Lattice QCD and Particle Physics
Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).
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arXiv subjects
Boram Yoon
Publications and source records attributed to Boram Yoon.
Quantum Algorithm Implementations for Beginners
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.
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AI and Theoretical Particle Physics
Theoretical particle physicists continue to push the envelope in both high performance computing and in managing and analyzing large data sets. For example, the goals of sub-percent accuracy in predictions of quantum chromodynamics (QCD) using large scale simulations of lattice QCD and in finding signals of rare events and new physics in exabytes of data produced by experiments at the high luminosity large hadron collider (LHC) require new tools beyond just developments in hardware. Machine learning and artificial intelligence offer the promise of dramatically reducing the computational cost and time. This chapter reviews selected areas where AI/ML tools could have a major impact, provides an overview of the challenges, and discusses how new ideas such as normalizing flows can speed up the generation of gauge configurations needed in lattice QCD calculations; the growth of ML in surrogate models and pattern matching to reduce the cost of event generators and in the analysis of experimental data; and in the search for viable vacua in the landscape of string theories. While such approaches transform aspects of particle theory into computational problems, and thus black boxes, we argue that physics-aware development of these tools combined with algorithms that ensure that the results are bias free will continue to require a deep understanding of the physics. We see this broader transformation as akin to formulating and extracting observables from simulations of lattice QCD, a numerical integration of the path integral formulation of QCD that nevertheless requires a deep understanding of the underlying quantum field theory, the standard model of particle physics and effective field theory methods.
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Improved data analysis on two-point correlation function with sequential Bayesian method
We report our progress in data analysis on two-point correlation functions of the $B$ meson using sequential Bayesian method. The data set of measurement is obtained using the Oktay-Kronfeld (OK) action for the bottom quarks (valence quarks) and the HISQ action for the light quarks on the MILC HISQ lattices. We find that the old initial guess for the $χ^2$ minimizer in the fitting code is poor enough to slow down the analysis somewhat. In order to find a better initial guess, we adopt the Newton method. We find that the Newton method provides a natural test to check whether the $χ^2$ minimizer finds a local minimum or the global minimum, and it also reduces the number of iterations dramatically.
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The pion-nucleon sigma term from Lattice QCD
We summarize recent evidence, both from lattice QCD and chiral perturbation theory, that suggests that larger-than-expected excited-state contamination could be the reason for the tension between phenomenological determinations and previous direct lattice-QCD calculations of the pion--nucleon sigma term $σ_{πN}$. In addition, we extend the $χ$PT analysis by calculating the corrections due to including the $Δ(1232)$ resonance as an explicit degree of freedom. This correction is found to be small, thereby corroborating the excited-state effects found in the $Δ$-less calculation and the result for $σ_{πN}$.
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Flavor Diagonal Nucleon Charges
This talk provides an update on the calculation of matrix elements of flavor diagonal axial, scalar and tensor quark bilinear operators between the nucleon ground state. The simulations are done using Wilson-clover fermions on a sea of eight 2+1+1-flavor HISQ ensembles generated by the MILC collaboration. We discuss the signal in the connected and disconnected contributions, calculation of the renormalization constants and mixing in the RI-sMOM scheme, and control over the simultaneous chiral-continuum-finite-volume fit used to extract the final charges.
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Excited states and precision results for nucleon charges and form factors
The exponentially falling signal-to-noise ratio in all nucleon correlation functions, and the presence of towers of multihadron excited states with relatively small mass gaps makes extraction of matrix elements of various operators within the ground state nucleon challenging. Theoretically, the allowed positive parity states with the smallest mass gaps are the $N(\bm p)π(-\bm p)$, $N(\bm 0)π(\bm 0)π(\bm 0)$, $N(\bm p)π(\bm 0)$, $N(\bm 0)π(\bm p),\ \ldots$, states. A priori, the contribution of these states arises at one loop in chiral perturbation theory ($χ$PT), however, in many cases the contributions are enhanced. In this talk, I will review four such cases: the correlation functions from which the axial form factors, electric and magnetic form factors, the $Θ$-term contribution to neutron electric dipole moment (nEDM), and the pion-nucleon sigma term are extracted. Including appropriate multihadron states in the analysis can lead to significantly different results compared to standard analyses with the mass gaps taken from fits to 2-point functions. The $χ$PT case for $N π$ states is the most clear in the axial/pseudoscalar form factors which need to satisfy the PCAC relation between them. Our analyses, supported by $χ$PT, suggests similarly large effects in the calculations of the $Θ$-term and the pion-nucleon sigma term that have significant phenomenological implications.
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Precision Nucleon Charges and Form Factors Using 2+1-flavor Lattice QCD
We present high statistics results for the isovector nucleon charges and form factors using seven ensembles of 2+1-flavor Wilson-clover fermions. The axial and pseudoscalar form factors obtained on each ensemble satisfy the PCAC relation once the lowest energy $Nπ$ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the $Nππ$ excited state contributes to the correlation functions with the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parameterization of the experimental electric and magnetic data. Our final estimates for the isovector charges are $g_{A}^{u-d} = 1.31(06)(05)_{sys}$, $g_{S}^{u-d} = 1.06(10)(06)_{sys}$, and $g_{T}^{u-d} = 0.95(05)(02)_{sys}$, where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, ${\langle r_A^2 \rangle}^{u-d}=0.428(53)(30)_{sys}\ {\rm fm}^2$, (ii) the induced pseudoscalar charge, $g_P^\ast=7.9(7)(9)_{sys}$, (iii) the pion-nucleon coupling $g_{π{\rm NN}} = 12.4(1.2)$, (iv) the electric charge radius squared, ${\langle r_E^2 \rangle}^{u-d} = 0.85(12)(19)_{sys} \ {\rm fm}^2$, (v) the magnetic charge radius squared, ${\langle r_M^2 \rangle}^{u-d} = 0.71(19)(23)_{\rm sys} \ {\rm fm}^2$, and (vi) the magnetic moment $μ^{u-d} = 4.15(22)(10)_{\rm sys}$. All our results are consistent with phenomenological/experimental values but with larger errors. Lastly, we present a Padé parameterization of the axial, electric and magnetic form factors over the range $0.04< Q^2 <1$ GeV${}^2$ for phenomenological studies.
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Calculation of neutron electric dipole moment due to the QCD topological term, Weinberg three-gluon operator and the quark chromoelectric moment
We present results for the neutron electric dipole moment due to the dimension 4 and dimension 6 gluonic CP violation, and the isovector quark chromoelectric dipole moment using clover valence quarks on HISQ dynamical ensembles generated by the MILC Collaboration. For the gluonic operators, we use the gradient flow scheme to obtain divergence-free continuum results. For the chromoelectric dipole moment operator, we use the unflowed local operator but discuss how the quadratically divergent mixing with the pseudoscalar operator can be controlled nonperturbatively.
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Effects of Virtual Room Size and Objects on Relative Translation Gain Thresholds in Redirected Walking
This paper investigates how the size of virtual space and objects within it affect the threshold range of relative translation gains, a Redirected Walking (RDW) technique that scales the user's movement in virtual space in different ratios for the width and depth. While previous studies assert that a virtual room's size affects relative translation gain thresholds on account of the virtual horizon's location, additional research is needed to explore this assumption through a structured approach to visual perception in Virtual Reality (VR). We estimate the relative translation gain thresholds in six spatial conditions configured by three room sizes and the presence of virtual objects (3 X 2), which were set according to differing Angles of Declination (AoDs) between eye-gaze and the forward-gaze. Results show that both size and virtual objects significantly affect the threshold range, it being greater in the large-sized condition and furnished condition. This indicates that the effect of relative translation gains can be further increased by constructing a perceived virtual movable space that is even larger than the adjusted virtual movable space and placing objects in it. Our study can be applied to adjust virtual spaces in synchronizing heterogeneous spaces without coordinate distortion where real and virtual objects can be leveraged to create realistic mutual spaces.
cs.HC↗
Nucleon isovector momentum fraction, helicity and transversity moment using Lattice QCD
We present our recent high precision calculations (Phys. Rev. D102 (2020) no.5, 054512 and JHEP 04 (2021) 044, JHEP 21 (2020) 004) of the first moment of nucleon isovector polarized, unpolarized and transversity distributions, i.e., momentum fraction, helicity and transversity moment, respectively. We use the standard method for the calculation of these moments (via matrix elements of twist two operators), and carry out a detailed analysis of the sources of systematic uncertainty, in particular of excited state contributions. Our calculations have been performed using two different lattice setups (Clover-on-HISQ and Clover-on-Clover), each with several ensembles. They give consistent results that are in agreement with global fit analyses.
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The pion-nucleon sigma term from lattice QCD
We present an analysis of the pion-nucleon $σ$-term, $σ_{πN}$, using six ensembles with 2+1+1-flavor highly improved staggered quark action generated by the MILC collaboration. The most serious systematic effect in lattice calculations of nucleon correlation functions is the contribution of excited states. We estimate these using chiral perturbation theory ($χ$PT), and show that the leading contribution to the isoscalar scalar charge comes from N$π$ and N$ππ$ states. Therefore, we carry out two analyses of lattice data to remove excited-state contamination, the standard one and a new one including N$π$ and N$ππ$ states. We find that the standard analysis gives $σ_{πN} = 41.9(4.9)$ MeV, consistent with previous lattice calculations, while our preferred $χ$PT-motivated analysis gives $σ_{πN} = 59.6(7.4)$ MeV, which is consistent with phenomenological values obtained using $π$N scattering data. Our data on one physical pion mass ensemble was crucial for exposing this difference, therefore, calculations on additional physical mass ensembles are needed to confirm our result and resolve the tension between lattice QCD and phenomenology.
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Prediction and compression of lattice QCD data using machine learning algorithms on quantum annealer
We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables into a sparse coding machine learning algorithm. The trained correlation pattern is used to predict lattice QCD observables of unseen lattice configurations from other observables measured on the lattice. In the compression algorithm, we define a mapping from lattice QCD data of floating-point numbers to the binary coefficients that closely reconstruct the input data from a set of basis vectors. Since the reconstruction is not exact, the mapping defines a lossy compression, but, a reasonably small number of binary coefficients are able to reconstruct the input vector of lattice QCD data with the reconstruction error much smaller than the statistical fluctuation. In both applications, we use D-Wave quantum annealers to solve the NP-hard binary optimization problems of the machine learning algorithms.
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Lossy compression of statistical data using quantum annealer
We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3.5 times better compression performance than the algorithms based on a neural-network autoencoder and principal component analysis. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.
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Strange and charm contributions to nucleon charges and moments
We present preliminary results for strange and charm contributions to nucleon charges and moments. The scalar, axial and tensor charges, and unpolarized first moments are calculated using clover-on-HISQ formulation and cover four lattice spacings, $a=\{0.06,0.09,0.12, 0.15\}$~fm, and three pion masses, $M_π=\{310,220,130\}$~MeV. The renormalization factors are calculated nonperturbatively using the RI-sMOM scheme. We carry out a chiral and continuum extrapolation to obtain physical results.
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Moments of nucleon isovector structure functions in $2+1+1$-flavor QCD
We present results on the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{Δu-Δd}$, and the transversity moment, $\langle x \rangle_{δu-δd}$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC collaboration using $2+1+1$-flavors of dynamical highly improved staggered quarks (HISQ). The correlation functions are calculated using the Wilson-Clover action and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI${}^\prime$-MOM scheme. The data have been collected at lattice spacings $a \approx 0.15,\ 0.12,\ 0.09,$ and 0.06 fm and $M_π\approx 310,\ 220$ and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the $\overline{MS}$ scheme at 2 GeV, are $\langle x \rangle_{u-d} = 0.173(14)(07)$, $\langle x \rangle_{Δu-Δd} = 0.213(15)(22)$ and $\langle x \rangle_{δu-δd} = 0.208(19)(24)$, where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.
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Contribution of the QCD $Θ$-term to nucleon electric dipole moment
We present a calculation of the contribution of the $Θ$-term to the neutron and proton electric dipole moments using seven 2+1+1-flavor HISQ ensembles. We also estimate the topological susceptibility for the 2+1+1 theory to be $χ_Q = (66(9)(4) \rm MeV)^4$ in the continuum limit at $M_π= 135$ MeV. The calculation of the nucleon three-point function is done using Wilson-clover valence quarks. The CP-violating form factor $F_3$ is calculated by expanding in small $Θ$. We show that lattice artifacts introduce a term proportional to $a$ that does not vanish in the chiral limit, and we include this in our chiral-continuum fits. A chiral perturbation theory analysis shows that the $N(0) π(0)$ state should provide the leading excited state contribution, and we study the effect of such a state. Detailed analysis of the contributions to the neutron and proton electric dipole moment using two strategies for removing excited state contamination are presented. Using the excited state spectrum from fits to the two-point function, we find $d_n^Θ$ is small, $|d_n^Θ| \lesssim 0.01 \overline Θe$ fm, whereas for the proton we get $|d_p^Θ| \sim 0.02 \overline Θe$ fm. On the other hand, if the dominant excited-state contribution is from the $N π$ state, then $|d_n^Θ|$ could be as large as $0.05 \overline Θe$ fm and $|d_p^Θ| \sim 0.07 \overline Θe$ fm. Our overall conclusion is that present lattice QCD calculations do not provide a reliable estimate of the contribution of the $Θ$-term to the nucleon electric dipole moments, and a factor of ten higher statistics data are needed to get better control over the systematics and possibly a $3σ$ result.
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A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer
We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on a D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as a combined vector, and encode the high-order correlations between them into a dictionary optimized for sparse reconstruction. On a test dataset, the dependent variable is initialized to its average value and then a sparse reconstruction of the combined vector is obtained in which the dependent variable is typically shifted closer to its true value, as in a standard inpainting or denoising task. Here, a quantum annealer, which can presumably exploit a fully entangled initial state to better explore the complex energy landscape, is used to solve the highly non-convex sparse coding optimization problem. The regression algorithm is demonstrated for a lattice quantum chromodynamics simulation data using a D-Wave 2000Q quantum annealer and good prediction performance is achieved. The regression test is performed using six different values for the number of fully connected logical qubits, between 20 and 64. The scaling results indicate that a larger number of qubits gives better prediction accuracy.
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