The strong CP problem revisited

The strong CP-violating θ parameter, the problem of strong CP violation and their status are reviewed. Among all possibilities, two natural solutions to the strong CP puzzle are thoroughly discussed and emphasized: the axion-type mechanism for hard CP violation and the non-Peccei-Quinn scheme for spontaneous CP nonconservation. Basic properties of the axion are derived from the modified Peccei-Quinn symmetry. Astrophysical and cosmological constraints are described for two different types of invisible axions. In nonaxion solutions, CP is spontaneously broken at the grand-unification scale and the CP phase is transmitted down to the low energy sector by quantum effects or by fermion mixing effects. As a by-product, the cosmological baryon asymmetry, which is caused by the same source of CP violation ultimately responsible for the kaon ε parameter, is generated adequately at the one-loop level.     

A solution to the strong CP problem in the SU(5) model

The possibility of naturally suppressing strong CP violation in the grand unified SU(5) model is examined. We show that a recent solution to the quark-lepton mass ratio problem by Georgi and Jarlskog can be extended in such a way as to yield a zero strong CP-violating parameter θ at the tree level and a small value for it coming from higher-order effects, along with reasonable mass ratios and mixing angles. Several phenomenological implications of the model are noted.     

Can the quark mass matrix be real?

We study the possibility of solving the strong CP problem in a theory where CP is broken spontaneously and the quark mass matrix, M_ij, not just its determinant, remains real to one part in 10⁸. We find that it is difficult to build natural models consistent with the known CP violation phenomenology. We find that such models require new fermions and possess a hierarchy problem. We present an SO(10) example which succeeds at the one-loop level, however, two-loop effects will introduce phases into M_ij.     

K 0 → \bar K^0 and B 0 → \bar B^0 transitions in the minimal supersymmetric standard model involving explicit CP violation in the Higgs sector

Mixing in the systems of neutral K ⁰ and B ⁰ mesons is considered within the minimal supersymmetric standard model (MSSM) containing a type-II Yukawa sector and featuring an explicitCP violation in the Higgs potential. In the case of a strong mixing of CP-even and CP-odd states, the model admits the presence of a light charged Higgs boson. Basic mixing parameters are calculated. These include the mass difference Δm _LS between neutral kaons and the parameter ε, which characterizes the amount of an indirect CP violation (that is, that which arises owing to an ultraweak mixing of CP-invariant and CP-noninvariant components). In the limit of the low-energy one-loop approximation, it is shown that, for the K ⁰ mesons, the contribution of nonstandard-physics effects to the mass splitting of the neutral kaons and an indirect CP violation are very small and are weakly dependent on the mass of the charged Higgs boson. Under certain conditions, the nonstandard contributions for the B ⁰- $ \bar B_d^0 $ and B ⁰- $ \bar B_s^0 $ systems may become somewhat more substantial, which constrains the MSSM parameter space.     

The rate difference between the weak decays of t and in supersymmetry

We find that the CP-violating asymmetry

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at the one-loop order within the minimal supersymmetric extension of the standard model is of the order of few percent for maximal CP violation. It could be measured by considering the rate difference in the one-lepton events.     

Noncommutative linear sigma models

We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu–Goldstone symmetry realization is inconsistent with continuum renormalization. Specifically we find no violation of Goldstone's theorem at one-loop for the U(N) models with the quartic term ordering consistent with possible noncommutative gauging of the model. The difference is due to terms involving noncommutative commutator interactions, which vanish in the commutative limit. We also examine the U(2), and O(4) linear sigma models with matter in the adjoint representation, and find that the former is consistent with Goldstone's theorem at one-loop if we include only trace invariants consistent with possible noncommutative gauging of the model, while the latter exhibits violations of Goldstone's theorem of the kind seen in the fundamental of O(N) for N>2.     

Majorana neutrinos and CP violation in the leptonic sector

A set of weak-basis-independent necessary conditions is derived for CP conservation in the leptonic sector of the SU(2) × U(1) gauge theory with an arbitrary number of generations, when both Majorana and Dirac neutrino mass terms are present. In the case of two and three generations of left-handed Majorana neutrinos, weak-basis-independent conditions are given which are necessary and sufficient for CP invariance in the leptonic sector. It is also shown that for three or more generations of Majorana neutrinos, there may be CP violation even in the limit of complete neutrino-mass degeneracy.     

Spontaneous breakdown of CP symmetry,cabbibo angle in nuclear and hypernuclear physics

Following a suggestion of Salam and Strathdee that CP violation disappears and the Cabbibo angle vanishes at high magnetic fields we infer that no CP (or T) violation should be observed in nuclear beta decays and that stable hypernuclei are in principle possible.     

Unitarity polygons and CP violation areas and phases in the standard electroweak model

A geometrical interpretation of CP violation in terms of areas of unitarity triangles is presented, in the standard electroweak model with three families of quarks. The extension of the results to the case of four families is investigated. A special case is worked out in detail where it is shown how one determines the CP violating invariant phases and the areas of the CP violation triangles as functions of the moduli of the elements of the quark mixing matrix. For the most general four-family case, which is found to be rather involved, the necessary formulae, for determining the invariant phases and the CP violation areas, are given.     

Spontaneous CP violation and minimal coupling to supergravity

In the framework of minimal coupling to supergravity, it is found that the assumption of spontaneous CP violation allows one to generate naturally real couplings between the high-energy and the low-energy sectors of the theory, at the grand unification scale M_x. These boundary conditions for the renormalization group equations imply sufficiently small imaginary parts of these couplings at the weak scale M_w, to ensure that the experimental bound on the electric dipole moment of the neutron is respected.     

Photoproduction of massive gauge bosons in high energy electron-proton collisions

A self-consistent renormalization scheme at finite temperature and zero momentum is used together with the finite temperature renormalization group to study the temperature dependence of the mass and the coupling to one-loop order in the (φ ³)₆- and (φ ⁴)₄-models. It is found that the critical temperature is shifted relative to the naive one-loop result and the coupling constants at the critical temperature get large corrections. In the high temperature limit of the (φ ⁴)₄-model the coupling decreases.     

Quantum effects on t\rightarrow H^{+}\,b in the MSSM: a window to “virtual” supersymmetry?

We analyze the one-loop effects (strong and electroweak) on the unconventional top quark decay mode within the MSSM. The results are presented in the on-shell renormalization scheme with a physically well motivated definition of . The study of this process at the quantum level is useful to unravel the potential supersymmetric nature of the charged Higgs emerging from that decay. As compared with the standard mode , the corrections to are large, slowly decoupling and persist at a sizeable level even for all sparticle masses well above the LEP 200 discovery range. As a matter of fact, the potential size of the SUSY effects, which amount to corrections of several ten percent, could counterbalance the standard QCD corrections and even make them to appear with the “wrong” sign. Therefore, if the charged Higgs decay of the top quark is kinematically allowed – a possibility which is not excluded by the existing measurements of the branching ratio at the Tevatron – it could be an invaluable laboratory to search for “virtual” supersymmetry. While a first significant test of these effects could possibly be performed at the upgraded Tevatron, a more precise verification would most likely be carried out in future experiments at the LHC. Received: 18 April 1997 / Revised version: 18 June 1997     

Continuum regularization of quantum field theory

As an extension of our earlier one-loop renormalization studies at the regularized Schwinger-Dyson level, we report here on equivalent renormalization programs for regularized Langevin systems. Proper structure is discussed, and proper one-loop renormalizations of the Green functions of φ ₆ ³ and QCD₄ are given. An optional apparent?-renormalization is discussed as a technical simplificaiton for gauge theories with Zwanziger's gauge-fixing.     

Weakened constraints from b-->sgamma on supersymmetry flavor mixing due to next-to-leading-order corrections

We examine the process B-->X(s)gamma in minimal supersymmetry (SUSY) with general squark flavor mix-ings. We include all relevant next-to-leading order (NLO) QCD corrections and dominant NLO SUSY effects from the gluino. We find that gluino-squark corrections to down-type quark masses induce large NLO corrections to the dominant Wilson coefficients whose size is often similar to those at LO, es-pecially at large tan(beta. For micro>0, destructive interference and suppression by the renormalization group running lead to a "focusing effect" of reducing the size of gluino corrections to the branching ratio, and also of reducing the LO sensitivity to flavor mixings among squarks. Constraints from B(B-->X(s)gamma) on the SUSY-breaking scale can become significantly weakened relative to the minimal flavor violation case, even, at large tan(beta, for small flavor mixings. The case of micro<0 also becomes allowed.     

On gauge independence in quantum gravity

We prove the gauge independence of the one-loop path integral for on-shell quantum gravity obtained in the framework of the modified geometric approach. We use a projector on pure gauge directions constructed via the quadratic form of the action. This enables us to formulate the proof entirely in terms of determinants of non-degenerate elliptic operators without reference to any renormalization procedure. The role of the rotation of the conformal factor in achieving gauge independence is discussed. Direct computations on CP² in a general three-parameter background gauge are presented. We comment on the gauge dependence of previous results by Ichinose.     

Some phenomenological implications of string loop effects

We investigate low energy implications of string loop corrections to supergravity couplings which break a possible flavor universality of the tree level. If supersymmetry is broken by the dilaton F-term, universal soft scalar masses arise at the leading order but string loop corrections generically induce flavor-non-diagonal soft terms. Constraints from flavor changing neutral currents (FCNC) and CP violation then require a large supersymmetry breading scale and thus heavy gluinos and squarks. If supersymmetry is broken by moduli F-terms, universality at the string tree level can only be guaranteed by extra conditions on the Kahler potential. A large hierarchy between the gluino and squark masses ensures that FCNC and CP-violation constraints are satisfied. If the soft scalar masses vanish at the string tree level, the cosmological problems related to light moduli can be evaded. However, generic string loop corrections violate FCNC bounds and require very heavy squark masses (∼ 100 TeV).     

Results from GRACE/SUSY at one-loop

We report the recent development on the SUSY calculations with the help of GRACE system. GRACE/SUSY/1LOOP is the computer code which can generate Feynman diagrams in the MSSM automatically and compute one-loop amplitudes in the numerical way. We present new results of various two-body decay widths and chargino pair production at ILC (international linear collider) at one-loop level.      

CP violation and Fritzsch mass matrices

We discuss a form for the quark mass matrices which produces maximal weak but no string CP violation. The quark mass matrices are of the Fritzsch type, with all phases equal to multiples of $\text{1}\text{2}\text{π}$. We show that these matrices can be produced in an SO(10) model with CP violated spontaneously at the GUT scale. The model successfully predicts the entire K-M matrix. Radiative corrections to $\text{θ}$, however, are several orders of magnitude too large in the model, and $\text{θ}$ is naturally of O(10^?5).     

Isospin invariance,CP violation and B−B̄ mixing

With large B⁰−B̄⁰ mixing, the CP asymmetry of certain B decays become nearly maximal. However, the clear identification of relevant B meson decays required for experimental observation of such effects is difficult. We point out that symmetry relations among various B meson decay channels lead to additional constraints which can be useful in extracting CP violating amplitudes. As an example, we consider decay amplitudes to final states containing both a J/ψ and a K_S, whose interference terms provide information on CP violation. We show that these decays are ΔI=0 transitions and obtain isospin relations between the direct terms in the amplitude and experimental results from corresponding decays involving charged kaons.     

Analytic expressions for threshold corrections to the finite-temperature higgs potential in the minimal supersymmetric standard model

Within the minimal supersymmwtric standard model (MSSM) featuring an explicit CP violation, one-loop corrections to the parameters of the effective two-doublet potential are calculated at finite temperature for various scales of the mass parameters in the sector of soft supersymmetry breaking. It is shown that the splitting of scalar-quark masses has a strong effect on the effective parameters of the potential and that, in the limiting case where all mass parameters of the squark sector are degenerate and where the temperature is zero, the potential parameters reduce to the results obtained previously.