arXiv subjects
Publications and source records attributed to A. H. Fariborz.
First, recent work on light scalar mesons, which is of possible interest in connection with the strong coupling region of QCD is briefly discussed. Then a very short highlighting of a paper concerned with an application to the eta -> 3 pi problem is presented.
Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = sigma(e^+ e^- --> hadrons)/sigma(e^+ e^- --> mu^+ mu^-), as obtained from the imaginary part of the purely-perturbative vector-current correlation function. We present explicit solutions for the summation of leading and up to three subsequent subleading orders of logarithms. The summations accessible from the four-loop vector-correlator not only lead to a substantial reduction in sensitivity to the renormalization scale, but necessarily impose a common infrared bound on perturbative approximations to R(s), regardless of the infrared behaviour of the true QCD couplant.
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 192π^3Γ(b\to u\barν_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm GeV^5} and 192π^3Γ(b\to c\ell^-\barν_\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).
QCD contributions to the $b \to u \ell^- \barν_\ell$ decay rate, which are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient dependence on the renormalization mass $μ$ to compromise phenomenological predictions for inclusive semileptonic $B \to X_u$ processes. Such scale dependence is ameliorated by the renormalization-group (RG) extraction and summation of all leading and RG-accessible subleading logarithms occurring subsequent to two-loop order in the perturbative series. This optimal RG-improvement of the known portion of the perturbative series virtually eliminates $μ$-dependence as a source of theoretical uncertainty in the predicted semileptonic $B \to X_u$ inclusive rate.
The renormalization-scale ($μ$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\barν_\ell$ decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MS-bar scheme. Three-loop contributions to the decay rate are estimated by developing Pade approximant techniques particularly suited to perturbative calculations in the pole mass scheme. An optimized Pade estimate of the three-loop contributions is obtained by comparison of the Pade estimates with the three-loop terms determined by renormalization-group invariance. The resulting three-loop estimate in the pole-mass scheme exhibits minimal sensitivity to the renormalization scale near $μ=1.0 GeV$, leading to an estimated decay rate of $192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)=992\pm 217 GeV^5$ inclusive of theoretical uncertainties and non-perturbative effects.
For any perturbative series that is known to $k$-subleading orders of perturbation theory, we utilise the process-appropriate renormalization-group (RG) equation in order to obtain all-orders summation of series terms proportional to $α^n \log^{n-k}(μ^2)$ with $k = {0,1,2,3}$, corresponding to the summation to all orders of the leading and subsequent-three-subleading logarithmic contributions to the full perturbative series. These methods are applied to the perturbative series for semileptonic $b$-decays in both MS-bar and pole-mass schemes, and they result in RG-summed series for the decay rates which exhibit greatly reduced sensitivity to the renormalization scale $μ$. Such summation via RG-methods of all logarithms accessible from known series terms is also applied to perturbative QCD series for vector- and scalar-current correlation functions, the perturbative static potential function, the (single-doublet standard-model) Higgs decay amplitude into two gluons, as well as the Higgs-mediated high-energy cross-section for $W^+W^-\to ZZ$ scattering. The resulting RG-summed expressions are also found to be much less sensitive to the renormalization scale than the original series for these processes.
The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group invariant quantities. This technique is applied to the inclusive semileptonic process $b\to u \barν_\ell\ell^-$ (explicitly known to two-loop order) to obtain bounds on the three- and four-loop perturbative coefficients that are not accessible via the renormalization group. Using the principle of minimal sensitivity, an estimate is obtained for the perturbative contributions to $Γ(b\to u \barν_\ell\ell^-)$ that incorporates theoretical uncertainty from as-yet-undetermined higher order QCD corrections.
We first briefly review a treatment of the scalars in meson meson scattering based on a non-linear chiral Lagrangian, with unitarity implemented by a "local" modification of the scalar propagators. It is shown that the main results are confirmed by a treatment in the SU(3) linear sigma model in which unitarity is implemented "globally". Some remarks are made on the speculative subject of the scalars' quark structure.
The three flavor linear sigma model is studied as a ``toy model'' for understanding the role of possible light scalar mesons in the ππ, πK and πηscattering channels. The approach involves computing the tree level partial wave amplitude for each channel and unitarizing by a simple K-matrix prescription which does not introduce any new parameters. If the renormalizable version of the model is used there is only one free parameter. While this highly constrained version has the right general structure to explain ππscatteirng, it is ``not quite'' right. A reasonable fit can be made if the renormalizability (for the {\it effective} Lagrangian) is relaxed while chiral symmetry is maintained. The occurence of a Ramsauer Townsend mechanism for the f_0(980) region naturally emerges. The effect of unitarization is very important and leads to ``physical'' masses for the scalar nonet all less than about 1 GeV. The a_0(1450) and K_0^*(1430) appear to be ``outsiders'' in this picture and to require additional fields. Comparison is made with a scattering treatment using a more general non-linear sigma model approach. In addition some speculative remarks and a highly simplified larger toy model are devoted to the question of the quark substructure of the light scalar mesons.
We propose a simple Ansatz for the three generation neutrino mass matrix $M_ν$ which is motivated from an SO(10) grand unified theory. The Ansatz can be combined with information from neutrino oscillation experiments and bounds on neutrinoless double beta decay to determine the neutrino masses themselves and to reconstruct, with some assumptions, the matrix $ M_ν$ .
A Hoelder inequality analysis of the QCD Laplace sum-rule which probes the non-strange (n\bar n) components of the I={0,1} (light-quark) scalar mesons supports the methodological consistency of an effective continuum contribution from instanton effects. This revised formulation enhances the magnitude of the instanton contributions which split the degeneracy between the I=0 and I=1 channels. Despite this enhanced isospin splitting effect, analysis of the Laplace and finite-energy sum-rules seems to preclude identification of a_0(980) and a light broad sigma-resonance state as the lightest isovector and isoscalar spin-zero $n\bar n$ mesons. This apparent decoupling of sigma [\equiv f_0(400-1200)] and a_0(980) from the quark n\bar n scalar currents suggests either a non-q \bar q or a dominantly s\bar s interpretation of these resonances, and further suggests the possible identification of the f_0(980) and a_0(1450) as the lightest I={0,1} scalar mesons containing a substantial n\bar n component.
Motivated by the $1/N_c$ expansion, we study a simple model in which the pi-K scattering amplitude is the sum of a current-algebra contact term and resonance pole exchanges. This phenomenological model is crossing symmetric and, when a putative light strange scalar meson, kappa, is included, satisfies the unitarity bounds to well above 1 GeV. The model also features chiral dynamics, vector meson dominance and appropriate interference between the established scalar K*(1430) resonance and its predicted background. We briefly discuss the physical significance of the results and directions for further work.
We investigate lowest-lying scalar meson properties predicted from QCD Laplace sum rules based upon isovector and isoscalar non-strange $\bar{q}q$ currents. The hadronic content of these sum rules incorporates deviations from the narrow resonance approximation anticipated from physical resonance widths. The field theoretical content of these sum rules incorporates purely-perturbative QCD contributions to three-loop order, the direct single-instanton contribution in the instanton liquid model, and leading contributions from QCD-vacuum condensates. In the isovector channel, the results we obtain are compatible with a$_0$(1450) being the lowest-lying $q\bar{q}$ resonance, and are indicative of a non-$q\bar{q}$ interpretation for a$_0$(980). In the isoscalar channel, the results we obtain are compatible with the lowest lying $q\bar{q}$ resonance being f$_0$(980) or a state somewhat lighter than f$_0$(980) whose width is less than half of its mass. The dilaton scenario for such a narrower $σ$-resonance is discussed in detail, and is found compatible with sum rule predictions for the resonance coupling only if the anomalous gluon-field portion of $Θ_μ^μ$ dominates the matrix element $<σ|Θ_μ^μ|0>$. A linear sigma-model interpretation of the lowest-lying resonance's coupling, when compared to the coupling predicted by sum rules, is indicative of a renormalization-group invariant light-quark mass between 4 and 6 MeV.
A QCD Laplace sum rule framework is employed to investigate the relationship between the mass and the decay width of the sigma, the lowest-lying isoscalar resonance in the spin-zero meson channel. Our analysis differs from prior analyses, not only by incorporating finite-width departures from the narrow resonance approximation, but also through the inclusion of direct-instanton contributions and three-loop-order perturbative effects. Assuming that the sigma is the dominant subcontinuum resonance in this channel, the least upper bound we obtain for the sigma-mass is shown to increase with the sigma-width, and suggests that a sigma lighter than 800 MeV should have a total width substantially smaller than its mass.
There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We first discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We then show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension > 6 condensates containing at least one q-bar q pair. We extract the direct single-instanton contribution to the F_1 sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass resonance contributions within the pseudoscalar channel.
Global fits to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters are performed, leading to predictions for the pion-resonance mass and decay constant. Two scenarios are considered which differ only in their treatment of the dimension-six quark condensate $< O_6>$. The first scenario assumes an effective scale for $< O_6>$ from other sum-rule applications which is assumed to be independent of the physical value of the quark mass, while the second scenario requires self-consistency between the value of $< O_6>$ and the current algebra constraint $2m< \bar q q>=-f_π^2m_π^2$. Predictions of the pion-resonance mass $M_π$ and decay constant $F_π$ are obtained in these two scenarios. A byproduct of this analysis is a prediction of the renormalization-group invariant quark mass $(\hat m_u+\hat m_d)/2$.
A global fit to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters is performed, leading to predictions for the pion-resonance mass and decay constant. This fit leads to predictions of $M_π = 1.15 \pm 0.15 GeV$ for the pion-resonance mass, and $F_π^2=(4.5\pm 2.1).(f_π^2m_π^4/M_π^4)$ for the pion-resonance decay constant.
We consider the first pion excitation as a sub-continuum resonance in the pseudoscalar channel, and we obtain parameters characterizing this resonance through a global fit of the Borel-parameter dependence of the field-theoretical pseudoscalar Laplace sum rule to its hadronic (pion + pion-excitation + QCD-continuum) content. Our analysis incorporates finite-width deviations from the narrow resonance approximation, instanton effects, and higher-loop perturbative contributions to the pseudoscalar correlator. We obtain the following values (uncertainties reflect 90% confidence levels): mass $M_Π= 1.15 \pm 0.28 GeV$, width $Γ_Π= < 0.48 GeV$, decay constant $r \equiv [F_ΠM_Π^2 / f_πm_π^2]^2 = 4.7 \pm 2.8$.