Jonathan Richard Ellis

Radiative corrections to the masses of supersymmetric Higgs bosons

Abstract The lightest neutral Higgs boson in the minimal supersymmetric extension of the standard model has a tree-level mass less than that of the Z 0 . We calculate radiative corrections to its mass and to that of the heavier CP -even neutral Higgs boson. We find large corrections that increase with the top quark and squark masses, and vary with the ratio of vacuum expectation values ν 2 / ν 1 . These radiative corrections can be as large as O(100) GeV, and have the effect of (i) invalidating lower bounds on ν 2 / ν 1 inferred from unsuccessful Higgs searches at LEP I, (ii) in many cases, increasing the mass of the lighter CP -even Higgs boson beyond m z , (iii) often, increasing the mass of the heavier CP -even Higgs boson beyond the LEP reach, into a range more accessible to the LHC or SSC.

A phenomenological profile of the Higgs boson

A discussion is given of the production, decay and observability of the scalar Higgs boson H expected in gauge theories of the weak and electromagnetic interactions such as the Weinberg-Salam model. After reviewing previous experimental limits on the mass of the Higgs boson, we give a speculative cosmological argument for a small mass. If its mass is similar to that of the pion, the Higgs boson may be visible in the reactions π−p → Hn or γp → Hp near threshold. If its mass is ≲300 MeV, the Higgs boson may be present in the decays of kaons with a branching ratio O(10−7), or in the decays of one of the new particles: 3.7 → 3.1 + H with a branching ratio O(10−4). If its mass is ⩽4 GeV, the Higgs boson may be visible in the reaction pp → H + X, H → μ+μ−. If the Higgs boson has a mass ⩽2mμ, the decays H → e+e− and H → γγ dominate, and the lifetime is O(6 × 10−4 to 2 × 10−12) seconds. As thresholds for heavier particles (pions, strange particles, new particles) are crossed, decays into them become dominant, and the lifetime decreases rapidly to O(10−20) sec for a Higgs boson of mass 10 GeV. Decay branching ratios in principle enable the quark masses to be determined.

Aspects of the Flipped Unification of Strong, Weak and Electromagnetic Interactions

We study issues arising in attempts to unify strong and other elementary particle interactions. The proton lifetime is estimated in theories with second-order baryon number violation, and found to be O(103–104) longer than naive dimensional counting suggested. The renormalization of quark and lepton masses below the grand unification mass is considered in some detail. Application is made to the SU(5) model of Georgi and Glashow, and we find strange and bottom quark masses: ms ≈ 0.4–0.5 GeV, mb ≈ 4.8–5.6 GeV . Inputs are the values of the strong interactions coupling constant favoured by electroproduction and charmonium analyses, and the observed muon and heavy lepton (τ) masses. These estimates are substantially increased if there are more than six flavours of quark. Symmetry breaking in the SU(5) model is studied, including radiative corrections to the effective Higgs potential.

Probing the desert using gauge coupling unification

Abstract We present analytic one-loop expressions for sin 2 θ w , the unification scale M x , and the coupling at the unification scale α ( M x ), in supersymmetric grand-unified models with arbitrary intermediate scales. We correct these expressions to agree with a two-loop calculation for central values of the inputs. Our general results quickly determine whether a particular model has hope of compatibility with the low energy couplings. We then apply these results to traditional supersymmetric SU (5) and to supersymmetric flipped SU (5) × U (1). These results translate into a narrow bound on a function of the extra intermediate scales. In particular, we conclude that even allowing for the experimental uncertainties in low-energy couplings and effects of supersymmetric and Higgs thresholds, traditional supersymmetric SU (5) grand unification without extra thresholds is about one standard deviation away from the measured value of sin 2 θ w . We also calculate the range of proton decay in minimal flipped SU (5) × U (1) allowing for uncertainties in the low-energy couplings and the effects of supersymmetric and Higgs thresholds. Non-observation of proton decay gives a bound on another function of additional intermediate scales beyond the minimal model.

No Scale Supersymmetric Guts

We construct locally supersymmetric GUTs in which radiative corrections determine all the mass scales which are hierarchically smaller than the Planck mass: m32 = O(mW) = exp (−O(1)αt)mp, etc. Such no-scale GUTs are based on a hidden sector with a flat potential guaranteed by SU(1, 1) conformal invariance. This is extended to include observable chiral fields in an SU(n, 1)/SU(n) × U(1) structure reminiscent of N ⩾ 5 extended supergravity theories. Tree-level supersymmetry breaking is present only for the gravitino, and for the light gaugino masses through non-minimal kinetic terms reminiscent of N⩾4 extended supergravity theories. Radiative corrections generate squark and slepton masses which are phenomenologically acceptable, and the right value of mW is obtained if mt ≈ 50 GeV in the simplest such model.

The flipped SU(5)×U(1) string model revamped

Abstract We present a refined version of our three-generation flipped ,SU(5)×U(1) string model with the following properties. • -The complete massless spectrum is derived and shown to be free of all gauge and mixed anomalies apart from a single anomalous U(1). • -The imaginary part of the dilaton supermultiplet is eaten by the anomalous U(1) gauge boson, and the corresponding D-term is cancelled by large VEVs for singlet fields that break surplus U(1) gauge factors, leaving a supersymmetric vacuum with an SU(5)×U(1) visible gauge group and an SO(10)×SO(6) hidden gauge group. • -There are sufficient Higgs multiplets to break the visible gauge symmetry down to the standard model in an essentially unique way. • -All trilinear superpotential couplings have been calculated and there are in particular some giving m t , m b , m τ ≠0. • -A renormalization group analysis shows that m t m b ≅3 m τ . • -Light Higgs doublets are split automatically from heavy Higgs triplets, leaving no residual dimension-five operators for baryon decay, and the baryon lifetime τ B ∼ 2×10 34±2 yr. • -There are no tree-level flavour-changing neutral currents, but μ → eγ may occur at a detectable level: B ( μ → eγ ) ∼ 10 −11 −10 −14 .

Phenomenological SU(1,1) Supergravity

We investigate the structure of phenomenological supergravity models which permit the hierarchy problem to be “solved” in the sense that m32 and mW are determined dynamically to be exp [-O(1)/α] × mP. Such models must have a flat hidden sector potential, which is only possible if the theory has an underlying SU(1, 1) invariance. Flat SU(1, 1) theories necessarily have a zero cosmological constant and the hidden sector is an Einstein space with Rzz∗ = 23Gzz∗. The SU(1, 1) invariance is necessarily broken down to U(1) by the gravitino mass. If m32 is the only source of SU(1, 1) breaking then the tree-level gaugino masses are small and A = 32, while values of A up to 3 and non-zero gaugino masses are possible if other sources of SU(1, 1) breaking are tolerated. Yukawa couplings may scale as some power of m32mP in these models where m32 is generated dynamically, which may explain the hierarchy of Higgs-fermion Yukawa couplings: mfmW = O(mWmP)λ>0? These models also permit the spontaneous violation of CP in the Yukawa coupling matrix. Numerical studies yield 20 GeV < mt < 100 GeV in these phenomenological SU(1, 1) supergravity models. Speculations are presented about their relation to a fundamental theory based on extended supergravity.

The cosmology of decaying gravitinos

Abstract We consider the cosmological constraints on unstable particles with masses O( m W ). Constraints from the energy density during primordial nucleosynthesis, from subsequent entropy generation, and from perturbations of the microwave background are not as restrictive as bounds from the dissociation of light elements. Most restrictive is the need to avoid over-production of D and 3 He through the photo-dissociation of 4 He. When applied to gravitinos, this bound imposes an upper limit of O(10 8 ) GeV on the reheating temperature after inflation, which could create problems for baryosynthesis in supersymmetric theories. These problems can be avoided if the photino is heavier than the gravitino.

Flavour-changing neutral interactions in broken supersymmetric theories

Abstract We point out that in order to ensure an efficient “super-GIM” suppression of flavour-changing neutral interactions, the supersymmetric partners of conventional fermions (squarks and sleptons) must be almost degenerate in mass. The strongest constraints on squark mass differences of Δm 2 sq m 2 sq −3 ) come from the K 1 -K 2 mass matrix, while the non-observation of μ→ eγ imposes m 2 sl m 2 sl −3 ) if the supersymmeric partners of the SU(2) and SU(1) bosons have masses O(100) GeV. These results help motivate a susy gauge theory with an extra Ũ(1) symmetry spontaneously broken at low energy, perhaps of a non-minimal type.

Search for gluons in e+e− annihilation

Abstract We study the deviations to be expected at high energies from the recently observed two-jet structure of hadronic final states in e + e − annihilation. Motivated by the approximate validity of the naive parton model and by asymptotic freedom, we suggest that hard gluon bremsstrahlung may be the dominant source of hadrons with large momenta transverse to the main jet axes. This process should give rise to three-jet final states. These may be observable at the highest SPEAR or DORIS energies, and should be important at the higher PETRA or PEP energies.