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Research

My research interests are all connected by lattice field theory, but they span several topics within high energy theory and software development. I try to describe each project and link some relevant literature.

HVP contribution to muon anomalous magnetic moment

The muon anomalous magnetic moment \(a_\mu\) has been measured to extremely high precision, most recently at Fermilab by the Muon \(g-2\) collaboration. On the theoretical side, it can be subdivided into QED, electroweak, and hadronic contributions, the latter of which cannot be obtained perturbatively. The hadronic vacuum polarization (HVP) contribution can be computed using lattice QCD or using the dispersive method, a data-driven approach that takes experimentally measured cross sections as input. \(a_\mu\) has been of particular interest to the community, as state-of-the-art experimental results compared to theoretical results extracted using the dispersive approach exhibited about \(4.2\sigma\) tension in 2020. If that discrepancy were confirmed, it may indicate another possible signal for physics beyond the Standard Model (SM). Since then, a lattice determination by the BMW Collaboration fell between the dispersive and experimental results, which has been updated to favor the experimental result, albeit using some additional experimental input. Meanwhile the situation for the dispersive approach has become somewhat ambiguous, as new measurements from CMD-3 lie in tension with older results. Independent lattice input is urgently needed, and I help the Fermilab-HPQCD-MILC collaboration to that end.

Publications
  • 2024: A. Bazavov, C. W. Bernard, D. A. Clarke, C. T. H. Davies, C. DeTar, et al. "Hadronic vacuum polarization for the muon \(g-2\) from lattice QCD: Long-distance and full light-quark connected contribution" arXiv: 2412.18491.
  • 2024: A. Bazavov, D. A. Clarke, C. T. H. Davies, C. DeTar, A. X. El-Khadra et al. "Hadronic vacuum polarization for the muon \(g-2\) from lattice QCD: Complete short and intermediate windows", arXiv: 2411.09656.
Presentations

QCD phase diagram at pure imaginary baryon chemical potential

At \(\mu_B>0\), the lattice QCD Boltzmann factor becomes complex, rendering simulation through Markov chains no longer viable. At purely imaginary \(\mu_B\) the Boltzmann factor is again a well defined probability distribution, and one can infer results about real \(\mu_B\) from imaginary \(\mu_B\). We use multi-point Padé approximants to look out for singularities in the complex \(\mu_B\) plane, gleaning information about the convergence radius of Taylor expansions about \(\mu_B=0\) and looking out for signatures of phase transitions like the chiral transition.

Publications

  • 2024: S. Singh, F. Di Renzo, D. A. Clarke, P. Dimopoulos, J. Goswami et al. "What we can learn about Lee-Yang zeros from lattice simulations of QCD", PoS EuroPLEx2023 (2024) 025, DOI: 10.22323/1.451.0025.

  • 2024: D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt et al. "Searching for the QCD critical point using multi-point Padé approximations", arXiv: 2405.10196.

  • 2024: F. Di Renzo, D. A. Clarke, P. Dimopoulos, C. Schmidt, J. Goswami et al. "Detecting Lee-Yang/Fisher singularities by multi-point Padè", 453 PoS(LATTICE2023)169, DOI: 10.22323/1.453.0169 arXiv: 2401.09619.

  • 2024: D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt et al. "Searching for the QCD critical point using Lee-Yang edge singularities", 453 PoS(LATTICE2023)168, DOI: 10.22323/1.453.0168 arXiv: 2401.08820.

  • 2024: C. Schmidt, D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami et al. "Universal scaling and the asymptotic behaviour of Fourier coefficients of the baryon-number density in QCD", 453 PoS(LATTICE2023)167, DOI: 10.22323/1.453.0167 arXiv: 2401.07790.

  • 2024: J. Goswami, D. A. Clarke, P. Dimopoulos, F. Di Renzo, C. Schmidt et al. "Exploring the Critical Points in QCD with Multi-Point Padé and Machine Learning Techniques in (2+1)-flavor QCD", EPJ Web Conf. 296, 06007, DOI: 10.1051/epjconf/202429606007 arXiv: 2401.05651.

  • 2023: K. Zambello, D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami et al. "Determination of Lee-Yang edge singularities in QCD by rational approximations", 430 PoS(LATTICE2022)164, DOI: 10.22323/1.430.0164 arXiv: 2301.03952.

  • 2022: C. Schmidt, D. A. Clarke, P. Dimopoulos, J. Goswami, G. Nicotra et al. "Detecting critical points from Lee-Yang edge singularities in lattice QCD", Acta Phys. Pol. B Proc. Suppl. 16, 1-A52, DOI: 10.5506/APhysPolBSupp.16.1-A52 arXiv: 2209.04345.

Presentations

QCD phase diagram at non-zero real baryon chemical potential

A popular strategy to circumvent the sign problem is to access the QCD grand partition function \(Z_{\text{QCD}}\) through Taylor expansion about \(\mu_B=0\). Here we use state-of-the-art, eighth-order Taylor expansions to provide bounds on the location of a possible critical endpoint in the QCD phase diagram. We also use \(Z_{\text{QCD}}\) to determine bulk thermodynamic observables for \(\mu_B>0\).

Publications

  • 2024: D. A. Clarke, J. Goswami, F. Karsch, and P. Petreczky. "QCD material parameters at zero and non-zero chemical potential from the lattice", EPJ Web Conf. 296 (2024) 14005 DOI: 10.1051/epjconf/202429614005 arXiv: 2312.16703.

  • 2023: D. Bollweg, D. A. Clarke, J. Goswami, O. Kaczmarek, F. Karsch et al.
    "Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density" DOI: 10.1103/PhysRevD.108.014510 arXiv: 2212.09043.

  • 2022: D. A. Clarke. "Isothermal and isentropic speed of sound in (2+1)-flavor QCD at non-zero baryon chemical potential", 430 PoS(LATTICE2022)147, DOI: 10.22323/1.430.0147 arXiv: 2212.10009.

Presentations

Deep learning phases of matter

Deep learning has proven capable of distinguishing phases of matter in classical statistical physics systems. For example the output layer of a convolutional neural network can be treated as an effective order parameter and used to extract critical parameters. We explore the capabilities and limitations of deep learning with the eventual goal of examining the width of the QCD crossover transition.

Publications
  • 2025: A. Abuali, D. A. Clarke, M. Hjorth-Jensen, I. Konstantinidis, C. Ratti et al. "Deep learning of phase transitions with minimal examples", arXiv: 2501.05547.

Gluonic observables in the chiral limit of (2+1)-flavor QCD

In the infinite quark mass limit, one can interpret the Polyakov loop as the order parameter for the deconfinement transition, corresponding to global \(\mathbb{Z}_3\) symmetry breaking. At finite quark mass, there is no clear global symmetry to link to deconfinement, which makes its interpretation less clear. Interestingly, we found the Polyakov loop to be sensitive to the chiral transition near and below physical quark mass; i.e. near the chiral transition point, it scales according to the O(2) universality class. To make the connection with the chiral transition clearer, we are extending this analysis to other gluonic observables.

Publications

  • 2021: D. A. Clarke, O. Kaczmarek, F. Karsch, A. Lahiri, and M. Sarkar. "Imprint of chiral symmetry restoration on the Polyakov loop and the heavy quark free energy", 396 PoS(LATTICE2021)184, DOI: 10.22323/1.396.0184 arXiv: 2111.09844.

  • 2021: D. A. Clarke, O. Kaczmarek, A. Lahiri, and M. Sarkar. "Sensitivity of the Polyakov loop to chiral symmetry restoration", Acta Phys. Pol. B Proc. Suppl. 14, 311 DOI: 10.5506/APhysPolBSupp.14.311 arXiv: 2010.15825.

  • 2021: D. A. Clarke, O. Kaczmarek, F. Karsch, A. Lahiri, and M. Sarkar. "Sensitivity of the Polyakov loop and related observables to chiral symmetry restoration", Phys. Rev. D, 103 DOI: 10.1103/PhysRevD.103.L011501 arXiv: 2008.11678.

  • 2020: D. A. Clarke, O. Kaczmarek, F. Karsch, and A. Lahiri. "Polyakov loop susceptibility and correlators in the chiral limit", 363 PoS(LATTICE2019)194, DOI: 10.22323/1.363.0194 arXiv: 1911.07668.

Presentations

Topology in pure SU(N) lattice gauge theory

As a graduate student, I helped demonstrate that for pure SU(2), the cooling and gradient scales have similar scaling behavior. Comparing these scales we estimated systematic error due to choice of reference scale at finite lattice spacing. We also showed that cooling scales calculated in different topological charge sectors agree within our statistics and provided a new estimate for the SU(2) topological susceptibility in the continuum limit.

Publications

  • 2018: B. A. Berg and D. A. Clarke. "Topological charge and cooling scales in pure SU(2) lattice gauge theory", Phys. Rev. D, 97, DOI: 10.1103/PhysRevD.97.054506 arXiv: 1710.09474.

  • 2017: B. A. Berg and D. A. Clarke. "Deconfinement, gradient, and cooling scales for pure SU(2) lattice gauge theory", Phys. Rev. D, 95, DOI: 10.1103/PhysRevD.95.094508 arXiv: 1612.07347.

Presentations

SIMULATeQCD

SIMULATeQCD is a (Si)mple, (Mu)lti-GPU (Lat)ice code for (QCD) calculations, is a multi-GPU, multi-node, highly modularized code base, written using modern C++. It supports \(N_f=2+1\) HISQ and pure SU(3) gauge actions, and it includes modules for measurement of various observables. It can run on both NVIDIA and AMD GPUs.

Publications
  • 2023: L. Mazur, D. Bollweg, D. A. Clarke, L. Altenkort, O. Kaczmarek et al. "SIMULATeQCD: A simple multi-GPU lattice code for QCD calculations", Comput. Phys. Commun, 300, DOI:10.1016/j.cpc.2024.109164, arXiv:2306.01098.
  • 2021: D. Bollweg, L. Altenkort, D. A. Clarke, O. Kaczmarek, L. Mazur et al. "HotQCD on Multi-GPU Systems", 396 PoS(LATTICE2021)196, DOI: 0.22323/1.396.0196 arXiv: 2111.10354.

AnalysisToolbox

The AnalysisToolbox is a set of Python tools for analyzing physics data, in particular targeting lattice QCD. It includes statistics modules, such as general jackknife and bootstrap error bar calculators; physics modules, for instance allowing hadron resonance gas model calculations; and it also includes moderate interfacing with HotQCD and MILC software.

Publications
  • 2023: L. Altenkort, D. A. Clarke, J. Goswami, H. Sandmeyer. "Streamlined data analysis in Python", 453 PoS(LATTICE2023)136, DOI: 10.22323/1.453.0136 arXiv: 2308.06652.