Superfluids as higher-form anomalies

We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid - its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higher-form symmetries and their anomalies instead of how the symmetries are realized. This treatment is more general and, in particular, includes the case of BKT transitions. As an application of this formalism we construct the hydrodynamic theories of conventional (0-form) and 1-form superfluids.

Baryons and chiral symmetry

The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of [Formula: see text] term and strangeness. The third one is the role of chiral [Formula: see text] anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.

Quark and Glue Components of the Proton Spin from Lattice Calculation

The status of lattice calculations of the quark spin, the quark orbital angular momentum, the glue angular momentum and glue spin in the nucleon is summarized. The quark spin calculation is recently carried out from the anomalous Ward identity with chiral fermions and is found to be small mainly due to the large negative anomaly term which is believed to be the source of the ‘proton spin crisis’. We also present the first calculation of the glue spin at finite nucleon momenta.

SCALAR AND PSEUDOSCALAR GLUEBALLS

We employ two simple and robust results to constrain the mixing matrix of the isosinglet scalar mesons f0(1710), f0(1500), f0(1370): one is the approximate SU (3) symmetry empirically observed in the scalar sector above 1 GeV and confirmed by lattice QCD, and the other is the scalar glueball mass at 1710 MeV in the quenched approximation. In the SU (3) symmetry limit, f0(1500) becomes a pure SU (3) octet and is degenerate with a0(1450), while f0(1370) is mainly an SU (3) singlet with a slight mixing with the scalar glueball which is the primary component of f0(1710). These features remain essentially unchanged even when SU (3) breaking is taken into account. The observed enhancement of ωf0(1710) production over ɸf0(1710) in hadronic J/ψ decays and the copious f0(1710) production in radiative J/ψ decays lend further support to the prominent glueball nature of f0(1710). We deduce the mass of the pseudoscalar glueball G from an η-η′-G mixing formalism based on the anomalous Ward identity for transition matrix elements. With the inputs from the recent KLOE experiment, we find a solution for the pseudoscalar glueball mass around (1.4±0.1) GeV, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. This affirms that η(1405), having a large production rate in the radiative J/ψ decay and not seen in γγ reactions, is indeed a leading candidate for the pseudoscalar glueball. It is much lower than the results from quenched lattice QCD (> 2.0 GeV) due to the dynamic fermion effect. It is thus urgent to have a full QCD lattice calculation of pseudoscalar glueball masses.

COMMENTS ON THE VACUUM ORIENTATIONS IN QCD

We study the QCD vacuum orientation angles in correlation with the strong CP phases. A vacuum alignment equation of the dynamical chiral symmetry breaking is derived based on the anomalous Ward identity. It is emphasized that a chiral rotation of the quark field causes a change of the vacuum orientation and a change in the definition of the light pseudoscalar generators. As an illustration of the idea, η→2π decays are carefully studied in different chiral frames.