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Register a new userThe energy-dependent $pi^+ pi^+ pi^+$ scattering amplitude from QCD
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Focusing on three-pion states with maximal isospin ($pi^+pi^+pi^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.
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The results of an amplitude analysis of the charmless three-body decay $B^+ rightarrow pi^+pi^+pi^-$, in which $C!P$-violation effects are taken into account, are reported. The analysis is based on a data sample corresponding to an integrated luminosity of $3 text{fb}^{-1}$ of $pp$ collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behaviour of the $pi^+ pi^-$ S-wave contribution, which is achieved by using three complementary approaches based on the isobar model, the K-matrix formalism, and a quasi-model-independent procedure. Additional resonant contributions for all three methods are described using a common isobar model, and include the $rho(770)^0$, $omega(782)$ and $rho(1450)^0$ resonances in the $pi^+pi^-$ P-wave, the $f_2(1270)$ resonance in the $pi^+pi^-$ D-wave, and the $rho_3(1690)^0$ resonance in the $pi^+pi^-$ F-wave. Significant $C!P$-violation effects are observed in both S- and D-waves, as well as in the interference between the S- and P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of $C!P$-violation effects in $B^+ rightarrow pi^+pi^+pi^-$ decays.
Utilizing the data set corresponding to an integrated luminosity of $3.19$ fb$^{-1}$ collected by the BESIII detector at a center-of-mass energy of 4.178 GeV, we perform an amplitude analysis of the $D_s^+topi^+pi^-pi^+$ decay. The sample contains 13
,797 candidate events with a signal purity of $sim$80%. We use a quasi-model-independent approach to measure the magnitude and phase of the $D_s^+topi^+pi^-pi^+$ decay, where the ${cal P}$ and ${cal D}$ waves are parameterized by a sum of three Breit-Wigner amplitudes $rho(770)^0$, $rho(1450)^0$, and $f_2(1270)$. The fit fractions of different decay channels are also reported.
In this project, we will compute the form factors relevant for $B to K^*(to K pi)ell^+ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B to K pi$ matrix elements, the $K pi$ scattering amplitude needs to be determined using Luschers method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^*$ resonance mass and the $K^* K pi$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.
We present a lattice QCD study of the phase shift of $I{=}2$ $pipi$ scattering on the basis of two different approaches: the standard finite volume approach by Luscher and the recently introduced HAL QCD potential method. Quenched QCD simulations are performed on lattices with extents $N_s{=}16,24,32,48$ and $N_t{=}128$ as well as lattice spacing $a{sim}0.115,mathrm{fm}$ and a pion mass of $m_pi{sim}940,mathrm{MeV}$. The phase shift and the scattering length are calculated in these two methods. In the potential method, the error is dominated by the systematic uncertainty associated with the violation of rotational symmetry due to finite lattice spacing. In Luschers approach, such systematic uncertainty is difficult to be evaluated and thus is not included in this work. A systematic uncertainty attributed to the quenched approximation, however, is not evaluated in both methods. In case of the potential method, the phase shift can be calculated for arbitrary energies below the inelastic threshold. The energy dependence of the phase shift is also obtained from Luschers method using different volumes and/or nonrest-frame extension of it. The results are found to agree well with the potential method.
Using a data sample of 2.59 x 10^7 psi(2S) decays obtained with the CLEO-c detector, we perform amplitude analyses of the complementary decay chains chi_c1 -> eta pi+ pi- and chi_c1 -> eta pi+ pi-. We find evidence for a P-wave eta pi scattering amplitude, which, if interpreted as a resonance, would have exotic J^PC = 1^-+ and parameters consistent with the pi_1(1600) state reported in other production mechanisms. We also make the first observation of the decay a_0(980) -> eta pi and measure the ratio of branching fractions B(a_0(980) -> eta pi)/B(a_0(980) -> eta pi) = 0.064 +- 0.014 +- 0.014. The pi pi spectrum produced with a recoiling eta is compared to that with eta recoil.
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