Proton decay

The lifetimes and branching ratios of the proton and bound neutron are calculated in the SO(10) grand unified theory by taking into account the form factor effect (by making use of SU(6) symmetric wave functions for the nucleons and mesons) and the generation mixing, based on the assumption that the ΔB = ? 1 decay interaction is generated by the exchange of superheavy leptoquark gauge bosons, D (X and Y) and E (X' and Y'). In our approach there is a free parameter M_D/M_E, which should be determined by experiment. The branching ratio of the inclusive decay of an I = 0 nucleus into neutrinos and anything is found to be most dependent on the ratio M_D/M_E. The nucleon lifetime is τ_N = [M_D (GeV)/5 × 10¹⁴]⁴ × (0.0015,2.5,4.6) × (1_?0.4⁺²) × 10³⁰ year, for M_D/M_E = (10,1,0.1). Only the cases in which M_DapM_E are found to be possible for Λ_ms[? 0.26 GeV and τ_N ? 5 × 10³⁰ year if there is not a fourth generation of light fermions, technicolored particles nor supersymmetric particles.     

Proton decay in supersymmetric models

We discuss proton decay in supersymmetric theories. We find that it is possible to obtain rates which are comparable with those of standard SU(5). In the presence of a discrete symmetry which occurs in an SU(5) supersymmetric unified model we obtain a definite prediction for the dominant decay mode, i.e. p → K^+?ν_μ and n → K^0?ν_μ.     

Proton decay in E6

It is shown that nucleon decay modes mediated by E₆ gauge bosons are identical to those occuring in O(10).     

Fast proton decay

We consider proton decay in the testable flipped SU(5)×UX₍₁₎$\mathit{SU}(5)\times U{(1)}_X$ models with TeV-scale vector-like particles which can be realized in free fermionic string constructions and F-theory model building. We significantly improve upon the determination of light threshold effects from prior studies, and perform a fresh calculation of the second loop for the process p→e⁺π⁰$p\to e^{+}{\pi }^0$ from the heavy gauge boson exchange. The cumulative result is comparatively fast proton decay, with a majority of the most plausible parameter space within reach of the future Hyper-Kamiokande and DUSEL experiments. Because the TeV-scale vector-like particles can be produced at the LHC, we predict a strong correlation between the most exciting particle physics experiments of the coming decade.     

Proton decay in locally supersymmetric GUT

Proton decay is studied in the supergravity model with “the hidden sector” as the source of supersymmetry breaking. Each dimension-five operator is found to accompany ΔB ≠ 0 four-scalar interactions. The Higgs fermion exchange for loop diagrams at low energies can be as important as the gauge fermion exchange, if the associated Yukawa coupling is significant as suggested by the radiatively induced SU(2) × U(1) breaking mechanism. The experimental bound for p → K⁰μ⁺ gives the lower bound of the order of 10¹⁶ GeV for the mass of the baryon-number violating Higgs particle.     

Proton decay and horizontal symmetry

Proton decay can teach us about the so-called horizontal or family symmetry.     

Proton diffusion in proton conducting oxides

Quasielastic neutron scattering was used to study the atomistic proton diffusion mechanism in Yb-doped SrCeO₃, a proton conducting perovskite, simultaneously in space and time. Proton diffusion consists of a sequence of trapping and free diffusion events. The free diffusion corresponds to the Grotthus mechanism including very fast rotations around oxygen ions.     

Supersymmetry and proton decay

Using supergraph techniques it is shown that all one-loop contributions to the proton decay amplitude, which are suppressed by only one power of the unification mass and are not of fourth order in Higgs couplings, vanish in a general supersymmetric grand unification setting. Corrections to this statement due to soft supersymmetry breaking are analysed.     

Proton decay in four dimensional superstring models

In this paper, we discuss the contraints that emerge from baryon nonconserving processes in theSU(4)×O(4) andSU(5)×U(1) models derived in the fermionic formulation of the four dimensional superstring. We examine dimension five baryon violating operators arising a) from Higgs exchange diagrams, and b) from non-renormalisable terms which arise from the exchange of massive string states. Both kinds of the above operators put non-trivial constraints on the matter field assignments and on the vevs of various singlet fields of the string models under consideration.     

Baryon poles in proton decay amplitudes

The decay rate of the p→π⁰e⁺ mode is calculated in SU(5) grand unified theory using a pole model with proton and $\text{1}\text{2}{}^{\mathrm{?}}$ baryon poles. Baryon-to-vacuum amplitudes are calculated in the framework of the MIT bag model. It is found that the partial decay rate [～(5×10³¹ yr)^?)] is close to the partial decay rates calculated by different methods.     

Chiral quarks and proton decay

In this paper we calculate the hadronic matrix elements of baryon decay operators using a chiral effective lagrangian with quarks, gluons and Goldstone boson fields. We study in detail the cases where the ΔB = 1 operators arise from supersymmetric SU(5) GUT as well as the minimal SU(5) GUT model. In each model the results depend on two parameters. In particular there is a range of values for the two parameters, where the dominant decay modes in the minimal SU(5) GUT are: p → ηe⁺ and n → π^? e⁺.     

Role of hadronic dynamics in proton decay

Aspects of hadronic dynamics which play a crucial role in proton decay (exclusive and inclusive) are examined in the context of a comprehensive Bethe-Salpeter (BS) formalism forq \(\bar q\) andqqq systems, under harmonic confinement. The BS model which is characterized by two basic parameters—the universal spring constant \(\tilde \omega \) GeV and the quark massm _q =0.28 GeV, has already provided an impressive set of agreements in respect of a large number and variety of hadronic observables (mass spectra, and an extensive list of e.m. and pionic couplings of both mesons and baryons). TheSU(5) GUT parameters, on the other hand, are kept fixed at the ‘standard’ values, (see e.g. Langacker's review). The absolute normalization of the baryon, which is rather crucial in this case, is fixed with reference to the (topologically equivalent) process of its ‘dissociation’ into three quarks by a hard photon, which makes use of the structure function sum rule \(\int\limits_0^1 {dxF_2^p (x)/x = \sum {Q_i^2 } } \) , instead of the usual BS normalization (which amounts to the conservation of charge). Thee ⁺ inclusive rate, which is about three times that of thee ⁺π⁰ mode, works out at0.54×10 ^?33 yr ^?1 which is smaller than most contemporary calculations by two orders of magnitude. Other exclusive modes are also consistent with the above estimate. The theoretical implications of these results vis a vis contemporary calculations as well as current experimental searches are discussed.     

Proton decay,annihilation or fusion?

The proton decay candidatep→μ⁺η of Kamioka NDE in Japan, if seriously taken, probably means that fusion is the only mechanism of proton decay. A model based on the work of Pati-Salam-Sarkar is discussed in detail.     

Proton decay in terms of an effective baryon-lepton transition

We calculate the two-body decay rates for the hadronic and electromagnetic decays of proton and neutron in terms of the effective baryon-lepton transition matrix element. Further ingredients like PCAC and vector meson dominance are used. We compute these transition amplitudes within the framework of a relativistic quark model involving Bethe-Salpeter amplitudes and present the nucleon lifetimes and branching ratios of various decay modes for three different grand unification models.     

Still more on proton decay in supersymmetric theories

It is shown, contrary to the recent claim in literature, that gluino exchange in supersymmetric proton decay does not vanish in general. In N=1 supergravity theory it could be an important or even dominant contribution, which would imply the often-mentioned model independent main mode . We also summarize the situation in the case of charged W-ino exchange incorporating the new measurement of B meson lifetimes.