Francesco Knechtli

The strange quark mass and Lambda parameter of two flavor QCD

We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r0 in physical units as well as an improved determination of the renormalization constant ZA.

Non-perturbative quark mass renormalization in two-flavor QCD

Abstract The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O ( a ) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schrodinger functional scheme. Using existing data for the scale r 0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.

Non-perturbative renormalization of the axial current with dynamical Wilson fermions

We present a new normalization condition for the axial current, derived from the PCAC relation with non-vanishing quark mass. This condition is expected to reduce mass effects in the chiral extrapolation of the results for the normalization factor ZA. The application to the two-flavor theory with improved Wilson fermions shows that this expectation is indeed fulfilled. Using the Schrodinger functional setup we calculate ZA(g02) as well as the vector current normalization factor ZV(g02) for β = 6/g02 ≥ 5.2.

Determination of the static potential with dynamical fermions

Abstract We present in detail a technique to extract the potential between a static quark and anti-quark pair from Wilson loops measured on dynamical configurations. This technique is based on HYP smearing and leads to an exponential improvement of the noise-to-signal ratio of Wilson loops. We explain why the correct continuum potential is obtained and show numerical evidence that the cut-off effects are small. We present precise results for the non-perturbative potential. As applications, we determine the scale r 0 / a and study the shape of the static potential in the range of distances around r 0 , where it can be compared with phenomenological potential models.

String breaking in SU(2) gauge theory with scalar matter fields

Abstract We investigate the static potential in the confinement phase of the SU(2) Higgs model on the lattice, where this model is expected to have properties similar to QCD. We observe that Wilson loops are inadequate to determine the potential at large distances, where the formation of two color-neutral mesons is expected. Introducing smeared fields and a suitable matrix correlation function, we are able to overcome this difficulty. We observe string breaking at a distance rb≈1.8r0, where the length scale r0 has a value r 0 ≈0.5 fm in QCD. The method presented here may lead the way towards a treatment of string breaking in QCD.

Simulating the Schrödinger functional with two pseudo-fermions

We report on simulations with two flavors of O(a) improved degenerate Wilson fermions with Schrodinger functional boundary conditions. The algorithm which is used is Hybrid Monte Carlo with two pseudo-fermion fields as proposed by M. Hasenbusch. We investigate the numerical precision and sensitivity to reversibility violations of this algorithm. A gain of a factor two in CPU cost is reached compared with one pseudo-fermion field due to the larger possible step-size.

Locality with staggered fermions

Abstract We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes. A definition of such a theory necessitates an underlying local fermion operator with the same determinant and the corresponding Greens functions to establish causality and unitarity. We illustrate this point by studying analytically and numerically the square root of the staggered fermion operator. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.

On the phase structure of five-dimensional SU(2) gauge theories with anisotropic couplings

Abstract The phase diagram of five-dimensional SU(2) gauge theories is explored using Monte Carlo simulations of the theory discretized on a Euclidean lattice using the Wilson plaquette action and periodic boundary conditions. We simulate anisotropic gauge couplings which correspond to different lattice spacings a 4 in four dimensions and a 5 along the extra dimension. In particular we study the case where a 5 > a 4 . We identify a line of first order phase transitions which separate the confined from the deconfined phase. We perform simulations in large volume at the bulk phase transition staying in the confined vacuum. The static potential measured in the hyperplanes orthogonal to the extra dimension hints at dimensional reduction. We also locate and analyze second order phase transitions related to breaking of the center along one direction.

Nonperturbative definition of five-dimensional gauge theories on the R4×S1/Z2 orbifold

Abstract We construct a Z 2 orbifold projection of SU ( N ) gauge theories formulated in five dimensions with a compact fifth dimension. We show through a nonperturbative argument that no boundary mass term for the Higgs field, identified with some of the fifth-dimensional components of the gauge field, is generated, which would be quadratically divergent in the five-dimensional ultraviolet cutoff. This opens the possibility of studying these theories nonperturbatively in order to establish if they can be used as effective weakly interacting theories at low energies. We make preparations for a study on the lattice. In particular we show that only Dirichlet boundary conditions are needed, which specify the breaking pattern of the gauge group at the orbifold fixpoints.

A new model for confinement

Abstract We propose a new approach towards the understanding of confinement. Starting from an anisotropic five-dimensional pure gauge theory, we approach a second order phase transition where the system reduces dimensionally. Dimensional reduction is realized via localization of the gauge and scalar degrees of freedom on four-dimensional branes. The gauge coupling deriving from the brane Wilson loop observable runs like an asymptotically free coupling at short distance, while it exhibits clear signs of string formation at long distance. The regularization used is the lattice. We take the continuum limit by keeping the ratio of the lattice spacing in the brane over the lattice spacing along the extra dimension constant and smaller than one.