Center for Theoretical Physics Publications

We present an update of the Fermilab Lattice and MILC Collaborations project to compute the form factors for semileptonic \(B_{(s)}\)-meson decays. Our calculation uses the highly improved staggered quark (HISQ) action for sea and valence quarks, and ensembles with up, down, strange, and charm quarks in the sea. Using a highly improved action with the MILC Collaboration's gauge ensembles with lattice spacings down to \(a\approx0.03\) fm, allows the heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows for absolutely normalized vector currents, bypassing the need for perturbative matching, which has been a source of uncertainty in previous calculations of \(B\)-meson decay form factors by our collaboration. All preliminary form-factor results are blinded.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by \(\epsilon < 1\) is introduced. It is shown that while Pauli \(Z\)-errors are not recoverable without additional resources, Pauli \(X\) and \(Y\) errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length \(O(2^k c^{k^2} d)\) is sufficient to correct any length-\(d\) QSP with \(c\) unique phases to \(k^{th}\)-order in error \(\epsilon\). Allowing an additional assumption, a lower bound of \(\Omega(cd)\) is shown, which is tight for \(k = 1\), on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

With the vast data-collecting capabilities of current and future high-energy collider experiments, there is an increasing demand for computationally efficient simulations. Generative machine learning models enable fast event generation, yet so far these approaches are largely constrained to fixed data structures and rigid detector geometries. In this paper, we introduce EPiC-GAN - equivariant point cloud generative adversarial network - which can produce point clouds of variable multiplicity. This flexible framework is based on deep sets and is well suited for simulating sprays of particles called jets. The generator and discriminator utilize multiple EPiC layers with an interpretable global latent vector. Crucially, the EPiC layers do not rely on pairwise information sharing between particles, which leads to a significant speed-up over graph- and transformer-based approaches with more complex relation diagrams. We demonstrate that EPiC-GAN scales well to large particle multiplicities and achieves high generation fidelity on benchmark jet generation tasks.

In this note, we prove that the one-loop pfaffian of the non-perturbative superpotential generated by Euclidean D-branes in type II compactifications on orientifolds of Calabi-Yau threefolds is determined by the moduli integral of the new supersymmetric index defined by Cecotti, Fendley, Intriligator, and Vafa. As this quantity can be computed via topological string theory, Chern-Simons theory, matrix models, or by solving the holomorphic anomaly equation, this result provides a method to directly compute the one-loop pfaffian of the non-perturbative superpotential. The relation between the one-loop pfaffian, threshold corrections to the gauge coupling, and the one-loop partition function of open topological string theory is discussed.

One of the greatest challenges in quantum chromodynamics is understanding the hadronization mechanism, which is also crucial for carrying out precision physics with jet substructure. In this Letter, we combine recent advancements in our understanding of the field theory-based nonperturbative structure of the soft drop jet mass with precise perturbative calculations of its multi-differential variants at next-to-next-to-leading logarithmic (NNLL) accuracy. This enables a systematic study of its hadronization power corrections in a completely model-independent way. We calibrate and test hadronization models and their interplay with parton showers by comparing our universality predictions with various event generators for quark and gluon initiated jets in both lepton-lepton and hadron-hadron collisions. We find that hadronization models perform better for quark jets relative to gluon jets. Our results provide the necessary toolkit for precision studies with the soft drop jet mass motivating future analyses using real world collider data. The nontrivial constraints derived in our framework are useful for improving the modeling of hadronization and its interface with parton showers in next generation event generators.

First-principles calculations of multi-hadron dynamics are a crucial goal in lattice QCD. Significant progress has been achieved in developing, implementing, and applying theoretical tools that connect finite-volume quantities to their infinite-volume counterparts. Here, I review some recent theoretical developments and numerical results regarding multi-particle quantities in a finite volume. These results include \(N\pi\) scattering, systems of two and three mesons at maximal isospin, three-body resonances in a toy model, and the formulation of effective theories in finite volume for multi-nucleon systems.

We present lattice-QCD calculations of the hadronic form factors for the semileptonic decays \(D\to\pi\ell\nu\), \(D\to K\ell\nu\), and \(D_s\to K\ell\nu\). Our calculation uses the highly improved staggered quark (HISQ) action for all valence and sea quarks and includes \(N_f=2+1+1\) MILC ensembles with lattice spacings ranging from \(a\approx0.12\) fm down to \(0.042\) fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The HISQ action allows all the quarks to be treated with the same relativistic light-quark action, allowing for nonperturbative renormalization using partial conservation of the vector current. We combine our results with experimental measurements of the differential decay rates to determine \(|V_{cd}|^{D\to\pi}=0.2238(11)^{\rm Expt}(15)^{\rm QCD}(04)^{\rm EW}(02)^{\rm SIB}[22]^{\rm QED}\) and \(|V_{cs}|^{D\to K}=0.9589(23)^{\rm Expt}(40)^{\rm QCD}(15)^{\rm EW}(05)^{\rm SIB}[95]^{\rm QED}\) This result for \(|V_{cd}|\) is the most precise to date, with a lattice-QCD error that is, for the first time for the semileptonic extraction, at the same level as the experimental error. Using recent measurements from BES III, we also give the first-ever determination of \(|V_{cd}|^{D_s\to K}=0.258(15)^{\rm Expt}(01)^{\rm QCD}[03]^{\rm QED}\) from \(D_s\to K \ell\nu\). Our results also furnish new Standard Model calculations of the lepton flavor universality ratios \(R^{D\to\pi}=0.98671(17)^{\rm QCD}[500]^{\rm QED}\), \(R^{D\to K}=0.97606(16)^{\rm QCD}[500]^{\rm QED}\), and \(R^{D_s\to K}=0.98099(10)^{\rm QCD}[500]^{\rm QED}\), which are consistent within \(2\sigma\) with experimental measurements. Our extractions of \(|V_{cd}|\) and \(|V_{cs}|\), when combined with a value for \(|V_{cb}|\), provide the most precise test of second-row CKM unitarity, finding agreement with unitarity at the level of one standard deviation.

In this paper, we compare several event classification architectures defined on the point cloud representation of collider events. These approaches, which are based on the frameworks of deep sets and edge convolutions, circumvent many of the difficulties associated with traditional feature engineering. To benchmark our architectures against more traditional event classification strategies, we perform a case study involving Higgs boson decays to tau leptons. We find a 2.5 times increase in performance compared to a baseline ATLAS analysis with engineered features. Our point cloud architectures can be viewed as simplified versions of graph neural networks, where each particle in the event corresponds to a graph node. In our case study, we find the best balance of performance and computational cost for simple pairwise architectures, which are based on learned edge features.

We present a new way of deriving effective theories of dynamical electromagnetic fields in general media. It can be used to give a systematic formulation of magnetohydrodynamics (MHD) with strong magnetic fields, including systems with chiral matter and Adler-Bell-Jackiw (ABJ) anomaly. We work in the regime in which velocity and temperature fluctuations can be neglected. The resulting chiral anomalous MHD incorporates and generalizes the chiral magnetic effect, the chiral separation effect, the chiral electric separation effect, as well as recently derived strong-field MHD, all in a single coherent framework. At linearized level, the theory predicts that the chiral magnetic wave survives strong dynamical magnetic fields, and predicts the wave velocity. We also introduce a simple, but solvable nonlinear model to explore the fate of the chiral instability.

The Hamiltonian limit of lattice gauge theories can be found by extrapolating the results of anisotropic lattice computations, i.e., computations using lattice actions with different temporal and spatial lattice spacings (\(a_t\neq a_s\)), to the limit of \(a_t\to 0\). In this work, we present a study of this Hamiltonian limit for a Euclidean \(U(1)\) gauge theory in 2+1 dimensions (QED3), regularized on a toroidal lattice. The limit is found using the renormalized anisotropy \(\xi_R=a_t/a_s\), by sending \(\xi_R \to 0\) while keeping the spatial lattice spacing constant. We compute \(\xi_R\) in \(3\) different ways: using both the ``normal'' and the ``sideways'' static quark potential, as well as the gradient flow evolution of gauge fields. The latter approach will be particularly relevant for future investigations of combining quantum computations with classical Monte Carlo computations, which requires the matching of lattice results obtained in the Hamiltonian and Lagrangian formalisms.

The Heavy Quark Expansion (HQE) gives an expansion of inclusive decay rates of \(b\)-hadrons as a simultaneous series in \(\alpha_s\) and \(1/m_b\), in terms of perturbatively defined coefficients and non-perturbative matrix elements. Spectator effects arise from the dimension-\(6\) operators in the HQE in which along with the heavy quark, a light spectator quark from the hadron participates in the weak decay. In this work, we provide a lattice determination of the bare matrix elements that contribute to the spectator effects for the \(B^+\)-meson, \(B_d\)-meson and the \(\Lambda_b\)-baryon. The computations were performed on two separate lattice spacings of the RBC-UKQCD (2+1)-flavor Domain Wall Fermion ensembles. Renormalization and continuum extrapolation of the matrix elements have not yet been computed, and are left to future work.

Dark matter (DM) in the Milky Way halo may annihilate or decay to photons, producing monochromatic gamma rays. We search for DM-induced spectral lines using 14 years of data from the Large Area Telescope onboard the Fermi Gamma-ray Space Telescope (\(\textit{Fermi}\)-LAT) between \(10\,\mathrm{GeV}\) and \(2\,\mathrm{TeV}\) in the inner Milky Way leveraging both the spatial and spectral morphology of an expected signal. We present new constraints as strong as \(\langle \sigma v \rangle \lesssim 6\times 10^{-30}\, \mathrm{cm}^3/\mathrm{s}\) for the two-to-two annihilations and \(\tau \gtrsim 10^{30}\,\mathrm{s}\) for one-to-two decays, representing leading sensitivity between \(10\,\mathrm{GeV}\) and \(\sim\)\(500\,\mathrm{GeV}\). We consider the implications of our line-constraints on the Galactic Center Excess (GCE), which is a previously-observed excess of continuum \(\sim\)GeV gamma-rays that may be explained by DM annihilation. The Higgs portal and neutralino-like DM scenarios, which have been extensively discussed as possible origins of the GCE, are constrained by our work because of the lack of observed one-loop decays to two photons. More generally, we interpret our null results in a variety of annihilating and decaying DM models, such as neutralinos, gravitinos, and glueballs, showing that in many cases the line search is more powerful than the continuum, despite the continuum annihilation being at tree level.

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the \(U(1)\) degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous \(U(1)\) system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

This paper is essentially a verbatim reconstruction of lectures that I gave at the Los Alamos School on Relativistic Dynamics and Quark Nuclear Physics in 1985. They were published in the school proceedings, but the book is not widely available. The Los Alamos School took place at the height of the first wave of interest in the quark substructure of nuclei, stimulated by the 1983 discovery of the EMC Effect. Interest in this subject has been increasing for years and the prospect of a dedicated Electron Ion Collider within the decade guarantees even greater attention to quarks and gluons in nuclei among both theorists and experimentalists. Recently, to my surprise, I learned that copies of my old lectures have been circulating and been found useful by the relatively few people who know about them. The are, of course, dated: experiments have far outstripped what was available 37 years ago and theory has progressed too. However, the rest frame derivation of the parton model, the derivation and discussion of the convolution formalism for nucleons, nucleon correlations, and other, virtual, constituents of nuclei, and sections on scaling violation and the operator product expansion have aged pretty well and seem to still be useful. With the help and encouragement of Richard Milner, I have recreated the LaTeX files necessary to post the 1985 Lectures on the arXiv, making them available to the nuclear and particle physics community. Apart from correcting some typographical errors, I have made no attempt to edit, improve, or update these lectures. I hope readers will nevertheless find them useful.

In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from the naive shift and center symmetries. Since the Gauss law is anomalous, there is no conserved, gauge-invariant, and quantized electric charge. Rather, using half higher gauging, we find a non-invertible Gauss law associated with a non-invertible 1-form global symmetry, which is related to the Page charge. These symmetries act invertibly on the axion field and Wilson line, but non-invertibly on the monopoles and axion strings, leading to selection rules related to the Witten effect. We also derive various crossing relations between the defects. Finally, we show that the non-invertible 0- and 1-form global symmetries mix with other invertible symmetries in a way reminiscent of a higher-group symmetry. Using this non-invertible higher symmetry structure, we derive universal inequalities on the energy scales where different infrared symmetries emerge in any renormalization group flow to the axion-Maxwell theory.

A central challenge in analog quantum simulation is to characterize desirable physical properties of quantum states produced in experiments. However, in conventional approaches, the extraction of arbitrary information requires performing measurements in many different bases, which necessitates a high level of control that present-day quantum devices may not have. Here, we propose and analyze a scalable protocol that leverages the ergodic nature of generic quantum dynamics, enabling the efficient extraction of many physical properties. The protocol does not require sophisticated controls and can be generically implemented in analog quantum simulation platforms today. Our protocol involves introducing ancillary degrees of freedom in a predetermined state to a system of interest, quenching the joint system under Hamiltonian dynamics native to the particular experimental platform, and then measuring globally in a single, fixed basis. We show that arbitrary information of the original quantum state is contained within such measurement data, and can be extracted using a classical data-processing procedure. We numerically demonstrate our approach with a number of examples, including the measurements of entanglement entropy, many-body Chern number, and various superconducting orders in systems of neutral atom arrays, bosonic and fermionic particles on optical lattices, respectively, only assuming existing technological capabilities. Our protocol excitingly promises to overcome limited controllability and, thus, enhance the versatility and utility of near-term quantum technologies.

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many \(n\)-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the \(n\)-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

The presence of symmetries can convert an otherwise computationally hard task into an efficient one. In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts. As an example, we show that simulating and finding the ground state of permutation invariant Hamiltonians can be efficiently performed in polynomial classical time, further restricting the possible set of symmetries that provide quantum advantage.

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. This article describes the progress in the lattice QCD calculation of the fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion (HOPE).

We propose a variational quantum eigensolver suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. The parametric ansatz circuit we design is capable of incorporating the symmetries of the model, present in certain parameter regimes, which allows for reducing the number of variational parameters substantially. Moreover, the ansatz circuit can be implementated on both measurement-based and circuit-based quantum hardware. We numerically demonstrate that our ansatz circuit is able to capture the phase structure of the model and allows for faithfully approximating the ground state. Our results show that our approach is suitable for current intermediate-scale quantum hardware and can be readily implemented on existing quantum devices.