Intermediate Mass Scale Research Articles

Limitations of the Press-Schechter Formalism

view Abstract Citations (43) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Limitations of the Press-Schechter Formalism Yano, Taihei ; Nagashima, Masahiro ; Gouda, Naoteru Abstract The Press-Schechter (PS) formalism for mass functions of the collapsed objects is reanalyzed. The factor of 2 in the Press-Schechter formalism is shown to be correct in the sharp k-space filter when we use the novel approach proposed by Jedamzik for the "cloud-in-cloud" problem which was first discussed by Peacock & Heavens and Bond et al. The spatial correlation of the density fluctuations, however, was either neglected or treated in an approximate manner in the previous works dealing with the cloud-in-cloud problem. In this paper the effect of spatial correlations is analyzed by using the Jedamzik formalism, taking explicitly into account the two-point correlations of density fluctuations, and it is found that this effect alters the PS mass function on some mass scales. For example, in the case of the initial power index n = 0, the difference between the modified mass function and the PS mass function is a factor of 1.4 at M = 0.1M_*_ and is 3 orders of magnitude at M = 10M_*_. With our new derivation of the mass function, we find that the probability of the effective overlap of the collapsed objects can be neglected either on very small or on large mass scales (for example, in the case of the initial power index n = 0, M <~ 0.1M_*_ or M ~> 10M_*_, where M_*_ is the characteristic mass scale on which the variance of density fluctuations equals unity), while it cannot be neglected on intermediate mass scales. Publication: The Astrophysical Journal Pub Date: July 1996 DOI: 10.1086/177488 arXiv: arXiv:astro-ph/9504073 Bibcode: 1996ApJ...466....1Y Keywords: COSMOLOGY: THEORY; GALAXIES: FORMATION; GALAXIES: LUMINOSITY FUNCTION; MASS FUNCTION; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; Astrophysics E-Print: 23 pages, uuencoded compressed Postscript full text sources arXiv | ADS |

Neutrinos and structure of the intermediate mass scale

Neutrino data lead via the see-saw mechanism to masses of the right handed neutrinos at the intermediate mass scale. A simple formalism is suggested which incorporates the quark-lepton symmetry and allows one to find properties of the intermediate scale (masses and mixing) from neutrino data. The averaged mass scale and the mass hierarchy parameter are introduced and fixed by the data. They determine natural ranges of masses and mixing at the intermediate scale. In particular, a scenario which includes the MSW solution of the solar neutrino problem and tau neutrino as the hot component of the dark matter in the Universe leads to M 2 = (2–4) × 10 10 GeV and M 3 = (4–8) × 10 12 GeV in agreement with the linear mass hierarchy. Strong deviations from these natural ranges imply fine tuning of parameters or/and certain symmetry of the Majorana mass matrix of the right handed neutrinos.

New scenario for string unification.

We present a new scenario for gauge coupling unification in flipped SU(5) string models, which identifies the ${M}_{32}$ scale of SU(3) and SU(2) unification with the empirical ${M}_{\mathrm{LEP}}\ensuremath{\sim}{10}^{15\ensuremath{-}16}\mathrm{GeV}$ scale, and the ${M}_{51}$ scale of SU(5) and U(1) unification with the theoretical ${M}_{\mathrm{string}}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{17}\mathrm{GeV}$ string unification scale. The vacuum shift necessary for the cancellation of the anomalous ${\mathrm{U}}_{A}\left(1\right)$ and an SU(4) hidden sector with fractionally charged particles play a crucial role in the dynamical determination of all intermediate mass scales in this scenario.

Chaotic inflation and a radiatively generated intermediate scale in the supersymmetric standard model

We consider a phenomenological extension of the minimal supersymmetric standard model which incorporates chaotic inflation and a radiatively generated intermediate mass scale. Initially a period of chaotic inflation is driven by a quartic potential associated with the right-handed electron sneutrino. Supersymmetry relates the quartic coupling of the inflationary potential to the electron Majorana neutrino Yukawa coupling, h 1. The microwave background temperature anisotropy determines this coupling to be h 1 ⋍ 10 −7 , which is similar in magnitude to the electron Dirac Yukawa coupling. A U(1) Peccei-Quinn (PQ) symmetry is broken by radiative corrections at an intermediate scale ⋍ 10 12 GeV when the universe cools to a temperature T ≲ 10 3 GeV. This leads to an invisible axion, a weak scale μ-term and an electron Majorana neutrino mass M N 1 ⋍ 10 5 GeV. A second inflationary period can also occur via a flat-direction field. In this case the universe can be reheated to a temperature T RH ⋍ 10 6 GeV, without restoring PQ symmetry. Baryogenesis will then occur via out-of-equilibrium neutrino decay.

Top quark mass in supersymmetric SO(10) unification.

The successful prediction of $\sin^2\theta_W$ suggests that the effective theory beneath the GUT scale is the two-Higgs MSSM. If we further assume that the unified gauge group contains SO(10), that the two light Higgs doublets lie mostly in a single irreducible SO(10) representation, and that the $t$, $b$ and $\tau$ masses originate in renormalizable Yukawa interactions of the form $16_3 O 16_3$, then also the top quark mass can be predicted in terms of the MSSM parameters. To compute $m_t$ we present a precise analytic approximation to the solution of the 2-loop renormalization group equations, and study supersymmetric and GUT threshold corrections and the input value of the $b$ quark mass. The large ratio of top to bottom quark masses derives from a large ratio, $\tan\beta$, of Higgs vacuum expectation values. We point out that when $\tan\beta$ is large, so are certain corrections to the $b$ quark mass prediction, unless a particular hierarchy exists in the parameters of the model. With such a hierarchy, which may result from approximate symmetries, the top mass prediction depends only weakly on the spectrum. Our results may be applied to any supersymmetric SO(10)-like model as long as $\lambda_t\simeq \lambda_b\simeq\lambda_\tau$ at the GUT scale and there are no intermediate mass scales in the desert.

Baryogenesis via B− L violation in SO(10) unified models

We discuss the problem of baryon number generation in the framework of a class of SO(10) grand unified models with an intermediate mass scale. In these theories the neutrino mass spectrum allows for the τ neutrino to be a good candidate for the hot component of the dark matter and, at the same time, an implementation of the MSW mechanism is possible. We show that an adequate matter-antimatter asymmetry is achievable through the interplay of B− L violating decays of scalar bosons into massive right-handed neutrinos with the anomalous B+ L violating processes mediated by sphalerons.

Supergravity Grand Unification(a).

A review of the recent proposal of Supergravity Grand Unification is given. Topics include the structure of Supergravity GUTS, symmetry breaking through Supergravity induced effects, protection at low energy from intermediate and superheavy mass scales, effective potential and the particle spectrum at low energy. Experimental consequences of Supergravity GUTS and in particular the decays of W and Z into photino, Wino and Zino modes and their branching ratios in various channels are also discussed.

Anomalous discrete symmetries and the domain-well problem

String theory frequently leads to four-dimensional models containing discrete symmetries which carry QCD anomalies and break spontaneously at an intermediate mass scale m. The domain walls associated with the spontaneous of breaking of such anomalous discrete symmetries are potentially cosmologically disastrous. We find that this cosmological catastrophe is avoided if and only if m ≲ 10 7 GeV. We also show that this stringent bound on m can be circumvented if the anomalous discrete symmetry happens to be effectively embedded in an “accidental” approximate anomalous global U(1) symmetry. A specific model which exhibits this mechanism is presented. Although we restricted ourselves to string models, our discussion can be readily applied to other gauge models with spontaneously broken anomalous discrete symmetries too.

Radiative breaking of Peccei-Quinn symmetry at the intermediate mass scale

We construct a supersymmetric (SUSY) extension of an invisible axion model, in which the Peccei-Quinn symmetry is broken naturally at the intermediate mass scale 10 10−10 12 GeV by radiative corrections from right-handed neutrino loops. The SUSY-invariant mass of doublet Higgs supermultiplets is forbidden by the Peccei-Quinn symmetry, whose breaking, however, generates an invariant Higgs mass of the order of the Fermi scale. In this model the right-handed neutrinos acquire large Majorana masses which are in a favored range for the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem.

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

SO(10) FOR GRAND UNIFICATION?

In this brief review, we present the arguments both theoretical and experimental in favor of the simple group SO(10) as the first approximation towards grand unification. The physical phenomena of the solar neutrino problem which motivate existence of neutrino mass, the recent LEP data which rule out the simple SU(5) (and perhaps supersymmetric SU(5) if tied also to the solar neutrino problem) model for which vanishing neutrino masses would be logical, coupled with attractive features like accommodating the invisible axion and a τ neutrino mass acceptable to cosmology, converge towards a two-step SO(10) model with intermediate mass scale of order 1011 GeV . We comment on the status of a second Z′ in a model of the spontaneous breakdown of SO(10) which is particularly conservative in that very little of the standard picture is altered.

Light Higgs bosons in three-generation Calabi-Yau superstring theory.

An analysis of the Higgs sector is given in three-generation superstring models which arise via Calabi-Yau compactifications where the flux breaking at the compactification scale reduces the ${\mathrm{E}}_{6}$ grand unified group to ${[\mathrm{S}\mathrm{U}(3)]}^{3}$ and a further spontaneous breaking at an intermediate scale ${M}_{I}$ reduces this symmetry down to the standard-model gauge group symmetry $\mathrm{SU}{(3)}_{C}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$. The analysis is carried out within the framework of matter parity invariance which is needed for proton stability and the assumption that spontaneous breaking at the intermediate scale is triggered by supersymmetry breaking. Conditions for the existence of a pair of light Higgs doublets needed for the further breaking of the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$ electroweak symmetry are obtained. These conditions act as constraints on the moduli space of the theory in order that the ${(27)}^{3}$ interactions accommodate light Higgs bosons below the intermediate mass scale.

Higgs bosons inE 6 and intermediate mass scales

Considering the importance ofE 6 as the grand unification group in superstring theories, several breakdown patterns ofE 6 through maximal subgroups are studied. The Higgs which break the low energy group and give masses to the fermions are determined in each case. At each scale we consider minimal Higgs and apply extended survival hypothesis to determine the limits on the mass scales. The combination of intermediate mass scales that give rise to acceptable electroweak mixing angle and unification mass is determined. Proton decay rate is found to be acceptable in all cases except one.

Matter-parity constraints on particle spectrum in three-generation Calabi-Yau manifolds.

An analysis of the particle spectrum after intermediate scale breaking in the three-generation Calabi-Yau manifold CP/sup 3//times/CP/sup 2//Z/sub 3/ is given. The spectrum is investigated within the framework of intermediate scale breaking which preserves matter parity and breaks the rank-six gauge group SU(3)/sub /ital C///times/SU(3)/sub /ital L///times/SU(3)/sub /ital R// to the standard-model gauge group SU(3)/sub /ital C///times/SU(2)/sub /ital L///times/U(1)/sub /ital Y//. It is shown that a large number of particles and mirror particles associated with the extra families and mirror families on CP/sup 3//times/CP/sup 3//Z/sub 3/ can all be made superheavy through mass generation induced by nonrenormalizable interactions that are present in the superpotential below the compactification scale. The final spectrum of the compactified superstring below the intermediate-mass scale breaking is shown to be the spectrum of the standard /ital N/=1 supersymmetry theory and a few additional exotic leptons. Some of these exotic leptons are hybrid structures containing equal mixture of leptons and mirror leptons.

Symmetry breaking in three-generation Calabi-Yau manifolds.

The spontaneous breaking of [SU(3)${]}^{3}$ symmetry to SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1) due to nonrenormalizable interactions in the three-generation Calabi-Yau superstring model is considered. It is seen that these models lead naturally to intermediate scales ${M}_{I}$\ensuremath{\sim}${10}^{15}$ GeV with simultaneous formation of N and ${\ensuremath{\nu}}^{c}$ vacuum expectation values (VEV's). The lowest-lying extrema automatically preserve matter parity and hence protect the model against too rapid proton decay. Models with matter parity also protect against electroweak Higgs VEV's from forming at ${M}_{I}$. The intermediate mass scale produces some particles with mass O(${M}_{I}$). It also implies the existence of others with mass \ensuremath{\sim}1 TeV, which are possibly accessible to low-energy experiments.

Cosmological higgsino densities in SUSY models with intermediate mass scales

We study the density of light stable higgsinos which arise in SUSY models with flat potentials for a scalar field φ which gains a large VEV, when the higgsinos freeze out during a period when the total energy density is dominated by coherent oscillations of φ and where the radiation energy density is dominated by radiation from φ decays. For the case where the higgsino density arises from freezing out of chemical equilibrium, it is shown that the lower bound on the higgsino mass is reduced compared with standard cosmology, and that the number density of higgsinos at present is proportional to M h −6 compared with M h −3 in the standard case. In the case where higgsinos arise from direct decay of the φ oscillations to higgsino pairs, it is shown that in order not to have an unacceptable present higgsino density, either the temperature at which the oscillation dominated period ends must be larger than a critical temperature O(1 GeV), or the branching ratio to higgsino pairs must be constrained to be ⩽10 −6( M φ 2M h ) . We comment on the implications of the results for higgsino dark matter when freeze-out occurs during oscillation domination.

NEUTRINO MASSES IN SUPERSTRING THEORIES WITH INTERMEDIATE SCALES

Three generation superstring models require intermediate mass scales to be consistent with perturbative unification. We study the problem of neutrino masses in theories with intermediate mass scales which can evolve in the low energy limit of superstring theories.

A cosmologically acceptable hadronic axion in a superstring-inspired model

A cosmologically acceptable harmless hadronic axion is generated in a superstring-inspired model with an intermediate mass scale, through the heavy-quark mechanism. The heavy quarks required to implement this scheme are naturally identified with the exoticD fields contained in the fundamental representations of the gauge groupE6. The axion couplings with ordinary matter are discussed.

Intermediate mass scale in rank-six superstring models.

The current experimental lower limit on proton lifetime from the decay mode p\ensuremath{\rightarrow}\ensuremath{\nu}\ifmmode\bar\else\textasciimacron\fi{}+${K}^{+}$ is used to obtain a limit on the intermediate mass scale in superstring-inspired models with rank-six groups. It is shown that the intermediate mass scale breaking in these models can be as low as 1\ifmmode\times\else\texttimes\fi{}${10}^{14}$ GeV without violating current proton-decay data, provided the Yukawa couplings of superstring models are no larger than the corresponding couplings in SU(5) supergravity models. Scalar-quark masses are then larger than 1 TeV and the photino mass is no more than a few gigaelectronvolts.

Intermediate-mass scales and one-loop corrections in superstring-inspired models

We extend a previous analysis about the mechanism for generating radiatively a gauge symmetry breaking at an intermediate-mass scale, in the framework ofE6 superstring-inspired models. The breaking is obtained driving the squared masses of some standard-model singlet scalars from the «survivor»\(b_{1,1} (\underline {27} + \underline {\overline {27} } )\) to negative values, by means of Yukawa couplings of sufficient magnitude. Performing a numerical calculation, the effect is shown on the intermediate-mass scaleMI of the one-loop corrections to the effective scalar potential, varying the Yukawa couplings both in the27 and in the\({\overline {27} }\) sector of the survivors.