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Register a new userLow Mass $S$-wave $Kpi$ and $pipi$ System
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B. Meadows
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Knowledge of the details of the $S$-wave $Kpi$ and $pipi$ systems limits the precision of measurements of heavy quark meson properties. This talk covers recent experimental developments in parametrizing and measuring these waves, and examines possibilities for the future.
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In this work, we provide estimates of the branching ratios, direct $CP$ asymmetries and triple product asymmetries in $B_{(s)} to (pipi)(Kpi)$ decays in the perturbative QCD approach, where the $pipi$ and $Kpi$ invariant mass spectra are dominated by the vector resonances $rho(770)$ and $K^*(892)$, respectively. Some scalar backgrounds, such as $f_0(500,980) to pipi$ and $K^*_0(1430) to Kpi$ are also accounted for. The $rho(700)$ is parametrized by the Gounaris-Sakurai function. The relativistic Breit-Wigner formula for the $f_0(500)$ and Flatte model for the $f_0(980)$ are adopted to parameterize the time-like scalar form factors $F_S(omega^2)$. We also use the D.V. Bugg model to parameterize the $f_0(500)$ and compare the relevant theoretical predictions from different models. While in the region of $Kpi$ invariant mass, the $K^*_0(1430)$ is described with the LASS lineshape and the $K^*(892)$ is modeled by the Breit-Wigner function. We find that the decay rates for the considered decay modes agree with currently available data within errors. As a by-product, we extract the branching ratios of two-body decays $B_{(s)} to rho(770)K^*(892)$ from the corresponding four-body decay modes and calculate the relevant polarization fractions. Our prediction of longitudinal polarization fraction for $B^0to rho(770)^0 K^*(892)^0$ decay deviates a lot from the recent LHCb measurement, which should be resolved. It is shown that the direct $CP$ asymmetries are large due to the sizable interference between the tree and penguin contributions, but they are small for the tree-dominant or penguin-dominant processes. The PQCD predictions for the triple product asymmetries are small which are expected in the standard model, and consistent with the current data reported by the LHCb Collaboration.Our results can be tested by the future precise data from the LHCb and Belle II experiments.
We present results for the isospin-0 $pipi$ s-wave scattering length calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge configurations. We use three $N_f = 2$ ensembles with unitary (valence) pion mass at its physical value (250$sim$MeV), at 240$sim$MeV (320$sim$MeV) and at 330$sim$MeV (400$sim$MeV), respectively. By using the stochastic Laplacian Heaviside quark smearing method, all quark propagation diagrams contributing to the isospin-0 $pipi$ correlation function are computed with sufficient precision. The chiral extrapolation is performed to obtain the scattering length at the physical pion mass. Our result $M_pi a^mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions. Since we only use one lattice spacing, certain systematics uncertainties, especially those arising from unitary breaking, are not controlled in our result.
The COMPASS collaboration has collected the currently largest data set on diffractively produced $pi^-pi^-pi^+$ final states using a negative pion beam of 190 GeV/c momentum impinging on a stationary proton target. This data set allows for a systematic partial-wave analysis in 100 bins of three-pion mass, $0.5 < m_{3pi} < 2.5$ GeV/c$^2$ , and in 11 bins of the reduced four-momentum transfer squared, $0.1 < t < 1.0$ (GeV/c)$^2$ . This two-dimensional analysis offers sensitivity to genuine one-step resonance production, i.e. the production of a state followed by its decay, as well as to more complex dynamical effects in nonresonant $3pi$ production. In this paper, we present detailed studies on selected $3pi$ partial waves with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{-+}$, $2^{++}$, and $4^{++}$. In these waves, we observe the well-known ground-state mesons as well as a new narrow axial-vector meson $a_1(1420)$ decaying into $f_0(980) pi$. In addition, we present the results of a novel method to extract the amplitude of the $pi^-pi^+$ subsystem with $I^{G}J^{PC} = 0^+ 0^{++}$ in various partial waves from the $pi^-pi^-pi^+$ data. Evidence is found for correlation of the $f_0(980)$ and $f_0(1500)$ appearing as intermediate $pi^- pi^+$ isobars in the decay of the known $pi(1800)$ and $pi_2(1880)$.
We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $Kpi$ scattering amplitudes as a function of the center-of-mass energy using Luschers method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $sqrt{3}frac{2pi}{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $kappa$ resonance in the $S$-wave and the narrow $K^*(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of $317.2(2.2)$ and $175.9(1.8)$ MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $kappa$-resonance pole positions are found to be $left[0.86(12) - 0.309(50),iright]:{rm GeV}$ at the heavier pion mass and $left[0.499(55)- 0.379(66),iright]:{rm GeV}$ at the lighter pion mass. The $P$-wave $K^*$-resonance pole positions are found to be $left[ 0.8951(64) - 0.00250(21),i right]:{rm GeV}$ at the heavier pion mass and $left[0.8718(82) - 0.0130(11),iright]:{rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^* Kpi}=5.02(26)$ and $g_{K^* Kpi}=4.99(22)$, respectively.
Using the perturbative QCD amplitudes for $Bto pipi$ and $Bto Kpi$, we have performed an extensive study of the parameter space where the theoretical predictions for the branching ratios are consistent with recent experimental data. From this allowed range of parameter space, we predict the mixing induced CP asymmetry for $B to pi^+pi^-$ with about 11% uncertainty and the other CP asymmetries for $Bto pipi$, $Kpi$ with 40% ~ 47% uncertainty. These errors are expected to be reduced as we restrict the parameter space by studying other decay modes and by further improvements in the experimental data.
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