MIT Center for Theoretical Physics — a Leinweber Institute Publications

Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N${}^{}$LL) resummation. To our knowledge, this is the first N${}^{}$LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes.

In the high energy limit, $s\gg -t$, amplitudes in planar gauge theories Reggeize, with power law behavior $(\frac{s}{-t}{)}^{\alpha \left(t\right)}$ governed by the Regge trajectory $\alpha \left(t\right)$. Beyond the planar limit this simplicity is violated by "Regge cuts", for which practical organizational principles are still being developed. We use a top-down effective field theory organization based on color projection in the $t$ channel and rapidity evolution equations for collinear impact factors, to sum large $s\gg -t$ logarithms for Regge cut contributions. The results are matrix equations which are closed within a given color channel. To illustrate the method we derive in QCD with $SU\left(N_c\right)$ for the first time a closed 6$\times$6 evolution equation for the "decupletons" in the $\text{10}\oplus \overline{\text{10}}$ Regge color channel, a 2$\times$2 evolution equation for the "triantapentons" in the $\text{35}\oplus \overline{\text{35}}$ color channel, and a scalar evolution equation for the "tetrahexaconton" in the 64 color channel. More broadly, our approach allows us to describe generic Reggeization phenomena in non-planar gauge theories, providing valuable data for the all loop structure of amplitudes beyond the planar limit.

We construct algebras of diff-invariant observables in a global de Sitter universe with two observers and a free scalar QFT in two dimensions. We work in the strict $G_N\to 0$ limit, but allow the observers to have an order one mass in cosmic units. The observers are fully quantized. In the limit when the observers have infinite mass and are localized along geodesics at the North and South poles, it was shown in previous work \cite{CLPW} that their algebras are mutually commuting type II${}_1$ factors. Away from this limit, we show that the algebras fail to commute and that they are type I non-factors. Physically, this is because the observers' trajectories are uncertain and state-dependent, and they may come into causal contact. We compute out-of-time-ordered correlators along an observer's worldline, and observe a Lyapunov exponent given by $\frac{4\pi }{{\beta }_{\text{dS}}}$, as a result of observer recoil and de Sitter expansion. This should be contrasted with results from AdS gravity, and exceeds the chaos bound associated with the de Sitter temperature by a factor of two. We also discuss how the cosmological horizon emerges in the large mass limit and comment on implications for de Sitter holography.

We investigate the effects of Chern-Simons-Gauss-Bonnet gravity on fundamental metrics. This theory involves perturbative corrections to general relativity, as well as two scalar fields, the axion and the dilaton, which arise from Chern-Simons and Gauss-Bonnet gravity modifications respectively. The combined Chern-Simons-Gauss-Bonnet gravity is motivated by a wide range of theoretical and phenomenological perspectives, including particle physics, string theory, and parity violation in the gravitational sector. In this work, we provide the complete set of field equations and equations of motion of the Chern-Simons-Gauss-Bonnet modified gravity theory for a suite of fundamental metrics (Friedmann-Lemaître-Robertson-Walker, Schwarzschild, spherically symmetric, and perturbed Minkowski), under no prior assumptions on the behavior of the fields. The full set of field equations and equations of motion can be numerically solved and applied to specific observables under certain assumptions, and can be used to place constraints on the Chern-Simons-Gauss-Bonnet modified gravity theory.

The subtraction function plays a pivotal role in calculations involving the forward Compton amplitude, which is crucial for predicting the Lamb shift in muonic atoms, as well as the proton-neutron mass difference. In this Letter, we present a lattice QCD calculation of the subtraction function using two domain wall fermion gauge ensembles near the physical pion mass. We utilize a recently proposed subtraction point, demonstrating its advantage in mitigating statistical and systematic uncertainties by eliminating the need for ground-state subtraction. Our results reveal significant contributions from $N\pi$ intermediate states to the subtraction function. Incorporating these contributions, we compute the proton, neutron, and nucleon isovector subtraction functions at photon momentum transfer $Q^2\in [0,2]{\mathrm{GeV}}^2$. For the proton subtraction function, we compare our lattice results with chiral perturbation theory prediction at low $Q^2$ and with the results from the perturbative operator-product expansion at high $Q^2$. Finally, using these subtraction functions as input, we determine their contribution to two-photon exchange effects in the Lamb shift and isovector nucleon electromagnetic self-energy.

Lattice quantum field theory calculations may potentially combine the advantages of Hamiltonian formulations with the scalability and control of conventional Lagrangian frameworks. However, such hybrid approaches need to consider (1) the differences in renormalized coupling values between the two formulations, and (2) finite-volume and discretization effects when the Hamiltonian component of the calculation is characterized by a smaller volume or coarser lattice spacing than the Lagrangian component. This work investigates the role of both factors in the application of Hamiltonian-optimized interpolating operator constructions for the conventional Lagrangian framework. The numerical investigation is realized for the pseudoscalar meson in the Schwinger model, using tensor-network and Monte-Carlo calculations. It is demonstrated that tensor-network-optimized constructions are robust to both (1) and (2). In particular, accurate optimized constructions for the pseudoscalar meson can be obtained from calculations with a smaller number of Hamiltonian lattice sites, even when the meson mass itself receives significant finite-volume corrections. To the extent that these results generalize to theories with more complicated spectra, the method holds promise for near-term applications in large-scale calculations of lattice quantum field theory.

We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over space-time and is equivariant under Lorentz transformations. The underlying architecture is a versatile and scalable transformer, which is able to break symmetries if needed. We demonstrate the power of L-GATr for amplitude regression and jet classification, and then benchmark it as the first Lorentz-equivariant generative network. For all three LHC tasks, we find significant improvements over previous architectures.

A number of new balloon or space-based $\gamma$-ray observatories have been proposed to close a “MeV gap” in sensitivity to $\gamma$ rays in the MeV–GeV energy band. One aspect of the science case for these instruments is their ability to constrain or discover decaying or annihilating dark matter. In this work, we forecast the sensitivity of these instruments for dark matter annihilation or decay for a range of possible Standard Model final states and compare to existing bounds.

The Cabibbo-Kobayashi-Maskawa (CKM) matrix, which controls flavor mixing between the three generations of quark fermions, is a key input to the standard model of particle physics. In this paper, we identify a surprising connection between quantum entanglement and the degree of quark mixing. Focusing on a specific limit of $2\to 2$ quark scattering mediated by electroweak bosons, we find that the quantum entanglement generated by scattering is minimized when the CKM matrix is almost (but not exactly) diagonal, in qualitative agreement with observation. With the discovery of neutrino masses and mixings, additional angles are needed to parametrize the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix in the lepton sector. Applying the same logic, we find that quantum entanglement is minimized when the PMNS matrix features two large angles and a smaller one, again in qualitative agreement with observation, plus a hint for suppressed $CP$ violation. We speculate on the (unlikely but tantalizing) possibility that minimization of quantum entanglement might be a fundamental principle that determines particle physics input parameters.

The phase diagram of QCD may contain a moat regime in a large region of temperature $T$ and chemical potential $\mu \ne 0$. A moat regime is characterized by quasiparticle moatons (pions) whose energy is minimal at nonzero spatial momentum. At $\mu \ne 0$, higher mass dimension operators play a critical role in a moat regime. At dimension six, there are nine possible gauge invariant couplings between scalars and photons. For back-to-back dilepton production, only one operator contributes, which significantly enhances production near a moat threshold. This enhancement is an experimental signature of moatons.

Tree tensor network states (TTNS) generalize the notion of having low Schmidt-rank to multipartite quantum states, through a parameter known as the bond dimension. This leads to succinct representations of quantum many-body systems with a tree-like entanglement structure. In this work, we study the task of testing whether an unknown pure state is a TTNS on $n$ qudits with bond dimension at most $r$, or is far in trace distance from any such state. We first establish that, independent of the physical dimensions, $O\left(n{r}^2\right)$ copies of the state suffice to acccomplish this task with one-sided error, as in the matrix product state (MPS) test of Soleimanifar and Wright. We then prove that $\Omega \left(n{r}^2/\log n\right)$ copies are necessary for any test with one-sided error whenever $r\ge 2+\log n$. In particular, this closes a quadratic gap in the previous bounds for MPS testing in this setting, up to log factors. On the other hand, when $r=2$ we show that $\Theta \left(\sqrt{n}\right)$ copies are both necessary and sufficient for the related task of testing whether a state is a product of $n$ bipartite states having Schmidt-rank at most $r$, for some choice of physical dimensions. We also study the performance of tests using measurements performed on a small number of copies at a time. In the setting of one-sided error, we prove that adaptive measurements offer no improvement over non-adaptive measurements for many properties, including TTNS. We then derive a closed-form solution for the acceptance probability of an $(r+1)$-copy rank test with rank parameter $r$. This leads to nearly tight bounds for testing rank, Schmidt-rank, and TTNS when the tester is restricted to making measurements on $r+1$ copies at a time. For example, when $r=2$ there is an MPS test with one-sided error which uses $O\left(n^2\right)$ copies and measurements performed on just three copies at a time.

Entanglement is a resource to improve the sensitivity of quantum sensors. In an ideal case, using an entangled state as a probe to detect target fields, we can beat the standard quantum limit by which all classical sensors are bounded. However, since entanglement is fragile against decoherence, it is unclear whether entanglement-enhanced metrology is useful in a noisy environment. Its benefit is indeed limited when estimating the amplitude of dc magnetic fields under the effect of parallel Markovian decoherence, where the noise operator is parallel to the target field. In this paper, on the contrary, we show an advantage to using an entanglement over the classical strategy under the effect of parallel Markovian decoherence when we try to detect ac magnetic fields. We consider a scenario to induce a Rabi oscillation of the qubits with the target ac magnetic fields. Although we can, in principle, estimate the amplitude of the ac magnetic fields from the Rabi oscillation, the signal becomes weak if the qubit frequency is significantly detuned from the frequency of the ac magnetic field. We show that, by using the Greenberger-Horne-Zeilinger (GHZ) states, we can significantly enhance the signal of the detuned Rabi oscillation even under the effect of parallel Markovian decoherence. Our method is based on the fact that the interaction time between the GHZ states and ac magnetic fields scales as $1/L$ to mitigate the decoherence effect, where $L$ is the number of qubits, which contributes to improving the bandwidth of the detectable frequencies of the ac magnetic fields. Our results pave the way for new applications of entanglement-enhanced ac magnetometry.

Long-range attractive interactions between dark matter particles can significantly enhance their annihilation, particularly at low velocities. This Sommerfeld enhancement'' is typically computed by evaluating the deformation of the two-particle wavefunction due to the long-range potential, while ignoring the physics associated with the annihilation, and then scaling the appropriate annihilation matrix elements by factors that depend on the wavefunction in the limit where the particles approach zero relative separation. It has long been recognized that this approach is a valid approximation only in the limit where the annihilation rate is small, and breaks down in the regime where the enhanced annihilation rate approaches the unitarity bound, in which case ignoring the impact of the annihilation physics on the two-particle wavefunction cannot be justified and leads to apparent violations of unitarity. In the case where the physics relevant to annihilation occurs at a parametrically shorter distance scale (higher energy scale) compared with the long-range potential, we provide a simple prescription for correcting the Sommerfeld enhancement for the effects of the short-range physics, valid for all partial waves and for systems where multiple states are coupled by the long-range potential.

Energy correlators have recently come to the forefront of jet substructure studies at colliders due to their remarkable properties: they naturally separate physics at different scales, are robust to contamination from soft radiation, and offer a direct connection with quantum field theory. The current parametrization used for energy correlators, however, is based on redundant pairwise angles with complex phase space restrictions. In this Letter, we introduce a new parametrization of energy correlators that features a simpler phase space structure and preserves information about the orientation of jet constituents. Further, our parametrization drastically reduces the computational cost to compute energy correlators on experimental data; whereas the time to compute a traditional projected N-point energy correlator scales as M^N/N! on a jet with M particles, our new parametrization achieves a scaling of M^2 log(M) independently of N. Theoretical calculations for our new energy correlators differ from those of traditional parametrizations only at next-to-next-to-leading logarithmic accuracy and beyond, and we expect that our simpler phase space structure will simplify those calculations. We also discuss how to extend our parametrization to resolved N-point energy correlators that encode angular distances between greater numbers of particles, and we propose two possible generalizations for probing multi-prong jets and testing jet scaling behaviour.

Quantum simulation is one of the methods that have been proposed and used in practice to bypass computational challenges in the investigation of lattice gauge theories (LGTs). While most of the proposals rely on truncating the infinite dimensional Hilbert spaces that these models feature, we propose a truncation-free method based on the exact analogy between the local Hilbert space of lattice quantum electrodynamics and that of a Josephson junction. We provide several proposals, mostly semi-analog, arranged according to experimental difficulty. Our method can simulate a quasi-2D system of up to $2\times N$ plaquettes, and we present an approximate method that can simulate the fully-2D theory, but is more demanding experimentally and not immediately feasible. This sets the ground for analog quantum simulation of LGTs with superconducting circuits, in a completely Hilbert space truncation-free procedure, for continuous gauge groups.

A hallmark of far-from-equilibrium systems is the emergence of a spectral cascade, where energy is transferred across length-scales following a simple power law. The universal nature of this phenomenon has led to advances in a range of disciplines, including climate forecasting, foreign exchange trading, and the modelling of neurological activity. For many diverse far-from-equilibrium scenarios, the scaling laws of steady states have been successfully predicted by the statistical theory of weak wave turbulence, originally developed by considering the leading order interactions between waves on a fluid surface. However, the predictive power of weak wave turbulence breaks down in the presence of large amplitudes, high dissipation, and finite-size effects. We offer new insight into these regimes by experimentally tracking the formation of a spectral cascade under these conditions in an externally driven fluid-fluid interface. We resolve individual wave modes and observe their time evolution from one to few to many, a process culminating in a steady state with a spectral density characterised by a power-law scaling. Our findings confirm that interfacial dynamics can be effectively modelled by a weakly nonlinear Lagrangian theory, a predictive framework encompassing both underlying wave interaction and emergent behaviours of the system. Such nonlinear interactions are experimentally quantified through statistical correlations, revealing a hierarchy in wave-mixing order that confirms a key assumption of weak wave turbulence. The Lagrangian formulation further aids our time-evolution analysis; specific interactions are tracked through time, and we predict the timescale until a cascade emerges. Our findings are transferable to other far-from-equilibrium systems, which we demonstrate by providing a mapping to reheating scenarios following cosmic inflation in the early Universe.

Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.

The Energy Mover’s Distance (EMD) has seen use in collider physics as a metric between events and as a geometric method of defining infrared and collinear safe observables. Recently, the Spectral Energy Mover’s Distance (SEMD) has been proposed as a more analytically tractable alternative to the EMD. In this work, we obtain a closed-form expression for the Riemannian-like p = 2 SEMD metric between events, eliminating the need to numerically solve an optimal transport problem. Additionally, we show how the SEMD can be used to define event and jet shape observables by minimizing the distance between events and parameterized energy flows (similar to the EMD), and we obtain closed-form expressions for several of these observables. We also present the Specter framework, an efficient and highly parallelized implementation of the SEMD metric and SEMD-derived shape observables as an analogue of the previously-introduced Shaper for EMD-based computations. We demonstrate that computing the SEMD with Specter can be up to a thousand times faster than computing the EMD with standard optimal transport libraries.

Lattice gauge fixing is required to compute gauge-variant quantities, for example those used in RI-MOM renormalization schemes or as objects of comparison for model calculations. Recently, gauge-variant quantities have also been found to be more amenable to signal-to-noise optimization using contour deformations. These applications motivate systematic parameterization and exploration of gauge-fixing schemes. This work introduces a differentiable parameterization of gauge fixing which is broad enough to cover Landau gauge, Coulomb gauge, and maximal tree gauges. The adjoint state method allows gradient-based optimization to select gauge-fixing schemes that minimize an arbitrary target loss function.

This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations.