The large number of scalar meson states below 2 GeV contradicts the expected number derived from a quark-antiquark description. One possibility is that one or more of the light scalar mesons can be described as four quark states composed of quark-antiquark pairs. This scenario has been explored with sum-rule methods in Quantum Chromodynamics (QCD) to leading-order in the strong coupling constant. Higher loop contributions are significant in the QCD sum-rule analysis of quark-antiquark scalar states and a similar situation could occur in the four-quark case. In this thesis the leading order and pieces of the second order terms of the correlation function, as needed to study properties of a four-quark state via a QCD sum-rule, is calculated in the chiral limit (i.e. massless quarks) in QCD. Operator mixing related to renormalization of the composite operators appearing in the correlation function first contributes at second order. The result for the second order contributions to the correlation function indicate that operator mixing must be addressed before using proper dispersion relations to link this calculation with the mass of an existing state.

The large number of scalar meson states below 2 GeV contradicts the expected number derived from a quark-antiquark description. One possibility is that one or more of the light scalar mesons can be described as four quark states composed of quark-antiquark pairs. This scenario has been explored with sum-rule methods in Quantum Chromodynamics (QCD) to leading-order in the strong coupling constant. Higher loop contributions are significant in the QCD sum-rule analysis of quark-antiquark scalar states and a similar situation could occur in the four-quark case. In this thesis the leading order and pieces of the second order terms of the correlation function, as needed to study properties of a four-quark state via a QCD sum-rule, is calculated in the chiral limit (i.e. massless quarks) in QCD. Operator mixing related to renormalization of the composite operators appearing in the correlation function first contributes at second order. The result for the second order contributions to the correlation function indicate that operator mixing must be addressed before using proper dispersion relations to link this calculation with the mass of an existing state.

In 2003 the Belle collaboration announced the discovery of the X(3872) particle. This was confirmed shortly thereafter by the CDF, D0 and BaBar collaborations, and later by the LHCb collaboration. Based on the decay modes that have been observed to date, it is clear that this particle is a hadron, that is, a composite particle that experiences the strong nuclear force. The X(3872) was found within a family of well understood hadrons called charmonia. Interestingly, it is quite difficult to interpret the X(3872) as a charmonium state. For this reason it has been widely speculated that the X(3872) cannot be understood in terms of the quark model, unlike the vast majority of hadrons observed to date. Such hitherto unobserved particles are called exotic hadrons. Since the discovery of the X(3872), many similarly anomalous charmonium-like particles have been discovered. As would be expected, some unanticipated hadrons have also been found in the closely related bottomonium spectrum. These particles are collectively referred to as heavy quarkonium-like. Evidence is growing that at least some of these particles are exotic hadrons. If confirmed, this would have dramatic implications for our understanding of the strong nuclear force. A major experimental and theoretical effort is now underway in the field of hadron spectroscopy to determine the identities of the heavy quarkonium-like states. In order to investigate the possibility that some of these states could be exotic hadrons, theoretical calculations are needed to firmly establish their properties. One of the main arguments for the existence of exotic hadrons is that they are predicted by the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Therefore it is desirable to predict the properties of exotic hadrons using a theoretical approach that is firmly based in QCD. One such method is QCD sum rules (QSR). The research presented here uses the QSR technique to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher order calculations. This research has implications for the Y(3940), X(3872), Zc(3895), Yb(10890), Zb(10610) and Zb(10650) particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states.

Neste trabalho usamos as regras de soma da QCD para calcular as massas e constantes de acoplamento ou decaimento dos estados exóticos theta+(1540) e cascata--(1862) (pentaquarks), dos mesons escalares charmosos DsJ+(2317), D0(2308) e D0(2405) e do meson axial X(3872). Os mesons foram também tratados como estados exóticos de quatro quarks (tetraquarks). Dois métodos de regra de soma foram aplicados e uma atenção especial foi dada aos limites de validade e incertezas da regra de soma. Em todos os casos encontramos resultados compatíveis com os dados experimentais existentes, mas no caso dos pentaquarks e dos mesons escalares as regras de soma têm algumas de suas condições violadas, levantando a questão sobre a existência das ressonâncias na forma em que foram propostas. Fizemos também uma previsão para um méson axial Xb, que é uma expansão para o setor botônico do modelo assumido para o X(3872). / In this work the QCD Sum Rules have been used to obtain masses and coupling or decay constants of the theta+(1540) and cascade--(1862) pentaquarks, the DsJ+(2317), D0(2308) and D0(2405) charmed scalar mesons and the X(3872) axial meson. The mesons have been treated as 4-quark exotic states (tetraquarks). Two sum rules methods have been used with special attention given to the limits and uncertainties of the sum rules. Results consistent with experimental data have been found in all cases, but some of the sum rules constraints have been violated in the calculation of the pentaquarks and scalar mesons, leaving questions about the existence of the states as they have been built here. A prediction was also made for the mass of a state expanding the model used for X(3872) to the botton sector, named Xb.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Physics." Includes bibliographical references (p. 117-119).

The correlation function is the critical ingredient for Quantum Chromodynamics (QCD) sum-rule methods that are used to predict hadronic properties. Thus, in order to perform a sum-rule analysis of hybrids, we need to compute a correlation function involving an operator that probes hybrid states composed to quark-antiquark pair with a gluonic excitation. Using particular combinations of quark and gluon fields and Dirac matrices, we construct currents that probe hybrid states with various J^{PC} quantum numbers. We compute the correlation function to order g_s^3 in QCD, obtaining both perturbative and condensate contributions. The focus here is on light quarkonium and strangeonium hybrids, which involve quark masses small compared to the external momentum scale (m_q^2 << Q^2). While for light quarkonium the calculations are performed in the massless limit, for strangeonium we include a strange quark mass correction to the perturbative result. While the details of the calculations outlined throughout this thesis are outlined for J^{PC} = 0^{+-} and 1^{--} due to interest in the exotic quantum numbers 0^{+-}, ultimately the correlation function is computed for all J^{PC} values with J=0,1. Comparison with existing results for a subset of these J^{PC} quantum numbers provides a validation of our calculations.

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [114]-116).

Neste trabalho usamos as regras de soma da QCD para calcular as massas e constantes de acoplamento ou decaimento dos estados exóticos theta+(1540) e cascata--(1862) (pentaquarks), dos mesons escalares charmosos DsJ+(2317), D0(2308) e D0(2405) e do meson axial X(3872). Os mesons foram também tratados como estados exóticos de quatro quarks (tetraquarks). Dois métodos de regra de soma foram aplicados e uma atenção especial foi dada aos limites de validade e incertezas da regra de soma. Em todos os casos encontramos resultados compatíveis com os dados experimentais existentes, mas no caso dos pentaquarks e dos mesons escalares as regras de soma têm algumas de suas condições violadas, levantando a questão sobre a existência das ressonâncias na forma em que foram propostas. Fizemos também uma previsão para um méson axial Xb, que é uma expansão para o setor botônico do modelo assumido para o X(3872). / In this work the QCD Sum Rules have been used to obtain masses and coupling or decay constants of the theta+(1540) and cascade--(1862) pentaquarks, the DsJ+(2317), D0(2308) and D0(2405) charmed scalar mesons and the X(3872) axial meson. The mesons have been treated as 4-quark exotic states (tetraquarks). Two sum rules methods have been used with special attention given to the limits and uncertainties of the sum rules. Results consistent with experimental data have been found in all cases, but some of the sum rules constraints have been violated in the calculation of the pentaquarks and scalar mesons, leaving questions about the existence of the states as they have been built here. A prediction was also made for the mass of a state expanding the model used for X(3872) to the botton sector, named Xb.

No description available.

We present and explore a new formulation of perturbative QCD based not on the renormalised coupling but on the dimensional transmutation parameter of the theory and the property of asymptotic scaling. The approach yields a continued function, the iterated function being that involved in the solution of the two-loop β-function equation. In the so-called large-b limit the continued function reduces to a continued fraction and the successive approximants are diagonal Padé approximants. We investigate numerically the convergence of successive approximants using the leading-b approximation, motivated by renormalons, to model the all-orders result. We consider the Adler D-function of vacuum polarisation, the Polarised Bjorken and Gross-Llewellyn Smith sum rules, the (unpolarised) Bjorken sum rule, and the Minkowskian quantities R(_r) and the R-ratio of e(^+)e(^-) annihilation. In contrast to diagonal Fade approximants the truncated continued function method gives remarkably stable large-order approximants in cases where infra-red renormalon effects are important. We also use the new approach to determine the QCD fundamental parameters from the R(_r) and the R-ratio measurements, where we find Ā(^(3))(_MS)=516±48 MeV (which yields a(_s)(µ=m(_r))=0.360(^+0.021)(_=0.020)), and Ā(^(5))(_MS)=299(^+6)(_-7) MeV (which yields a(_s)(µ=m(_zo)=0.1218±0.0004), respectively. The evolution of the former value to the m(_zo) energy results in a(_s)(µ= m(_zo)) = 0.123 ± 0.002. These values are in line with other determinations available in the literature. We implement the Complete Renormalisation Group Improvement (CORGI) scheme throughout all the calculations. We report on how the mathematical concept of Stieltjes series can be used to assess the convergence of Padé approximants of perturbative series. We find that the combinations of UV renormalons which occur in perturbative QCD may or may not be Stieltjes series depending on the renormalisation scheme used.