One-loop chiral amplitudes of Møller scattering process

The high energy amplitudes of the large angles Møller scattering are calculated in the frame of chiral basis in Born and 1-loop QED level. Taking into account as well the contribution from emission of soft real photons the compact relations free from infrared divergences are obtained. The expressions for the contributions to the cross section of individual chiral amplitudes are in agreement with renormalization group predictions.     

Two-loop electroweak vertex corrections for polarized Møller scattering

The contributions to the electron-electron-photon vertex of two-loop electroweak corrections are calculated. The relative correction to the parity-violating asymmetry of Møller scattering for the case of 11 GeV electron scattered off the electron at rest is found to be about–0.0034 and should be taken into account at future experiment MOLLER at JLab.     

Constructing Hadamard States via an Extended Møller Operator

We consider real scalar field theories, whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential V. By means of an extension of the standard definition of Møller operator, we construct an isomorphism between the associated spaces of smooth solutions and between the associated algebras of observables. On the one hand, such isomorphism is non-canonical, since it depends on the choice of a smooth time-dependant cut-off function \({\chi}\). On the other hand, given any quasi-free Hadamard state for a theory with a given V, such isomorphism allows for the construction of another quasi-free Hadamard state for a different potential. The resulting state preserves also the invariance under the action of any isometry, whose associated Killing field \({\xi}\) is complete and fulfilling both \({\mathcal{L}_\xi V=0 \,\, {\rm and} \,\, \mathcal{L}_\xi\chi=0}\). Eventually, we discuss a sufficient condition to remove on static spacetimes, the dependence on the cutoff via a suitable adiabatic limit.     

Møller Energy-Momentum Distribution of Higher Dimensional Vaidya Space-Time

In this paper, we intend to clarify the energy-momentum problem of higher dimensional Vaidya space-time in the general theory of relativity. In this connection, Møller energy and momentum for the higher dimensional Vaidya space-time are evaluated in the frame of general relativity. We have obtained that the Møller energy distribution of higher dimensional Vaidya space-time is equal to zero, while the Møller momentum distribution of higher dimensional Vaidya space-time is not equal to zero.     

One-loop approximation of Møller scattering in generalized Krein-space quantization

It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime. In this processes ultraviolet and infrared divergences have been automatically eliminated. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λφ ⁴) has been achieved through the consideration of the negative-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field theory without any divergences. Pursuing this approach, we express Wick’s theorem and calculate Møller scattering in the one-loop approximation in generalized Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.     

Precision measurement of the weak mixing angle in Møller scattering

We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (M?ller) scattering: A(PV) = [-131 +/- 14(stat) +/- 10(syst)] x 10(-9), leading to the determination of the weak mixing angle sin2(thetaW(eff) = 0.2397 +/- 0.0010(stat) +/- 0.0008(syst), evaluated at Q2 = 0.026 GeV2. Combining this result with the measurements of sin2(thetaW(eff) at the Z0 pole, the running of the weak mixing angle is observed with over 6sigma significance. The measurement sets constraints on new physics effects at the TeV scale.     

Electroweak radiative corrections to polarized Møller scattering at high energies

The cross section for with arbitrary electron polarizations is calculated within the Electroweak Standard Model for energies large compared to the electron mass, including the complete virtual and soft-photonic radiative corrections. The relevant analytical results are listed, and a numerical evaluation is presented for the unpolarized and polarized cross sections as well as for polarization asymmetries. The relative weak corrections are typically of the order of 10%. At low energies, the bulk of the corrections is due to the running of the electromagnetic coupling constant. For left-handed electrons, at high energies the vertex and box corrections involving virtual W bosons become very important. The polarization asymmetry is considerably reduced by the weak radiative corrections. Received: 22 July 1998 / Published online: 8 September 1998     

Analytical nuclear gradients of the explicitly correlated Møller–Plesset second-order energy

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller–Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree–Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller–Plesset theory outperforms conventional second-order Møller–Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level.     

Complete calculation of electroweak corrections for polarized Møller scattering at high energies

A complete calculation of electroweak radiative corrections to observables of polarized Møller scattering at high energies was performed. This calculation took explicitly into account contributions caused by hard bremsstrahlung. A FORTRAN code that permitted including radiative corrections to high-energy Møller scattering under arbitrary electron-detection conditions was written. It was shown that the electroweak corrections caused by hard bremsstrahlung were rather strongly dependent on the choice of experimental cuts and changed substantially the polarization asymmetry in the region of high energies and over a broad interval of scattering angles.     

Bhabha versus Møller scattering as a contact-interaction analyzer at a polarized Linear Collider

We discuss electron-electron contact-interaction searches in the processes and at planned Linear Colliders run in the e ⁺ e ^- and e ^- e ^- modes with both beams longitudinally polarized. Our analysis is based on the measurement, for the two processes, of polarized differential cross sections, and allows one to simultaneously take into account the general set of electron contact-interaction couplings as independent, non-zero, parameters thus avoiding the simplifying choice of a model. We evaluate the corresponding model-independent constraints on the contact coupling constants, emphasizing the role of the available beam polarization and the complementarity, as far as the chirality of the constants is concerned, of the two processes in giving the best constraints. Received: 15 October 2002, Revised: 28 April 2003, Published online: 18 June 2003     

A new class of Fermionic Projectors: Møller operators and mass oscillation properties

Recently, a new functional analytic construction of quasi-free states for a self-dual CAR algebra has been presented in Finster and Reintjes (Adv Theor Math Phys 20:1007, 2016). This method relies on the so-called strong mass oscillation property. We provide an example where this requirement is not satisfied, due to the nonvanishing trace of the solutions of the Dirac equation on the horizon of Rindler space, and we propose a modification of the construction in order to weaken this condition. Finally, a connection between the two approaches is built.     

One-loop electroweak corrections for polarized Møller scattering at different renormalization schemes and conditions

Using two different approaches, we perform detailed calculations of the one-loop (Next-to-Leading Order (NLO)) electroweak radiative corrections to the parity violating e ^? e ^? → e ^? e ^?(γ) scattering asymmetry. First approach, more classical, relies on calculations “by hand” with reasonable approximations, second approach relies on program packages FeynArts, FormCalc, LoopTools, and FORM. The detailed numerical analysis of the various contributions is provided for a wide range of energies relevant for the ultraprecise 11 GeV MOLLER experiment planned at the JLab, as well as future experiments at the International Linear Collider (ILC). The numerical results obtained within the on-shell renormalization scheme using two different sets of renormalization conditions are in excellent agreement. We also calculate the total NLO correction in the Constrained Differential Renormalization (CDR) scheme. Analysis of the results, along with the increasing experimental precision, shows that it is feasible that the corrections at the Next-to-Next-to-Leading Order (NNLO) level may be important for the next generation of experiments.     

Parity-violating M?ller scattering

The A4 collaboration at the MAMI accelerator at Mainz investigates the contribution of strange quarks to the form factors of the nucleon by measuring the parity violating asymmetry A _PV in the cross section of elastic scattering of longitudinally polarized electrons off hydrogen and deuterium. Recently, measurements at backward angles at a four momentum transfer of Q ²?=?0.22 GeV² were completed. Together with previous results at forward angles at the same momentum transfer, the strange electric and magnetic form factors $G_E^s$ and $G_M^s$ can be disentangled.     

Observation of parity nonconservation in møller scattering

We report a measurement of the parity-violating asymmetry in fixed target electron-electron (M?ller) scattering: A(PV)=[-175+/-30(stat)+/-20(syst)] x 10(-9). This first direct observation of parity nonconservation in M?ller scattering leads to a measurement of the electron's weak charge at low energy Q(e)(W)=-0.053+/-0.011. This is consistent with the standard model expectation at the current level of precision: sin((2)theta(W)(M(Z))((-)MS)=0.2293+/-0.0024(stat)+/-0.0016(syst)+/-0.0006(theory).     

Møller’s Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane

Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and depends only on the generalized (effective) mass and charge which incorporate corrections of first order in the noncommutativity parameter.