We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and ...N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.
We report on the progress of understanding spatial correlation functions in
high temperature QCD. We study isovector meson operators in $N_f=2$ QCD using
domain-wall fermions on lattices of $N_s=32$ ...and different quark masses. It has
previously been found that at $\sim 2T_c$ these observables are not only
chirally symmetric but in addition approximately $SU(2)_{CS}$ and $SU(4)$
symmetric. In this study we increase the temperature up to $5T_c$ and can
identify convergence towards an asymptotically free scenario at very high
temperatures.
Operators for simulating the scattering of two particles with spin are constructed. Three methods are shown to give the consistent lattice operators for PN, PV, VN and NN scattering, where P, V and N ...denote pseudoscalar meson, vector meson and nucleon. The projection method leads to one or several operators \(O_{\Gamma,r,n}\) that transform according to a given irreducible representation \(\Gamma\) and row r. However, it gives little guidance on which continuum quantum numbers of total J, spin S, orbital momentum L or single-particle helicities \(\lambda_{1,2}\) will be related with a given operator. This is remedied with the helicity and partial-wave methods. There first the operators with good continuum quantum numbers \((J,P,\lambda_{1,2})\) or \((J,L,S)\) are constructed and then subduced to the irreps \(\Gamma\) of the discrete lattice group. The results indicate which linear combinations \(O_{\Gamma,r,n}\) of various n have to be employed in the simulations in order to enhance couplings to the states with desired continuum quantum numbers. The total momentum of two hadrons is restricted to zero since parity P is a good quantum number in this case.
In this talk I present the formalism we have used to analyze Lattice data on two meson systems by means of effective field theories. In particular I present the results obtained from a reanalysis of ...the lattice data on the \(KD^{(*)}\) systems, where the states \(D^*_{s0}(2317)\) and \(D^*_{s1}(2460)\) are found as bound states of \(KD\) and \(KD^*\), respectively. We confirm the presence of such states in the lattice data and determine the contribution of the \(KD\) channel in the wave function of \(D^*_{s0}(2317)\) and that of \(KD^*\) in the wave function of \(D^*_{s1}(2460)\). Our findings indicate a large meson-meson component in the two cases.
Charmonia in moving frames Prelovsek, S; Bali, G; Collins, S ...
arXiv.org,
10/2017
Paper, Journal Article
Odprti dostop
Lattice simulation of charmonium resonances with non-zero momentum provides additional information on the two-meson scattering matrices. However, the reduced rotational symmetry in a moving frame ...renders a number of states with different \(J^P\) in the same lattice irreducible representation. The identification of \(J^P\) for these states is particularly important, since quarkonium spectra contain a number of states with different \(J^P\) in a relatively narrow energy region. Preliminary results concerning spin-identification are presented in relation to our study of charmonium resonances in flight on the Nf=2+1 CLS ensembles.
Based on a complete set of \(J = 0\) and \(J=1\) spatial isovector correlation functions calculated with \(N_F = 2\) domain wall fermions we identify an intermediate temperature regime of \(T \sim ...220 - 500\) MeV (\(1.2T_c\)--\(2.8T_c\)), where chiral symmetry is restored but the correlators are not yet compatible with a simple free quark behavior. More specifically, in the temperature range \(T \sim 220 - 500\) MeV we identify a multiplet structure of spatial correlators that suggests emergent \(SU(2)_{CS}\) and \(SU(4)\) symmetries, which are not symmetries of the free Dirac action. The symmetry breaking effects in this temperature range are less than 5%. Our results indicate that at these temperatures the chromo-magnetic interaction is suppressed and the elementary degrees of freedom are chirally symmetric quarks bound into color-singlet objects by the chromo-electric component of the gluon field. At temperatures between 500 and 660 MeV the emergent \(SU(2)_{CS}\) and \(SU(4)\) symmetries disappear and one observes a smooth transition to the regime above \(T \sim 1\) GeV where only chiral symmetries survive, which are finally compatible with quasi-free quarks.
We present a lattice QCD study of charmonium resonances and bound states with \(J^{PC}=1^{--}\) and \(3^{--}\) near the open-charm threshold, taking into account their strong transitions to \(\bar ...DD\). Vector charmonia are the most abundant in the experimentally established charmonium spectrum, while recently LHCb reported also the first discovery of a charmonium with likely spin three. The \(\bar DD\) scattering amplitudes for partial waves \(l=1\) and \(l=3\) are extracted on the lattice by means of the L\"uscher formalism, using multiple volumes and inertial frames. Parameterizations of the scattering amplitudes provide masses and widths of the resonances, as well as the masses of bound states. CLS ensembles with 2+1 dynamical flavors of non-perturbatively \(O(a)\) improved Wilson quarks are employed with \(m_\pi\simeq 280\) MeV, a single lattice spacing of \(a\simeq0.086\) fm and two lattice spatial extents of \(L=24\) and \(32\). Two values of the charm quark mass are considered to examine the influence of the position of the \(\bar{D}D\) threshold on the hadron masses. For the lighter charm quark mass we find the vector resonance \(\psi(3770)\) with mass \(m=3780(7)\) MeV and coupling \(g=16.0(^{+2.1}_{-0.2})\) (related to the width), both consistent with their experimental values. The vector \(\psi(2S)\) appears as a bound state with \(m=3666(10)\) MeV. The charmonium resonance with \(J^{PC}=3^{--}\) is found at \(m=3831(^{+10}_{-16})\) MeV, consistent with the \(X(3842)\) recently discovered by LHCb. At our heavier charm-quark mass the \(\psi(2S)\) as well as the \(\psi(3770)\) are bound states and the \(X(3842)\) remains a resonance. We stress that all quoted uncertainties are only statistical, while lattice spacing effects and the approach to the physical point still need to be explored. This study of conventional charmonia sets the stage for more challenging future studies of unconventional charmonium-like states.
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