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Register a new userPhase shifts in I=2 {pi}{pi}-scattering from two lattice approaches
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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.
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The $I=1$ $p$-wave and $I=2$ $s$-wave elastic $pi$-$pi$ scattering amplitudes are calculated from a first-principles lattice QCD simulation using a single ensemble of gauge field configurations with $N_{mathrm{f}} = 2+1$ dynamical flavors of anisotropic clover-improved Wilson fermions. This ensemble has a large spatial volume $V=(3.7mathrm{fm})^3$, pion mass $m_{pi} = 230mathrm{MeV}$, and spatial lattice spacing $a_s = 0.11mathrm{fm}$. Calculation of the necessary temporal correlation matrices is efficiently performed using the stochastic LapH method, while the large volume enables an improved energy resolution compared to previous work. For this single ensemble we obtain $m_{rho}/m_{pi} = 3.350(24)$, $g_{rhopipi} = 5.99(26)$, and a clear signal for the $I=2$ $s$-wave. The success of the stochastic LapH method in this proof-of-principle large-volume calculation paves the way for quantitative study of the lattice spacing effects and quark mass dependence of scattering amplitudes using state-of-the-art ensembles.
In this paper we report on results for the s-wave scattering length of the $pi$-$K$ system in the $I=3/2$ channel from $N_f=2+1+1$ Lattice QCD. The calculation is based on gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about $230$ to $450,text{MeV}$ at three values of the lattice spacing. Our main result reads $M_{pi},a_0^{3/2,text{phys}} = -0.059(2)$. Using chiral perturbation theory we are also able to estimate $M_{pi},a_0^{1/2,text{phys}} = 0.163(3)$. The error includes statistical and systematic uncertainties, and for the latter in particular errors from the chiral and continuum extrapolations.
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.
Phase shifts for $s$-wave $pipi$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3times 64$. These results support our recent study of direct CP violation in $Ktopipi$ decay cite{Abbott:2020hxn}, improving our earlier 2015 calculation cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $pipi$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $pipi$ interpolating operators including a scalar bilinear $sigma$ operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.
Pi-Pi scattering is investigated for the first time for Nf=2+1+1 dynamical quark flavours using Wilson twisted mass fermions. Luschers finite size method is used to relate energy shifts in finite volume to scattering quantities like the scattering length in the I=2 channel. The computation is performed at several pion masses and lattice spacings utilising the stochastic LapH method.
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