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We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the presence of a merging phenomenon between non-trivial fixed points for which the a theorem has not been tested so far.
We consider the leading-order expression at weak-coupling for a single-site large-N gauge theory coupled to adjoint fermions. We study the case of overlap and wilson fermions. We extend the theory to real values of the number of fermion flavors and restrict ourselves to asymptotically free theories. Using a four-dimensional density function for the distribution of the eigenvalues of the link variables, we show that it is possible to recover the infinite-volume continuum limit for a certain range of fermion flavors if we use fermions with a bare mass of zero. Our use of the four-dimensional density function is supported by a direct analysis of the lattice action.
In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.
Composite dark matter candidates, which can arise from new strongly-coupled sectors, are well-motivated and phenomenologically interesting, particularly in the context of asymmetric generation of the relic density. In this work, we employ lattice calculations to study the electromagnetic form factors of electroweak-neutral dark-matter baryons for a three-color, QCD-like theory with Nf = 2 and 6 degenerate fermions in the fundamental representation. We calculate the (connected) charge radius and anomalous magnetic moment, both of which can play a significant role for direct detection of composite dark matter. We find minimal Nf dependence in these quantities. We generate mass-dependent cross-sections for dark matter-nucleon interactions and use them in conjunction with experimental results from XENON100, excluding dark matter candidates of this type with masses below 10 TeV.
Lattice simulations for the electromagnetic form factors of the nucleon yield insights into the internal structure of hadrons. The logarithmic divergence of the charge radius in the chiral limit poses an interesting challenge in achieving reliable predictions from finite-volume lattice simulations. Recent results near the physical pion mass are examined in order to confront the issue of how the chiral regime is approached. The electric charge radius of the nucleon presents a forum for achieving consistent finite-volume corrections. Newly-developed techniques within the framework of chiral effective field theory are used to achieve a robust extrapolation of the electric charge radius to the physical pion mass, and to infinite volume. The chiral extrapolations exhibit considerable finite-volume dependence; lattice box sizes of L > 7 fm are required in order to achieve a direct lattice simulation result within 2% of the infinite-volume value at the physical point. Predictions of the volume-dependence are provided to guide the interpretation of future lattice results.
We present a lattice QCD calculation of form factors for the decay $Λ_b \to p μ^- \barν$, which is a promising channel for determining the CKM matrix element $|V_{ub}|$ at the Large Hadron Collider. In this initial study we work in the limit of static b quarks, where the number of independent form factors reduces to two. We use dynamical domain-wall fermions for the light quarks, and perform the calculation at two different lattice spacings and at multiple values of the light-quark masses in a single large volume. Using our form factor results, we calculate the $Λ_b \to p μ^- \barν$ differential decay rate in the range $14 GeV^2 \leq q^2 \leq q^2_{max}$, and obtain the integral $\int_{14 GeV^2}^{q^2_{max}} [dΓ/dq^2] dq^2 / |V_{ub}|^2 = 15.3 \pm 4.2 ps^{-1}$. Combined with future experimental data, this will give a novel determination of $|V_{ub}|$ with about 15\% theoretical uncertainty. The uncertainty is dominated by the use of the static approximation for the b quark, and can be reduced further by performing the lattice calculation with a more sophisticated heavy-quark action.
We extract the next-to-leading-order low-energy constants \bar\ell_3 and \bar\ell_4 of SU(2) chiral perturbation theory, based on precise lattice data for the pion mass and decay constant on ensembles generated by the Wuppertal-Budapest Collaboration for QCD thermodynamics. These ensembles feature 2+1 flavors of two-fold stout-smeared dynamical staggered fermions combined with Symanzik glue, with pion masses varying from 135 to 435 MeV, lattice scales between 0.7 and 2.0 GeV, while m_s is kept fixed at its physical value. Moderate taste splittings and the scale being set through the pion decay constant allow us to restrict ourselves to the taste pseudoscalar state and to use formulas from continuum chiral perturbation theory. Finally, by dropping the data points near 135 MeV from the fits, we can explore the range of pion masses that is needed in SU(2) chiral perturbation theory to reliably extrapolate to the physical point.
We investigate differences and similarities between fundamental fermions and adjoint fermions in SU(N) gauge theories. The gauge theory with fundamental fermions possesses ZN symmetry only in the limit of infinite fermion mass, whereas the gauge theory with adjoint fermions does have the symmetry for any fermion mass. The flavor-dependent twisted boundary condition (FTBC) is then imposed on fundamental fermions so that the theory with fundamental fermions can possess ZN symmetry for any fermion mass. We show similarities between FTBC fundamental fermions and adjoint fermions, using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. In the mean-field level, the PNJL model with FTBC fundamental fermions has dynamics similar to the PNJL model with adjoint fermions for the confinement/deconfinement transition related to ZN symmetry. The chiral property is somewhat different between the two models, but there is a simple relation between chiral condensates in the two models. As an interesting high-energy phenomenon, a possibility of the gauge symmetry breaking is studied for FTBC fundamental fermions.
Motivated by the search for new observables in nonperturbative quantum gravity, we consider Causal Dynamical Triangulations (CDT) in 2+1 dimensions with the spatial topology of a torus. This system is of particular interest, because one can study not only the global scale factor, but also global shape variables in the presence of arbitrary quantum fluctuations of the geometry. Our initial investigation focusses on the dynamics of the scale factor and uncovers a qualitatively new behaviour, which leads us to investigate a novel type of boundary conditions for the path integral. Comparing large-scale features of the emergent quantum geometry in numerical simulations with a classical minisuperspace formulation, we find partial agreement. By measuring the correlation matrix of volume fluctuations we succeed in reconstructing the effective action for the scale factor directly from the simulation data. Apart from setting the stage for the analysis of shape dynamics on the torus, the new set-up highlights the role of nontrivial boundaries and topology.
We investigate the critical properties of the two-dimensional Z(5) vector model. For this purpose, we propose a new cluster algorithm, valid for Z(N) models with odd values of N. The two-dimensional Z(5) vector model is conjectured to exhibit two phase transitions with a massless intermediate phase. We locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices and compare the results with analytical predictions.
We investigate both analytically and numerically the renormalization group equations in 2D Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index ν is computed. For N=7, 17 the critical points are located by Monte Carlo simulations and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.
We present a reliable nonperturbative calculation of the QCD correction, at leading order in the electromagnetic coupling, to the anomalous magnetic moment of the electron, muon, and tau leptons using two-flavor lattice QCD. We use multiple lattice spacings, multiple volumes, and a broad range of quark masses to control the continuum, infinite-volume, and chiral limits. We examine the impact of the commonly ignored disconnected diagrams and introduce a modification to the previously used method that results in a well-controlled lattice calculation. We obtain 1.513(43) 10^(-12), 5.72(16) 10^(-8), and 2.650(54) 10^(-6) for the leading-order two-flavor QCD correction to the anomalous magnetic moment of the electron, muon, and tau, respectively, each accurate to better than 3%.
I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional negative adjoint plaquette term that lessens this problem. I also introduce a new analysis method for the 2-lattice matching Monte Carlo renormalization group technique that significantly reduces finite volume effects. The combination of these two improvements allows me to measure the bare step scaling function in a region of the gauge coupling where it is clearly negative, indicating a positive renormalization group $β$ function and infrared conformality.
Using methods of numerical Lattice Gauge Theory we show that in the limit of a large number of colors, properly regularized Wilson loops have an eigenvalue distribution which changes non-analytically as the overall size of the loop is increased. This establishes a large-N phase transition in continuum planar gauge theory, a fact whose precise implications remain to be worked out.
We present a light-front determination of the pionic contribution to the nucleon self-energy, $Σ_π$, to second-order in pion-baryon coupling constants that allows the pion-nucleon vertex function to be treated in a model-independent manner constrained by experiment. The pion mass $μ$ dependence of $Σ_π$ is consistent with chiral perturbation theory results for small values of $μ$ and is also linearly dependent on $μ$ for larger values, in accord with the results of lattice QCD calculations. The derivative of $Σ_π$ with respect to $μ^2$ yields the dominant contribution to the pion content, which is consistent with the $\bar{d}-\bar{u}$ difference observed experimentally in the violation of the Gottfried sum rule.
The semileptonic decay channel B -> D tau nu is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently the BaBar experiment reported the first observation of the exclusive semileptonic decay B -> D tau nu, finding an approximately 2-sigma disagreement with the Standard-Model prediction for the ratio R(D)=BR(B->D tau nu)/BR(B->D l nu), where l=e,mu. We compute this ratio of branching fractions using hadronic form factors computed in unquenched lattice QCD and obtain R(D) = 0.316(12)(7), where the errors are statistical and total systematic, respectively. This result is the first Standard-Model calculation of R(D) from ab initio full QCD. Its error is smaller than that of previous estimates, primarily due to the reduced uncertainty in the scalar form factor f_0(q^2). Our determination of R(D) is approximately 1-sigma higher than previous estimates and, thus, reduces the tension with experiment. We also compute R(D) in models with electrically charged scalar exchange, such as the type II two-Higgs doublet model. Once again, our result is consistent with, but approximately 1-sigma higher than, previous estimates for phenomenologically relevant values of the scalar coupling in the type II model. As a byproduct of our calculation, we also present the Standard-Model prediction for the longitudinal polarization ratio P_L (D)= 0.325(4)(3).
We perform non-perturbative calculation of the π^0 to γγ transition form factor and the associated decay width using lattice QCD. The amplitude for two-photon final state, which is not an eigenstate of QCD, is extracted through an Euclidean time integral of the relevant three-point function. We utilize the all-to-all quark propagator technique to carry out this integral as well as to include the disconnected quark diagram contributions. The overlap fermion formulation is employed on the lattice to ensure exact chiral symmetry on the lattice. After examining various sources of systematic effects except for possible discretization effect, we obtain Γ=7.83(31)(49) eV for the pion decay width, where the first error is statistical and the second is our estimate of the systematic error.
We use Monte Carlo methods to study spinons in two-dimensional quantum spin systems, characterizing their intrinsic size $λ$ and confinement length $Λ$. We confirm that spinons are deconfined, $Λ\to \infty$ and $λ$ finite, in a resonating valence-bond spin-liquid state. In a valence-bond solid, we find finite $λ$ and $Λ$, with $λ$ of a single spinon significantly larger than the bound-state---the spinon is soft and shrinks as the bound state is formed. Both $λ$ and $Λ$ diverge upon approaching the critical point separating valence-bond solid and Néel ground states. We conclude that the spinon deconfinement is marginal in the lowest-energy state in the spin-1 sector, due to weak attractive spinon interactions. Deconfinement in the vicinity of the critical point should occur at higher energies.