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تسجيل مستخدم جديدEmergence of the NMSGUT
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تأليف
Charanjit S. Aulakh
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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.
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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 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.
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.
Superheavy threshold corrections to the matching condition between matter Yukawa couplings of the effective Minimal Supersymmetric Standard Model (MSSM) and the New Minimal Supersymmetric (SO(10)) GUT(NMSGUT) provide a novel and generic mechanism for
reducing the long standing and generically problematic operator dimension 5 Baryon decay rates. In suitable regions of the parameter space strong wave function renormalization of the effective MSSM Higgs doublets due to the large number of heavy fields can take the wave function renormalization of the MSSM Higgs field close to the dissolution value ($Z_{H,overline{H}}=0$). Rescaling to canonical kinetic terms lowers the SO(10) Yukawas required to match the MSSM fermion data. Since the same Yukawas determine the dimension 5 B violation operator coefficients, the associated rates can be suppressed to levels compatible with current limits. Including these threshold effects also relaxes the constraint $ y_b-y_tausimeq y_s-y_mu$ operative between $textbf{10} -textbf{120} $ plet generated tree level MSSM matter fermion Yukawas $y_f$. We exhibit accurate fits of the MSSM fermion mass-mixing data in terms of NMSGUT superpotential couplings and 5 independent soft Susy breaking parameters specified at $10^{16.25},$ GeV with the claimed suppression of Baryon decay rates. As before, our s-spectra are of the mini split supersymmetry type with large $|A_0|,mu,m_{H,overline H} > 100,,$ TeV, light gauginos and normal s-hierarchy. Large $A_0,mu$ and soft masses allow significant deviation from the canonical GUT gaugino mass ratios and ensure vacuum safety. Even without optimization, prominent candidates for BSM discovery such as the muon magnetic anomaly, $brightarrow sgamma$ and Lepto-genesis CP violation emerge in the preferred ball park.
With discovery of the Higgs boson, science has located the source for $lesssim 2$% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining $gtrsim 98$%. The instruments at work here must be ca
pable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.
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