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Register a new userE6 GUT through Effects of Dimension-5 Operators
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In the effective field theory framework, quantum gravity can induce effective dimension-5 operators, which have important impacts on grand unified theories. Interestingly, one of main effects is the modification of the usual gauge coupling unification condition. We investigate the gauge coupling unification in $E_{6}$ under modified gauge coupling unification condition at scales $M_X$ in the presence of one or more dimension-5 operators. It is shown that nonsupersymmetric models of $E_6$ unification can be obtained and can easily satisfy the constraints from the proton lifetime. For constructing these models, we consider several maximal subgroups $H=SO(10)times U(1), H=SU(3)times SU(3)times SU(3)$, and $H=SU(2)times SU(6)$ of $E_{6}$ and the usual breaking chains for a specific maximal subgroup, and derive all of the Clebsch-Gordan coefficients $Phi^{(r)}_{s,z}$ associated with $E_6$ breaking to the Standard Model, which are given in Appendix A.
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The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate the group theoretic nature of them for the well known E(6) model. Considering the breaking chains $E_{6}mapsto H=SO(10)times U_{V}(1)mapsto SU(5)times U_{V}(1)times U_{V}(1)mapsto SU(3)times SU(2)times U_{Z}(1)times U_{V}(1)times U_{V}(1)$ and $E_{6}mapsto H=SO(10)times U_{V}(1)mapsto SU(4)times SU_{L}(2)times SU_{R}(2)times U_{V}(1)mapsto SU(3)times SU_{L}(2)times SU_{R}(2)times U_{S}(1)times U_{V}(1)$, we derive and give all of the Clebsch-Gordan coefficients $Phi^{(r)}_{s,z}$ associated with $E_6$ breaking to the standard model. Some applications of the results are discussed shortly.
We study the off-shell mixing and renormalization of flavor-diagonal dimension-5 T- and P-odd operators involving quarks, gluons, and photons, including quark electric dipole and chromo-electric dipole operators. We present the renormalization matrix to one-loop in the $bar{rm MS}$ scheme. We also provide a definition of the quark chromo-electric dipole operator in a regularization-independent momentum-subtraction scheme suitable for non-perturbative lattice calculations and present the matching coefficients with the $bar{rm MS}$ scheme to one-loop in perturbation theory, using both the naive dimensional regularization and t Hooft-Veltman prescriptions for $gamma_5$.
We study the effects of including Yukawa-like dimension-5 operators in the Georgi-Machacek model where the Standard Model is augmented with triplet scalars. We focus only on the charged Higgs sector and investigate the constraints arising from radiative B-meson decays, neutral B-meson mixing and precision measurement of Zbb vertex. We observe that the inclusion of the dimension-5 operators causes substantial alteration of the limits on the charged Higgs masses and the vacuum expectation value of the triplets, derived otherwise using only the dimension-4 operators.
The $B$-meson light-cone distribution amplitude (LCDA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory (HQET) and is a building block of QCD factorization formula for exclusive $B$-meson decays. When the corresponding bilocal HQET operator has a light-like distance $t$ between the quark and antiquark fields, the scale $sim 1/t$ separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat the bilocal HQET operator based on the operator product expansion (OPE), disentangling the singularities from the IR and UV regions systematically. The matching at the next-to-leading order $alpha_s$ is performed in the $overline{rm MS}$ scheme with a complete set of local operators of dimension $d le 5$, through a manifestly gauge-invariant calculation organizing all contributions in the coordinate space. The result exhibits the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This OPE yields the $B$-meson LCDA for $t$ less than $sim 1$ GeV$^{-1}$, in terms of $bar{Lambda}= m_B - m_b$ and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive $B$ decays, $lambda_B$, is also discussed.
We minimally extend the Standard Model field content by adding new vector-like fermions at the TeV scale to allow gauge coupling unification at a realistic scale. We embed the model into a $SU(5)$ grand unified theory that is asymptotically safe and features an interacting fixed point for the gauge coupling. There are no Landau poles of the $U(1)$ gauge and Higgs couplings. Gauge, Yukawa and Higgs couplings are retraced from the fixed point and matched at the grand unification scale to those of the Standard Model rescaled up to the same energy. All couplings, their fixed point values and critical exponents always remain in the perturbative regime.
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