Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSupersymmetric QCD on the Lattice: An Exploratory Study
70
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric ${cal N}{=}1$ QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Greens functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is $SU(N_c)$, while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $alpha$, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant ($Z_g$) and of the quark ($Z_psi$), gluon ($Z_u$), gluino ($Z_lambda$), squark ($Z_{A_pm}$), and ghost ($Z_c$) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.
rate research
Read More
We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4$d$ overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of $am_happrox 0.4$, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range $2.0-5.7,mathrm{GeV}$. We observe very mild $a^2$ scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.
We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric ${cal N}{=}1$ QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Greens functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is $SU(N_c)$, while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $alpha$, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant ($Z_g$) and of the quark ($Z_psi$), gluon ($Z_u$), gluino ($Z_lambda$), squark ($Z_{A_pm}$), and ghost ($Z_c$) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.
We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+topi^+ ubar{ u}$ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.
In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+topi^+ ubar{ u}$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+topi^+ ubar{ u}$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of O(5%) in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the $K^+topi^+ ubar{ u}$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3times32$) and at unphysical pion, kaon and charm quark masses, $m_pi=420$ MeV, $m_K=563$ MeV and $m_c^{overline{mathrm{MS}}}(mbox{2 GeV})=863$ MeV, the techniques presented in this work can readily be applied to a future realistic calculation.
We study the performance of all-mode-averaging (AMA) when used in conjunction with a locally deflated SAP-preconditioned solver, determining how to optimize the local block sizes and number of deflation fields in order to minimize the computational cost for a given level of overall statistical accuracy. We find that AMA enables a reduction of the statistical error on nucleon charges by a factor of around two at the same cost when compared to the standard method. As a demonstration, we compute the axial, scalar and tensor charges of the nucleon in $N_f=2$ lattice QCD with non-perturbatively O(a)-improved Wilson quarks, using O(10,000) measurements to pursue the signal out to source-sink separations of $t_ssim 1.5$ fm. Our results suggest that the axial charge is suffering from a significant amount (5-10%) of excited-state contamination at source-sink separations of up to $t_ssim 1.2$ fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
