The lattice gradient flow at tree-level and its improvement
A bstractThe Yang-Mills gradient flow and the observable 〈E(t)〉, defined by the square of the field strength tensor at t > 0, are calculated at finite lattice spacing and tree-level in the gauge coupling. Improvement of the flow, the gauge action and the observable are all considered. The results are relevant for two purposes. First, the discretization of the flow, gauge action and observable can be chosen in such a way that O(a2), O(a4) or even O(a6) improvement is achieved. Second, simulation results using arbitrary discretizations can be tree-level improved by the perturbatively calculated correction factor normalized to one in the continuum limit.

title: Twelve fundamental and two sextet fermion flavors
abstract: We report extended simulation results and their new analysis in two important gauge theories with twelve fermion flavors in the fundamental SU(3) color representation and two fermions in the sextet representation. We probe the $N_f=12$ model with respect to the conformal window using mass deformed finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Our results at fixed gauge coupling show problems with the conformal scenario of the $N_f=12$ model. In the sextet model with two flavors, under the conformal hypothesis, we determine large values for the anomalous fermion mass dimension with $\gamma\geq 1$. Since our sextet analysis favors the chiral symmetry breaking hypothesis without conformality, the large exponent $\gamma$ could play an important role in understanding the composite Higgs mechanism. The new results discussed here include our extended data sets and exceed what was presented at the conference.

title: Baryon spectrum in the composite sextet model
abstract: The strongly coupled near-conformal gauge theory with two fermion flavors in the two-index symmetric (sextet) representation of SU(3) is potentially a minimal realization of the composite Higgs mechanism. We discuss the staggered fermion construction of baryonic states, present our first numerical results and comment on implications for dark matter.

title: Can the nearly conformal sextet gauge model hide the Higgs impostor
abstract: New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β -function (DeGrand et al.  ). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β -function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.

title: The ﬁnite volume spectrum of excited states from lattice QCD simulations
abstract: We present results for the spectrum of excited mesons obtained from temporal correlations of spatially-extended single-hadron and multi-hadron operators computed in lattice QCD. The stochastic LapH algorithm is implemented on anisotropic, dynamical lattices for isovectors for pions of mass 390 MeV. A large correlation matrix with single-particle and two-particle probe operators is diagonalized to identify resonances. The masses of excited states in the I = 1,S = 0,T 1u channel as well as the mixing of single and multi-particle probe operators are presented.

title: Pion-pion scattering phase shifts with the stochastic LapH method
abstract: Progress in calculating scattering phase shifts on $N_f=2+1$ anisotropic clover Wilson lattices is described. The stochastic LapH method facilitates computations in large volumes and for light pion masses. Results for pion masses down to 240 MeV, keeping $m_\pi L > 4$, are presented.

title: Magnetic States at Short Distances
abstract: 3 P ++ 0 states admit two types of eigenstates with drastically different behaviors for the radial wave function u = rψ. One type of states, with u growing as r �+1 at small r, will be called usual states. The other type of states with u growing as rwill be called peculiar states. Both of the usual and peculiar eigenstates have admissible behaviors at short distances. Remarkably, the solutions for both sets of 1 S0 states can be written out analytically. The usual bound 1 S0 states possess attributes the same as those one usually encounters in QED and QCD, with bound state energies explicitly agreeing with the standard perturbative results through order α 4 . In contrast, the peculiar bound 1 S0 states, yet to be observed, not only have different behaviors at the origin, but also distinctly different bound state properties (and scattering phase shifts). For the peculiar 1 S0 ground state of fermion-antifermion pair with fermion rest mass m, the root-mean-square radius is approximately 1/m, binding energy is approximately (2 p 2)m, and rest mass approximately p 2m. On the other hand, the (n+1) 1 S0 peculiar state with principal quantum number (n + 1) is nearly degenerate in energy and approximately equal in size with the n 1 S0 usual states. For the 3 P0 states, the usual solutions lead to the standard bound state energies and no resonance, but resonances have been found for the peculiar states whose energies depend on the description of the internal structure of the charges, the mass of the constituent, and the coupling constant. The existence of both usual and peculiar eigenstates in the same system leads to the non- self-adjoint property of the mass operator and two non-orthogonal complete sets. As both sets of states are physically admissible, the mass operator can be made self-adjoint with a single complete set of admissible states by introducing a new peculiarity quantum number and an enlarged Hilbert space that contains both the usual and peculiar states in different peculiarity sectors. Whether or not these newly-uncovered quantum-mechanically acceptable peculiar 1 S0 bound states and 3 P0 resonances for point fermion-antifermion systems correspond to physical states remains to be further investigated.

title: Quarkonia and quark drip lines in a quark-gluon plasma
abstract: We extract the Q-Q potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give spontaneous dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a Q-Q potential, we examine the quarkonium states in a quark-gluon plasma and determine the "quark drip lines" which separate the region of bound color-singlet Q Q states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound Q Q states with light quarks to temperatures close to the phase transition temperature. Bound quarkonia with light quarks may exist very near the phase transition temperature if their effective quark mass is of the order of 300-400 MeV and higher.

title: Effects of dynamical quarks on the stability of heavy quarkonia in quark-gluon plasma
abstract: To study the stability of heavy quarkonia in quark-gluon plasma, we use a color-singlet Q-Qbar potential determined previously to be a well-defined linear combination of the free energy F_1 and the internal energy U_1. Using the lattice gauge results of Kaczmarek et al., the dissociation temperatures of J/psi and chi_b in quenched QCD are found to be 1.62Tc and 1.18Tc respectively, in good agreement with spectral function analyses. The dissociation temperature of J/psi in full QCD with 2 flavors is 1.42Tc. Thus, the presence of dynamical quarks in full QCD lowers the dissociation temperature of J/psi, but J/psi remains bound up to 1.42Tc.

title: Quantum Treatment of the Multiple Scattering and Collective Flow in Intensity Interferometry
abstract: We apply the path‐integral method to study the multiple scattering and collective flow in intensity interferometry in high‐energy heavy‐ion collisions. We show that the Glauber model and eikonal approximation in an earlier quantum treatment are special examples of the more general path‐integral method. The multiple scattering and collective flow lead essentially to an initial source at a shifted momentum, with a multiple collision absorption factor that depends on the pion absorption cross section and a phase factor that depends on the deviations of the in‐medium particle momenta from their asymptotic values.

title: Heavy quarkonia in quark-gluon plasma
abstract: Q in quenched QCD, we study the binding energies and wave functions of heavy quarkonia in a quark-gluon plasma. By minimizing the grand potential in a simplified schematic model, we find that the proper color-singlet Q- ¯ Q potential can be obtained from the total internal energy U1 by subtracting the gluon internal energy contributions. We carry out this subtraction in the local energy-density approximation in which the gluon energy density can be related to the local gluon pressure by the quark-gluon plasma equation of state. We find in this approximation that the proper color-singlet Q- ¯ Q potential is approximately F1 for T ∼ Tc and it changes to 3 F1 + 1 U1 at high temperatures. In this potential model, the J/ ψ is weakly bound above the phase-transition temperature Tc, and it dissociates spontaneously above 1.62Tc, whereas χc and ψ � are unbound in the quark-gluon plasma. The bottomium states ϒ, χb ,a ndϒ � are bound in the quark-gluon plasma and they dissociate at 4.1Tc, 1.18Tc, and 1.38Tc respectively. For comparison, we evaluate the heavy quarkonium binding energies also in other models using the free energy F1 or the total internal energy U1 as the Q- ¯ Q potential. The comparison shows that the model with the new Q- ¯ Q potential proposed here gives dissociation temperatures that agree best with those from spectral function analyses. We evaluate the cross section for σ (g + J/ ψ → c + ¯ c) and its inverse process to determine the J/ ψdissociation width and the rate of J/ ψ production by recombining c and ¯ c in the quark-gluon plasma.