Two-Pion Decay Widths of Excited Charm Mesons

The widths for $\pi\pi$ decay of the L=1 charm mesons are calculated by describing the pion coupling to light constituents quarks by the lowest order chiral interaction. The wavefunctions of the charm mesons are obtained as solutions to the covariant Blankenbecler-Sugar equation. These solutions correspond to an interaction Hamiltonian modeled as the sum of a linear scalar confining and a screened one-gluon exchange (OGE) interaction. This interaction induces a two-quark contribution to the amplitude for two-pion decay, which is found to interfere destructively with the single quark amplitude. For the currently known L=1 $D$ mesons, the total $\pi\pi$ decay widths are found to be $\sim 1$ MeV for the $D_1(2420)$ and $\sim 3$ MeV for the $D^*_2(2460)$ if the axial coupling of the constituent quark is taken to be $g_A^q=1$. The as yet undiscovered spin singlet $D_1^*$ state is predicted to have a larger width of 7 - 10 MeV for $\pi\pi$ decay.Comment: 20 pages, uses Feynmf Submitted to Nuclear Physics A, published versio

Exchange Current Operators and Electromagnetic Dipole Transitions in Heavy Quarkonia

The electromagnetic E1 and M1 transitions in heavy quarkonia ($c\bar c$, $b\bar b$, $c\bar b$) and the magnetic moment of the $B_c^\pm$ are calculated within the framework of the covariant Blankenbecler-Sugar (BSLT) equation. The aim of this paper is to study the effects of two-quark exchange current operators which involve the $Q\bar Q$ interaction, that arise in the BSLT (or Schr\"odinger) reduction of the Bethe-Salpeter equation. These are found to be small for E1 dominated decays such as $\psi(nS)\to \chi_{cJ} \gamma$ and $\Upsilon(nS)\to \chi_{bJ} \gamma$, but significant for the M1 dominated transitions. It is shown that a satisfactory description of the empirical data on E1 and M1 transitions in charmonium and bottomonium requires unapproximated treatment of the Dirac currents of the quarks. Finally, it is demonstrated that many of the transitions are sensitive to the form of the $Q\bar Q$ wavefunctions, and thus require a realistic treatment of the large hyperfine splittings in the heavy quarkonium systems.Comment: 30 pages, 2 figures, uses Feynmf. Submitted to Nucl. Phys. A Accepted versio

Lattice field theory simulations of graphene

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling

Is graphene in vacuum an insulator?

We present evidence, from lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at αgcrit=1.11±0.06, where αg 2.16 in vacuum, and αg 0.79 on a SiO2 substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors 4<Nfcrit<6. Our data are consistent with a second-order transition

Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study

The low-energy theory of graphene exhibits spontaneous chiral symmetry breaking due to pairing of quasiparticles and holes, corresponding to a semimetal-insulator transition at strong Coulomb coupling. We report a lattice Monte Carlo study of the critical exponents of this transition as a function of the number of Dirac flavors Nf, finding δ=1.25±0.05 for Nf =0, δ=2.26±0.06 for Nf =2 and δ=2.62±0.11 for Nf =4, with γ1 throughout. We compare our results with recent analytical work for graphene and closely related systems and discuss scenarios for the fate of the chiral transition at finite temperature and carrier density, an issue of relevance for upcoming experiments with suspended graphene samples

Velocity renormalization in graphene from lattice monte carlo

We compute the Fermi velocity of the Dirac quasiparticles in clean graphene at the charge neu- Trality point for strong Coulomb coupling ag. We perform a Lattice Monte Carlo calculation within the low-energy Dirac theory, which includes an instantaneous, long-range Coulomb in- Teraction. We find a renormalized Fermi velocity vFR &gt; vF, where vF ≃ c=300. Our results are consistent with a momentum-independent vFR which increases approximately linearly with ag, although a logarithmic running with momentum cannot be excluded at present. At the predicted critical coupling agc for the semimetal-insulator transition due to excitonic pair formation, we find vFR=vF ≃ 3:3, which we discuss in light of experimental findings for vFR=vF at the charge neutrality point in ultra-clean suspended graphene

Strongly coupled Graphene on the Lattice

The two-dimensional carbon allotrope graphene has recently attracted a lot of attention from researchers in the disciplines of Lattice Field Theory, Lattice QCD and Monte Carlo calculations. This interest has been prompted by several remarkable properties of the conduction electrons in graphene. For instance, the conical band structure of graphene at low energies is strongly reminiscent of relativistic Dirac fermions. Also, due the low Fermi velocity of vF ≃ c/300, where c is the speed of light in vacuum, the physics of the conduction electrons in graphene is qualitatively similar to Quantum Electrodynamics in a strongly coupled regime. In turn, this opens up the prospect of the experimental realization of gapped, strongly correlated states in the electronic phase diagram of graphene. Here, we review the experimental and theoretical motivations for Lattice Field Theory studies of graphene, and describe the directions that such research is likely to progress in during the next few years. We also give a brief overview of the two main lattice theories of graphene, the hexagonal Hubbard theory and the low-energy Dirac theory. Finally, we describe the prospect of extracting response functions, such as the electric conductivity, using Lattice Field Theory calculations

The unitary Fermi gas at finite temperature: Momentum distribution and contact

The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD

Momentum distribution and contact of the unitary Fermi gas

We calculate the momentum distribution n(k) of the unitary Fermi gas by using quantum Monte Carlo calculations at finite temperature T/εF as well as in the ground state. At large momenta k/k F, we find that n(k) falls off as C/k4, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/εF and present a comparison with theory. At low T/εF, we find that C increases with temperature, and we tentatively identify a maximum around T/εF0.4. Our calculations are performed on lattices of spatial extent up to Nx=14 with a particle number per unit volume of 0.03-0.07

Graphene: From materials science to particle physics

Since its discovery in 2004, graphene, a two-dimensional hexagonal carbon allotrope, has generated great interest and spurred research activity from materials science to particle physics and vice versa. In particular, graphene has been found to exhibit outstanding electronic and mechanical properties, as well as an unusual low-energy spectrum of Dirac quasiparticles giving rise to a fractional quantum Hall effect when freely suspended and immersed in a magnetic field. One of the most intriguing puzzles of graphene involves the low-temperature conductivity at zero density, a central issue in the design of graphene-based nanoelectronic components. While suspended graphene experiments have shown a trend reminiscent of semiconductors, with rising resistivity at low temperatures, most theories predict a constant or even decreasing resistivity. However, lattice field theory calculations have revealed that suspended graphene is at or near the critical coupling for excitonic gap formation due to strong Coulomb interactions, which suggests a simple and straightforward explanation for the experimental data. In this contribution we review the current status of the field with emphasis on the issue of gap formation, and outline recent progress and future points of contact between condensed matter physics and Lattice QCD