RevModPhys.84.1477】Tests of the standard electroweak model at the energy frontier

Allowed by the gauge symmetries weinberg 1979 l5 cij

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Unformatted text preview: e symmetries (Weinberg, 1979), L5 ¼ cij iT ðL ÞCðT Lj Þ þ H:c:; à (1) where Li is the lepton doublet field of the ith generation and  is the Higgs-doublet field [the 2  2 matrix  and the 4  4 charge-conjugation matrix C are present to ensure invariance under SUð2ÞL and Lorentz transformations, respectively]. When the Higgs doublet acquires a vacuum-expectation value pffiffiffi hi ¼ ð0; v= 2Þ (v ¼ 246 GeV), this term gives rise to a (Majorana) mass for neutrinos, ij L5 ¼ À1M iT Cj þ H:c: 2 (2) ij where M ¼ cij v2 =à is the neutrino mass matrix. Because of the small inferred masses of neutrinos, the scale à lies around 1015 GeV, assuming cij is not much less than order unity. There are other indications that the SM is not a complete description of nature, most of them related to gravitation and cosmology. Even with massive neutrinos included, the SM particles only constitute 4.6% of the present Universe, with the remainder in mysterious dark matter (23%) and dark energy (72%). Neither dark matter nor dark energy are accommodated in the SM. There is no adequate mechanism for baryogenesis (the observed excess of baryons over Rev. Mod. Phys., Vol. 84, No. 4, October–December 2012 antibaryons) or inflation, which is the simplest explanation of the observed temperature fluctuations in the cosmic microwave background. The SM also provides no explanation of the strong CP problem: the lack of observed CP violation in the strong interaction, which is allowed by the SM. If physics beyond the SM lies at an energy scale less than 1 TeV, then we should be able to observe it directly at highenergy colliders. If it lies at a scale greater than 1 TeV, then we can parametrize its effects via higher-dimension operators, suppressed by inverse powers of the scale of new physics à exactly as in the case of neutrino masses described above. Other than the dimension-five operator responsible for neutrino masses, the lowest-dimension operators are of dimension six, and are therefore suppressed by two inverse powers of Ã. If à is of order 1015 GeV, as suggested by neutrino masses, then these operators are so suppressed that they are unobservable, with the possible exception of baryonnumber violating operators that mediate nucleon decay. However, there could be more than one scale of new physics, and if this scale is not much greater than 1 TeV, its effects could be observable via dimension-six operators. Operators of a dimension greater than six are suppressed by even more inverse powers of à and can be neglected. There are many dimension-six operators allowed by the SM gauge symmetry (Buchmuller and Wyler, 1986). There are three ways to detect the presence of these operators. The first is to observe phenomena that are absolutely forbidden (or extremely suppressed) in the SM, such as nucleon decay. The second is to make measurements with such great precision that the small effects of the dimension-six operators manifest themselves. The t...
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