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

Extended BRS Symmetry and Gauge Independence in On-Shell Renormalization Schemes

Extended BRS symmetry is used to prove gauge independence of the fermion renormalization constant $Z_2$ in on-shell QED renormalization schemes. A necessary condition for gauge independence of $Z_2$ in on-shell QCD renormalization schemes is formulated. Satisfying this necessary condition appears to be problematic at the three-loop level in QCD.Comment: latex2e, 7 pages, 3 embedded eps figur

Lower Bound on the Pion Polarizability from QCD Sum Rules

Making use of QCD sum rules a lower bound is found which relates the electromagnetic polarizability $\alpha_{_E}$ and mean-square radius $\langle r_\pi^2\rangle$ of charged pions through the intrinsic polarizability $\tilde\alpha_{_E}= \alpha_{_E}-\alpha\langle r_\pi^2\rangle/(3M_\pi)$. We find that if present constraints on the QCD continuum (duality) threshold are accepted, this lower bound on the intrinsic polarizability $\tilde\alpha_{_E}$ is incompatible with some previous determinations of $\alpha_{_E}$ and $\langle r_\pi^2\rangle$.Comment: 9 pages, RevTeX, 3 figures added as uu-encoded g-zipped tarred eps files, to appear in Phys. Lett

Constraints on QCD Sum-rules from the H\"older Inequalities

A new technique based on H\"older's integral inequality is applied to QCD sum-rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum-rules are to consistently describe integrated physical cross-sections, but these constraints do not require any experimental data and therefore can be applied to any hadronic spectral function. As an illustration of this technique the Laplace sum-rules of the light-quark correlation function for the vector and the axial-vector currents are examined in detail. We find examples of inconsistency between the inequalities and sum-rule parameters used in some previous analyses of the vector and axial-vector channels.Comment: 13 pages, RevTeX, 4 figures available upon request, to appear in Phys. Lett

Instanton Effects on the Role of the Low-Energy Theorem for the Scalar Gluonic Correlation Function

Instanton contributions to the Laplace sum-rules for correlation functions of scalar gluonic currents are calculated. The role of the constant low-energy theorem term, whose substantial contribution is unique to the leading Laplace sum-rule $L_{-1}$, is shown to be diminished by instanton contributions, significantly increasing the resulting mass bounds for the ground state of scalar gluonium and improving compatibility with results from higher-weight sum-rules.Comment: latex2e, 12 pages, 10 encapsulated postscript figures. Revised version includes additional analysis, figures, and reference

Pade/renormalization-group improvement of inclusive semileptonic B decay rates

Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS} scheme works favorably in the b \to u case whereas the pole mass scheme shows better convergence in the b \to c case. Upon the inclusion of the estimated three-loop contribution, we find the full perturbative decay rate to be 192\pi^3\Gamma(b\to u\bar\nu_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm GeV^5} and 192\pi^3\Gamma(b\to c\ell^-\bar\nu_\ell)/(G_F^2|V_{cb}|^2)= 992 \pm 198 {\rm GeV^5}, respectively. The errors are inclusive of theoretical uncertainties and non-perturbative effects. Ultimately, these perturbative contributions reduce the theoretical uncertainty in the extraction of the CKM matrix elements |V_{ub}| and |V_{cb}| from their respective measured inclusive semileptonic branching ratio(s).Comment: 3 pages, latex using espcrc2.sty. Write-up of talk given at BEACH 2002, UBC, Vancouve

Quark Effects in the Gluon Condensate Contribution to the Scalar Glueball Correlation Function

One-loop quark contributions to the dimension-four gluon condensate term in the operator product expansion (OPE) of the scalar glueball correlation function are calculated in the MS-bar scheme in the chiral limit of $n_f$ quark flavours. The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluonic condensate term represents the leading power corrections to the scalar glueball correlator and, therein, the one-loop logarithmic contributions provide the most important condensate contribution to those QCD sum-rules independent of the low-energy theorem (the subtracted sum-rules).Comment: latex2e, 6 pages, 7 figures embedded in latex fil

Stability of Subsequent-to-Leading-Logarithm Corrections to the Effective Potential for Radiative Electroweak Symmetry Breaking

We demonstrate the stability under subsequent-to-leading logarithm corrections of the quartic scalar-field coupling constant $\lambda$ and the running Higgs boson mass obtained from the (initially massless) effective potential for radiatively broken electroweak symmetry in the single-Higgs-Doublet Standard Model. Such subsequent-to-leading logarithm contributions are systematically extracted from the renormalization group equation considered beyond one-loop order. We show $\lambda$ to be the dominant coupling constant of the effective potential for the radiatively broken case of electroweak symmetry. We demonstrate the stability of $\lambda$ and the running Higgs boson mass through five orders of successively subleading logarithmic corrections to the scalar-field-theory projection of the effective potential for which all coupling constants except the dominant coupling constant $\lambda$ are disregarded. We present a full next-to-leading logarithm potential in the three dominant Standard Model coupling constants ($t$-quark-Yukawa, $\alpha_s$, and $\lambda$) from these coupling constants' contribution to two loop $\beta$- and $\gamma$-functions. Finally, we demonstrate the manifest order-by-order stability of the physical Higgs boson mass in the 220-231 GeV range. In particular, we obtain a 231 GeV physical Higgs boson mass inclusive of the $t$-quark-Yukawa and $\alpha_s$ coupling constants to next-to-leading logarithm order, and inclusive of the smaller $SU(2)\times U(1)$ gauge coupling constants to leading logarithm order.Comment: 21 pages, latex2e, 2 eps figures embedded in latex file. Updated version contains expanded analysis in Section

A Gaussian Sum-Rules Analysis of Scalar Glueballs

Although marginally more complicated than the traditional Laplace sum-rules, Gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading Gaussian sum-rule, the analysis of the lowest-weighted sum-rule (which contains a large scale-independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. However, the presence of instanton effects leads to approximately consistent mass scales in the lowest weighted and next-lowest weighted sum-rules. The analysis of the next-to-leading sum-rule demonstrates that a single narrow resonance model does not provide an adequate description of the hadronic spectral function. Consequently, we consider a wide variety of phenomenological models which distribute resonance strength over a broad region---some of which lead to excellent agreement between the theoretical prediction and phenomenological models. Including QCD uncertainties, our results indicate that the hadronic contributions to the spectral function stem from a pair of resonances with masses in the range 0.8--1.6 GeV, with the lighter of the two potentially having a large width.Comment: latex2e, 22 pages, 5 figures. Analysis extended in revised versio

Gaussian Sum-Rules and Prediction of Resonance Properties

Techniques for using Gaussian QCD sum-rules to predict hadronic resonance properties are developed for single-resonance and two-resonance phenomenological models, and criteria are developed for determining which of these models is required for analyzing a particular hadronic channel. The vector current sum-rule coupled to the $\rho$ meson is shown to be consistent with a single resonance model, and the Gaussian sum-rule analysis results in an accurate $\rho$ mass prediction which exhibits excellent agreement between the theoretical prediction of the Gaussian sum-rule and the phenomenological model. A two-resonance model is shown to be necessary for the Gaussian sum-rule for the non-strange quark scalar ($\bar n n$) currents. The two-resonance Gaussian sum-rule analysis of the isoscalar and isovector ($I=0,1$) $\bar n n$ scalar mesons exhibits excellent agreement between the theoretical prediction and phenomenological model. The prediction of the resonance properties of the $I=0,1$ $\bar n n$ scalar mesons in this two-resonance model provides valuable information for the interpretation of the scalar mesons, including the X(1775).Comment: latex2e, 29 pages, 10 eps figures embedded in latex2e. Revised version includes additions to reference [28] and correction to equation (56