University of Illinois Urbana-Champaign

The light-quark connected contribution to the muon’s anomalous magnetic moment

Lahert, Shaun

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LAHERT-DISSERTATION-2023.pdf

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https://hdl.handle.net/2142/121397

Description

Title
The light-quark connected contribution to the muon’s anomalous magnetic moment
Author(s)
Lahert, Shaun
Issue Date
2023-05-19
Director of Research (if dissertation) or Advisor (if thesis)
El-Khadra, Aida
Doctoral Committee Chair(s)
Pitts, Kevin
Committee Member(s)
  • Clark, Bryan
  • Noronha-Hostler, Jackie
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Physics
  • Muon
  • Magnetic
  • Moment
  • QCD
Abstract
Understanding the apparent disagreement between the experimental determination and theoretical prediction of the muon's anomolous magnetic moment, $a_\mu$, is a central goal of high energy physics. An ongoing experiment at Fermilab, E989, aims at reducing the uncertainty on the experimental value, already at 0.35~ppm, by a further factor of four (approximately). Alongside this, a new experiment at JPARC, E34, is under construction with comparable precision goals. Correspondingly, reduction of the theoretical prediction's uncertainty is a vital part understanding the apparent tension. The prediction is made using the Standard Model, our current best understanding of particle physics. The dominant source of uncertainty in this result arises from the leading-order hadronic vacuum polarization (HVP) contribution, $a_\mu^{\mathrm{HVP,LO}}$. There are currently two approaches for obtaining this contribution. The first is a data-driven approach, using a dispersion relation to obtain the HVP, which the accepted theoretical result is based upon. This approach takes, as input, experimental data of the cross section for electron-positron scattering to obtain the so-called R-ratio, a function related to the HVP. The second approach is a first principles method, lattice quantum chromodynamics (LQCD), where one puts the hadronic part of the standard model, quantum chromodynamics (QCD) on a discrete spacetime lattice. Within this approach, one calculates the Euclidean correlation function (roughly the fourier transform of the HVP) on the lattice and numerically integrates it over Euclidean time to obtain $a_\mu^{\mathrm{HVP,LO}}$. To date, one LQCD calculation, by the BMW collaboration, has reached the precision of the data-driven approach. Their prediction lies between the data-driven based prediction and the experimental result. Hence, additional lattice calculations are paramount to help shed light on these tensions. The work in this thesis is a series of calculations related to the dominant, light-quark (up and down) contribution to $a_\mu^{\mathrm{HVP,LO}}$ in the isospin-symmetric limit, $a_\mu^{ll}(\mathrm{conn.})$, using LQCD. In particular, a complete calculation of the continuum, infinite-volume, physical result for $a_\mu^{ll}(\mathrm{conn.})$, limited to an intermediate Euclidean time region, W, is presented. A value of $a^{ll,{\mathrm W}}_{\mu}(\mathrm{conn.})=206.5(1.0)$, is obtained which is found to be in excellent agreement with all other recent lattice determinations. A value for a secondary window region, W2, later in Euclidean time, more amenable to the effective-field-theory (EFT) based lattice-correction schemes, is computed. A value of $a^{ll,{\mathrm W}}_{\mu}(\mathrm{conn.})=100.7(3.1)$ is obtained, which again is found to be in good agreement with the single previous determination. Included in these calculations is a comprehensive treatment of the different EFT-based schemes and their applicability in different regions of Euclidean time. This work is performed using the highly-improved-staggered-quark (HISQ) formalism of LQCD on four different SU(3) gauge ensembles with lattice spacings spanning $0.15-0.06$ fm. Alongside this is a detailed study of the of the unique discretization effects associated with the staggered-quark formalism, namely the additional taste quantum number and the temporal oscillations in the correlation functions which are integrated to obtain $a_\mu^{ll}(\mathrm{conn.})$. Finally, a proof-of-principle calculation of the two-pion contribution to $a_\mu^{ll}(\mathrm{conn.})$ is performed at a lattice spacing of 0.15 fm. This calculation addresses the well-known signal-to-noise problem in the long-Euclidean-distance tail of the light-quark correlation function. Explicit two-pion operators are used to precisely resolve the low-lying two-pion state's energies and amplitudes through solving a generalized-eigenvalue problem. These energies and amplitudes are used to reconstruct correlation function in the long-distance region. This approach was found to reduce statistical uncertainty on $\amuL$ significantly.
Graduation Semester
2023-08
Type of Resource
Thesis
Handle URL
https://hdl.handle.net/2142/121397
Copyright and License Information
Copyright 2023 Shaun Lahert

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