Lattice QCD study analyzes key systematics in inclusive B_s to X_c l nu decays and isolates excited-state contributions by treating ground states exclusively to reduce uncertainties.
The M\"obius Domain Wall Fermion Algorithm
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abstract
We present a review of the properties of generalized domain wall Fermions, based on a (real) M\"obius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass ($m_{res}$) and the Ward-Takahashi identities. The M\"obius class interpolates between Shamir's domain wall operator and Bori\c{c}i's domain wall implementation of Neuberger's overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter ($\alpha$) reduces chiral violations at finite fifth dimension ($L_s$) but yields exactly the same overlap action in the limit $L_s \rightarrow \infty$. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling $\alpha(L_s)$, we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed $L_s$. At large $L_s$ we argue that the observed scaling for $m_{res} = O(1/L_s)$ for Shamir is replaced by $m_{res} = O(1/L_s^2)$ for the properly tuned M\"obius algorithm with $\alpha = O(L_s)$
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UNVERDICTED 9representative citing papers
Extended lattice simulations yield continuum-limit anomalous dimensions γ* = 0.170(6) for Nf=1 and γ* = 0.291(9) for Nf=2 adjoint SU(2), with chiral perturbation theory ruling out spontaneous chiral symmetry breaking.
New four-flavor smeared Möbius Domain Wall Fermion ensembles yield F_K/F_pi = 1.1962(34) as a precision test for inexpensive chiral fermion calculations in lattice QCD.
Lattice QCD yields the Ds to Xs l nu inclusive decay rate in agreement with experiment after full chiral and continuum extrapolations, with few-percent total uncertainty.
Lattice simulations with Möbius domain-wall fermions find the three-flavor QCD transition at mu_B=0 is a continuous crossover at pseudocritical quark masses of 184(10) MeV (Nt=6), 36-39 MeV (Nt=8), and 3.5-3.7 MeV (Nt=12) in the MSbar scheme.
Lattice simulations with Möbius domain-wall fermions find that conserved charge fluctuations in (2+1)-flavor QCD match hadron resonance gas predictions below the pseudocritical temperature and rise toward free-quark limits above it.
Lattice QCD finds evidence for effective U(1)_A symmetry restoration at 319(22) MeV, well above the chiral crossover.
Domain wall fermions recover exact chiral symmetry in the infinite fifth dimension limit and produce an effective four-dimensional operator satisfying the Ginsparg-Wilson relation.
Lecture notes on lattice methods for formal TASI students covering basics, confinement, chiral fermions, and case studies in the 3D Ising model and QCD.
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