Norman H. Christ
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Norman H. Christ has a total of 62 co-authors. Here are the top co-authors by number of shared publications:
- Christopher T. Sachrajda
Department of Physics and Astronomy Department of Physics and Astronomy Università di Roma "Tor Vergata" INFN sezione di Roma "Tor Vergata" Università di Roma Tre INFN sezione di Roma Tre Università di Roma "La Sapienza" INFN sezione di Roma University of Southampton University of Southampton INFN sezione di Roma Tre
7 shared publications - Xu Feng
Peking University
4 shared publications - Hantao Yin
Department of Physics Columbia University 10025 New York NY USA
3 shared publications - Luchang Jin
University of Connecticut
3 shared publications - Peter A. Boyle
University of Edinburgh
3 shared publications - Yikai Huo
Department of Physics Columbia University New York USA
3 shared publications
Latest Publications
- Open Access
- 14 February 2025
- Published by Sissa Medialab Srl
- Vol. 466, 239
Enhanced Lattice QCD Studies on $\epsilon_{K}$ and $\Delta M_{K}$Two second-order quantities related to K meson mixing, $\varepsilon_{K}$ and $\Delta M_K$, are Standard Model observables that are highly sensitive to possible new physics. The RBC and UKQCD collaborations have presented results for $\Delta M_{K}$ with physical quark masses and the first lattice calculation of the long-distance part of $\varepsilon_{K}$. Utilizing new-generation computers and new lattice configurations with an inverse lattice spacing of $2.7\ \mathrm{GeV}$ and physical quark masses, we can extend this previous work to obtain more precise results.- 14 February 2025
- Published by Sissa Medialab Srl
- Vol. 466, 239
Open AccessEnhanced Lattice QCD Studies on $\epsilon_{K}$ and $\Delta M_{K}$Two second-order quantities related to K meson mixing, $\varepsilon_{K}$ and $\Delta M_K$, are Standard Model observables that are highly sensitive to possible new physics. The RBC and UKQCD collaborations have presented results for $\Delta M_{K}$ with physical quark masses and the first lattice calculation of the long-distance part of $\varepsilon_{K}$. Utilizing new-generation computers and new lattice configurations with an inverse lattice spacing of $2.7\ \mathrm{GeV}$ and physical quark masses, we can extend this previous work to obtain more precise results. - Open Access
- 13 February 2025
- Published by Sissa Medialab Srl
- Vol. 466, 063
Studies of Gauge-fixed Fourier acceleration for SU(3) gauge theory
We report results from the application of Fourier acceleration to $SU(3)$ lattice gauge theory using softly-fixed Landau gauge. Acceleration of the HMC algorithm is studied on a $16^4$ lattice volume with the Wilson gauge action and different values of $\beta$. Two types of boundary conditions with fixed boundary links are explored. The boundary links are fixed either to unit matrices or to the matrices present on the boundaries of an initial gauge configuration equilibrated with periodic boundary conditions, anticipating a possible application in which a large lattice is continually divided into subvolumes that are evolved independently- 13 February 2025
- Published by Sissa Medialab Srl
- Vol. 466, 063
Open AccessStudies of Gauge-fixed Fourier acceleration for SU(3) gauge theory
We report results from the application of Fourier acceleration to $SU(3)$ lattice gauge theory using softly-fixed Landau gauge. Acceleration of the HMC algorithm is studied on a $16^4$ lattice volume with the Wilson gauge action and different values of $\beta$. Two types of boundary conditions with fixed boundary links are explored. The boundary links are fixed either to unit matrices or to the matrices present on the boundaries of an initial gauge configuration equilibrated with periodic boundary conditions, anticipating a possible application in which a large lattice is continually divided into subvolumes that are evolved independently - Open Access
- 10 February 2025
- Published by Sissa Medialab Srl
- Vol. 466, 045
Tuning the Riemannian Manifold Hybrid Monte Carlo with Fermions
The Riemannian Manifold HMC (RMHMC) is designed to tackle critical slowing down by utilizing a rational function of the SU(3) gauge covariant laplace operator in place of the canonical mass term in the HMC algorithm. The RMHMC has been demonstrated to be effective at increasing the rate of change of long-distance modes. We present the results of the recent studies done to tune the algorithm and improve its efficiency.
- 10 February 2025
- Published by Sissa Medialab Srl
- Vol. 466, 045
Open AccessTuning the Riemannian Manifold Hybrid Monte Carlo with Fermions
The Riemannian Manifold HMC (RMHMC) is designed to tackle critical slowing down by utilizing a rational function of the SU(3) gauge covariant laplace operator in place of the canonical mass term in the HMC algorithm. The RMHMC has been demonstrated to be effective at increasing the rate of change of long-distance modes. We present the results of the recent studies done to tune the algorithm and improve its efficiency.
- Open Access
- 5 May 2024
- Published by Sissa Medialab Srl
- Vol. 453, 042
Fourier Acceleration of SU(3) Pure Gauge Theory at Weak Coupling
In the hybrid Monte Carlo simulation of $\mathrm{SU}(3)$ pure gauge theory, we explore a Fourier acceleration algorithm to reduce critical slowing down. By introducing a soft-gauge-fixing term in the action, we can identify the eigenmodes in the weak-coupling expansion of the action and eliminate the differences in their evolution frequencies. A special unit-link boundary, in which the links lying in the boundary faces are fixed to be unit matrices, is also proposed to eliminate the $\mathbf{Z}_3$ symmetry and the tunneling between $\mathbf{Z}_3$ phases in which is not of interest here. We present the theoretical details and the numerical implementation of this algorithm, compare the autocorrelation times of certain observables with the usual hybrid Monte Carlo algorithm to show its acceleration effect for weak coupling and examine its potential application to physically relevant lattice spacings.- 5 May 2024
- Published by Sissa Medialab Srl
- Vol. 453, 042
Open AccessFourier Acceleration of SU(3) Pure Gauge Theory at Weak Coupling
In the hybrid Monte Carlo simulation of $\mathrm{SU}(3)$ pure gauge theory, we explore a Fourier acceleration algorithm to reduce critical slowing down. By introducing a soft-gauge-fixing term in the action, we can identify the eigenmodes in the weak-coupling expansion of the action and eliminate the differences in their evolution frequencies. A special unit-link boundary, in which the links lying in the boundary faces are fixed to be unit matrices, is also proposed to eliminate the $\mathbf{Z}_3$ symmetry and the tunneling between $\mathbf{Z}_3$ phases in which is not of interest here. We present the theoretical details and the numerical implementation of this algorithm, compare the autocorrelation times of certain observables with the usual hybrid Monte Carlo algorithm to show its acceleration effect for weak coupling and examine its potential application to physically relevant lattice spacings. - Open Access
- 4 May 2024
- Published by Sissa Medialab Srl
- Vol. 453, 266
Lattice Calculation of Electromagnetic Corrections to Kl3 decay
We describe a first-principles method to apply lattice QCD to compute the order $\alpha_{\mathrm{EM}}$ corrections to $K\to\pi\ell\nu_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: Phys.Rev.D 108 (2023) 1, 014501.- 4 May 2024
- Published by Sissa Medialab Srl
- Vol. 453, 266
Open AccessLattice Calculation of Electromagnetic Corrections to Kl3 decay
We describe a first-principles method to apply lattice QCD to compute the order $\alpha_{\mathrm{EM}}$ corrections to $K\to\pi\ell\nu_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: Phys.Rev.D 108 (2023) 1, 014501. - Open AccessLattice calculation of electromagnetic corrections to $K\ell3$ decayWe describe a first-principles method to apply lattice QCD to compute the order $α_{\mathrm{EM}}$ corrections to $K\toπ\ellν_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: arXiv:2304.08026.Open AccessLattice calculation of electromagnetic corrections to $K\ell3$ decayWe describe a first-principles method to apply lattice QCD to compute the order $α_{\mathrm{EM}}$ corrections to $K\toπ\ellν_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: arXiv:2304.08026.
- Open Access
- 8 January 2021
- Published by American Physical Society (APS) in Physical Review D
- Vol. 103 (1) , 014507
Finite-volume effects in long-distance processes with massless leptonic propagators
A method was proposed recently [X. Feng and L. Jin, Phys. Rev. D 100, 094509 (2019)] to calculate QED corrections to hadronic self-energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.- 8 January 2021
- Published by American Physical Society (APS) in Physical Review D
- Vol. 103 (1) , 014507
Open AccessFinite-volume effects in long-distance processes with massless leptonic propagators
A method was proposed recently [X. Feng and L. Jin, Phys. Rev. D 100, 094509 (2019)] to calculate QED corrections to hadronic self-energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections. - Open AccessCalculating the Two-photon Contribution to $π^0 \rightarrow e^+ e^-$ Decay AmplitudeWe develop a new method that allows us to deal with two-photon intermediate states in a lattice QCD calculation. We apply this method to perform a first-principles calculation of the $\pi^0 \rightarrow e^+ e^-$ decay amplitude. Both the real and imaginary parts of amplitude are calculated. The imaginary part is compared with the prediction of optical theorem to demonstrate the effectiveness of this method. Our result for the real part of decay amplitude is $19.68(52)(1.10) \ \text{eV}$, where the first error is statistical and the second is systematic.Open AccessCalculating the Two-photon Contribution to $π^0 \rightarrow e^+ e^-$ Decay AmplitudeWe develop a new method that allows us to deal with two-photon intermediate states in a lattice QCD calculation. We apply this method to perform a first-principles calculation of the $\pi^0 \rightarrow e^+ e^-$ decay amplitude. Both the real and imaginary parts of amplitude are calculated. The imaginary part is compared with the prediction of optical theorem to demonstrate the effectiveness of this method. Our result for the real part of decay amplitude is $19.68(52)(1.10) \ \text{eV}$, where the first error is statistical and the second is systematic.
- Open AccessIncluding electromagnetism in $K\toππ$ decay calculations
Because of the small size of the ratio A_2/A_0 of the I=2 to I=0 K -> pipi decay amplitudes (the Delta I=1/2 rule) the effects of electromagnetism on A_2 may be a factor of 20 larger than given by a naive O(alpha) estimate. Thus, if future calculations of A_2 and epsilon'/epsilon are to achieve 10% accuracy, these effects need to be included. Here we present the first steps toward including electromagnetism in a calculation of the standard model K -> pipi decay amplitudes using lattice QCD.
Open AccessIncluding electromagnetism in $K\toππ$ decay calculationsBecause of the small size of the ratio A_2/A_0 of the I=2 to I=0 K -> pipi decay amplitudes (the Delta I=1/2 rule) the effects of electromagnetism on A_2 may be a factor of 20 larger than given by a naive O(alpha) estimate. Thus, if future calculations of A_2 and epsilon'/epsilon are to achieve 10% accuracy, these effects need to be included. Here we present the first steps toward including electromagnetism in a calculation of the standard model K -> pipi decay amplitudes using lattice QCD.
- Open AccessLong 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.
Open AccessLong 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.