arXiv subjects

Norman Christ

Publications and source records attributed to Norman Christ.

33 records · Page 2Linked to original sources

arXiv2017

Testing algorithms for critical slowing down

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

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arXiv2017

Using infinite volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g - 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD collaboration. However, the calculation is expected to suffer from a significant finite volume error that scales like $1/L^2$ where $L$ is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite volume, continuum QED, resulting in a weighting function that is pre-computed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite volume effects arising from the hadronic part of the amplitude.

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arXiv2016

The connected and leading disconnected diagrams of the hadronic light-by-light contribution to muon $g - 2$

We report our recent lattice calculation of hadronic light-by-light contribution to muon $g-2$ using our recently developed moment method. The connected diagrams and the leading disconnected diagrams are included. The calculation is performed on a $48^3 \times 96$ lattice with physical pion mass and 5.5 fm box size. We expect sizable finite volume and finite lattice spacing corrections to the results of these calculations which will be estimated in calculations to be carried out over the next 1-2 years.

hep-lat↗

arXiv2016

Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass

We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the $48^3 \times 96$ ensemble generated with a physical-pion-mass and a 5.5 fm spatial extent by the RBC and UKQCD collaborations using the chiral, domain wall fermion (DWF) formulation. We find $a_μ^{\text{HLbL}} = 5.35 (1.35) \times 10^{- 10}$, where the error is statistical only. The finite-volume and finite lattice-spacing errors could be quite large and are the subject of on-going research. The omitted disconnected graphs, while expected to give a correction of order 10\%, also need to be computed.

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arXiv2016

Long distance contributions to the rare kaon decay $K\toπ\ell^{+}\ell^{-}$

The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. To discern such New Physics one must be able to control the errors on the Standard Model prediction of the decay amplitude. These particular decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long distance contributions to these rare decay amplitudes using lattice QCD, and present the numerical results of some exploratory studies using the Domain Wall Fermion ensembles of the RBC and UKQCD collaborations.

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arXiv2015

On calculating disconnected-type hadronic light-by-light scattering diagrams from lattice QCD

For reliable comparison of the standard model prediction to the muon g-2 with its experimental value, the hadronic light-by-light scattering (HLbL) contribution must be calculated by lattice QCD simulation. HLbL contribution has many types of disconnected-type diagrams. Here, we start with recalling the point that must be taken care of in every method to calculate them by lattice QCD, and present one concrete method called nonperturbative QED method.

hep-lat↗

arXiv2015

Hadronic Light by Light Contributions to the Muon Anomalous Magnetic Moment With Physical Pions

The current measurement of muonic $g - 2$ disagrees with the theoretical calculation by about 3 standard deviations. Hadronic vacuum polarization (HVP) and hadronic light by light (HLbL) are the two types of processes that contribute most to the theoretical uncertainty. The current value for HLbL is still given by models. I will describe results from a first-principles lattice calculation with a 139 MeV pion in a box of 5.5 fm extent. Our current numerical strategies, including noise reduction techniques, evaluating the HLbL amplitude at zero external momentum transfer, and important remaining challenges, in particular those associated with finite volume effects, will be discussed.

hep-lat↗

arXiv2015

Lattice Calculation of Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment

The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6\;\mathrm{fm})^3$ spatial volume using the $32^3\times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.

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arXiv2015

Lattice Calculation of the Connected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment

The anomalous magnetic moment of muon, $g-2$, is a very precisely measured quantity. However, the current measurement disagrees with standard model by about 3 standard deviations. Hadronic vacuum polarization and hadronic light by light are the two types of processes that contribute most to the theoretical uncertainty. I will describe how lattice methods are well-suited to provide a first-principle's result for the hadronic light by light contribution, the various numerical strategies that are presently being used to evaluate it, our current results and the important remaining challenges which must be overcome.

hep-lat↗

arXiv2014

Calculating the $K_L-K_S$ mass difference and $ε_K$ to sub-percent accuracy

The real and imaginary parts of the $K_L-K_S$ mixing matrix receive contributions from all three charge-2/3 quarks: up, charm and top. These give both short- and long-distance contributions which are accessible through a combination of perturbative and lattice methods. We will discuss a strategy to compute both the mass difference, $ΔM_K$ and $ε_K$ to sub-percent accuracy, looking in detail at the contributions from each of the three CKM matrix element products $V_{id}^*V_{is}$ for $i=u, c$ and $t$ as described in Ref. [1]

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arXiv2009

Controlling Residual Chiral Symmetry Breaking in Domain Wall Fermion Simulations

At stronger gauge-field couplings, the domain wall fermion (DWF) residual mass, a measure of chiral symmetry breaking, grows rapidly. This measure is largely due to near zero fermion eigenmodes of logarithm of the 4D transfer matrix along the fifth dimension, and these eigenmodes increase rapidly at strong coupling. To suppress these eigenmodes, we have added to the DWF path integral a multiplicative weighting factor consisting of a ratio of determinants of Wilson-Dirac fermions having a chirally twisted mass with a large negative real component and a small imaginary chiral component. Numerical results show that this weighting factor with an appropriate choice of twisted masses significantly suppresses the residual mass while allowing adequate topological tunneling.

hep-lat↗

arXiv2006

Non-perturbatively Determined Relativistic Heavy Quark Action

We present a method to non-perturbatively determine the parameters of the on-shell, $O(a)$-improved relativistic heavy quark action. These three parameters, $m_0$, $ζ$, and $c_B=c_E$ are obtained by matching finite-volume, heavy-heavy and heavy-light meson masses to the exact relativistic spectrum through a finite-volume, step-scaling recursion procedure. We demonstrate that accuracy on the level of a few percent can be achieved by carrying out this matching on a pair of lattices with equal physical spatial volumes but quite different lattice spacings. A fine lattice with inverse lattice spacing $1/a=5.4$ GeV and $24^3 \times 48$ sites and a coarse, $1/a=3.6$ GeV, $16^3 \times 32$ lattice are used together with a heavy quark mass $m$ approximately that of the charm quark. This approach is unable to determine the initially expected, four heavy-quark parameters: $m_0$, $ζ$, $c_B$ and $c_E$. This apparent non-uniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction $c_E=c_B$ is permitted through order $a|\vec p|$ and to all orders in $m a$ where $\vec p$ is the heavy quark's spatial momenta.

hep-lat↗

arXiv1998

Toward the Chiral Limit of QCD: Quenched and Dynamical Domain Wall Fermions

A serious difficulty in conventional lattice field theory calculations is the coupling between the chiral and continuum limits. With both staggered and Wilson fermions, the chiral limit cannot be realized without first taking the limit of vanishing lattice spacing. In this talk, we report on extensive studies of the domain wall formulation of lattice fermions, which avoids this difficulty at the expense of requiring that fermion propagators be computed in five dimensions. A variety of results will be described for quenched and dynamical simulations at both zero and finite temperature. Conclusions about the benefits of this new method and some new physical results will be presented. These results were obtained on the QCDSP machines recently put into operation at Columbia and the RIKEN Brookhaven Research Center.

hep-lat↗

arXiv1998

Anomalous Chiral Symmetry Breaking above the QCD Phase Transition

We study the anomalous breaking of U_A(1) symmetry just above the QCD phase transition for zero and two flavors of quarks, using a staggered fermion, lattice discretization. The properties of the QCD phase transition are expected to depend on the degree of U_A(1) symmetry breaking in the transition region. For the physical case of two flavors, we carry out extensive simulations on a 16^3 x 4 lattice, measuring a difference in susceptibilities which is sensitive to U_A(1) symmetry and which avoids many of the staggered fermion discretization difficulties. The results suggest that anomalous effects are at or below the 15% level.

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arXiv1995

Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

The QCD phase transition is studied on $16^3$ and $32^3 \times 4$ lattices both with and without quark loops. We introduce a new zero-flavor or quenched species of quark $ζ$ and study the resulting chiral condensate, $\azbz$ as a function of the $ζ$ mass, $m_ζ$. By examining $\azbz$ for $10^{-10} \le m_ζ\le 10$ we gain considerable information about the spectrum of Dirac eigenvalues. A comparison of $ma=0.01$ and 0.025 shows little dependence of the Dirac spectrum on such a light, dynamical quark mass, after an overall shift in $β$ is removed. The presence of sufficient small eigenvalues to support anomalous chiral symmetry breaking in the high temperature phase is examined quantitatively. In an effort to enhance these small eigenvalues, $\azbz$ is also examined in the pure gauge theory in the region of the deconfinement transition with unexpected results. Above the critical temperature, the three $Z_3$ phases show dramatically different chiral behavior. Surprisingly, the real phase shows chiral symmetry, suggesting that a system with one flavor of staggered fermion at $N_t=4$ will possess a chiral a phase transition---behavior not expected in the continuum limit.

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