The Supersymmetric SO(10) theory (NMSO(10)GUT) based on thehfilbreak ${bf{210+126 +oot}}$ Higgs system proposed in 1982 has evolved into a realistic theory capable of fitting the known low energy Particle Physics data besides providing a Dark matter
candidate and embedding Inflationary Cosmology. It dynamically resolves longstanding issues such as fast dimension five operator mediated proton decay in Susy GUTs by allowing explicit and complete calculation of crucial threshold effects at $M_{Susy}$ and $M_{GUT}$ in terms of fundamental parameters. This shows that SO(10) Yukawas responsible for observed fermion masses as well as operator dimension 5 mediated proton decay can be highly suppressed on a Higgs dissolution edge in the parameter space of GUTs with rich superheavy spectra. This novel and generically relevant result highlights the need for every realistic UV completion model with a large/infinite number of heavy fields coupled to the light Higgs doublets to explicitly account for the large wave function renormalization effects on emergent light Higgs fields in order to be considered a quantitatively well defined candidate UV completion. The NMSGUT predicts large soft Susy breaking trilinear couplings and distinctive sparticle spectra. Measurable or near measurable level of tensor perturbations- and thus large Inflaton mass scale- may be accommodated by Supersymetric Seesaw inflation within the NMSGUT based on an LHN flat direction Inflaton if the Higgs component contains contributions from heavy Higgs components. Successful NMSGUT fits suggest a emph{renormalizable} Yukawon Ultra minimal gauged theory of flavor based upon the NMSGUT Higgs structure.
Bajc-Melfo(textbf{BM}) two field ($S,phi$) superpotentials define metastable F-term supersymmetry breaking vacua suitable as hidden sectors for calculable and realistic family and Grand Unification unification models. The undetermined vev $<S_s>$ of
the Polonyi field that breaks Supersymmetry can be fixed either by coupling to N=1 Supergravity or by radiative corrections. textbf{BM} hidden sectors extend to symmetric multiplets $(S,phi)_{ab}$ of a gauged $O(N_g)$ family symmetry, broken at the GUT scale, so that the $O(N_g)$ charged component vevs $<hat S_{ab}>$ are also undetermined before accounting for the $O(N_g)$ D-terms: which fix them by cancellation against D-term contributions from the visible sector. This facilitates Yukawon Ultra Minimal GUTs(YUMGUTs) proposed in [C.S.Aulakh and C.K.Khosa, Phys.Rev.D 90,045008(2014)] by relieving the visible sector from the need to give null D-terms for the family symmetry $ O(N_g)$. We analyze symmetry breaking and and spectra of the hidden sector fields in the Supergravity resolved case when $N_g=1,2,3$. Besides the Polonyi field $S_s$, most of the superfields $hat S_{ab}$ remain light, with fermions getting masses only from loop corrections. Such modes may yield novel dark matter lighter than 100 GeV. Possible Polonyi and moduli problems associated with the the fields $S_{ab}$ call for detailed investigation of loop effects due to the Yukawa and gauge interactions in the hidden sector and of post-inflationary field relaxation dynamics.
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.
Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of Yukawon Higgs multiplets. For concrete il
lustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $bf{210 oplus {overline{126}}oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $bf{{overline{126}},10}$($mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $phi,S $, of which the latters singlet part $S_s$ breaks supersymmetry and the traceless part $hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.
We show that Supersymmetric models with Type I seesaw neutrino masses support slow roll inflection point inflation. The inflaton is the D-flat direction labelled by the chiral invariant HLN composed of the Higgs(H), slepton(L) and conjugate sneutrino
(N) superfields. The scale of inflation and fine tuning is set by the conjugate neutrino Majorana mass $M_{ u^c} sim 10^6-10^{12}$ GeV. The cubic term in the (quartic) inflaton potential is dominantly from superpotential (not soft Susy breaking) couplings. The tuning conditions are thus insensitive to soft supersymmetry breaking parameters and are generically much less stringent than for previous `A-term inflation scenarios controlled by mass scales $sim TeV$. WMAP limits on the ratio of tensor to scalar perturbations limit the scale $M$ controlling inflection point inflation: $M <7.9 times 10^{13}$ GeV. `Instant preheating is operative and dumps the inflaton energy into MSSM modes giving a high reheat temperature : $T_{rh} approx M_{ u^c}^{3/4}, 10^{6}$ GeV $sim 10^{11}- 10^{15} $ GeV. A large gravitino mass $> 50 $ TeV is therefore required to avoid over closure by reheat produced gravitinos. `Instant preheating and NLH inflaton facilitate production of right handed neutrinos during inflaton decay and thus non-thermal leptogenesis in addition to thermal leptogenesis. We show that the embedding in the fully realistic New Minimal Supersymmetric SO(10) GUT requires use of the heaviest righthanded neutrino mass as the controlling scale but the possibility of a measurable tensor scalar perturbation ratio seems marginal. We examine the parametric difficulties remaining.
Supersymmetric Unified theories which incorporate a renormalizable Type I seesaw mechanism for small neutrino masses can also provide slow roll inflection point inflation along a flat direction associated with a gauge invariant combination of the Hig
gs, slepton and right handed sneutrino superfields. Inflationary parameters are related to the Majorana and Dirac couplings responsible for neutrino masses with the scale of inflation set by a right-handed neutrino mass $M_{ u^c} sim 10^6-10^{12}$ GeV. Tuning of the neutrino Dirac and Majorana superpotential couplings and soft Susy breaking parameters is required to enforce flatness of the inflationary potential. In contrast to previous inflection point inflation models the cubic term is dominantly derived from superpotential couplings rather than soft A-terms. Thus since $M_{ u^c}>>M_{Susy}$ the tuning condition is almost independent of the soft supersymmetry breaking parameters and therefore more stable. The required fine tuning is also less stringent than for Minimal SUSY Standard Model (MSSM) inflation or Dirac neutrino A-term inflation scenarios due to the much larger value of the inflaton mass. Reheating proceeds via `instant preheating which rapidly dumps all the inflaton energy into a MSSM mode radiation bath giving a high reheat temperature $T_{rh} approx M_{ u^c}^{3/4}, 10^{6}$ GeV $sim 10^{11}- 10^{15} $ GeV. Thus our scenario requires large gravitino mass $> 50 $ TeV to avoid a gravitino problem. The `instant preheating and Higgs component of the inflaton also imply a `non-thermal contribution to Leptogenesis due to facilitated production of right handed neutrinos during inflaton decay. We derive the tuning conditions for the scenario to work in the realistic New Minimal Supersymmetric SO(10) GUT and show that they can be satisfied by realistic fits.
We compare and contrast the computations that lead to the NMSGUT spectra and Yukawa couplings that appearedcite{nmsgut} in 2006 and a recent recalculation of the samecite{malinsky}. We argue that an explicit component based method of computation jeop
ardizes the power of SO(10) and its sub-groups to organize, in a unified and automatically phase correlated way, computations of dynamics beyond the basic mass matrix computation. The correct (one line) prescription for generating MSSM Yukawas from SO(10) ones was given in cite{ag2} and requires no computation beyond the identification of null vectors of the Higgs doublet mass matrix and the Clebsches given in cite{ag1,ag2}. It was already used to derive all fermion Yukawas and Majorana masses in cite{ag2,nmsgut}. We thus urge the adoption of a uniform notation and methodology based on descent from SO(10) to the SM through the Pati-Salam maximal subgroup of SO(10) to avoid Babel in this rapidly developing and highly promising subject.
We show that generic $ {bf{10oplus 120oplus {bar {126}}}}$ fits of fermion masses and mixings, using real superpotential couplings but with complex `Higgs fractions leading to complex yukawa couplings in the effective MSSM, emph{overdetermine}(by one
extra constraint) the superpotential parameters of the New Minimal Supersymmetric SO(10) GUTcite{nmsgut}. Therefore fits should properly be done by generating the 24 generic fit parameters from the 23 parameters of the NMSGUT superpotential, given $tanbeta$ as input. Each numerical fit then emph{fully specifies} the parameters of the NMSGUT. An analysis of all its implications, modulo only the residual uncertainty of supersymmetry breaking parameters, is now feasible. Thus the NMSGUT offers the possibility of a confrontation between the scale of gauge unification and the fit to fermion masses due to their extractable common dependence on the NMSGUT parameters. If and when `smoking gun discoveries of Supersymmetry and Proton decay occur they will find the NMSGUT fully vulnerable to falsification.
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.
