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Register a new userAngular momentum content of the rho-meson in lattice QCD
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The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the non-perturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the LSJ basis one may extract a partial wave content of a meson. We present results for the ground state of the rho-meson using quenched simulations as well as simulations with two dynamical quarks, all for lattice spacings close to 0.15 fm. We point out that these results indicate a simple 3S1-wave composition of the rho-meson in the infrared, like in the SU(6) flavor-spin quark model.
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The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the nonperturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the $^{2S+1}L_J$ basis one may extract the partial wave content of a meson. We present results for the $rho$- and $rho$-mesons using a simulation with $N_f=2$ dynamical quarks, all for lattice spacings close to 0.15 fm. Our results indicate a strong chiral symmetry breaking in the $rho$ state and its simple $^3S_1$-wave composition in the infrared. For the $rho$-meson we find a small chiral symmetry breaking in the infrared as well as a leading contribution of the $^3D_1$ partial wave, which is contradictory to the quark model.
It is possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark Fock component of a meson in the infrared, where mass is generated. Using the variational method and a set of interpolators that span a complete chiral basis we extract in a lattice QCD Monte Carlo simulation with two dynamical light quarks the orbital angular momentum and spin content of the rho-meson. We obtain in the infrared a simple 3S1 component as a leading component of the rho-meson with a small admixture of the 3D1 partial wave, in agreement with the SU(6) flavor-spin symmetry.
We identify the chiral and angular momentum content of the leading quark-antiquark Fock component for the $rho(770)$ and $rho(1450)$ mesons using a two-flavor lattice simulation with dynamical Overlap Dirac fermions. We extract this information from the overlap factors of two interpolating fields with different chiral structure and from the unitary transformation between chiral and angular momentum basis. For the chiral content of the mesons we find that the $rho(770)$ slightly favors the $(1,0)oplus(0,1)$ chiral representation and the $rho(1450)$ slightly favors the $(1/2,1/2)_b$ chiral representation. In the angular momentum basis the $rho(770)$ is then a $^3S_1$ state, in accordance with the quark model. The $rho(1450)$ is a $^3D_1$ state, showing that the quark model wrongly assumes the $rho(1450)$ to be a radial excitation of the $rho(770)$.
We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized $rho$ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between $0.060,text{fm}$ and $0.081,text{fm}$, different lattice volumes up to $m_pi L = 6.7$ and pion masses down to $m_pi=150,text{MeV}$. Bare lattice results are renormalized non-perturbatively using a variant of the RI-MOM scheme and converted to the $overline{text{MS}}$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants $f_rho^T/f_rho^{vphantom{T}} = 0.629(8)$ and the values of the second Gegenbauer moments $a_2^parallel = 0.132(27)$ and $a_2^perp = 0.101(22)$ at the scale $mu = 2,text{GeV}$ for the longitudinally and transversely polarized $rho$ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of $rhotopipi$ decay at the smaller pion masses is not taken into account.
In simulations with dynamical quarks it has been established that the ground state rho in the infrared is a strong mixture of the two chiral representations (0,1)+(1,0) and (1/2,1/2)_b. Its angular momentum content is approximately the 3S1 partial wave which is consistent with the quark model. Effective chiral restoration in an excited rho-meson would require that in the infrared this meson couples predominantly to one of the two representations. The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the non-perturbatively determined excited state at different resolution scales. We present results for the first excited state of the rho-meson using simulations with n_f=2 dynamical quarks. We point out, that in the infrared a leading contribution to rho= rho(1450) comes from (1/2,1/2)_b, in contrast to the rho. Its approximate chiral partner would be a h_1(1380) state. The rho wave function contains a significant contribution of the 3D1 wave which is not consistent with the quark model prediction.
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