Hadronic Width Research Articles

Sum rules for total hadronic widths of light mesonsand rectilinear stitch of the masses on the complex plane

Mass formulae for light meson multiplets derived by means of the exotic commutator technique are written for complex masses and considered as complex mass sum rules (CMSR). The real parts of the CMSR give the well known mass formulae for real masses (Gell-Mann-Okubo, Schwinger and ideal mixing ones) and the imaginary parts of CMSR give appropriate sum rules for the total hadronic widths - width sum rules (WSR). Most of the observed meson nonets satisfy the Schwinger mass formula (S nonets). The CMSR predict for the S nonet that the points $(m,\Gamma{})$ form a rectilinear stitch (RS) on the complex mass plane. For low-mass nonets the WSR are strongly violated due to "kinematical" suppression of the particle decays, but the violation decreases as the mass increases and disappears above $\sim 1.5$ GeV. The slope k s of the RS is not predicted, but the data show that it is negative for all S nonets and its numerical values are concentrated in the vicinity of the value -0.5. If k s is known for a nonet, we can evaluate "kinematical" suppressions of its individual particles. The masses and the widths of the S nonet mesons submit to some rules of ordering which matter in understanding the properties of the nonet. We give the table of the S nonets indicating masses, widths, mass and width orderings. We show also mass-width diagrams for them. We suggest to recognise a few multiplets as degenerate octets. In the appendix we analyze the nonets of the 1+ mesons.

Preliminary results on γγ → KsK±π∓ from e+e− scattering at CLEO

We analyzed 13.8 fb −1 of the integrated e + e − luminosity collected at 10.6 GeV center-of-mass energy with the CLEO II and II.V detectors to study exclusive two-photon production of single hadronic resonances. We searched for hadrons decaying into K s K ± π ∓ when both leptons remain undetected. In this analysis we studied the detection efficiency and evaluated systematic errors using independent data samples. We estimated 90% CL upper limits on the products of the two-photon partial widths of (pseudo)scalar hadrons with masses below 1.7 GeV/c 2 and their branching fractions into K s ( π + π −) K ± gp ∓. Our preliminary results are marginally consistent with the first observation of η(1440) in two-photon collisions by the L3 experiment.

Testing orbifold models of supersymmetric grand unification

In a model of supersymmetric SU(5) grand unification with a spatial dimension described by the orbifold S1/(Z2 × Z′2), proton decay is naturally suppressed at all orders. This is achieved by a suitable implementation of the discrete symmetries on the brane. But baryon number violating interactions are present in this model. We propose a few possible experimental tests of this model which exploit the effect of the baryon number violating couplings on low-energy observables such as neutron–antineutron oscillations, double nucleon decay into two kaons, hadronic decay widths of the Z boson and tt̄ production cross section in Run II of the Tevatron.

Inclusive decays of heavy quarkonium to light particles

We derive the imaginary part of the potential NRQCD Hamiltonian up to order 1/m^4, when the typical momentum transfer between the heavy quarks is of the order of Lambda_{QCD} or greater, and the binding energy E much smaller than Lambda_{QCD}. We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to O(mv^3 x (Lambda_{QCD}^2/m^2,E/m)) and O(mv^5) times a short-distance coefficient, for S- and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown non-perturbative parameters and, therefore, we obtain new model-independent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal non-perturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal non-perturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.

Determination ofmsand |Vus| from hadronic τ decays

The mass of the strange quark is determined from SU(3)-breaking effects in the τ hadronic width. Compared to previous analyses, the contributions from scalar and pseudoscalar spectral functions, which suffer from large perturbative corrections, are replaced by phenomenological parametrisations. This leads to a sizeable reduction of the uncertainties in the strange mass from τ decays. Nevertheless, the resulting ms value is still rather sensitive to the moment of the invariant mass distribution which is used for the determination, as well as the size of the quark-mixing matrix element |Vus|. Imposing the unitarity fit for the CKM matrix, we obtain ms(2 GeV) = 117 ± 17 MeV, whereas for the present Particle Data Group average for |Vus|, we find ms(2 GeV) = 103 ± 17 MeV. On the other hand, using an average of ms from other sources as an input, we are able to calculate the quark-mixing matrix element |Vus|, and we demonstrate that if the present measurement of the hadronic decay of the τ into strange particles is improved by a factor of two, the determination of |Vus| is more precise than the current world average.

Hadronic decays ofχbJinto light bottom squarks

We calculate the rates for inclusive hadronic decay of the three $\chi_{bJ}$ states into a pair of light bottom squarks as a function of the masses of the bottom squark and the gluino. We include color-singlet and color-octet configurations. The color-octet contribution is found to be insignificant for the $\chi_{b0}$ but can dominate in the $\chi_{b2}$ case if current lattice estimates are used for the color-octet matrix element. In comparison with the standard model values, bottom squark decays can increase the predicted hadronic width of the $\chi_{b0}$ by as much as 35%, for very small bottom squark masses and gluino masses in the range of 12 GeV, but make a small contribution in the cases of $\chi_{b1}$ and $\chi_{b2}$. Data from decays of the $\chi_{bJ}$ states could provide significant new bounds on the existence and masses of supersymmetric particles.

Global duality in heavy flavor hadronic decays

We show that heavy meson hadronic decay widths satisfy quark-hadron duality when smeared over the heavy quark mass, M, to an accuracy of order 1/M^2.

Scaling of hadron masses and widths in thermal models for ultrarelativistic heavy-ion collisions

By means of a simple rescaling, modifications of hadron masses and widths are incorporated into the thermal analysis of particle ratios in ultra-relativistic heavy-ion collisions. We find that moderate, up to 20%, changes of hadron masses do not spoil the quality of the fits, which remain as good as those obtained without modifications. The fits with the modified masses yield, however, modified values of the optimal temperature and baryon chemical potential. In particular, with decreasing masses of all hadrons (except for pseudo-Goldstone bosons) the fitted values of the temperature and the baryon chemical potential are lowered, with the change approximately proportional to the scaling of masses. In addition, we find that the broadening of the hadron widths by less than a factor of two practically does not affect the fits.

Resummation of the hadronic tau decay width with the modified Borel transform method

A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast to the ordinary Borel transform, the integrand of the Borel integral is renormalization--scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Pade approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain $\alpha_s(M^z) = 0.1192 +- 0.0007_{exp.} +- 0.0010_{EW+CKM} +- 0.0009_{th.} +- 0.0003_{evol.}$. These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead.

Bilocal expansion of the Borel amplitude and the hadronic tau decay width

The singular part of Borel transform of a QCD amplitude near the infrared renormalon can be expanded in terms of higher order Wilson coefficients of the operators associated with the renormalon. In this paper we observe that this expansion gives nontrivial constraints on the Borel amplitude that can be used to improve the accuracy of the ordinary perturbative expansion of the Borel amplitude. In particular, we consider the Borel transform of the Adler function and its expansion around the first infrared renormalon due to the gluon condensate. Using the next-to-leading order Wilson coefficient of the gluon condensate operator, we obtain an exact constraint on the Borel amplitude at the first IR renormalon. We then extrapolate, using judiciously chosen conformal transformations and Pade approximants, the ordinary perturbative expansion of the Borel amplitude in such a way that this constraint is satisfied. This procedure allows us to predict the $O(\alpha_s^4)$ coefficient of the Adler function, which gives a result consistent with the estimate by Kataev and Starshenko using a completely different method. We then apply this improved Borel amplitude to the tau decay width, and obtain the strong coupling constant $\alpha_s(M_Z) =0.1193 \pm 0.0007_{exp.} \pm 0.0010_{EW+CKM} \pm 0.0009_{meth.} \pm 0.0003_{evol.}$. We then compare this result with those of other resummation methods.

Strange quark mass from the invariant mass distribution of Cabibbo-suppressed tau decays

Quark mass corrections to the tau hadronic width play a significant role only for the strange quark, hence providing a method for determining its mass. The experimental input is the vector plus axial-vector strange spectral function derived from a complete study of tau decays into strange hadronic final states performed by ALEPH. New results on strange decay modes from other experiments are also incorporated. The present analysis determines the strange quark mass at the Mtau mass scale using moments of the spectral function. Justified theoretical constraints are applied to the nonperturbative components and careful attention is paid to the treatment of the perturbative expansions of the moments which exhibit convergence problems. The result obtained, m_s(Mtau^2) = (120 +- 11_exp +- 8_Vus +- 19_th) MeV = (120^+21_-26) MeV, is stable over the scale from Mtau down to about 1.4 GeV. Evolving this result to customary scales yields m_s(1 GeV^2) = (160^+28_-35) MeV and m_s(4 GeV^2) = (116^+20_-25) MeV.

Coupling of baryon resonances to the Nω channel

We estimate the resonance coupling strength f RNω and f RNρ from a Vector Meson Dominance (VMD) analysis. The isoscalar and isovector part of the photon coupling are obtained separately from helicity amplitudes. The reliability of this approach is tested by comparing VMD predictions for f RNρ with values obtained from fitting the hadronic decay widths into Nρ. A reasonable agreement is found, but VMD tends to underestimate the coupling constants. In order to confirm consistency with experimental data, we calculate the cross-sections for photon- and pion-induced reactions within a Breit–Wigner model. Finally, we study how the properties of ω mesons in nuclear matter are affected from the excitation of resonance–hole loops. For an ω at rest, we find a broadening of about 40 MeV, while at higher momenta the effect of resonance excitations is reduced.

Transition form factors and probabilities of the semileptonic decays of B and D mesons within covariant light-front dynamics

Electroweak form factors for the decays of heavy B and D mesons are considered within the covariant formulation of light-front dynamics. With the aid of this approach, it is possible to separate the physical and unphysical contributions to the form factors. An analytic expression is obtained for gluon corrections to the electroweak vertex of the vector and the vector-axial quark current, and it is shown that, for constructing a quantitative description of available experimental data, it is important to take into account such corrections to the decay widths of heavy hadrons. The effect of contact interaction on the transition form factors is analyzed, and the importance of taking into account contact interaction for 0− → 1− transitions is demonstrated numerically. The elements |Vbc|, |Vbu|, |Vcs|, and |tVcd| of the Cabibbo-Kobayashi-Maskawa matrix are determined from an analysis of the entire body of data on 0− → 0− and 0− → 1− semileptonic decays. Within the experimental errors, the results obtained in this way are intrinsically consistent and comply with world-averaged data.

Exclusive hadronic τ decays in the resonance effective action of QCD

Until present the study of the form factors associated to the vector and axial-vector components of the hadronic weak current has been carried out with a plethora of modelizations of the underlying strong interactions. While of importance to get an understanding of the dynamics involved, the amount and quality of the experimental data start to show some discrepancies with the analysed models. Moreover, and from a theoretical point of view, most of these models are not consistent with quantum chromodynamics (QCD). We propose a QCD-based model-independent procedure to analyse those decays through the use of the resonance chiral theory, the low-energy effective action of QCD in the relevant resonance region. Within this framework we study the hadronic off-shell width of the ϱ meson and the vector form factor of pion in τ − → π −π 0ν τ. We also comment on the τ − → (πππ) −ν τ decay.

Strange quark mass from τ decays

Mass corrections to the τ hadronic width play a signicant role only for the strange quark. A complete determination of the τ decays into strange hadronic final states has been performed by ALEPH and the total strange spectral function determined. The analysis leading to the determination of m s is revisited using reasonable theoretical constraints on the nonperturbative components and incorporating new results on strange decay modes from other experiments. The result, m s ( m 2 τ) = (112 ± 23) MeV, is stable over the scale from m 2 τ down to about 2 GeV 2.

V-A hadronic tau decays : a QCD laboratory

Recent ALEPH/OPAL data on the V-A spectral functions from hadronic τ decays are used for fixing the QCD continuum threshold at which the first and second Weinberg sum rules should be satisfied in the chiral limit, and for predicting the values of the low-energy constants f π, m π + − m π 0 and L 10. Some DMO-like sum rules and the τ-total hadronic widths R τ, V-A are also used for extracting the values of the D = 6, 8 QCD vacuum condensates and the corresponding (in the chiral limit) electroweak kaon penguin matrix elements 〈 Q 3 2 8,7 > 2π, where a deviation from the vacuum saturation estimate has been obtained. Combining these results with the one of the QCD penguin matrix element 〈 Q 1 2 6〉 2π obtained from a (maximal) q̄q-gluonium mixing scheme from the scalar meson sum rules, we deduce, in the Electroweak Standard Model (ESM), the conservative upper bound for the CP-violating ratio: ϵ′/ϵ ≤ (22 ± 9)10 −4, in agreement with the present measurements.

New QCD-estimate of the kaon penguin matrix elements and

Firstly, we use the recent ALEPH/OPAL data on the V-A spectral functions for fixing the continuum threshold with which the first and second Weinberg sum rules should be satisfied in the chiral limit. Then, we predict the values of the low-energy constants m_{\pi^+}-m_{\pi^0}, {L}_{10}, and test the values of the electroweak kaon penguin matrix elements <Q^{3/2}_{8,7}>_{2\pi} obtained from DMO--like sum rules. Secondly, we use the data on the \tau-total hadronic width R_{\tau,V/A} for extracting <Q_8^{3/2}_{2\pi}>, in the {MS}\bar scheme, and propose some new sum rules for < Q_7^{3/2}>_{2\pi} in the chiral limit, where the latter require more accurate data for the spectral functions near the $\tau$-mass. Thirdly, we analyze the effects to the matrix element <Q_6^{1/2}>_{2\pi}, of the S_2\equiv(\bar uu+\bar dd) component of the I=0 scalar meson, with its parameters fixed from QCD spectral sum rules. Our results should stimulate a further attention on the r\^ole of the (expected large) gluonium component of the I=0 scalar meson and of the associated operator in the K--->\pi\pi amplitude. Finally, using our previous determinations, we deduce, in the Standard Model (SM), the conservative upper bound for the CP-violating ratio: \epsilon'/\epsilon < (22\pm 9) 10^{-4}, which is in agreement with the present measurements.

Hadronic off-shell width of meson resonances

Within the resonance chiral effective theory we study the dressed propagators of the spin-1 fields, which arise from a Dyson-Schwinger resummation perturbatively constructed from loop diagrams with absorptive contributions in the s channel. We apply the procedure to the vector pion form factor and elastic $\ensuremath{\pi}\ensuremath{\pi}$ scattering to obtain the off-shell width of the ${\ensuremath{\rho}}^{0}$ meson. We adopt a definition of the off-shell width of spin-1 meson resonances that satisfies the requirements of analyticity, unitarity, chiral symmetry, and asymptotic behavior ruled by QCD. To satisfy these constraints the resummation procedure cannot consist only of self-energy diagrams. Our width definition is shown to be independent of the formulation used to describe the spin-1 meson resonances.

Heavy quark expansion and preasymptotic corrections to decay widths in the ’t Hooft model

We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}),$ with the emphasis on the ``spectator-dependent'' effects, i.e., those sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the 't Hooft equation. We show that the ${1/m}_{Q}$ expansion of both the weak annihilation and Pauli interference widths coincides with the OPE predictions to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of the summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the ${1/m}_{Q}$ expansion in the 't Hooft model.

Strange quark mass determination from Cabibbo-suppressed tau decays

We present a general analysis of SU(3) breaking effects in the semi-inclusive tau hadronic width. The recent ALEPH measurements of the inclusive Cabibbo--suppressed decay width of the tau and several moments of its invariant mass distribution are used to determine the value of the strange quark mass. We obtain, in the MS scheme, m_s(M_\tau^2) = (119\pm 24) MeV to O(\alpha_s^3), which corresponds to m_s (1 GeV^2) = (164 \pm 33) MeV, m_s(4 GeV^2) = (114\pm 23) MeV .