115167324
Multi-operator brackets acting thrice
We generalize an identity first found by Bremner for Nambu 3-brackets. For odd N-brackets built from associative operator products, we show that for any fixed A, when totally antisymmetrized over all the Bs.
115164400
Classical and quantal ternary algebras
We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.
119142727
Approximate Solutions of Functional Equations
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by construction of approximate continuous functional iterates for , sin x, and λx(1 − x). Simple functional conjugation by these functions, and their inverses, substantially improves the numerical accuracy of formal series approximations for their continuous iterates.
118336670
Lattice QCD with 12 Degenerate Quark Flavors
We report on new data from additional zero temperature simulations of QCD with 12 flavors. This is a continuation of previous studies using the DBW2 gauge action and naive staggered fermions. With the use of the force gradient integrator and a multiple-quark-mass preconditioned HMC, we have done simulations with input quark masses from mq = 0:003 to mq = 0:008. We have observed a metastable, first order, bulk transition that occurs at small input quark masses. As the quark mass increases, this first order bulk transition ends at a second order critical point, and, for still heavier quark masses, becomes the cross-over we have previously reported. We present measurements of hadron masses, decay constants and other low energy observables in the small quark mass region on the weak coupling side of the bulk transition. Our results show that the behavior of the system is still consistent with spontaneously broken chiral symmetry. We also discuss a preliminary investigation into the behavior of the bulk transition itself. We have found that, as the system approaches the second order critical end point, the scalar singlet meson becomes lighter. Thus it appears that the critical endpoint corresponds to a continuum limit theory only involving scalars and, following known triviality arguments, this is likely a free field theory. The presence of this critical endpoint could influence scaling of lattice observables in the conventional continuum limit.
118449163
Lattice QCD with 12 Quark Flavors: A Careful Scrutiny
With a substantial amount of simulations, we have explored the system across a wide range of lattice scales. We have located a lattice artifact, first order bulk transition, have studied its properties, and found that the flavor-singlet scalar meson mass vanishes at the critical endpoint. We will discuss the lattice phase diagrams and the continuum limits for both a spontaneous chiral symmetry breaking phase and an infrared conformal phase, and compare results with other groups.
118389195
Scalar correlators near the 3-flavor thermal critical point
We investigate screening masses at both sides of the first order finite temperature transition with 3 quark flavors using the nonperturbatively improved clover fermion action and the Iwasaki gauge action. We have developed the method of hierarchical truncations with stochastic probing to accelerate the noise estimator for evaluating quark loops at every spatial lattice slices. At parameter values we study, the flavor singlet scalar meson has a screening mass about half of the pion screening mass. It becomes lighter as the system approaches the critical endpoint.
118550101
Stealth Dark Matter: Dark scalar baryons through the Higgs portal
We present a new model of "Stealth Dark Matter": a composite baryonic scalar of an SU(ND) strongly coupled theory with even ND ≥ 4. All mass scales are technically natural, and dark matter stability is automatic without imposing an additional discrete or global symmetry. Constituent fermions transform in vectorlike representations of the electroweak group that permit both electroweak-breaking and electroweak-preserving mass terms. This gives a tunable coupling of stealth dark matter to the Higgs boson independent of the dark matter mass itself. We specialize to SU(4), and investigate the constraints on the model from dark meson decay, electroweak precision measurements, basic collider limits, and spin-independent direct detection scattering through Higgs exchange. We exploit our earlier lattice simulations that determined the composite spectrum as well as the effective Higgs coupling of stealth dark matter in order to place bounds from direct detection, excluding constituent fermions with dominantly electroweak-breaking masses. A lower bound on the dark baryon mass mB ≳ 300 GeV is obtained from the indirect requirement that the lightest dark meson not be observable at LEP II. Furthermore, we briefly survey some intriguing properties of stealth dark matter that are worthy of future study, including collider studies of dark mesonmore » production and decay; indirect detection signals from annihilation; relic abundance estimates for both symmetric and asymmetric mechanisms; and direct detection through electromagnetic polarizability, a detailed study of which will appear in a companion paper.« less