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Register a new userAcceleration of an unpolarized proton along a uniform magnetic field: Casimir momentum of leptons
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Authors
Manuel Donaire
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It has been recently shown that a chiral molecule accelerates linearly along a spatially uniform magnetic field, as a result of the parity-time symmetry breaking induced in its QED self-interaction. In this work we extend this result to fundamental particles which present EW self-interaction, in which case parity is violated by the EW interaction itself. In particular, we demonstrate that, in a spatially uniform and adiabatically time-varying magnetic field, an unpolarized proton coupled to the leptonic vacuum acquires a kinetic momentum antiparallel to the magnetic field, whereas virtual leptons gain an equivalent $Casimir$ $momentum$ in the opposite direction. That momentum is proportional to the magnetic field and to the square of Fermis constant. We prove that the kinetic energy of the proton is a magnetic energy which forms part of its EW self-energy.
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It is commonly assumed that a charged particle does not accelerate linearly along a spatially uniform magnetic field. We show that this is no longer the case if the interaction of the particle with the quantum vacuum is chiral, in which case parity and time-reversal symmetries are simultaneously broken. In particular, this is the situation of an electroweak interacting particle in the presence of a uniform magnetic field. We demonstrate first that, in a spatially uniform and adiabatically time-varying magnetic field, a proton coupled to the leptonic vacuum acquires a kinetic momentum antiparallel to the magnetic field, whereas virtual leptons gain an equivalent Casimir momentum in the opposite direction. Remarkably, leptons remain virtual throughout the process, which means that the proton acceleration is not caused by the recoil associated to the emission of any actual particle. The kinetic energy of the proton is part of its electroweak self-energy, which is provided by the source of magnetic field. In addition we find that, in a constant and uniform magnetic field, the adiabatic spin-relaxation of a single proton is accompanied by its acceleration along the magnetic field. We estimate that, at the end of the spin-polarization process, the proton reaches a velocity of the order of $mu$m/s. The latter finding may lie within the scope of experimental observations.
As is the case for all light coloured Standard Model particles, also photons and charged leptons appear as constituents in ultrarelativistic hadron beams, and admit a parton density function (PDF). It has been shown recently that the photon PDF can be given in terms of the structure functions and form factors for electron-proton scattering. The same holds for lepton PDFs. In the present work we set up a calculation of the lepton PDFs at next-to-leading order, using the same data input needed in the photon case. A precise knowledge of the lepton densities allows us to study lepton-initiated processes even at a hadron collider, with all possible combinations of same-charge, opposite-charge, same-flavour, different-flavour leptons and leptons-quarks, most of which cannot be realized in any other foreseeable experiment. The lepton densities in the proton are extremely small, so that their contribution to Standard Model processes is generally shadowed by processes initiated by coloured partons. We will show, however, that there are cases where these processes can be relevant, giving rise to rare Standard Model signatures and to new production channels, that can enlarge the discovery potential of New Physics at the LHC and future high energy colliders with hadrons in the initial state.
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