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T. Blum

Publications and source records attributed to T. Blum.

At least 73 records · Page 4Linked to original sources
arXiv2001

Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions

In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath, {\it et al.} we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, $β=6.0$, larger lattices, $16^4$, and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitude of the chirality density, $|ψ^\dagger(x)γ^5ψ(x)|$, and the normal density, $ψ^\dagger(x)ψ(x)$, for the low-lying Dirac eigenvectors.

hep-lat↗
arXiv2001

Non-perturbative Renormalisation of Domain Wall Fermions: Quark Bilinears

We find the renormalisation coefficients of the quark field and the flavour non-singlet fermion bilinear operators for the domain wall fermion action, in the regularisation independent (RI) renormalisation scheme. Our results are from a quenched simulation, on a 16^3x32 lattice, with beta=6.0 and an extent in the fifth dimension of 16. We also discuss the expected effects of the residual chiral symmetry breaking inherent in a domain wall fermion simulation with a finite fifth dimension, and study the evidence for both explicit and spontaneous chiral symmetry breaking effects in our numerical results. We find that the relations between different renormalisation factors predicted by chiral symmetry are, to a good approximation, satisfied by our results and that systematic effects due to the (low energy) spontaneous chiral symmetry breaking and zero-modes can be controlled. Our results are compared against the perturbative predictions for both their absolute value and renormalisation scale dependence.

hep-lat↗
arXiv2000

$K\toππ$ Decays with Domain Wall Fermions: Lattice Matrix Elements

We present a lattice calculation of the $K\toπ$ and $K\to 0$ matrix elements of the $ΔS=1$ effective weak Hamiltonian which can be used to determine $ε^\prime/ε$ and the $ΔI=1/2$ rule for $K$ decays in the Standard Model. The matrix elements for $K\toππ$ decays are related to $K\toπ$ and $K\to 0$ using lowest order chiral perturbation theory. We also present results for the kaon $B$ parameter, $B_K$. Our quenched domain wall fermion simulation was done at $β=6.0$ ($a^{-1}\approx 2$ GeV), lattice size $16^3\times 32\times 16$, and domain wall height $M_5=1.8$.

hep-lat↗
arXiv2000

Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit

Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and $16^3 \times 32$ and three couplings, $β=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass ($\mres$) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings much larger values of $L_s$ are required to achieve a given physical value of $\mres$. For $β=6.0$ and $L_s=16$, we find $\mres/m_s=0.033(3)$, while for $β=5.7$, and $L_s=48$, $\mres/m_s=0.074(5)$, where $m_s$ is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of $m_π^2$ in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in $f_π$ over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.

hep-lat↗
arXiv2000

Polarized structure functions from the lattice

We give a brief sketch of lattice structure function calculations and review previous results for the axial coupling $g_A$. We outline a new technique for treating fermions on the lattice that preserves chiral symmetry, domain wall fermions. Finally, we give preliminary results for the nucleon spectrum using this new technique. Remarkably, a large mass splitting between the $N$ and $N^*$, roughly consistent with experiment, is produced in the calculation. These results are encouraging for proposed calculations of nucleon structure functions.

hep-lat↗
arXiv1999

Resonant Processes in a Frozen Gas

We present a theory of resonant processes in a frozen gas of atoms interacting via dipole-dipole potentials that vary as $r^{-3}$, where $r$ is the interatomic separation. We supply an exact result for a single atom in a given state interacting resonantly with a random gas of atoms in a different state. The time development of the transition process is calculated both on- and off-resonance, and the linewidth with respect to detuning is obtained as a function of time $t$. We introduce a random spin Hamiltonian to model a dense system of resonators and show how it reduces to the previous model in the limit of a sparse system. We derive approximate equations for the average effective spin, and we use them to model the behavior seen in the experiments of Anderson et al. and Lowell et al. The approach to equilibrium is found to be proportional to $\exp (-\sqrt{γ_{eq}t}$), where the constant $γ_{eq}$ is explicitly related to the system's parameters.

cond-mat.dis-nn↗
arXiv1998

Domain wall fermions in vector gauge theories

I review domain wall fermions in vector gauge theories. Following a brief introduction, the status of lattice calculations using domain wall fermions is presented. I focus on results from QCD, including the light quark masses and spectrum, weak matrix elements, the $n_f=2$ finite temperature phase transition, and topology and zero modes and conclude with topics for future study.

hep-lat↗
arXiv1998

SU(3) Flavor Breaking in Hadronic Matrix Elements for $B - \bar B$ Oscillations

Results in the quenched approximation for SU(3) breaking ratios of the heavy-light decay constants and the $ΔF=2$ mixing matrix elements are reported. Using lattice simulations at $6/g^2=5.7$, 5.85, 6.0, and 6.3, we directly compute the mixing matrix element $M_{hl}=< \bar P_{hl}|\bar h γ_μ(1-γ_5)l \bar h γ_μ(1-γ_5)l|P_{hl}>$. Extrapolating to the physical B meson states, $B^0$ and $B_s^0$, we obtain $M_{bs}/M_{bd} =1.76(10)^{+57}_{-42}$. in the continuum limit. The systematic error includes the errors within the quenched approximation but not the errors of quenching. We also obtain the ratio of decay constants, $f_{bs}/f_{bd}=1.17(2)^{+12}_{-6}$. For the B parameters we find $B_{bs}(2 GeV)=B_{bd}(2 GeV)=1.02(13)$; we cannot resolve the SU(3) breaking effects in this case.

hep-lat↗
arXiv1997

Update on lattice QCD with domain wall quarks

Using domain wall fermions, we estimate B_K(mu approx 2 GeV)=0.602(38) in quenched QCD which is consistent with previous calculations. We also find ratios of decay constants that are consistent with experiment, within our statistical errors. Our initial results indicate good scaling behavior and support expectations that O(a) errors are exponentially suppressed in low energy (E<< a^{-1}) observables. It is also shown that the axial current numerically satisfies the lattice analog of the usual continuum axial Ward identity and that the matrix element of the four quark operator needed for B_K exhibits excellent chiral behavior.

hep-lat↗
arXiv1997

QCD with domain wall quarks

We present lattice calculations in QCD using a variant of Kaplan fermions which retain the continuum SU(N)xSU(N) chiral symmetry on the lattice in the limit of an infinite extra dimension. In particular, we show that the pion mass and the four quark matrix element related to K_0-K_0-bar mixing have the expected behavior in the chiral limit, even on lattices with modest extent in the extra dimension, e.g. N_s=10.

hep-lat↗
arXiv1997

Domain wall quarks and kaon weak matrix elements

We present lattice calculations of kaon matrix elements with domain wall fermions. Using lattices with beta=5.85, 6.0, and 6.3, we estimate B_K(approx 2 GeV)=0.628(47) in quenched QCD which is consistent with previous calculations. At beta=6.0 and 5.85 we find the ratio f_K/m_rho in agreement with the experimental value, within errors. These results support expectations that O(a) errors are exponentially suppressed in low energy (E<< a^{-1}) observables, and indicate that domain wall fermions have good scaling behavior at relatively strong couplings. We also demonstrate that the axial current numerically satisfies the lattice analog of the usual continuum axial Ward identity.

hep-lat↗
arXiv1997

Update on the hadron spectrum with two flavors of staggered quarks

We present an update on the MILC Collaboration's light hadron spectrum calculation with two flavors of dynamical, staggered quarks. We present extrapolations of the nucleon to rho mass ratio to the continuum limit for fixed values of the pi to rho mass ratio including the physical one.

hep-lat↗
arXiv1997

Lattice QCD with domain wall quarks and applications to weak matrix elements

Using domain wall fermions, we estimate $B_K(μ\approx 2 GeV)=0.628(47)$ in quenched QCD which is consistent with previous calculations. At $\gbeta=6.0$ and 5.85 we find the ratio $f_K/m_ρ$ in agreement with the experimental value, within errors. These results support expectations that $O(a)$ errors are exponentially suppressed in low energy ($E\ll a^{-1}$) observables, and indicate that domain wall fermions have good scaling behavior at relatively strong couplings. We also demonstrate that the axial current numerically satisfies the lattice analog of the usual continuum axial Ward identity.

hep-lat↗
arXiv1997

Critical Behavior at the Chiral Phase Transition

Quantum chromodynamics with two zero mass flavors is expected to exhibit a phase transition with O(4) critical behavior. Fixing the universality class is important for phenomenology and for facilitating the extrapolation of simulation data to physical quark mass values. At Lattice '96 the Tsukuba and Bielefeld groups reported results from new simulations with dynamical staggered quarks at $N_t = 4$, which suggested a departure from the expected critical behavior. We report observations of similar deviations and discuss efforts in progress to understand this phenomenon.

hep-lat↗
arXiv1997

A study of nonlocal conductivity in high-temperature superconductors

We examine nonlocal conductivity in high-temperature superconductors from a phenomenological point of view. One wants to deduce the properties of the conductivity, especially its inherent length scales, from the transport data. Although this is a challenging inverse problem, complicated further by the experimental data not being completely self-consistent, we have made some progress. We find that if a certain form for the conductivity is postulated then one requires positive "viscosity" coefficients to reproduce some of the experimental results. We are able to show that the effects of surfaces on the conductivity are likely to be important and draw comparisons with the treatment of the surface within the hydrodynamic approach put forth by Huse and Majumdar. We also develop an approximation scheme for the conductivity which is more robust than the hydrodynamic one, since it is stable for both positive and negative viscosity coefficients, and discuss the results obtained using it.

cond-mat.supr-con↗
arXiv1997

B Mixing on the Lattice: $f_B$, $f_{B_s}$ and Related Quantities

The MILC collaboration computation of heavy-light decay constants is described. Results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios are presented. These results are still preliminary, but the analysis is close to being completed. Sources of systematic error, both within the quenched approximation and from quenching itself, are estimated, although the latter estimate is rather crude. A sample of our results is: $f_B=153 \pm 10 {}^{+36}_{-13} {}^{+13}_{-0} MeV$, $f_{B_s}/f_B = 1.10 \pm 0.02 {}^{+0.05}_{-0.03} {}^{+0.03}_{-0.02}$, and $f_{B}/f_{D_s} = 0.76 \pm 0.03 {}^{+0.07}_{-0.04} {}^{+0.02}_{-0.01}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively. The largest source of error comes from the extrapolation to the continuum. The second largest source is the chiral extrapolation. At present, the central values are based on linear chiral extrapolations; a shift to quadratic extrapolations would for example raise $f_B$ by $\approx 20$ MeV and thereby make the error within the quenched approximation more symmetric.

hep-ph↗