Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid ³He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ～ 325 GeV. They together satisfy the Nambu sum rule M ₁ ² + M ₂ ² = 4M _t ² , where M _t ～ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ～210 GeV. In this case the Nambu sum rule is 2M ₁ ² + 2M ₂ ² = 4M _t ² . In addition, the properties of the Higgs modes in superfluid ³He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M ₊ ² + M _? ² = 4M _t ² .     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

Higgs mass and inflation

We show that the standard-model Higgs boson mass mh is correlated with the spectral index of density perturbation ns in the inflation scenario with the inflaton being identified with the B-L Higgs boson. The Higgs boson mass ranges from mh?120 GeV to 140 GeV for ns?0.95-0.96. In particular, as ns approaches to 0.96, the Higgs mass is predicted to be in the range of 125 GeV to 140 GeV in the case of relatively light gauginos, and 120 GeV to 135 GeV in the case where all SUSY particle masses are of the same order. This will be tested soon by the LHC experiment and the Planck satellite. The relation is due to the PeV-scale supersymmetry required by the inflationary dynamics. We also comment on the cosmological implications of our scenario such as non-thermal leptogenesis and dark matter.     

Inverse seesaw in NMSSM and 126 GeV Higgs boson

We consider extensions of the next-to-minimal supersymmetric model (NMSSM) in which the observed neutrino masses are generated through a TeV scale inverse seesaw mechanism. The new particles associated with this mechanism can have sizable couplings to the Higgs field which can yield a large contribution to the mass of the lightest CP-even Higgs boson. With this new contribution, a 126 GeV Higgs is possible along with order of 200 GeV masses for the stop quarks for a broad range of tan β. The Higgs production and decay in the diphoton channel can be enhanced due to this new contribution. It is also possible to solve the little hierarchy problem in this model without invoking a maximal value for the NMSSM trilinear coupling and without severe restrictions on the value of tan β.     

Baryogenesis at the weak phase transition

The weak phase transition of the hot big bang can produce quarks, leptons and weak bosons which are out of thermal equilibrium. In a simple extension of the standard model it is shown that the reactions following top quark decays can generate the cosmological baryon asymmetry. The top quark mass must be close to 80 GeV and the Higgs boson must be lighter than 1 GeV. This baryogenesis mechanism can be directly tested at e⁺e⁻ and hadron collider by searching for spectacular events containing six or more bottom quarks and a violation of baryon number at the decay vertex of a long lived neutral particle.     

The conflict between natural flavor conservation of Higgs couplings and cabibbo mixing in SU(2)L × U(1)

The general problem of conservation of strangeness and other quark flavors by the exchange of several neutral Higgs mesons is investigated in SU(2)_L × U(1). We find that the horizontal symmetries necessary to enforce this conservation conflict with the known Cabibbo mixing. In particular, if the quarks form an irreducible representation of the horizontal symmetry, the mixing angles are all trivial (i.e., 0 or $\text{π}\text{2}$); if they form a reducible representation, it is possible to have some nontrivial mixing angles, but only if there are several unmixed generations of quarks with exactly the same relative pattern of masses and mixings.     

Mass breaking in a relativistic quark model for mesons

We study symmetry breaking via quark mass differences in a relativistic quark model where mesons are built from heavy (m > 3 GeV) spin $\text{1}\text{2}$) quarks and antiquarks. The meson (squared-)mass differences are linearly related to the number of strange, charmed, etc. quarks in the mesons. We show that the previously assumed SU_n symmetry of the mesonic couplings holds, i.e., quark mass differences only show up in the masses of the external particles, not in the three meson vertex itself.     

Cosmology of spontaneously broken gauge family symmetry with axion solution of strong CP-problem

TheSU(3) _H model of spontaneously broken local family symmetry is considered as a simplest version of realistic quantum flavourdynamics, giving reasonable explanation of the mass hierarchy and mixing pattern of quarks and leptons. This scheme can naturally possess one or two additional globalU(1) symmetries, which can play the role of Peccei-Quinn symmetry. The model predicts: existence of the neutrino Majorana masses with definite hierarchy, existence of familon being simultaneously invisible axion (or arion) and Majoron, relationship between neutrino lifetimes relative to familon decays. Thereby, the model provides the unified physical ground for all the main types of dark matter, considered in the theory of large scale structure of the universe.     

Four-Generation Condensate Scheme Without the Fourth Generation of Leptons

The renormalization group (RG) analyses show that in the four-generation fermion condensate scheme of electroweak symmetry breaking without the extra fourth generation of leptons thelimitation to the compositeness scale Λ could be greatly loosened and up to Λ<10¹⁰ GeV if the masses of the extra fourth generation of quarks are demanded to be bigger than the topquark mass m_t = 180 GeV. However, the mass constraints 2(m_Q)_minh⁰<2(m_Q)_max between the Higgs boson h⁰ and its constituent Q-fermions are no longer totally valid for Λ>10⁵ GeV. The ~redicted masses of the fourth generation of quarks and the Higgs boson will be larger than the corresponding ones in the four-generation quark-lepton scheme. The stability of the results for variation of the compositeness boundary conditions could be explained more clearly.     

Asymptotic behavior of amplitudes for longitudinal-leptoquark processes and structure of the scalar sector in the minimal model involving four-color symmetry

Within the minimal model based on the four-color symmetry of quarks and leptons of the Pati-Salam type, the asymptotic behavior of amplitudes for processes involving longitudinal leptoquarks (and W or Z′ bosons) is investigated, together with the mechanism according to which the growth of these amplitudes at high energies is suppressed by scalar fields. It is shown that, within the Higgs mechanism of mass generation and of the mass splitting of quarks and leptons, the four-color symmetry of quarks and leptons requires that scalar-leptoquark doublets, scalar-gluon doublets, and an extra color-singlet scalar doublet exist in addition to the standard Higgs doublet.     

T-odd quarks at the large hadron collider: 2010-2012

We study the potential of the current Large Hadron Collider (LHC) 7 TeV run to search for heavy, colored vector-like fermions, which are assumed to carry a conserved Z₂ quantum number forcing them to be pair-produced. Each fermion is assumed to decay directly into a Standard Model quark and an invisible stable particle. T-odd quarks and the lightest T-odd particle (LTP) of the Littlest Higgs model with T-parity provide an example of this setup. We estimate the bounds based on the published CMS search for events with jets and missing transverse energy in the 35 pb−1 data set collected in the 2010 run. We find that T-odd quark masses below about 450 GeV are ruled out for the LTP mass about 100 GeV. This bound is somewhat stronger than the published Tevatron constraint. We also estimate the reach with higher integrated luminosities expected in the 2011-2012 run. If no deviation from the SM is observed, we expect that a bound on the T-odd quark mass of about 650 GeV, for the LTP mass of 300 GeV and below, can be achieved with 1 fb−1 of data. We comment on the possibility of using initial-state radiation jets to constrain the region with nearly-degenerate T-odd quark and LTP.     

Vector Gauge Boson Dark Matter for the SU(N) Gauge Group Model

The existence of dark matter is explained by a new neutral vector boson, C-boson, of mass (900 GeV), predicted by the Wu mechanisms for mass generation of gauge field. According to the Standard Model (SM) W, Z-bosons normally get their masses through coupling with the SM Higgs particle of mass 125 GeV. We compute the self-annihilation cross section of the vector gauge boson C-dark matter and calculate its relic abundance. We also study the constraints suggested by dark-matter direct-search experiments. The problem on the stability of C-particle is left as an open question for future research.     

The standard model process e^ + e^ - \to \nu \bar \nu b\bar b and its Higgs signal at LEP II

We present and study the results for the standard model process $e^ + e^ - \to \nu \bar \nu b\bar b$ at c.m. energies 150 ≤ √s(GeV) ≤ 240 and for Higgs boson masses 60 GeV ≤ m _H ≤ 110 GeV, obtained from all tree-level diagrams and including the most important radiative corrections. The matrix elements have been calculated by the ‘spinor bracket’ method without neglecting masses, which is presented in detail. The √s-dependence and the interference properties of the Higgs boson contributions and of various coherent background contributions to the total cross section are examined and compared. The important differential distributions for the Higgs boson and the background components are studied, providing information useful for choosing cuts in Higgs searches. We also examine the effect of a minimal set of cuts and evaluate the importance of the WW fusion for detecting a higher mass Higgs boson at LEP II.     

Relativity,noncommutative geometry,renormalization and particle physics

A. Connes and A. Chamseddine have proposed a new geometric version of the standard model including a noncommutative relativity action. We present a systematic analysis of the relations among masses and coupling constants in these approaches. At the tree level, for a given top mass, the Higgs mass m_H is constrained to lie in an interval. Moreover, playing with the noncommutative gauge couplings, we compare the influence of the Higgs mass renormalization in these effective theories. The existing intersection is m_H = 188–201 GeV.     

Associated production of heavy Higgs boson with top quarks

Associated production of a heavy Higgs boson (m_H > 100 GeV) with top quarks at Juratron energies is studied. It is natural to differentiate between the “light” (2m_t < m_H < 2m_W) and “heavy” (m_H > 2m_W) Higgs search. It is assumed that the mass value of the top quarks is in the interval m_t ≈ 30–80 GeV. m_W is the W-boson mass. If m_H < 2m_W a dangerous background is given by the QCD production of four top quarks. We have calculated the cross sections for both the Higgs production and the background reaction. The disappointing result found is that the background is overwhelmingly large. However the Higgs search in this mass region is not hopeless. The associated production of the Higgs boson with a W-boson may have a clear experimental signature, its background given by the reaction $\text{p}\text{+}\text{p}\text{→}\text{W}\text{+}\text{t}\text{+}\text{t}$ might be suppressed. The difficulty with this mechanism is that the rate is rather low. If m_H > 2m_W the background is different and its contribution is expected to be small. The associated production of a Higgs boson with a pair of top quarks might be a useful method in the Higgs search in this case.     

Quark mixing in the discrete dark matter model

We consider a model in which dark matter is stable as it is charged under a Z₂ symmetry that is residual after an A₄ flavour symmetry is broken. We consider the possibility to generate the quark masses by charging the quarks appropriately under A₄. We find that it is possible to generate the CKM mixing matrix by an interplay of renormalisable and dimension-six operators. In this set-up, we predict the third neutrino mixing angle to be large and the dark matter relic density to be in the correct range. Low energy observables - in particular meson-antimeson oscillations - are hard to facilitate. We find that only in a situation where there is a strong cancellation between the Standard Model contribution and the contribution of the new Higgs fields, B meson oscillations are under control.     

Cosmic-ray induced vacuum decay in the standard model

In the standard model, if the Higgs boson mass, m_H, and the top quark mass, m_t, satisfy the relationship m_t≳95GeV + 0.60 m_H, then the vacuum is unstable. However, if the top quark mass is less than 190 GeV, then the lifetime is greater than the age of the universe. There is thus a large region of parameter space in which the vacuum is unstable, but sufficiently long-lived. We examine the possibility that high energy cosmic ray collisions could induce the decay of the vacuum, and show that this region of parameter space can be excluded.     

Higgs boson emission in very rare decays of an extra vector boson

We explore the phenomenological structure of E ₆-inspired grand unified group with the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1), the emphasis being laid upon its implications for Higgs boson observation. In particular, we discuss the probability for the mass eigenstate Z ₂ to decay into a Higgs particle and a bound state composed of heavy quarks. Constraints on and relations between the Z ₂ and Higgs masses are presented.     

Combined fit of low energy constraints to minimal supersymmetry and discovery potential at LEP II

Within the Constrained Minimal Supersymmetric Standard Model (CMSSM) it is possible to predict the low energy gauge couplings and masses of the 3. generation particles from a few parameters at the GUT scale. In addition the MSSM predicts electroweak symmetry breaking due to large radiative corrections from Yukawa couplings, thus relating theZ ⁰ boson mass to the top quark mass. From ax ² analysis, in which these constraints can be considered simultaneously, one can calculate the probability for each point in the MSGUT parameter space. The recently measured top quark mass prefers two solutions for the mixing angle in the Higgs sector: tan?? in the range between 1 and 3 or alternatively tan????25?50. For both cases we find a uniquex ² minimum in the parameter space. From the corresponding most probable parameters at the GUT scale, the masses of all predicted particles can be calculated at low energies using the RGE, albeit with rather large errors due to the logarithmic nature of the running of the masses and coupling constants. Our fits include full second order corrections for the gauge and Yukawa couplings, low energy threshold effects, contributions of all (s)particles to the Higgs potential and corrections tom _b from gluinos and higgsinos, which exclude (in our notation) positive values of the mixing parameter?? in the Higgs potential for the large tan?? region. Further constraints can be derived from the branching ratio for the radiative (penguin) decay of theb-quark intos?? and the lower limit on the lifetime of the universe, which requires the dark matter density due to the Lightest Super-symmetric Particle (LSP) not to overclose the universe. For the low tan?? solution these additional constraints can be fulfilled simultaneously for quite a large region of the parameter space. In contrast, for the high tan?? solution the correct value for theb??s?? rate is obtained only for small values of the gaugino scale and electroweak symmetry breaking is difficult, unless one assumes the minimal SU(5) to be a subgroup of a larger symmetry group, which is broken between the Planck scale and the unification scale. In this case small splittings in the Yukawa couplings are expected at the unification scale and electroweak symmetry breaking is easily obtained, provided the Yukawa coupling for the top quark is slightly above the one for the bottom quark, as expected e.g. if the larger symmetry group would be SO(10). For particles, which are most likely to have masses in the LEP II energy range, the cross sections are given for the various energy scenarios at LEP II. For low tan?? the production of the lightest Higgs boson, which is expected to have a mass below 103 GeV, is the most promising channel, while for large tan?? the production of charginos and/or neutralinos covers the preferred parameter space.     

Speculations on a strongly interacting Higgs sector

Using the 1/N expansion, we argue that the O_2N Higgs-Goldstone model may be a good indicator of the behavior of the standard SU₂ ? U₁ electroweak model in the non-perturbative limit of a strongly interacting Higgs sector. We emphasize that there remains a physical scalar particle or resonance σ (Higgs remnant), whose mass (and width) will be set by the weak scale. However, its coupling to vector bosons is expected to be much stronger than the standard model Higgs of comparable mass. This provides evidence that there is an upper limit to the Higgs mass in the hundreds of GeV, regardless of whether naturalness constraints are imposed on the parameters of the effective lagrangian. We conclude with some comments about the possible relevance of this particle to the radiative events observed at the CERN $\text{p}\text{p}$ collider.