Search NASAβŒ• Search

Engineering topics

Christ, N. H.

Publications and source records attributed to Christ, N. H..

10 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Bootstrap-determined p values in lattice QCD

We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p -value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling T 2 methods based on the conventional Ο‡ 2 statistic do not apply, such as for uncorrelated fits. Specifically, we analyze q 2 , defined as the correlated Ο‡ 2 statistic obtained using an arbitrary covariance matrix estimator, and show how to use the bootstrap as a data-driven method to determine the expected distribution of q 2 for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p -value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p -value of estimating population parameters from a single ensemble of N samples. The overall method is accurate up to a 1 / N bias which we do not attempt to quantify. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Workshop summary: Kaons@CERN 2023

Kaon physics is at a turning point – while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop, held in September 2023 at CERN.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Lattice determination of 𝐼=0 and 2 πœ‹β’πœ‹ scattering phase shifts with a physical pion mass

Phase shifts for 𝑠-wave πœ‹β’πœ‹ scattering in both the 𝐼 =0 and 𝐼 =2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32 3 Γ—64. These results support our recent 2021 study of direct 𝐢⁒𝑃 violation in 𝐾 β†’ πœ‹β’πœ‹ decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving πœ‹β’πœ‹ systems, at three (𝐼 = 0) and four (𝐼 = 2) different total momenta. We implement several πœ‹β’πœ‹ interpolating operators including a scalar bilinear β€œπœŽβ€ operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Direct CP violation and the Ξ”I=1/2 rule in K→ππ decay from the standard model

We present a lattice QCD calculation of the Ξ” I = 1 / 2 , K β†’ Ο€ Ο€ decay amplitude A 0 and Ο΅ ' , the measure of direct C P violation in K β†’ Ο€ Ο€ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 32 3 Γ— 64 lattice with an inverse lattice spacing of a - 1 = 1.3784 ( 68 ) GeV . However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the Ο€ Ο€ ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re ( A 0 ) = 2.99 ( 0.32 ) ( 0.59 ) Γ— 10 - 7 GeV and Im ( A 0 ) = - 6.98 ( 0.62 ) ( 1.44 ) Γ— 10 - 11 GeV , where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re ( A 0 ) = 3.3201 ( 18 ) Γ— 10 - 7 GeV . These results for A 0 can be combined with our earlier lattice calculation of A 2 [2] to obtain Re ( Ο΅ ' / Ο΅ ) = 21.7 ( 2.6 ) ( 6.2 ) ( 5.0 ) Γ— 10 - 4 , where the third error represents omitted isospin breaking effects, and Re ( A 0 ) / Re ( A 2 ) = 19.9 ( 2.3 ) ( 4.4 ) . The first agrees well with the experimental result of Re ( Ο΅ ' / Ο΅ ) = 16.6 ( 2.3 ) Γ— 10 - 4 . A comparison of the second with the observed ratio Re ( A 0 ) / Re ( A 2 ) = 22.45 ( 6 ) , demonstrates the standard model origin of this β€œ Ξ” I = 1 / 2 rule” enhancement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Low energy constants of S U ( 2 ) partially quenched chiral perturbation theory from N f = 2 + 1 domain wall QCD

Here, we have performed fits of the pseudoscalar masses and decay constants, from a variety of the RBC-UKQCD Collaboration’s domain wall fermion ensembles, to SU(2) partially quenched chiral perturbation theory at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low-energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low-energy constants to make predictions for mass splittings due to QCD isospin-breaking effects and the S-wave ππ scattering lengths. Lastly, we conclude that, for the range of pseudoscalar masses explored in this work, 115 MeV≲mPS≲430 MeV, the NNLO SU(2) expansion is quite robust and can fit lattice data with percent-scale accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Standard Model Prediction for Direct C P Violation in K β†’ Ο€ Ο€ Decay

In this paper, we report the first lattice QCD calculation of the complex kaon decay amplitude A 0 with physical kinematics, using a 32 3 x 64 lattice volume and a single lattice spacing a, with 1/a = 1.3784(68) GeV. We find Re(A 0 ) = 4.66(1.00)(1.26) x 10 -7 GeV and Im(A 0 ) = -1.90(1.23)(1.08) x 10 -11 GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A 0 ) = 3.3201(18) x 10 -7 GeV, while the second can be used to compute the direct CP-violating ratio Re(Ο΅'/Ο΅) = 1.38(5.15)(4.59) x 10 -4 , which is 2.1Οƒ below the experimental value 16.6(2.3) x 10 -4 . Finally, the real part of A 0 is CP conserving and serves as a test of our method while the result for Re(Ο΅'/Ο΅) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Effects of finite volume on the K L – K S mass difference

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of LΓΌscher and Lellouch and LΓΌscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the K L – K S mass difference Ξ”M K and the CP-violating parameter Ξ΅K are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.

Christ, N. H.β†—