Pinning down the New Minimal Supersymmetric GUT

We show that generic ${\bf{10\oplus 120\oplus {\bar {126}}}}$ 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) GUT\cite{nmsgut}. Therefore fits should properly be done by generating the 24 generic fit parameters from the 23 parameters of the NMSGUT superpotential, given $\tan\beta$ 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.Comment: Minor changes : (1) Abstract : Phrase "complex Higgs doublet vevs" made more precise and a conjunction deleted (2)References : Umlauts inserted in an author nam

MSGUT a la Pati-Salam : from Futility to Precision

We compute the complete gauge and chiral superheavy mass spectrum and couplings of the Minimal Susy GUT (based on the \bf {210- \oot- 126-10} irreps as the Higgs system) by decomposing SO(10) labels in terms of Pati Salam subgroup labels. The spectra are sensitive functions of the single complex parameter that controls MSGUT symmetry breaking. We scan for the dependence of the threshold corrections to the Weinberg angle and Unification scale as functions of this parameter. We find that for generic values of the GUT scale parameters the modifications are within 10% of the one loop values and can be much smaller for significant regions of the parameter space. This shows that contrary to longstanding conjectures, high precision calculations are not futile but rather necessary and feasible in the MSGUT. The couplings of the matter supermultiplets are made explicit and used to identify the channels for exotic ($\Delta B\neq 0$) processes and to write down the associated bare $d=5$ operators (some of both are novel). The mass formulae for all matter fermions are derived. This sets the stage for a comprehensive RG based phenomenological analysis of the MSGUT.Comment: Version published in Nuclear Physics B with title changed to : "SO(10) MSGUT : spectra, couplings and threshold effects". Additional notes added on consistency checks. Factor of Sqrt 2 in eqns. 78-79 of Journal version correcte

The New Minimal Supersymmetric GUT : Spectra, RG analysis and Fermion Fits

The supersymmetric SO(10) GUT based on the ${\bf{210\oplus 10\oplus 120\oplus 126\oplus {\bar {126}}}}$ Higgs system provides a minimal framework for the emergence of the R-parity exact MSSM at low energies and a viable supersymmetric seesaw explanation for the observed neutrino masses and mixing angles. We present formulae for MSSM decomposition of the superpotential invariants, tree level light charged fermion effective Yukawa couplings, Weinberg neutrino mass generation operator, and the $d=5,\Delta B=\Delta L \neq 0$ effective superpotential in terms of GUT parameters. We use them to determine fits of the 18 available fermion mass-mixing data in terms of the superpotential parameters of the NMSGUT and SUGRY(NUHM) type soft supersymmetry breaking parameters ($\{m_{\tilde f},m_{1/2},A_0,M^2_{H,\bar H}\}$) specified at the MSSM one loop unification scale $M_X^0=10^{16.33}$ GeV. Our fits are compatible with electroweak symmetry breaking and Unification constraints and yield right-handed neutrino masses in the leptogenesis relevant range : $10^8-10^{13}$ GeV. Matching the SM data requires lowering the strange and down quark Yukawas in the MSSM via large $\tan\beta$ driven threshold corrections and characteristic soft Susy breaking spectra. The Susy spectra have light pure Bino LSP, heavy exotic Higgs(inos) and large $\mu,A_0,M_{H,\bar{H}}$ parameters $\sim 100$ TeV. Typically third generation sfermions are much \emph{heavier} than the first two generations. The smuon is often the lightest charged sfermion thus offering a Bino-CDM co-annihilation channel. The parameter sets obtained are used to calculate B violation rates which are found to be generically much faster($\sim 10^{-28}\, yr^{-1}$) than the current experimental limits. Improvements which may allow acceptable B violation rates are identified.Comment: Latex2e, 45 pages, 4 Appendices, 14 Tables. This is the final merged version of hep-ph/0612021 AND 0807.0917 and is identical with the version to be published in Nuclear Physics B. The fits have been updated in the light of LHC 1Fb^-1 data. Calculational details and plots omitted in this published version can be found in the previous arXiv version

On the Consistency of MSGUT Spectra

We show explicitly that, once convention dependent phases are properly accounted for, the mass spectra evaluated by us in hep-ph\0204097 and hep-ph\0405074 satisfy the Trace, SU(5) reassembly and Goldstone counting consistency checks. Furthermore proper phase accounting shows that the transposition symmetry called "Hermiticity" will be manifest only up to signs arising from the product of six phase factors which must be reinserted if the symmetry is to be verified also as regards signs. Thus the claims of hep-ph/0405300 and hep-ph/0412348 concerning the inconsistency of our results are completely mistaken. The Chiral multiplet spectra of the two calculations are equivalent. However our method also gives all gauge and gauge chiral spectra as well as a MSSM decomposition of all SO(10) MSGUT couplings, for both tensors and spinors, which are unavailable, even in principle, using the methods of the above papers.Comment: 9, pages 2 column, revtex

Fermion mass relations in a supersymmetric SO(10) theory

Neutrino and charged fermion masses provide important constraints on grand unified theories. We illustrate this by focusing on a renormalizable, supersymmetric SO(10) theory proposed long ago, that recently attracted great interest in view of its minimality. We show how the nature of the light Higgs, which depends on the GUT scale fields, gets reflected on the precise predictions for fermion masses and mixings. We exemplify this on the case of dominant Type II see-saw, which gets severely constrained and is likely to fail.Comment: Based on talks given by G. Senjanovic in the plenary session of PASCOS05 Conference and by A. Melfo at the 2005 Gran Sasso Summer Institut

Charged Topological Solitons in 4+1 Dimensional YMCS Theory

We show that when a Chern-Simons term is added to the action of $SU(N)$ ($N\geq 3$) Yang-Mills theory in 5 dimensions the usual self-dual topological solitons present in the theory necessarily pick up a (topological) electric charge.Comment: 11p [Replaced version N.B Some minor typos have been corrected and a note added