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Register a new userChiral symmetry breaking and the spin content of hadrons
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From the parton distributions in the infinite momentum frame one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term spin crisis. Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal $bar q q$ chiral basis and a unitary transformation from the chiral basis to the (2S+1)LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson we measure in dynamical lattice simulations a ratio of couplings of interpolarors with different chiral structure. For the rho meson we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?
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Using interpolators with different SU(2)_L times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $qbargamma^i{tau}q$ and $qbarsigma^{0i}{tau}q$ interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ~1 fm. In the ground state rho meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1) + (1,0) and (1/2,1/2)_b chiral representations with the former being the leading contribution. In contrast, in the rho meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)_b. Using a unitary transformation from the chiral basis to the {2S +1}L_J basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The rho meson is practically a 3S_1 state with no obvious trace of a spin crisis. The rho meson has a sizeable contribution of the 3D_1 wave, which implies that the rho meson cannot be considered as a pure radial excitation of the rho meson.
The nucleon is naturally viewed as a bipartite system of valence spin -- defined by its non-vanishing chiral charge -- and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the resulting entanglement entropy acts as an order parameter of chiral symmetry breaking in the nucleon. In the large-$N_c$ limit, the entanglement entropy vanishes and the valence spin accounts for all of the nucleon spin, while in the limit of maximal entanglement entropy, the nucleon loses memory of the valence spin and consequently has spin dominated by the sea. The nucleon state vector in the chiral basis, fit to low-energy data, gives a valence spin content consistent with experiment and lattice QCD determinations, and has large entanglement entropy.
The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which shows oscillations with a period that scales as 1/V and an amplitude that diverges exponentially with the volume $V=L^4$. We find that the discontinuity of the chiral condensate is due to the whole oscillating region rather than to an accumulation of eigenvalues at the origin. These results also extend beyond the microscopic regime to chemical potentials $mu sim 1/L$.
We review heavy quark flavor and spin symmetries, their exploitation in heavy meson effective theories and the flavored couplings of charmed and light mesons in the definition of their effective Lagrangians. We point out how nonperturbative continuum QCD approaches based on Dyson-Schwinger and Bethe-Salpeter equations can be used to calculate strong and leptonic decays of open-charm mesons and heavy quarkonia. The strong decay $D^*to Dpi$ serves as a benchmark, as it is the only physical open-charm observable that can be related to the effective Lagrangians couplings. Nonetheless, a quantitative comparison of $D^*Dpi$, $rho DD$, $rho D^*D$ and $rho D^* D^*$ couplings for a range of off-shell momenta of the $rho$-meson invalidates SU(4)$_F$ symmetry relations between these couplings. Thus, besides the breaking of flavor symmetry by mass terms in the Lagrangians, the flavor-symmetry breaching in couplings and their dependence on the $rho$-meson virtuality cannot be ignored. We also take the opportunity to present new results for the effective $J/psi DD$ and $J/psi D^*D$ couplings. We conclude this contribution with a discussion on how the description of pseudoscalar and vector $D$, $D_s$, $B$ and $B_s$ meson properties can be drastically improved with a modest modification of the flavor-dependence in the Bethe-Salpeter equation.
We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.
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