Odd Magne Ogreid

A bstract: We investigate CP violation in the process H ^± → W ^± Z within the framework of the two-Higgs-Doublet model (2HDM). Amplitudes are expressed transparently in terms of physical couplings. Our analysis qualitatively confirms recent results by Kanemura and Mura, for the interference between one-loop bosonic and fermionic amplitudes. Furthermore, we identify additional sources of CP violation arising from internal interference among the bosonic and also among the fermionic loop amplitudes. In the alignment limit, the asymmetry would vanish in the absence of fermionic loop contributions when the sum of the masses of the additional neutral scalars is higher than the mass of the Z . Our results allow for generic Yukawa couplings, and cover both explicit and spontaneous CP violation. For inclusive W ^± and Z decays, the CP violation will only manifest itself as a charge asymmetry.

A bstract: We investigate in detail a new class (GOOFy) of transformations for bosonic and fermionic fields that leave relevant parts of the Lagrangian density unchanged. The transformations act upon complex scalar fields Φ and Φ ^† employing generalized charge conjugation ( C ) transformation in a non-consistent manner , i.e. allowing for Φ ^† → (Φ ^† ) ′ ≠ (Φ ′ ) ^† . Requiring invariance of the kinetic terms under such transformations specifies the form of (Φ ^† ) ′ . An analogous strategy is also adopted for fermionic fields. This offers a systematic way to construct new GOOFy-invariant field-theoretical models. It turns out that theories which are invariant with respect to these GOOFy transformations satisfy relations among parameters that are found to be RGE-stable up to two and three loop orders, thus constituting fixed-points under running of the RGE. This has been verified for various theories containing different numbers of bosonic and fermionic fields. In particular it has been shown that the Standard Model (SM) can not be a viable electroweak theory if demanding invariance under GOOFy transformations. However, the two-Higgs-Doublet Model (2HDM) may be invariant under GOOFy transformations (Yukawa couplings included), providing an interesting phenomenological example of physics beyond the SM. The most striking aspect of this study is the RGE stability of new relations between model parameters in a wide class of field theories. We also present a set of new relations between 2HDM potential parameters that constitute a fixed point under the running of the RGE up to at least three loop order.

Recently, a hitherto unknown class of renormalization group stable relations between parameters of bosonic field theories has been identified and dubbed as the r 0 or “GOOFy” symmetries. Here, one-loop properties of the r 0 invariant two-Higgs doublet model and a minimal symmetric model are discussed. It is concluded that the symmetry is present at the one-loop provided the UV cutoff squared transforms nontrivially under r 0 . The minimal model requires the presence of two real fields.

We investigate in detail a new class (GOOFy) of transformations for bosonic and fermionic fields that leave the Lagrangian density unchanged. The transformations act upon complex scalar fields Φand Φ^\dagger employing generalized charge conjugation (C) transformation in a non-consistent manner, i.e. allowing for Φ\dagger \to (Φ\dagger)^\prime \neq (Φ^\prime)^\dagger. Requiring invariance of the kinetic terms under such transformations specifies the form of (Φ\dagger)^\prime. An analogous strategy is also adopted for fermionic fields. This offers a systematic way to construct new GOOFy-invariant field-theoretical models. It turns out that theories which are invariant with respect these GOOFy transformations satisfy relations among parameters that are found to be RGE-stable up to two and three loop orders, thus constituting fixed-points under running of the RGE. This has been verified for various theories containing different numbers of bosonic and fermionic fields. In particular it has been shown that the Standard Model (SM) can not be a viable electroweak theory if demanding invariance under GOOFy transformations. However, the two-Higgs-Doublet Model (2HDM) may be invariant under GOOFy transformations (Yukawa couplings included), providing an interesting phenomenological example of physics beyond the SM. The most striking aspect of this study is the RGE stability of new relations between model parameters in a wide class of field theories. We also present a set of new relations between 2HDM potential parameters that constitute a fixed point under the running of the RGE up to at least three loop order.

We investigate CP violation in the process H^\pm \to W^\pm Z within the framework of the two-Higgs-Doublet model (2HDM). Amplitudes are expressed transparently in terms of physical couplings. Our analysis qualitatively confirms recent results by Kanemura and Mura, for the interference between one-loop bosonic and fermionic amplitudes. Furthermore, we identify additional sources of CP violation arising from internal interference among the bosonic and also among the fermionic loop amplitudes. In the alignment limit, the asymmetry would vanish in the absence of fermionic loop contributions when the sum of the masses of the additional neutral scalars is higher than the mass of the Z. Our results allow for generic Yukawa couplings, and cover both explicit and spontaneous CP violation. For inclusive W^\pm and Z decays, the CP violation will only manifest itself as a charge asymmetry.

We explore the phenomenology of Weinberg’s ℤ ₂ × ℤ ₂ symmetric three-Higgs-doublet potential, allowing for spontaneous violation of CP due to complex vacuum expectation values. An overview of all possible ways of satisfying the stationary-point conditions is given, with one, two or three non-vanishing vacuum expectation values, together with conditions for CP conservation in terms of basis invariants. All possible ways of satisfying the conditions for CP conservation are given. Scans of allowed parameter regions are given, together with measures of CP violation, in terms of the invariants. The light states identified in an earlier paper are further explored in terms of their CP-violating couplings. Loop-induced CP violation in WWZ couplings, as well as charge-asymmetric scattering are also commented on.

Recently, a hitherto unknown class of RG-stable relations between parameters of bosonic field theories have been identified and dubbed as the r0 or 'GOOFy' symmetries. Here, 1-loop properties of the r0 invariant 2-Higgs Doublet Model and a minimal symmetric model are discussed. It is concluded that the symmetry is present at the 1-loop provided the UV cut-off squared transforms non-trivially under r0. The minimal model requires the presence of two real fields.