Grand unification in RS1

We study unification in the Randall-Sundrum scenario for solving the hierarchy problem, with gauge fields and fermions in the bulk. We calculate the one-loop corrected low-energy effective gauge couplings in a unified theory, broken at the scale M_GUT in the bulk. We find that, although this scenario has an extra dimension, there is a robust (calculable in the effective field theory) logarithmic dependence on M_GUT, strongly suggestive of high-scale unification, very much as in the (4D) Standard Model. Moreover, bulk threshold effects are naturally small, but volume-enhanced, so that we can accommodate the measured gauge couplings. We show in detail how excessive proton decay is forbidden by an extra U(1) bulk gauge symmetry. This mechanism requires us to further break the unified group using boundary conditions. A 4D dual interpretation, in the sense of the AdS/CFT correspondence, is provided for all our results. Our results show that an attractive unification mechanism can combine with a non-supersymmetric solution to the hierarchy problem.     

The role of 75H in fermion mass hierarchy

It is pointed out that the second generation fermions can have a natural mass relation m_μ = 3m_s at M_GUT if SU(5) symmetry breaking occurs through 75_H and 5_H. It is a first order supergravity effect and a small Yukawa coupling is not necessary.     

Radiative corrections in compactified superstring models

One-loop corrections to the effective potential in models obtained from compactification of ten-dimensional superstring theories are calculated. It is found that no masses are generated for gauge non-singlet scalars even in the presence of supersymmetry breaking terms induced by gauge and gaugino condensation, but that the gravitino mass is determined at one loop. The scales of grand unification, supersymmetry breaking and condensation are fixed by the gauge singlet scalars and are found to be close to Planck scale. Requiring M_GUT<M_Planck restricts the other parameters of the theory. The one-loop effective potential at scales between the condensate and compactification scales is also discussed, with possible implications for the allowed particle content of the effective theory.     

Some rare processes in a model of composite quarks and leptons

The branching ratios of some rare processes, i.e. meson →μe, meson →meson μe, baryon → baryon μe, are calculated in a composite quark and lepton model. Use is made of an effective Hamiltonian which originates from hypercolor singlet 0^? and 1^? bound state exchange mechanism, acting at a mass scaleM _P andM _V respectively. Under the reasonable assumptionM _P =M _V onlyK _L →μe puts a significant limit on the composite scale.     

Resurrecting no-scale supergravity phenomenology

In the context of phenomenological models in which the soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT, it is possible that all the scalar mass parameters m ₀, the trilinear couplings A ₀ and the bilinear Higgs coupling B ₀ vanish simultaneously, as in no-scale supergravity. Using these no-scale inputs in a renormalisation-group analysis of the minimal supersymmetric SU(5) GUT model, we pay careful attention to the matching of parameters at the GUT scale. We delineate the region of M _in, m _1/2 and tan?β where the resurrection of no-scale supergravity is possible, taking due account of the relevant phenomenological constraints such as electroweak symmetry breaking, m _h ,b→s γ, the neutralino cold dark matter density Ω _χ h ² and g _μ ?2. No-scale supergravity survives in an L-shaped strip of parameter space, with one side having m _1/2?200 GeV, the second (orthogonal) side having M _in?5×10¹⁶ GeV. Depending on the relative signs and magnitudes of the GUT superpotential couplings, these may be connected to form a triangle whose third side is a hypotenuse at larger M _in, m _1/2 and tan?β, whose presence and location depend on the GUT superpotential parameters. We compare the prospects for detecting sparticles at the LHC in no-scale supergravity with those in the CMSSM and the NUHM.     

Leading logarithmic corrections to the weak leptonic and semi-leptonic low-energy hamiltonian

If one defines the parameters of the Weinberg-Salam theory at a momentum scale M = O(M_W, M_Z), the weak effective hamiltonian at a momentum scale μ ? M has logarithmically enhanced corrections, of order αln(M²/μ²). We present a computation of these corrections, for that part of the hamiltonian which leads to detectable weak-electromagnetic interference effects. The largest correction can be absorbed into a running sin²θ(μ). Other, smaller, corrections are estimated, taking into account the effect of strong interactions.An estimate of the non-logarithmically enhanced corrections is also given, by evaluating them in the limit sin²θ → 0. From the SLAC e - d asymmetry it was found sin²θ = 0.224 ± 0.020 at μ² ? 2 GeV². In correspondence, we find sin²θ(M) = 0.217 ± 0.020. This value, however, is subject to uncertainties deriving from the effect of the strange and of the antiquark parton sea.     

Neutrino production of M+ and E+ heavy leptons (I)

A theoretical study is made of M⁺ and E⁺ heavy lepton production in inclusive neutrino reactions. The production cross sections on protons are found to be enhanced over those for isoscalar targets and can in principle exceed the cross sections for the ordinary v_μ+p→μ^?+X process at high energies. New estimates are given for the decay branching ratios taking into account the SPEAR data on electron positron annihilation. Monte Carlo techniques are employed to calculate q² ? v spectra and y distributions for both the production process where v_μ→M⁺ and the effective process where v_μ→μ⁺. The normalized results are rather insensitive to the set of structure functions used.     

What if supersymmetry breaking unifies beyond the GUT scale?

We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT. We assume that the scalar masses and gaugino masses have common values, m ₀ and m _1/2 respectively, at M _in. We use the renormalisation-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to M _GUT, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as M _in increases. This has the consequence, as we show in (m _1/2,m ₀) planes for several different values of tan?β, that the stau-coannihilation region shrinks as M _in increases, and we delineate the regions of the (M _in,tan?β) plane where it is absent altogether. Moreover, as M _in increases, the focus-point region recedes to larger values of m ₀ for any fixed tan?β and m _1/2. We conclude that the regions of the (m _1/2,m ₀) plane that are commonly favoured in phenomenological analyses tend to disappear at large M _in.     

Gauge boson masses and lepton mixing inO(4)⊗U(1) gauge model

The Cabibbo angle is introduced as a mixing angle of the gauge bosonsW ^± andX ^± in anO(4)?U(1) gauge model. Masses of gauge bosons are calculated to beM _W=82 (input), \(M_z = \sqrt 2 M_W s\gamma = 130\) (γ is mixing angle, sin² γ=0.21),M _x=666, andM _Y=660, in units GeV. TheW _μ ^± andZ _μ ⁰ couple to the familiar charged and neutral currents, respectively. The effective neutrino oscillation angle is found to be the Cabibbo angle.     

Renormalization scheme dependence of electroweak radiative corrections

We compare two renormalization schemes of the electroweak standard model: the on-shell scheme withe, M _W ,M _Z ,M _H , and the fermion masses {m _f } as free parameters, and an intermediate scheme where theW boson self energy is renormalized atq ²=0 instead ofq ²=M _W ². TheM _W ?M _Z interdependence, and the differentiale ⁺ e ^?→μ ⁺ μ ^? cross section including polarized beams are calculated in both schemes to one-loop order. We find striking differences between the forward-backward asymmetries and the polarization asymmetries near theZ resonance after inclusion of weak and QED corrections.     

Lower limit for heavy muon mass obtained from the data of the CERN neutrino experiment

A lower limit for the heavy muon (heavy lepton omega′^? which can have the same lepton number as omega^? and ν_omega) mass M_μ′ > 1.8 GeV at 90% confidence level is obtained with the help of the bubble chamber “Gargamelle” data in the CERN neutrino experiment. This limit should not be confused with the known limit for an M⁺ (heavy lepton M⁺ which can have the same lepton number as μ^? and ν_μ).     

Electromagnetic corrections to neutrino processes in the leading logarithmic approximation,the value of sin θ and the W and Z masses

The parameters of the Weinberg-Salam model can be defined by amplitudes at a momentum scale M = O(M_W, M_Z). We derive the leading logarithmic e.m. correction to the relations giving the neutrino amplitudes at a momentum scale μ ? M in terms of sin²θ(M), α(M), M_W and M_Z. For leptonic processes, the Fermi constant is not corrected, but a running, universal, sin²θ(μ) > sin²θ(M) should be used. The Fermi constant for semileptonic processes is renormalized by a factor $\text{?(μ) > 1}$, for charged currents, and is not renormalized, for neutral current processes. The latter are described by the same sin²θ(μ) as the leptonic ones. We estimate that sin²θ(M) is about 0.013 smaller than the value of sin²θ obtained from semileptonic data with no correction, thereby improving the agreement with grand unified theories. The prediction for W (Z) masses and widths in terms of the low energy parameters are discussed. Using previous calculations at order α, we obtain predictions for the masses which are accurate up to and including terms of order (αlnM²)².     

A measurement of the ratio GE/GE of the proton form factors at very low momentum transfer

The ratioμG _EG_M of the proton form factors was determined by measuring the electron scattering cross section of the proton relative to that of¹²C. Data were taken atq ²=0.09, 0.16, 0.25, and 0.36 fm^?2, yielding a weighted mean ofμG _E/G_M=1.01±0.03.     

Quark confinement and the baker-ball-zachariasen approximation

The Yang-Mills effective action ?1/4∫dxxF _μv ^a (D ²/M ²)F _μv ^a recently proposed by Baker et al., and also much earlier by the author and R.L. Stuller, is considered. An extension of the effective action to include Fermions is constructed in which quarks can be confined. The Schwinger-Dyson equation for the quark propagator is studied, and conditions are derived for the quark mass to be driven selfconsistently to infinity.     

Magnetic properties of half-metallic semi Heusler Co1−xCuxMnSb compounds

A study of the half-metallic character of the semi Heusler alloys Co_1−xCu_xMnSb (0?x?0.9) is presented. We investigated the saturation magnetization M_S at temperatures from 5 K to room temperature and the temperature dependence of the DC magnetic susceptibility χ above Curie temperature T_C. The magnetic moments at 5 K, for most compositions are very close to the quantized value of 4 μ_B for Mn³⁺ ion, the compound with 90% Co substituted by Cu is still ferromagnetic with M_S (5 K)=3.78 μ_B/f.u. These results emphasize the role of Co atoms in maintaining the ferromagnetic order in the material. The Curie temperature is decreased from 476 K to about 300 K as the Cu content increases from 0% to 90%. Above T_C, the χ⁻¹ vs T curves follow very well the Curie–Weiss law. The effective moment μ_eff and paramagnetic Curie temperature θ are derived. A comparison between the values of M_S at 5 K and μ_eff shows a transition from localized to itinerant spin system in these compounds.     

Effective gauge theory and the effect of heavy quarks in Higgs boson decays

A general framework is given for evaluating the contributions of as yet undiscovered heavy quarks to the gluonic decay rate of the Weinberg-Salam type Higgs boson. Since the Yukawa coupling of the Higgs boson to a quark pair is proportional to the quark mass, loop graphs involving heavy quarks have a non-vanishing effect on the gluonic decay width of the Higgs boson. This effect of heavy quarks with massesM _j(j=t,...) much greater than the Higgs boson massm _H is calculated in an effective gauge theory. The effects of two different kinds of large logarithms, lnM _j ² /μ m _h ² /μ ² are separated and summed up by the renormalization group method. It is found that the higher order QCD corrections are large and that the gluonic contribution to the hadronic decay width is significant if there are more than three generations. The Higgs decay width can therefore be used to probe the number of generations of heavy quarks.     

Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M Z 2 )

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muona _μ≡(g _μ?2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of theg?2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at theZ-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently availablee ⁺e^? data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately forg?2 of the muon and the τ-lepton and for α(M _Z ² ). We obtain the resultsa _μ ^had* =(725±16)×10^?10 anda _τ ^had* =(351±10)×10^?8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant atM _Z=91.1888 GeV we obtainΔα _had ⁽⁵⁾ =0.0280±0.0007 and α(M _Z ² )^?1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements ofe ⁺e^? cross-sections at energies below about 12 GeV in future experiments.     

Exotic decays of the muon and heavy leptons in gauge theories

We have studied the decay ?₁ → ?₂ + γ for arbitrary like charged spin $\text{1}\text{2}$ leptons in a manner which is applicable to a large class of models. Our computations assume that this process is induced by one loop diagrams. When the leading effect is cancelled by a leptonic G.I.M. mechanism, we find an extremely large enhancement of O(M_W⁴/M_L⁴) in Λ(μ^?→e^?+e⁺e^?)/Λ(μ^?→e^?+γ) if the intermediate lepton is charged.     

Semi-leptonic decays of charmed mesons produced in γN collisions

We report here on a study of the characteristics of the semileptonic decay spectra from a pair of charmed hadrons produced via photoproduction. The inclusive production of charmed hadrons is phenomenologically parametrized as e^?aze^?bp_t2. Their decays are described by (i) decay of free charm quark in GIM, (ii) K¹ dominant mode, $\text{D}\text{→}\text{K}{}^1\text{l}\text{ν}$, and (iii) pure leptonic decays. We deduce that 〈M_eμ²〉 = 0.18 M_D² for free quark decay and 〈M_eμ²〉 = ?0.35 +-0.24 M_D² for K¹ dominant decay. For the specific purpose of the photoproduction experiment at FNAL whicc is currently searching for μe events, we incorporate the incident photon spectrum, and the decay distributions with and without the experimental acceptance criteria are presented.