Chiral symmetry breaking in QCD with two light flavors.

A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of M(π)(2)F(π)(2)/2 with respect to the quark mass m in the chiral limit, where M(π) and F(π) are the mass and the decay constant of the Nambu-Goldstone bosons. We compute the spectral density of the (Hermitian) Dirac operator, the quark mass, the pseudoscalar meson mass, and decay constant by numerical simulations of lattice QCD with two light degenerate Wilson quarks. We use lattices generated by the Coordinated Lattice Simulation (CLS) group at three values of the lattice spacing in the range 0.05-0.08 fm, and for several quark masses corresponding to pseudoscalar mesons masses down to 190 MeV. Thanks to this coverage of parameters space, we can extrapolate all quantities to the chiral and continuum limits with confidence. The results show that the low quark modes do condense in the continuum as expected by the Banks-Casher mechanism, and the rate of condensation agrees with the Gell-Mann-Oakes-Renner relation. For the renormalization-group-invariant ratios we obtain [Σ(RGI)](1/3)/F=2.77(2)(4) and Λ(M̅S)/F=3.6(2), which correspond to [Σ(M̅S)(2 GeV)](1/3)=263(3)(4) MeV and F=85.8(7)(20) MeV if F(K) is used to set the scale by supplementing the theory with a quenched strange quark.

Equation of state of a relativistic theory from a moving frame.

We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame, an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to computing the expectation value of the off-diagonal components T(0k) of the energy-momentum tensor in the presence of shifted boundary conditions. The entropy is, thus, easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9T(c)-20T(c). At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, we also determine the ultraviolet finite renormalization constant of T(0k) by imposing suitable Ward identities. These findings establish this strategy as a solid, simple, and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in T.

Stereocomplementary routes to hydroxylated nitrogen heterocycles: total syntheses of casuarine, australine, and 7-epi-australine.

Addition of lithiated 1-benzyloxyallene to a D-arabinose-derived cyclic nitrone occurred with perfect diastereoselectivity furnishing a bicyclic 1,2-oxazine derivative, which is an excellent precursor for pyrrolizidine alkaloids hydroxylated at C-7 with optional configuration at this stereogenic center. Depending on the stage of the N-O bond cleavage and ring re-closure, 7-hydroxypyrrolizidines with 7R or 7S configuration were obtained, as a result of completely selective addition reactions occurring complementarily at the bottom or top face of the endocyclic C-C double bond in six- and five-membered B rings, respectively. Applicability of these stereodivergent routes to obtain polyhydroxy pyrrolizidine alkaloids is demonstrated by the efficient syntheses of casuarine and australine as examples of the two classes of diversely configured 7-hydroxypyrrolizidine alkaloids. An alternative synthesis of australine and two strategies for the preparation of 7-epi-australine are also reported, which demonstrate that the stereoselectivity of hydride reduction of an exocyclic C-O double bond is independent of the ring size, occurring preferentially from the top face either in a six- or five-membered ring.

Thermal momentum distribution from path integrals with shifted boundary conditions.

For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.

Topological susceptibility in SU(3) gauge theory.

We compute the topological susceptibility for the SU(3) Yang-Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r(4)(0)chi = 0.059(3), which corresponds to chi = (191 +/- 5 MeV)(4) if F(K) is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the eta(').

BK from quenched QCD with exact chiral symmetry.

We present a calculation of the standard model DeltaS=2 matrix element relevant to indirect CP violation in K-->pipi decays which uses Neuberger's chiral formulation of lattice fermions. The computation is performed in the quenched approximation on a 16(3) x 32 lattice that has a lattice spacing a approximately 0.1 fm. The resulting bare matrix element is renormalized nonperturbatively. Our main result is B(RGI)(K)=0.87(8)+2+14-1-14, where the first error is statistical, the second is systematic, and the third is Sharpe's estimate of quenching and flavor-SU(3) breaking uncertainties.