SUSY see-saw and NMSO(10)GUT inflation after BICEP2

Supersymmetric see-saw slow roll inflection point inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, slepton and right-handed sneutrino at a scale set by the right-handed neutrino mass \(M_{{\nu }^{c}} \sim 10^{6}\!\,-\,\!10^{13}\) GeV. The tensor to scalar perturbation ratio r～10^?3 can be achieved in this scenario. However, this scenario faced difficulty in being embedded in the realistic new minimal supersymmetric SO(10) grand unified theory (NMSO(10)GUT). The recent discovery of B-mode polarization by BICEP2, changes the prospects of NMSO(10)GUT inflation. Inflection point models become strongly disfavoured, as the trilinear coupling of SUSY see-saw inflation potential gets suppressed relative to the mass parameter favoured by BICEP2. Large values of r≈0.2 can be achieved with super-Planck scale inflaton values and mass scales of inflaton ≥10 ¹³ GeV. In NMSO(10)GUT, this can be made possible with an admixture of heavy Higgs doublet fields, i.e., other than MSSM Higgs field, which are present and have masses of order GUT scale.     

Higgs mechanism without Higgs particle

Until now there has been no empirical evidence for the existence of the Higgs particle, although the Higgs mechanism of symmetry breaking is very successful. We propose a scalar-tensor theory of gravity with the Higgs field of theSU(3)×SU(2)×U(1) standard model of the elementary particles as scalar field, which results finally in Einstein's gravity and in theSU(3)×SU(2)×U(1) standard model without any influence of the excited Higgs field.     

Top–bottom mass hierarchy, s-\mu puzzle and gauge coupling unification with split multiplets

Supersymmetric 5D SU(5) grand unification is considered. SU(5) is broken down to by the assignment of the bulk field(s). The matter fields are located at the fixed point(s). In the bulk, a Higgs multiplet (containing the bottom doublet ) and the SU(5) gauge multiplet are located. At one fixed point, (the top doublet) and the standard model matter multiplets are presented. Because of the difference of the locations of and , one can obtain a hierarchy between top and bottom Yukawa couplings. We also present a possible way to understand the s– mass puzzle in this framework of the split multiplet. Received: 10 December 2001 / Revised version: 22 January 2002 / Published online: 5 April 2002     

On Nambu monopole dynamics in a SU(2) lattice Higgs model

It is shown that an SU(2) Higgs model on a lattice is equivalent to the Georgi-Glashow model in the limit of a small coupling constant between the Higgs and gauge fields. It can therefore be concluded that the transition between the confinement and symmetric phases in a 3 + 1 dimensional SU(2) Higgs model at finite temperature is accompanied by condensation of Nambu monopoles. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 577–580 (10 November 1997)     

New physics contribution to neutral trilinear gauge boson couplings

We study the one-loop new physics effects to the CP even triple neutral gauge boson vertices γ ^⋆ γ Z, γ ^⋆ Z Z, Z ^⋆ Z γ and Z ^⋆ ZZ in the context of Little Higgs models. We compute the contribution of the additional fermions in Little Higgs models in the framework of direct product groups where [SU(2)×U(1)]² gauge symmetry is embedded in SU(5) global symmetry and also in the framework of the simple group where SU(N)×U(1) gauge symmetry breaks down to SU(2) _L ×U(1). We calculate the contribution of the fermions to these couplings when T parity is invoked. In addition, we re-examine the MSSM contribution at the chosen point of SPS1a′ and compare with the SM and Little Higgs models.     

Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges

Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m in terms of the simultaneous existence of electric and magnetic charges along with their Yang-Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four-gauge symmetry SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m . Accordingly, we have made an attempt to obtain the abelian and non-Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)×U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W ^± and Z ⁰ bosons fields and the Higgs scalar fields.     

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N_g) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using \({\mathbf {10}}\oplus {\mathbf {210}} \oplus {\mathbf {126}} \oplus {\overline {\mathbf {126}}}\) Higgs irrep, ignoring the contribution of 120-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix \(\mathcal {H}\). A consistency condition on the doublet ([1,2,±1]) mass matrix (\(\text {Det}(\mathcal {H})=\) 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of \(\mathcal {H}\) are of generic kind required by the MSSM. A hidden sector with a pair of (S_ab; ?_ab) fields breaks supersymmetry and facilitates \(D_{O(N_{g})}\hspace *{-1pt}=\) 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.     

Quaternionic-valued Gravitation in 8D, Grand Unification and Finsler Geometry

A unification model of 4D gravity and SU(3)×SU(2)×U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP ²=SU(3)/U(2) symmetric space. We proceed to explore the nonlinear connection formalism used in Finsler geometry to show how ordinary gravity in D=4+2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU(5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S ². This is an appealing result because SU(5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU(3)×SU(2)×U(1)⊂SU(5)⊂SU(∞).     

Three Flavor Neutrino Mixing and Dark Energy Above GUT Scale

Neutrino mixing lead to a non zero contribution to the dark energy of the universe. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. The mechanism of neutrino mixing is a possible candidate to contribute the cosmological dark energy. Quantum gravitational (Planck scale) effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor. In this paper, we discuss the three flavor neutrino mixing and cosmological dark energy contributes due to Planck scale effects.     

Origin and phenomenology of weak-doublet spin-1 bosons

We study phenomenological consequences of the Standard Model extension by the new spin-1 fields with the internal quantum numbers of the electroweak Higgs doublets. We show, that there are at least three different classes of theories, all motivated by the hierarchy problem, which predict appearance of such vector weak-doublets not far from the weak scale. The common feature for all the models is the existence of an SUW(3) gauge extension of the weak SUW(2) group, which is broken down to the latter at some energy scale around TeV. The Higgs doublet then emerges as either a pseudo-Nambu-Goldstone boson of a global remnant of SUW(3), or as a symmetry partner of the true eaten-up Goldstone boson. In the third class, the Higgs is a scalar component of a high-dimensional SUW(3) gauge field. The common phenomenological feature of these theories is the existence of the electroweak doublet vectors (Z^?,W^?), which in contrast to well-known Z^′ and W^′ bosons posses only anomalous (magnetic moment type) couplings with ordinary light fermions. This fact leads to some unique signatures for their detection at the hadron colliders.     

Supersymmetric flipped SU(5) revitalized

We describe a simple N = 1 supersymmetric GUT based on the group SU(5)×U(1) which has the following virtues: the gauge group is broken down to the SU(3)_C×SU(2)_L×U(1)_Y of the standard model using just 10, $\text{10}$ Higgs representations, and doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin²θ_w can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring.     

Mass relations in the two Higgs doublet model from the absence of quadratic divergences

By setting the quadratic divergences to zero, four mass relations are obtained for the Standard Model generalized to two Higgs doublets. These four mass relations are obtained most simply in terms of the original fields in the Lagrangian, before spontaneousSU(2)×U(1) symmetry breaking is applied. Unlike the case of the Standard Model, the Higgs tadpoles of the two Higgs doublet theory do not furnish a complete set of mass relations, giving only three of the four.Work supported in part by the U.S. Department of Energy under Grant DE-FG02-84ER40158     

Triple and quartic interactions of Higgs bosons in the two-Higgs-doublet model with <Emphasis Type="Italic">CP</Emphasis>-violation

We consider the two-Higgs-doublet model with explicit CP-violation, where the effective Higgs potential is not CP-invariant at the tree level. The three neutral Higgs bosons of the model are the mixtures of CP-even and CP-odd bosons which exist in the CP-conserving limit of the theory. The mass spectrum and tree-level couplings of the neutral Higgs bosons to gauge bosons and fermions are significantly dependent on the parameters of the Higgs boson mixing matrix. We calculate the Higgs-gauge boson, Higgs-fermion, triple and quartic Higgs self-interactions in the MSSM with explicit CP-violation in the Higgs sector and CP-violating Yukawa interactions of the third generation scalar quarks. In some regions of the MSSM parameter space substantial changes of the self-interaction vertices take place, leading to significant suppression or enhancement of the multiple Higgs boson production cross sections. Received: 13 June 2002 / Revised version: 20 November 2002 / Published online: 14 March 2003     

Does CP Phase Exist Above the GUT Scale

We consider non-reormalizable interaction term as a perturbation of the conventional neutrino mass matrix. Quantum gravitational (Planck scale )effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. In particular, for the $\theta_{13}'$ range 0.00005–0.28, indicates the existence of CP violating phase above the GUT scale. We assume that the gravitational interaction is flavor blind. In this paper, we further investigate the possibility of CP phase exist from Quantum gravity.     

A numerical estimate of the upper limit for the Higgs boson mass

TheSU (2) Higgs model with a scalar doublet field is studied by Monte Carlo calculations on 12⁴ and 16⁴ lattices. The gauge coupling is chosen to be similar in magnitude to the physical value in the standard model. The numerical results at large scalar self-coupling imply an upper limitm _H /m _W ?9 for the ratio of the Higgs boson mass to the W-mass.     

Compactifications of the heterotic string with unitary bundles

We describe a large new class of four‐dimensional supersymmetric string vacua defined as compactifications of the E₈ × E₈ and the SO(32) heterotic string on smooth Calabi‐Yau threefolds with unitary gauge bundles and heterotic five‐branes. The conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of non‐flat line bundles into the ten‐dimensional gauge group, thus opening up the way for phenomenologically interesting string compactifications on simply connected manifolds. After a detailed analysis of the four‐dimensional effective theory we exemplify the general framework by means of a couple of explicit examples involving the spectral cover construction of stable holomorphic bundles. As for the SO(32) heterotic string, the resulting vacua can be viewed, in the S‐dual Type I picture, as a generalisation of magnetized D9/D5‐brane models. In the case of the E₈ × E₈ string, we find a natural way to construct realistic MSSM‐like models, either directly or via a flipped SU(5) GUT scenario.     

Final results from DELPHI on the searches for SM and MSSM neutral Higgs bosons

These final results from DELPHI searches for the Standard Model (SM) Higgs boson, together with benchmark scans of the Minimal Supersymmetric Standard Model (MSSM) neutral Higgs bosons, used data taken at centre-of-mass energies between 200 and 209 GeV with a total integrated luminosity of 224 pb^-1. The data from 192 to 202 GeV are reanalysed with improved b-tagging for MSSM final states decaying to four b-quarks. The 95% confidence level lower mass bound on the Standard Model Higgs boson is 114.1 GeV/c ². Limits are also given on the lightest scalar and pseudo-scalar Higgs bosons of the MSSM.Received: 7 March 2003, Revised: 30 September 2003, Published online: 3 December 2003     

Fine tuning as an indication of physics beyond the MSSM

We investigate the amount of fine tuning of the electroweak scale in the presence of new physics beyond the MSSM, parametrized by higher dimensional operators. We show that these significantly reduce the MSSM fine tuning to Δ<10 for a Higgs mass between the LEPII bound and 130 GeV, and a corresponding scale M_* of new physics as high as 30 to 65 times the higgsino mass. If the fine-tuning criterion is indeed of physical relevance, the findings indicate the presence of new physics in the form of new states of mass of that generated the effective operators in the first instance. At small tanβ these states can be a gauge singlet or a SU(2) triplet. We derive analytical results for the EW scale fine-tuning for the MSSM with higher dimensional operators, including the quantum corrections which are also applicable to the pure MSSM case in the limit the coefficients of the higher dimension operators vanish. A general expression for the fine-tuning is also obtained for an arbitrary two-Higgs doublet potential.     

THE CONSTRUCTION OF A TWO-LOOP FINITE SUPERSYMMETRY SU(5) MODEL

By solving the constraint equations of two-loop finiteness another type of two-loop finite SU(5) ground unified model is given in this paper.There is only one pair of light Higgs doublet,and the other Higgs particles are all superheavy (～M_x).The ordinary CKM-mixing can be obtained only in the low energy region.     

Nonlinear local supersymmetric SU(5)-model

We construct a realistic nonlinear supersymmetric SU(5) model without superpartner particles in curved space and investigate the Higgs sector in the limit of flat space. We need at least an adjoint-, a quintuplet- and an antiquintuplet-Higgs multiplet. In order to obtain a realistic breakdown of SU(5) to SU(3) × U(1) at tree level we have to modify the vacuum structure of the adjoint representation in comparison to other SU(5)-models. This model requires an “elegant” fine-tuning. We determine the mass spectrum of the electroweak Higgs sector.