QCD Sum-Rule Bounds on the Light Quark Masses

QCD sum-rules are related to an integral of a hadronic spectral function, and hence must satisfy integral inequalities which follow from positivity of the spectral function. Development of these Holder inequalities and their application to the Laplace sum-rule for pions lead to a lower bound on the average of the non-strange 2 GeV light-quark masses in the MS-bar scheme.Comment: latex2e, 8 pages. Write-up of talk presented at MRST 200

Trailing Edge Unification via an Intermediate Pati-Salam Group

We demonstrate to two-loop order that an intermediate symmetrically embedded Pati-Salam $SU(2)_L \times SU(2)_R \times SU(4)$ level of symmetry is all that is necessary to accommodate empirical values of $\alpha(M_z), \alpha_s(M_z)$ and $\sin^2\theta_w(M_z)$ within a grand unification context but with a high (10^{14} GeV) intermediate mass scale and with a concomitant higher GUT scale.Comment: 7 pages, 4 embedded eps figur

Analysis of Exotic Hybrid eta pion, eta-prime pion Decays

Investigations of the mass and decays of the exotic hybrid are reviewed, including calculation of the pion1 to eta pion, eta-prime pion decay widths within the QCD sum rules technique. In this calculation, the recently-proposed eta, eta-prime quark mixing scheme is employed. The results indicate that the decay width Gamma(pion1 to eta pion) around 250 MeV is large compared with the decay width Gamma(pion1 to eta-prime pion) around 20 MeV. Inspired by these results, some phenomenological approaches are suggested to gain an understanding of the underlying mechanism of eta pion and eta-prime pion hybrid decays.Comment: 4 pages, talk presented at the 10th International Symposium on Meson-Nucleon Physics and the Structure of the Nucleon(MENU2004), Beijing, China, August 29 to September 4, 200

Hoelder Inequalities and QCD Sum-Rule Bounds on the Masses of Light Quarks

QCD Laplace Sum-Rules must satisfy a fundamental Hoelder inequality if they are to consistently represent an integrated hadronic spectral function. The Laplace sum-rules of pion currents is shown to violate this inequality unless the $u$ and $d$ quark masses are sufficiently large, placing a lower bound on $m_u+m_d$, the SU(2)-invariant combination of the light-quark masses.Comment: 3 pages, latex, write-up of talk presented at DPF 200

Two-Loop QCD Renormalization and Anomalous Dimension of the Scalar Diquark Operator

The renormalization of the scalar diquark operator and its anomalous dimension is calculated at two-loop order in QCD, enabling higher-order QCD studies of diquarks. As an application of our result, the two-loop diquark anomalous dimension in the $\bar{{\rm MS}}$ scheme is used to study the QCD renormalization scale dependence of diquark matrix elements of the $\Delta S=1$ effective weak Hamiltonian.Comment: Version 3 corrects an error in Table 1 and associated results. 7 pages, 4 embedded eps figure

Gaussian Sum-Rule Analysis of Scalar Gluonium and Quark Mesons

Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum-rules, including instanton effects, for scalar gluonic and non-strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum-rules are remarkably consistent in their prediction of masses of approximately 1.0 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons.Comment: latex2e using amsmath, 11 pages, 4 eps figures embedded in latex file. Write-up of presentation for the 2003 SUNY IT (Utica) workshop on scalar meson

Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV Higgs Mass?

The mechanism of radiative electroweak symmetry breaking occurs through loop corrections, and unlike conventional symmetry breaking where the Higgs mass is a parameter, the radiatively-generated Higgs mass is dynamically predicted. Pade approximations and an averaging method are developed to extend the Higgs mass predictions in radiative electroweak symmetry breaking from five- to nine-loop order in the scalar sector of the Standard Model, resulting in an upper bound on the Higgs mass of 141 GeV. The mass predictions are well-described by a geometric series behaviour, converging to an asymptotic Higgs mass of 124 GeV consistent with the recent ATLAS/CMS observations. Similarly, we find that the Higgs self-coupling converges to $\lambda=0.23$, which is significantly larger than its conventional symmetry breaking counterpart for a 124 GeV Higgs mass. In addition to this significant enhancement of the Higgs self-coupling and $HH\rightarrow HH$ scattering, we find that Higgs decays to gauge bosons are unaltered and the scattering processes $W_{L}^{+}W_{L}^{+}\rightarrow HH$, $Z_{L}Z_{L}\rightarrow HH$ are also enhanced, providing signals to distinguish conventional and radiative electroweak symmetry breaking mechanisms.Comment: 5 pages, 3 eps figures included with LaTeX source. v3 contains extended analysis and discussio

Masses of Open-Flavour Heavy-Light Hybrids from QCD Sum-Rules

We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrid's constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of several hybrid interpolating currents, taking into account QCD condensates up to dimension-six, and extract hybrid mass predictions for all $J^P\in\{0^{\pm},\,1^{\pm}\}$, as well as explore possible mixing effects with conventional quark-antiquark mesons. Within theoretical uncertainties, our results are consistent with a degeneracy between the heavy-nonstrange and heavy-strange hybrids in all $J^P$ channels. We find a similar mass hierarchy of $1^+$, $1^{-}$, and $0^+$ states (a $1^{+}$ state lighter than essentially degenerate $1^{-}$ and $0^{+}$ states) in both the charm and bottom sectors, and discuss an interpretation for the $0^-$ states. If conventional meson mixing is present the effect is an increase in the hybrid mass prediction, and we estimate an upper bound on this effect.Comment: 24 pages, 8 figures. Mass predictions updated from previous version to reflect corrected sign error in sum rule analysis. Mixing analysis and examination of higher weight sum-rules added. To be published in JHE