria, can be used to significantly constrain the photon parton distribution functions, such as those from the CTEQ, MRST, and NNPDF collaborations. We compare the data with predictions using these photon distributions, as well as the new LUXqed photon distribution. We study the impact of including these data on the NNPDF2.3QED, NNPDF3.0QED and CT14QEDinc fits. We find that these data place a useful and complementary cross-check on the photon distribution, which is consistent with LUXqed prediction while suggesting that the NNPDF photon error band should be significantly reduced. Additionally, we propose a simple model for describing the two-photon production of W + W − at the LHC. Using this model, we constrain the amount of inelastic photon that remains after the experimental cuts are applied. PACS numbers: 12.15.Ji, 12.38 Cy, 13.85.Qk With the start of the 13 TeV run of the Large Hadron Collider (LHC), more precise theory calculations are needed to correctly interpret the present and upcoming experimental data. Calculations at the next-to-nextto-leading order (NNLO) in Quantum Chromodynamics (QCD) are becoming the standard, so that the theoretical uncertainty can be reduced to the same order as the experimental uncertainty. At this level of precision, the leading-order electroweak correction is also important, because the square of the coupling of the strong interaction (α s ) is of the same order of magnitude as the electromagnetic coupling (α). Therefore, it becomes necessary to include electroweak corrections in the calculations.One particular electroweak correction of interest is that due to photons coming from the proton in the initial state. This requires the inclusion of the photon as a parton inside the proton, with an associated parton distribution function (PDF). This is necessary both for consistency when electroweak corrections are included and because the photon-initiated processes can become significant at high energies. The treatment of the photon PDF in a global analysis was first performed by the MRST collaboration [1]. Since then, both NNPDF and CTEQ collaborations have introduced photon PDFs [2, 3], along with PDF evolution at leading order (LO) in QED and next-to-leading order (NLO) or NNLO in QCD. The MRST2004QED set contains photon PDFs with a parametrization based on radiation off of "primordial" up and down quarks, with the photon radiation cut off at either the current quark masses (MRST0), or the constituent quark masses (MRST1) [1]. The NNPDF2.3QED set uses a more general photon parametrization, which was then constrained by Drell-Yan data at the LHC [2]. This was recently updated in the NNPDF3.0QED set [4]. The CT14QED set also uses the r...
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