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Register a new userRenormalization and Mixing of the Gluino-Glue Operator on the Lattice
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We study the mixing of the Gluino-Glue operator in ${cal N}$=1 Supersymmetric Yang-Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not only multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Greens functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $overline{textrm{MS}}$ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilsons formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $N_c$, the gauge parameter, $beta$, and the clover coefficient, $c_{rm SW}$, are left as free parameters.
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We study the Gluino-Glue operator in the context of Supersymmetric ${cal N}{=}1$ Yang-Mills (SYM) theory. This composite operator is gauge invariant, and it is directly connected to light bound states of the theory; its renormalization is very important as a necessary step for the study of low-lying bound states via numerical simulations. We make use of a Gauge-Invariant Renormalization Scheme (GIRS). This requires the calculation of the Greens function of a product of two Gluino-Glue operators, situated at distinct space-time points. Within this scheme, the mixing with non-gauge invariant operators which have the same quantum numbers is inconsequential. We compute the one-loop conversion factor relating the GIRS scheme to $overline{rm MS}$. This conversion factor can be used in order to convert to $overline{rm MS}$ Greens functions which are obtained via lattice simulations and are renormalized nonperturbatively in GIRS.
The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with $d leq 5$ will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with $d<5$) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Greens functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the $K-pi$ matrix element are being performed in simulations with 4 dynamical ($N_f = 2+1+1$) twisted mass fermions and the Iwasaki improved gluon action.
By introducing an additional operator into the action and using the Feynman-Hellmann theorem we describe a method to determine both the quark line connected and disconnected terms of matrix elements. As an illustration of the method we calculate the gluon contribution (chromo-electric and chromo-magnetic components) to the nucleon mass.
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 study the strangeness contribution to nucleon matrix elements using Nf=2+1 dynamical clover fermion configurations generated by the CP-PACS/JLQCD collaboration. In order to evaluate the disconnected insertion (DI), we use the Z(4) stochastic method, along with unbiased subtraction from the hopping parameter expansion which reduces the off-diagonal noises in the stochastic method. Furthermore, we find that using many nucleon sources for each configuration is effective in improving the signal. Our results for the quark contribution to the first moment <x>_q in the DI, and the strangeness magnetic moment show that the statistical errors are under control with these techniques. We also study the gluonic contribution to the nucleon using the overlap operator to construct the gauge field tensor, F_{mu,nu}. The application to the calculation of first moment, <x>_G, gives a good signal in quenched lattice QCD.
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