Nonperturbative Light-Front QCD

In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum Electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the Constituent Quark Model with the complexities of Quantum Chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses, which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.Comment: 56 pages (REVTEX), Report OSU-NT-94-28. (figures not included, available via anaonymous ftp from pacific.mps.ohio-state.edu in subdirectory pub/infolight/qcd

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding $10^{10}$ on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to $N_\mathrm{max} = 22$ and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.Comment: Minor revisions.Accepted for publication in Physical Review

Pion-less effective field theory for atomic nuclei and lattice nuclei

We compute the medium-mass nuclei $^{16}$O and $^{40}$Ca using pionless effective field theory (EFT) at next-to-leading order (NLO). The low-energy coefficients of the EFT Hamiltonian are adjusted to experimantal data for nuclei with mass numbers $A=2$ and $3$, or alternatively to results from lattice quantum chromodynamics (QCD) at an unphysical pion mass of 806 MeV. The EFT is implemented through a discrete variable representation in the harmonic oscillator basis. This approach ensures rapid convergence with respect to the size of the model space and facilitates the computation of medium-mass nuclei. At NLO the nuclei $^{16}$O and $^{40}$Ca are bound with respect to decay into alpha particles. Binding energies per nucleon are 9-10 MeV and 30-40 MeV at pion masses of 140 MeV and 806 MeV, respectively.Comment: 26 page

The Zero-Bin and Mode Factorization in Quantum Field Theory

We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In non-relativistic field theories, the subtractions remove unphysical pinch singularities in box type diagrams, and give a derivation of the known pull-up mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formul\ae occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays.Comment: 92 pages, v4- Journal version. Some improvements to language in sections I, IIA, VI

A Consistency Test of EFT Power Countings from Residual Cutoff Dependence

A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented. The Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the breakdown scale of an EFT, on the low-momentum scales, and on the order of the calculation. Passing this test is a necessary but not sufficient consistency criterion for a suggested power counting whose exact nature is disputed. In Chiral Effective Field Theory (ChiEFT) with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the convergence pattern in results. This led to proposals which predict different sets of Low Energy Coefficients (LECs) at the same chiral order, and at times even predict a different ordering long-range contributions. The method may independently check whether an observable is renormalised at a given order, and proves estimates of both the breakdown scale and the momentum-dependent order-by-order convergence pattern. Conversely, it helps identify those LECs (and long-range pieces) which ensure renormalised observables at a given order. I also discuss assumptions and the relation to Wilson's Renormalisation Group; useful observable and cutoff choices; the momentum window with likely best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting LECs to data; and caveats as well as limitations. Since the test is designed to minimise the use of data, it quantitatively falsifies if the EFT has been renormalised consistently. This complements other tests which quantify how an EFT compares to experiment. Its application in particular to the 3P0 and P2-3F2 partial waves of NN scattering in ChiEFT may elucidate persistent power-counting issues.Comment: 15 pages LaTeX2e (pdflatex) including 5 figures as .pdf files using includegraphics. Final version to appear in Europ. J. Phys. A topical issue "The Tower of Effective (Field) Theories and the Emergence of Nuclear Phenomena". arXiv admin note: substantial text overlap with arXiv:1511.00490 Author's note: substantial corrections in key argument and expansions. Version appearing in Eur Phys J

Light-Front QCD and the Constituent Quark Model

A general strategy is described for deriving a constituent approximation to QCD, inspired by the constituent quark model and based on light-front quantization. Some technical aspects of the approach are discussed, including a mechanism for obtaining a confining potential and ways in which spontaneous chiral symmetry breaking can be manifested. (Based on a talk presented by K.G. Wilson at ``Theory of Hadrons and Light-Front QCD,'' Polana Zgorzelisko, Poland, August 1994.)Comment: 14 pages, LaTeX, no figure

Diffusion and Decoherence of Squarks and Quarks During the Electroweak Phase Transition

To estimate the diffusion constant $D$ of particles in a plasma, we develop a method that is based on the mean free path $\lambda$ for scatterings with momentum transfer $q >~ T$. Using this method, we estimate $\lambda$ and $D$ for squarks and quarks during the electroweak phase transition. Assuming that Debye and magnetic screening lengths provide suitable infrared cutoffs, our calculations yield $\lambda <~ 18/T$ and $D <~ 5/T$ for both squarks and quarks. Our estimate of $\lambda$ suggests that suppressions of charge transport due to decoherence of these strongly interacting particles during the electroweak phase transition are not severe and that these particles may contribute significantly to electroweak baryogenesis.Comment: 11 pages. Expanded discussion of our method and approximations, reference adde