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تسجيل مستخدم جديدCorrecting alpha_3(M_Z) in the NMSGUT
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We show that superheavy threshold corrections in the New Minimal Supersymmetric GUT based on the SO(10) Higgs system ${bf{210oplus 126oplus {bar {126}}oplus 10 oplus 120}} $ can comfortably correct the prediction for the value of $alpha_3(M_Z)$ from the relatively large value predicted by the two loop RG equations to the central value determined by the current world average. The unification scale is raised above the one loop value over almost all of the viable parameter space.
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We trace the emergence of the ``New Minimal supersymmetric SO(10) GUT (NMSGUT) out of the debris created by our demonstration that the MSGUT is falsified by the data. The NMSGUT is based on ${bf{210oplus 10oplus 120oplus 126oplus {bar {126}}}}$ Higgs
system. It has only spontaneous CP violation and Type I seesaw. With only 24 real superpotential parameters it is the simplest model capable of accommodating the known 18 parameter fermion mass data set and yet has enough freedom to accommodate the still unknown Leptonic CP violation and neutrino mass scale parameters. Our focus is on the two most salient features uncovered by our analysis: the domination of the ${bf{bar{126}}}$ Yukawa couplings by those of the ${bf{10,120}}$ (required for evasion of the no-go that trapped the MSGUT) and the inescapable raising of the Baryon violation scales(and thus suppression of proton decay) decreed by a proper inclusion of the threshold effects associated with the calculated superheavy spectra. These two structural features are shown to be complementary.
We revisit the analysis of the improved ladder Schwinger-Dyson (SD) equation for the dynamical chiral symmetry breaking in QCD with emphasizing the importance of the scale ambiguity. Previous calculation done so far naively used one-loop MSbar coupli
ng in the improved ladder SD equation without examining the scale ambiguity. As a result, the calculated pion decay constant f_pi was less than a half of its experimental value f_pi=92.4MeV once the QCD scale is fixed from the high energy coupling alpha_s(M_Z). In order to settle the ambiguity in a proper manner, we adopt here in the present paper the next-to-leading-order effective coupling instead of a naive use of the MSbar coupling. The pion decay constant f_pi is then calculated from high energy QCD coupling strength alpha_s(M_Z)=0.1172 pm 0.0020. Within the Higashijima-Miransky approximation, we obtain f_pi=85--106MeV depending on the value of alpha_s(M_Z) which agrees well with the experimentally observed value f_pi=92.4MeV. The validity of the improved ladder SD equation is therefore ascertained more firmly than considered before.
We list operators of the superpotential of the effective MSSM that emerges from the NMSGUT up to sextic degree. We give illustrative expressions for the coefficients in terms of NMSGUT parameters. We also estimate the impact of GUT scale threshold co
rrections on these effective operators in view of the demonstration that $B$ violation via quartic superpotential terms can be suppressed to acceptable levels after including such corrections in the NMSGUT. We find a novel $B, B-L$ violating quintic operator that leads to the decay mode $nto e^- K^+$. We also remark that the threshold corrections to the Type I seesaw mechanism make the deviation of right handed neutrino masses from the GUT scale more natural while Type II seesaw neutrino masses, which earlier tended to utterly negligible receive threshold enhancement. Our results are of relevance for analyzing $B-L$ violating operator based, sphaleron safe, Baryogenesis.
Consistency of trans-unification RG evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10) GUT (NMSGUT). We compute the 1-loop RGE $beta$ functions, simplifying generic formulae using constraints of gauge invar
iance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $beta$ functions involving large irreps. Use of the RGEs identifies a perturbative domain $Q < M_E$, where $M_E <M_{Planck}$ is the emph{scale of emergence} where the NMSGUT, with GUT compatible soft supersymmetry breaking terms emerges from the strong UV dynamics associated with the Landau poles in gauge and Yukawa couplings. Due to the strength of the RG flows the Landau poles for gauge and Yukawa couplings lie near a cutoff scale $Lambda_E $ for the perturbative dynamics of the NMSGUT which just above $M_E$. SO(10) RG flows into the IR are shown to facilitate small gaugino masses and generation of negative Non Universal Higgs masses squared needed by realistic NMSGUT fits of low energy data. Running the simple canonical theory emergent at $M_E$ through $M_X$ down to the electroweak scale enables tests of candidate scenarios such as supergravity based NMSGUT with canonical kinetic terms and NMSGUT based dynamical Yukawa unification.
We revisit the earlier determination of alpha_s(M_Z) via perturbative analyses of short-distance-sensitive lattice observables, incorporating new lattice data and performing a modified version of the original analysis. We focus on two high-intrinsic-
scale observables, log(W_11) and log(W_12), and one lower-intrinsic scale observable, log(W_{12}/u_0^6), finding improved consistency among the values extracted using the different observables and a final result, alpha_s(M_Z)=0.1192(11), 2 sigma higher than the earlier result, in excellent agreement with recent non-lattice determinations and, in addition, in good agreement with the results of a similar, but not identical, re-analysis by the HPQCD Collaboration. A discussion of the relation between the two re-analyses is given, focussing on the complementary aspects of the two approaches.
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