arXiv subjects

M. B. Oktay

Publications and source records attributed to M. B. Oktay.

48 records · Page 3Linked to original sources

arXiv2004

Semileptonic D->pi/K and B->pi/D decays in 2+1 flavor lattice QCD

We present results for form factors of semileptonic decays of $D$ and $B$ mesons in 2+1 flavor lattice QCD using the MILC gauge configurations. With an improved staggered action for light quarks, we successfully reduce the systematic error from the chiral extrapolation. The results for $D$ decays are in agreement with experimental ones. The results for B decays are preliminary. Combining our results with experimental branching ratios, we then obtain the CKM matrix elements $|V_{cd}|$, $|V_{cs}|$, $|V_{cb}|$ and $|V_{ub}|$. We also check CKM unitarity, for the first time, using only lattice QCD as the theoretical input.

hep-lat↗

arXiv2004

Semileptonic decays of $D$ mesons in three-flavor lattice QCD

We present the first three-flavor lattice QCD calculations for $D\to πlν$ and $D\to K lν$ semileptonic decays. Simulations are carried out using ensembles of unquenched gauge fields generated by the MILC collaboration. With an improved staggered action for light quarks, we are able to simulate at light quark masses down to 1/8 of the strange mass. Consequently, the systematic error from the chiral extrapolation is much smaller than in previous calculations with Wilson-type light quarks. Our results for the form factors at $q^2=0$ are $f_+^{D\toπ}(0)=0.64(3)(6)$ and $f_+^{D\to K}(0) = 0.73(3)(7)$, where the first error is statistical and the second is systematic, added in quadrature. Combining our results with experimental branching ratios, we obtain the CKM matrix elements $|V_{cd}|=0.239(10)(24)(20)$ and $|V_{cs}|=0.969(39)(94)(24)$, where the last errors are from experimental uncertainties.

hep-ph↗

arXiv2004

Universality in nontrivial continuum limits: a model calculation

We study numerically the continuum limit corresponding to the non-trivial fixed point of Dyson's hierarchical model. We discuss the possibility of using the critical amplitudes as input parameters. We determine numerically the leading and subleading critical amplitudes of the zero-momentum $2l$-point functions in the symmetric phase up to l=10 for randomly chosen local measures. In the infinite cutoff limit, the dimensionless renormalized coupling constants are in very good approximation universal (independent of the choice of the local measure). In addition, ratios of subleading amplitudes also appear to be universal. If we neglect very small log-periodic corrections, the non-universal features of the 2l-point functions appear to depend only the non-universal features of the 2-point function. We infer that when 2l becomes large, the dimensionless renormalized couplings grow as (2l)! despite the non-perturbative nature of our calculation, while the universal ratios of subleading amplitudes grow linearly.

hep-th↗

arXiv2003

A More Improved Lattice Action for Heavy Quarks

We extend the Fermilab formalism for heavy quarks to develop a more improved action. We give results of matching calculations of the improvement couplings at tree level. Finally, we estimate the discretization errors associated with the new action.

hep-lat↗

arXiv2002

A Relativistic $O(a^2)$ Improved Action for Heavy Quarks

We extend the Fermilab formalism for heavy quarks to develop an $O(a^2)$ improved relativistic action. We discuss our construction of the action, including the identification of redundant operators and the calculation of the improvement coefficients.

hep-lat↗

arXiv2000

Testing perturbative results with non-perturbative methods for the Hierarchical model

We present non-perturbative methods to calculate accurately the renormalized quantities for Dyson's Hierarchical Model. We apply this method and calculate the critical exponent gamma with 12 and 4 significant digits in the high and low temperature phases, respectively. We report accurate values for universal ratios of amplitudes and preliminary results concerning the comparison with perturbative results.

hep-lat↗

arXiv2000

Non-Gaussian numerical errors versus mass hierarchy

We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function (magnetic susceptibility). The actual calculations were performed with Dyson's hierarchical model and a simplified version of it. We compare the distributions of numerical values obtained from a large sample of rescaling factors with the (Gaussian by design) distribution of a random number generator and find significant departures from the Gaussian behavior. In addition, the average value differ (robustly) from the exact answer by a quantity which is of the same order as the standard deviation. We provide a simple model in which the errors made at shorter distance have a larger weight than those made at larger distance. This model explains in part the non-Gaussian features and why the central-limit theorem does not apply.

hep-lat↗

arXiv1999

Hyperscaling in the Broken Symmetry Phase of Dyson's Hierarchical Model

We use polynomial truncations of the Fourier transform of the local measure to calculate the connected q-point functions of Dyson's hierarchical model in the broken symmetry phase. We show that accurate values of the connected 1, 2 and 3 point functions can be obtained at large volume and in a limited range of constant external field coupled linearly to the field variable. We introduce a new method to obtain the correct infinite volume and zero external field extrapolations. We extract the leading critical exponents and show that they obey the scaling and hyperscaling relations with an accuracy ranging from 10^-5 to 5 10^-3. We briefly discuss how to improve the method of calculation.

hep-lat↗

arXiv1999

Symmetry Breaking, Duality and Fine-Tuning in Hierarchical Spin Models

We discuss three questions related to the critical behavior of hierarchical spin models: 1) the hyperscaling relations in the broken symmetry phase; 2) the combined use of dual expansions to calculate the non-universal quantities; 3) the fine-tuning issue in approximately supersymmetric models.

hep-lat↗

arXiv1998

High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.

hep-lat↗

arXiv1998

Accurate Checks of Universality for Dyson's Hierarchical Model

Using recently developed methods, we perform high-accuracy calculations of the susceptibility near beta_c for the D=3 version of Dyson's hierarchical model. Using linear fits, we estimate the leading gamma and subleading Delta exponents. Independent estimates are obtained by calculating the first two eigenvalues of the linearized renormalization group transformation. We found gamma = 1.29914073 (with an estimated error of 10^{-8}) and, Delta=0.4259469 (with an estimated error of 10^{-7}) independently of the choice of local integration measure (Ising or Landau-Ginzburg). After a suitable rescaling, the approximate fixed points for a large class of local measure coincide accurately with a fixed point constructed by Koch and Wittwer.

hep-lat↗

arXiv1997

A Guide to Precision Calculations in Dyson's Hierarchical Scalar Field Theory

The goal of this article is to provide a practical method to calculate, in a scalar theory, accurate numerical values of the renormalized quantities which could be used to test any kind of approximate calculation. We use finite truncations of the Fourier transform of the recursion formula for Dyson's hierarchical model in the symmetric phase to perform high-precision calculations of the unsubtracted Green's functions at zero momentum in dimension 3, 4, and 5. We use the well-known correspondence between statistical mechanics and field theory in which the large cut-off limit is obtained by letting beta reach a critical value beta_c (with up to 16 significant digits in our actual calculations). We show that the round-off errors on the magnetic susceptibility grow like (beta_c -beta)^{-1} near criticality. We show that the systematic errors (finite truncations and volume) can be controlled with an exponential precision and reduced to a level lower than the numerical errors. We justify the use of the truncation for calculations of the high-temperature expansion. We calculate the dimensionless renormalized coupling constant corresponding to the 4-point function and show that when beta -> beta_c, this quantity tends to a fixed value which can be determined accurately when D=3 (hyperscaling holds), and goes to zero like (Ln(beta_c -beta))^{-1} when D=4.

hep-lat↗