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We solve the dispersion relation for the P-wave {pi}{pi} amplitude. We discuss the role of the left-hand cut vs the Castillejo-Dalitz-Dyson pole contribution and compare the solution with a generic quark model description. We review the generic properties of analytical partial wave scattering and production amplitudes and discuss their applicability and fits of experimental data.
Charmed meson decays to a light pseudoscalar (P) and light vector (V) meson are analyzed taking account of {eta}-{eta}{sup '} mixing. A frequently-used octet-singlet mixing angle of 19.5 degree sign is compared with a value of 11.7 degree sign favored by a recent analysis of D{yields}PP decays.
We present a two-flavor linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate {pi}{pi} scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector-meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f{sub 0}(600) and a{sub 0}(980) mesons. We investigate this question by assigning the quark-antiquark {sigma} and a{sub 0} states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the {sigma}, which turns out to be too small. We also study the alternative assignment f{sub 0}(1370) and a{sub 0}(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the {pi}{pi} scattering length a{sub 0}{sup 0} is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.
In this work, we investigate the rescattering effects in the radiative decay {Upsilon}(5S){yields}{eta}{sub b}+{gamma}, which were suggested to be crucially important for understanding the anomalous largeness of the branching ratios B({Upsilon}(5S){yields}{Upsilon}(1S)+{pi}{pi}) and B({Upsilon}(5S){yields}{Upsilon}(1S)+{eta}). Our calculations show that the rescattering effects may enhance {Gamma}({Upsilon}(10860){yields}{eta}{sub b}+{gamma}) by four orders, but the tetraquark structure does not. Recently the BABAR and CLEO collaborations have measured the mass of {eta}{sub b} and the branching ratios B({Upsilon}(2S){yields}{eta}{sub b}+{gamma}), B({Upsilon}(3S){yields}{eta}{sub b}+{gamma}). We hope that very soon, {Upsilon}(10860){yields}{eta}{sub b}+{gamma} will be measured and it would be an ideal opportunity for testing whether the rescattering or the tetraquark structure is responsible for the anomaly of B({Upsilon}(5S){yields}{Upsilon}(nS){pi}{sup +}{pi}{sup -}(n=1,2,3)), i.e., the future measurements on the radiative decays of {Upsilon}(5S) might be a touchstone of the two mechanisms.
We make use of a self-consistent quark-model based study of four-quark charmonium-like states to interpret recent charmonium experimental data. We conclude that there exists a D*D* meson-meson molecule with quantum numbers (I{sup G})J{sup PC}=(1{sup -})2{sup ++}. Our study confirms the presence of charged charmonium-like resonances on the excited charmonium spectrum. We find support from recent experimental data by the Belle Collaboration [R. Mizuk et al. (Belle Collaboration), Phys. Rev. D 78, 072004 (2008)]. Confirmation of the experimental data by the Belle Collaboration and the determination of the quantum numbers of the new structures would help in discriminating among different theoretical models and would give further support to the theoretical analysis of T. Fernandez-Carames, A. Valcarce, and J. Vijande [Phys. Rev. Lett. 103, 222001 (2009)].
We discuss the importance of inelasticity in the P-wave {pi}{pi} amplitude on the Dalitz distribution of 3{pi} events in J/{psi} decay. The inelasticity, which becomes sizable for {pi}{pi} masses above 1.4 GeV, is attributed to KK{yields}{pi}{pi} rescattering. We construct an analytical model for the two-channel scattering amplitude and use it to solve the dispersion relation for the isobar amplitudes that parametrize the J/{psi} decay. We present comparisons between theoretical predictions for the Dalitz distribution of 3{pi} events with available experimental data.
Constraints from analyticity are combined with experimental electron-proton scattering data to determine the proton charge radius. In contrast to previous determinations, we provide a systematic procedure for analyzing arbitrary data without model-dependent assumptions on the form-factor shape. We also investigate the impact of including electron-neutron scattering data, and {pi}{pi}{yields}NN data. Using representative data sets we find r{sub E}{sup p}=0.870{+-}0.023{+-}0.012 fm using just proton scattering data; r{sub E}{sup p}=0.880{sub -0.020}{sup +0.017{+-}}0.007 fm adding neutron data; and r{sub E}{sup p}=0.871{+-}0.009{+-}0.002{+-}0.002 fm adding {pi}{pi} data. The analysis can be readily extended to other nucleon form factors and derived observables.
We propose a gauged U(1){sub H} horizontal symmetry around a TeV scale that is a subgroup of a SU(3){sub H} horizontal gauge symmetry broken at O(10{sup 14}) GeV. The breaking generates right-handed Majorana neutrino masses through a SU(3){sub H} sextet scalar. A particular Majorana right-handed neutrino mass matrix explicitly determines the remnant U(1){sub H} at low energy which only couples to b-s and {mu}-{tau} in the gauge eigenstate. The dangerous K-K, D-D mixing and B{sub s}{yields}{mu}{sup +}{mu}{sup -} are kept to be safe because the relevant couplings are suppressed through high powers of small mixing angles in the fermion rotation matrix. Our analysis which applies to the general case shows that the Tevatron di-muon anomaly can be explained through the B{sub s} and B{sub d} mixing while keeping all the other experimental constraints within 90% C.L. For the B meson decay, the B{sub s}{yields}{mu}{sup {+-}}{tau}{sup {+-}} is the leading leptonic decay channel which is several orders of magnitude below current experimental bounds.
We present an unquenched N{sub f}=2 lattice computation of the B{sub K} parameter which controls K{sup 0}-K{sup 0} oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder-Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the B{sub K} parameter which is both multiplicatively renormalizable and O(a) improved. Employing the nonperturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get B{sub K}{sup RGI}=0.729{+-}0.030, a number well in line with the existing quenched and unquenched determinations.
Based on a spin-flavor extension of chiral symmetry, a novel s-wave meson-meson interaction involving members of the {rho} nonet and of the {pi} octet is introduced, and its predictions are analyzed. The starting point is the SU(6) version of the SU(3)-flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry-breaking terms are then included to account for the physical meson masses and decay constants in a way that preserves (broken) chiral symmetry. Next, the T-matrix amplitudes are obtained by solving the Bethe-Salpeter equation in a coupled-channel scheme, and the poles are identified with their possible Particle Data Group counterparts. It is shown that most of the low-lying even-parity Particle Data Group meson resonances, especially in the J{sup P}=0{sup +} and 1{sup +} sectors, can be classified according to multiplets of SU(6). The f{sub 0}(1500), f{sub 1}(1420), and some 0{sup +}(2{sup ++}) resonances cannot be accommodated within this scheme, and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances (I{>=}3/2 and/or |Y|=2) with masses in the range of 1.4-1.6 GeV, which would complete the 27{sub 1}, 10{sub 3}, and 10{sub 3}* multiplets of SU(3) x SU(2).
No abstract prepared.
In this work we construct the {pi}{pi} scattering amplitude T{sub 0}{sup 0} with regular analytical properties in the s complex plane, which describes simultaneously the data on the {pi}{pi} scattering, {phi}{yields}{pi}{sup 0}{pi}0{gamma} decay, and {pi}{pi}{yields}KK reaction. The chiral shielding of the {sigma}(600) meson and its mixing with the f{sub 0}(980) meson are also taken into account. The data agrees with the four-quark nature of the {sigma}(600) and f{sub 0}(980) mesons. The amplitude in the range -5m{sub {pi}}{sup 2}<s<0.64 GeV{sup 2} also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.
We improve our description of {pi}{pi} scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K{sub l4} decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.
A set of once subtracted dispersion relations with imposed crossing symmetry condition for the {pi}{pi} D- and F-wave amplitudes is derived and analyzed. An example of numerical calculations in the effective two-pion mass range from the threshold to 1.1 GeV is presented. It is shown that these new dispersion relations impose quite strong constraints on the analyzed {pi}{pi} interactions and are very useful tools to test the {pi}{pi} amplitudes. One of the goals of this work is to provide a complete set of equations required for easy use. Full analytical expressions are presented. Along with the well-known dispersion relations successful in testing the {pi}{pi} S- and P-wave amplitudes, those presented here for the D and F waves give a complete set of tools for analyses of the {pi}{pi} interactions.
We develop a unitarized formalism to study tetraquarks using the triple flip-flop potential, which includes two meson-meson potentials and the tetraquark four-body potential. This can be related to the Jaffe-Wilczek and to the Karliner-Lipkin tetraquark models, where we also consider the possible open channels, since the four quarks and antiquarks may at any time escape to a pair of mesons. Here we study a simplified two-variable toy model and explore the analogy with a cherry in a glass, but a broken one where the cherry may escape from. It is quite interesting to have our system confined or compact in one variable and infinite in the other variable. In this framework we solve the two-variable Schroedinger equation in configuration space. With the finite difference method, we compute the spectrum, we search for localized states and we attempt to compute phase-shifts. We then apply the outgoing spherical wave method to compute in detail the phase-shifts and to determine the decay widths. We explore the model in the equal mass case, and we find narrow resonances. In particular the existence of two commuting angular momenta is responsible for our small decay widths.
We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts' mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the inverse amplitude method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also provide the estimation of uncertainties, which are dominated by those of the O(p{sup 6}) chiral parameters.