Limits on low scale gravity from e+e−→W+W−, ZZ and γγ

It has been proposed recently that the scale of quantum gravity (“the string scale”) can be M_S∼few TeV with n≥2 extra dimensions of size R≲mm so that, at distances greater than R, Newtonian gravity with M_Pl∼10¹⁸ GeV is reproduced if M_Pl²∼RⁿM_Sⁿ⁺². Exchange of virtual gravitons in this theory generates higher-dimensional operators involving SM fields, suppressed by powers of M_S. We discuss constraints on this scenario from the contribution of these operators to the processes e⁺e⁻→W⁺W⁻, ZZ, γγ. We find that LEP2 can place a limit M_S≈1 TeV from e⁺e⁻→W⁺W⁻, ZZ, γγ.     

SU(3) lattice Monte Carlo calculation of the glueball mass spectrum

We have calculated the glueball masses of various spins and parities in SU(3) gauge theory. Our first results give m_M(0⁺⁺)=(3.6±0.2)Λ_mom, m_E(0⁺⁺)=(4.3±0.3)Λ_mom, m(0^?+)=(7.2_?0.9^+1.6)Λ_mom, m_M(2⁺⁺)=(8.1±1.1)Λ_mom and m_E(2⁺⁺)=(8.3_?1.0^+1.6)Λ_mom as well as information on the glueball wave functions.     

Perturbative quantum gravity in analogy with Fermi theory of weak interactions using bosonic tensor fields

In this paper we work in perturbative quantum gravity and we introduce a new effective model for gravity. Expanding the Einstein–Hilbert Lagrangian in graviton field powers we have an infinite number of terms. In this paper we study the possibility of an interpretation of more than three graviton interacting vertices as effective vertices of a most fundamental theory that contain tensor fields. Here we introduce a Lagrangian model named I.T.B. (intermediate-tensor-boson) where four gravitational pseudo-currents that contain two gravitons couple to three massive tensorial fields of ranks one, three and five, respectively. We show that the exchange of those massive particles reproduces, at low energy, the interacting vertices for four or more gravitons. In a particular version, the model contains a dimensionless coupling constant g and the mass M of the intermediate bosons as free parameters. The universal gravitational constant G_N is shown to be proportional to the inverse of mass squared of mediator fields, particularly . A foresighting choice of the dimensionless coupling constant could lower the energy scale where quantum gravity aspects show up.     

Classical theory of a space-time sheet

By embedding the space-time V₄ in a higher-dimensional space M_N we can formulate a theory of gravity in which the true dynamical variables are the coordinates η^a(x) (a = 1,2,…, N) of V₄ with respect to M_N. Before constrained by the variational principle, which gives the equations of the four-surface V₄, all the coordinates η^a are independent. This enables the canonical formulation of the theory (without additional constraints except for the initial and boundary conditions on η^a and ones due to the reparametrization invariance) which is presented here. When expressed in terms of the metric tensor g_μ$\text{v}$ of the space-time four-surface V₄ the theory reduces to the Einstein general relativity.     

Nonlinear properties of vielbein massive gravity

We propose a nonlinear extension of the Fierz–Pauli mass for the graviton through a functional of the vielbein and an external Minkowski background. The functional generalizes the notion of the measure, since it reduces to a cosmological constant if the external background is formally sent to zero. Such a term and the explicit external background emerge dynamically from a bi-gravity theory, having both a massless and a massive graviton in its spectrum, in a specific limit in which the massless mode decouples, while the massive one couples universally to matter. We investigate the massive theory using the Stückelberg method and providing a ’t Hooft–Feynman gauge fixing, in which the tensor, vector and scalar Stückelberg fields decouple. We show that this model has the softest possible ultraviolet behavior that can be expected from any generic (Lorentz-invariant) theory of massive gravity, namely that it becomes strong only at the scale Λ₃=(m_g ²M_P)^1/3.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

A solution for galactic disks with Yukawian gravitational potential

We present a new solution for the rotation curves of galactic disks with gravitational potential of the Yukawa type. We follow the technique employed by Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new solution allows an easy comparison between the Newtonian solution and the Yukawian one. Therefore, constraints on the parameters of theories of gravitation can be imposed, which in the weak field limit reduce to Yukawian potentials. We then apply our formulae to the study of rotation curves for a zero-thickness exponential disk and compare it with the Newtonian case studied by Freeman in 1970. As an application of the mathematical tool developed here, we show that in any theory of gravity with a massive graviton (this means a gravitational potential of the Yukawa type), a strong limit can be imposed on the mass (m _g) of this particle. For example, in order to obtain a galactic disk with a scale length of b∼ 10 kpc, we should have a massive graviton of m _g ≪ 10⁻⁵⁹g. This result is much more restrictive than those inferred from solar system observations.     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

The glueball mass spectrum in QCD: First results of a lattice Monte Carlo calculation

We perform a variational calculation of the masses of glueballs of various spins and parities in SU(2) gauge theory. The quantum vacuum we use is generated by the lattice Monte Carlo technique. Our first results, obtained on medium sized lattices give m(0⁺) = (3.6 ± 0.35) Λ_mom, m(0^? = (6.0 ± 1.0)Λ_mom, m(2⁺) = (6.5^+1.8_?1.1)Λ_mom, various mass upper bounds and information on glueball wave functions.     

Quartic mass matrix and renormalization constants in supersymmetric Yang-Mills theories

We derive the general formula for the supertrace of the quartic mass matrix in a general supersymmetric gauge theory, with arbitrary representations for the chiral multiplets. This formula clarifies the non-renormalization theorems in presence of gauge interactions and gives “extended renormalization theorems” for N = 2 and N = 4 supersymmetric Yang-Mills theories. In particular we find the known result that g_ren = g_bare for the N = 4 theory and the new result m_ren = m_bare for the N = 2 gauge interactions of massive hypermultiplets. We give arguments to the extent that the latter non-renormalization theorem persists to all orders in perturbation theory.     

An effective lagrangian for multiphoton processes and a non-linear Born-Infeld lagrangian

An effective lagrangian for multiphoton processes (of Euler-Heisenberg type) is computed for an electromagnetic field interacting with massive scalar, fermion and vector particles. It is found that if the charges g_I, masses m_I and numbers N_I of massive particles satisfy the “supersymmetric” conditions, N_Sm_S⁴+3N_Vm_V⁴?2N_Fm_F⁴=0 and g_I²/m_I⁴ is I-independent, where I=S, F, V stands for scalars, fermions and vectors respectively, then not only quartic divergences (poles at n=0 in dimensional regularization) proportional to constant terms cancel out but also maximally helicity changing interaction terms vanish in the effective lagrangian. A possibility to relate a non-linear Born-Infeld lagrangian to the effective lagrangian is examined.     

The vacuum energy of QED with four-fermion interaction

We consider quantum electrodynamics in the quenched approximation including a four-fermion interaction with coupling constantg. The effective potential at stationary points is computed as a function of the coupling constants α andg and an ultraviolet cutoff Λ, showing a minimum of energy in the (α,g) plane for α=α _c =π/3 andg=∞. When we go to the continuum limit (Λ→∞), keeping finite the dynamical mass, the minimum of energy moves to (α=0,g=1), which correspond to a point where the theory is trivial.     

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=l,we calculate and discuss the influence of U bosons on the equation of state,mass-radius,moment of inertia and gravitational redshift of massive protoneutron stars(PNSs).The effective coupling constant gu of U bosons and nucleons is selected from 0 to 70 GeV~(-2).The results indicate that U bosons will stiffen the equation of state(EOS).The influence of U bosons on the pressure is more obvious at low density than high density,while the influence of U bosons on the energy density is more obvious at high density than low density.The U bosons play a significant role in increasing the maximum mass and radius of PNS.When the value of gu changes from 0 to 70 GeV~(-2),the maximum mass of a massive PNS increases from 2.11M_⊙ to 2.58M_⊙,and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km.The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS.For the PNS of the massive PSR J0348+0432,the radius and moment of inertia vary directly with gu,and the gravitational redshift varies approximately inversely with gu.     

Observation of a doubly charged charmed baryon in the reaction υp→μ−Σ++c

Evidence for the quasi-elastic production of the doubly charged charmed barron Σ⁺⁺_c has been observed in a vp interaction in BEBC. The mass of the Σ⁺⁺_c and of its decay product, the Λ⁺_c, are 2454±5 MeV and 2288±5 MeV, respectively. The mass difference M(Σ⁺⁺_c)? M(Λ⁺_c) is 166±1 MeV. Combining the Λ⁺_c mass value obtained here with the values obtained in the two Λ⁺_c events previously observed in this experiment, thevalue M(Λ⁺_c)=2283±3 MeV is deduced.     

Construction of Euclidean (QED)2 via lattice gauge theory

Let ν=det_ren(1+K _g ) be the renormalized Matthews-Salam determinant of (QED)₂, where \(K_g = ieA_{g,} S = \left( {\sum {\gamma _\mu \partial } _\mu + m} \right)^{ - 1} \) is euclidean fermion propagator of one of the following boundary conditions: (1) free, (2) periodic at ?Λ, Λ=[?L/2;L/2]², (3) anti-periodic at ?Λ, and \(A_g (x) = (\sum \gamma _\mu A_\mu (x))g(x)\) . Hereg(x)=1 ifxεΛ₀=[?r/2,r/2]² с Λ and 0 otherwise. Then we show

1. νεL ^p (dμ(A)), p>0. Further we prove a new determinant inequality which holds for the QED, QCD-type models containing fermions. This enables us to prove:
2. Z(Λ₀)=∫νdμ(A)≦exp[c|Λ₀|]. Similar volume dependence is shown for the Schwinger functions.

     

Proton decays and neutron oscillations in the rishon model

We analyze proton decays and neutron oscillations in the rishon model. Proton decay is forbidden in lowest order of the compositeness scale Λ_H. In a one-generation rishon model, the leading proton decays violate B?L (e.g., p→νπ⁺). The lifetime is given by τ_p～Λ_H⁸/(U_R²m_p⁷), where U_R～M(W_R) is the mass scale of the right-handed W boson and m_p is the proton mass. For U_R～500 GeV, the obtained limit for the compositeness scale is Λ_H?10⁸ GeV. Neutron oscillations are also proportional to Λ_H⁸ and cannot be detected in the foreseeable future. All of these predictions may depend strongly on the understanding of higher generations of quarks and leptons within the model.     

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2⁺ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2⁺ and 2⁻ particles of equal mass, as well as a massive pseudoscalar.     

A grand unified theory based onSU(n, 1)-minimal supergravity

We discuss a grand unified theory in the framework ofSU(n, 1) minimal supergravity with the Planck mass as the only input mass scale.M _W ≈m _3/2 is fixed by radiative corrections to be naturally ?M _P1. Due to the particular form of explicit soft supersymmetry breaking a light singlet can be used to obtain naturally light Higgs doublets and for a new mechanism for radiativeSU (2)×U(1) breaking. The low energy particle spectrum is very restricted withm _3/2≈10⁴ GeV.     

Renormalization group and dynamical symmetry breakdown in abelian gauge theories

Generalized renormalization group equations are used to analyze the dynamical mechanism of particle mass generation in terms of the Cornwall-Norton model both with and without cut-off. We look for solutions which contain non-zero physical masses of the two fermions (m₁, m₂) and of one of the vector bosons (μ) when the bare masses m_1Λ, m_2Λ, μ_Λ approach zero. For a theory without cut-off we obtain results which are similar to those of Cornwall. For a theory with cut-off the mass generation mechanism may only occur when a bare coupling constant α_Λ of the A_μ vector boson, which remains massless, exceeds some critical value α_c. In this case the fermion masses turn out to be of the superconductivity type.The model's “memory” of the nature of spontaneous symmetry breaking lim_{m1Λ, m2Λ → 0}m_1Λ/m_2Λ ≠ 1 is an indispensible factor for the vector boson to acquire a mass.     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.