MIT Center for Theoretical Physics — a Leinweber Institute Publications

In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses; however, biases induced by simulation-data mismodeling can be difficult to control within standard inference pipelines. In this work, we propose a Template-Adapted Mixture Model to confront this problem in the context of signal fraction estimation: inferring the population proportion of signal in a mixed sample of signal and background, both of which follow arbitrarily complex distributions. We harness many biased simulations to perform data-driven estimates of each process distribution in the signal region, substantially reducing the bias on the signal fraction due to the domain shift between simulation and reality. We explore different methodological choices, including model selection, feature representation, and statistical method, and apply them to a Gaussian toy example and to a semi-realistic di-Higgs measurement. We find that the presented methods successfully leverage the biased simulations to provide estimates with well-calibrated uncertainties.

We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single scalar before computing a parameter update. Sven treats each data point’s residual as a separate condition to be satisfied simultaneously, using the Moore-Penrose pseudoinverse of the loss Jacobian to find the minimum-norm parameter update that best satisfies all conditions at once. In practice, this pseudoinverse is approximated via a truncated singular value decomposition, retaining only the $k$ most significant directions and incurring a computational overhead of only a factor of $k$ relative to stochastic gradient descent. This is in comparison to traditional natural gradient methods, which scale as the square of the number of parameters. We show that Sven can be understood as a natural gradient method generalized to the over-parametrized regime, recovering natural gradient descent in the under-parametrized limit. On regression tasks, Sven significantly outperforms standard first-order methods including Adam, converging faster and to a lower final loss, while remaining competitive with LBFGS at a fraction of the wall-time cost. We discuss the primary challenge to scaling, namely memory overhead, and propose mitigation strategies. Beyond standard machine learning benchmarks, we anticipate that Sven will find natural application in scientific computing settings where custom loss functions decompose into several conditions.

In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus partition function of a 2d CFT is fixed by the spectrum of its primary operators and its chiral algebra, which we take to be the Virasoro algebra with $c>1$. We translate the requirement that this partition function is modular invariant into a loss function, which we then minimize to identify possible primary spectra. Our approach involves two technical innovations that facilitate finding reliable candidate CFTs. The first is a strategy to estimate the uncertainty associated with truncating the spectrum to the lowest dimension operators. The second is the use of a new singular-value-based optimizer (Sven) that is more effective than gradient descent at navigating the hierarchical structure of the loss landscape. We numerically construct candidate truncated CFT partition functions with central charges between 1 and $\frac{8}{7}$, a range devoid of known examples, and argue that these candidates likely come from a continuous space of modular bootstrap solutions. We also provide evidence for a more stringent constraint on the spectral gap near $c = 1$ than the existing bound of $Δ_{\rm gap} \le \frac{c}{6} + \frac{1}{3}$.

In this paper, we study various conceptual and practical aspects of using maximum-entropy reweighting to upgrade parton-shower event samples based on higher-accuracy theoretical constraints. Our approach produces strictly positive per-event weights that improve parton-shower predictions while preserving full event-level exclusivity, allowing any observable to be computed on the reweighted sample without rebinning or regeneration. On the conceptual side, we explain how theoretical principles can help determine which constraints to use and which kinds of priors lead to efficient reweighting. On the practical side, we perform a proof-of-concept study with hemisphere observables in $e^+e^-\!\to$ hadrons, and show that even when the parton-shower prior is purposefully degraded by removing the non-singular parts of the QCD splitting functions, a small set of precision calculations can nevertheless restore the desired physical behavior. We use energy flow polynomials (EFPs) as a systematic basis to organize infrared- and collinear-safe constraints, and study how information transfers from constrained observables to unconstrained ones. We find rapid information saturation, where constraints from a compact set of EFP moments achieve broad improvements across observable space, including for standard hemisphere observables never used in training. Physics-motivated basis reductions guided by collinear power counting achieve comparable performance to complete bases, and mixed moments combining polynomial and logarithmic terms outperform pure alternatives. These results suggest a systematic approach to improving parton-shower event generators, where theoretical constraints of highest accuracy can be translated into full phase-space predictions of experimental relevance.

We present a lattice quantum chromodynamics calculation of the $x$-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}_2$ moment of the twist-3 PDF $g_T(x)$ for the first time in the $\overline{\rm MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing $a$ = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta $P_z=\{0, 0.25, 1.02, 1.53\}$ GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for $g_T(x)$, we obtain $\tilde{d}_2^{u-d}(2\ {\rm GeV})=0.0024(46)$ at next-to-leading order in $\overline{\rm MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the $x$-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{\rm MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region $x\in[0.25,0.75]$ with controlled systematic uncertainties. The end-point regions are then parameterized, combined with the LaMET prediction at moderate $x$, and fitted to the short-distance matrix elements in coordinate space.

Exploding primordial black holes can source baryon asymmetry soon after the electroweak phase transition, as high-energy Hawking radiation drives ultrarelativistic shocks in the surrounding plasma. The shocks and their trailing rarefaction waves delineate two bubble-like walls around a shell of superheated fluid, in which electroweak symmetry is restored. These moving interfaces source chiral charge, which is converted to baryon number. Upon adding a simple CP-violating operator at the TeV scale, this mechanism yields the observed baryon asymmetry with minimal dependence on PBH model parameters.

Cosmic shear is a powerful probe of cosmological distances, matter abundance and clustering in the low-redshift Universe. Cosmological parameter extraction from cosmic shear data is limited by our understanding of baryonic astrophysics, which severely restricts the range of scales used in such analyses. We show that the remaining scales are largely perturbative and can be accurately described with two-loop effective field theory (EFT) predictions. We present the first consistent analysis of the public cosmic shear data from the DES-Y3 catalogs in EFT at the two-loop order, renormalizing small-scale sensitivity in cosmic-shear predictions via a lensing-counterterm expansion and accounting for the intrinsic alignments of galaxies with spin-2 EFT predictions. We constrain the lensing amplitude competitively with standard (empirically-modeled) methods, finding $S_8 = 0.783^{+0.038}_{-0.031}$ ($S_8 = 0.802^{+0.031}_{-0.026}$ with BAO). The perturbativity of cosmic shear suggests novel opportunities for testing new physics with ongoing and upcoming cosmic shear experiments like Roman, Euclid, and LSST. As an example, we derive matter clustering constraints within the dynamical dark energy model from a combination of our DES-EFT cosmic shear likelihood, early-universe CMB priors, DESI BAO, and supernovae data, finding $S_8 = 0.824\pm 0.029$, indicating no $S_8$ tension in the growth of cosmic structure regardless of the underlying cosmological model and expansion history.

We introduce a novel reformulation of three-dimensional gravity in terms of divergenceless vector frames, inspired by the double copy for Chern-Simons theory. This formulation is on-shell equivalent to conventional 3D gravity and provides a transparent geometric interpretation of the double-copy construction. We relate the resulting theory to a Chern-Simons-like action, propose a higher-dimensional origin, and explore extensions that give rise to $AdS_3$

Ultra-relativistic oxygen-oxygen (OO) collisions are a promising arena in which to probe rare, large-angle, high momentum-transfer $2\rightarrow2$ Molière scatterings between energetic jet partons and quasiparticles in quark-gluon plasma (QGP). As a jet propagates through the droplet of QGP formed in the same collision, its constituents lose energy to and excite wakes in the medium, and may scatter off quark- and gluon-like quasiparticles in QGP. Using the hybrid strong/weak coupling model, we show that including Molière scatterings between jet partons and medium quasiparticles is essential to reproduce recent CMS measurements of charged-particle suppression in OO collisions with this model. We then present the first theoretical study of how jet-medium interactions modify the internal structure of jets in OO collisions. We find that Molière scatterings broaden the Soft Drop splitting angle $R_g$, enhancing the population of $R=0.4$ and $R=0.8$ jets with $R_g\gtrsim0.2$ in OO collisions relative to pp collisions. Energy-energy correlators (EECs) provide a complementary probe, exhibiting enhanced large-angle correlations within jets due to jet-induced wakes and Molière scattering. In both cases, we propose an experimental measurement where the relevant OO/pp ratio can, if enhanced above unity in future data as in our calculations, be a distinctive, model-independent, detection of hard scattering off QGP quasiparticles. We furthermore use our calculations of EECs to show how the angular scale corresponding to the deflection of jet or medium partons by Molière scattering is imprinted in the EEC for jets with radius $R_{\rm jet}\sim0.8$ in OO collisions. These results demonstrate that jet substructure measurements in OO collisions are promising avenues to probe the quasiparticles that emerge at short distances within an otherwise strongly coupled medium.

Understanding the link between correlation functions (CFs) of local operators and measurable collider correlators has emerged as a new opportunity in the study of gauge theory dynamics at colliders. While in Conformal Field Theories (CFTs) this connection is established by the light transform, the non-conformal nature of QCD complicates its use beyond the lowest perturbative order. We show that a continuation of the CFs to the Wilson-Fisher fixed point can be used as a method to overcome these obstacles, serving as a conformal bridge for the evaluation of the light transform. At the fixed point, the renormalized CF of four local operators features a variable drop and only depends on two conformal cross ratios, in line with a genuine CFT quantity. This allows us to exploit CFT techniques to perform, for the first time, its light transform at higher loop orders. Remarkably, the resulting collider correlator in four dimensions can be recovered from this result simply by using lower-loop data. We demonstrate this method by computing the back-to-back limit of the charge-charge correlation (QQC) at two loops in QCD through the light transform of the CF of four vector currents in the sequential light-cone limit, reproducing a recent prediction.

We describe numerical simulations of the critical dynamics near the superfluid phase transition. The calculations are based on an implementation of a stochastic hydrodynamic theory known as model F in the classification of Hohenberg and Halperin. This theory is expected to describe dynamic scaling near the lambda transition in liquid $^4$He, Bose-Einstein condensation in ultracold atomic gases, and the superfluid transition in the unitary Fermi gas. Our simulation is based on a Metropolis algorithm previously applied to the critical endpoint of the liquid-gas phase transition in ordinary fluids. In the model E truncation of model F we obtain the expected dynamical exponent $z\simeq 3/2$. We observe the emergence of a propagating second sound mode at the phase transition. The second sound diffusivity $D_s$ is consistent with the scaling relation $D_s\sim ξ^{x_κ}$, where $ξ$ is the correlation length and $x_κ=1/2$.

We investigate how Hawking radiation from low-mass primordial black holes deposits energy into the early-universe plasma and show that the resulting phenomena are hydrodynamic rather than purely diffusive. Combining analytic arguments with relativistic hydrodynamic simulations, we find that the plasma first develops a quasi-steady outflow during the slow evaporation stage, while the final runaway phase of evaporation produces an expanding fireball that launches a shock wave into the surrounding medium. We characterize the thermalization scale of the Hawking products, the conditions under which shocks form, and the evolution and propagation of shocks. Additionally, we show that these shocks can locally restore electroweak symmetry, identifying exploding PBHs as a potentially important source of out-of-equilibrium dynamics in the early universe with profound phenomenological implications.

Hydrodynamic simulations of neutron star mergers rely on the clear separation between the strong-interaction, weak-interaction, and hydrodynamic timescales. In this effective framework, weak Urca interactions are typically the slowest microscopic processes, and therefore the Urca rate determines the bulk-viscous dissipation. This assumed hierarchy of dissipative mechanisms can be decisively altered, without invalidating hydrodynamics, if the trajectory of the matter in a neutron star merger passes through the vicinity of a possible low temperature QCD critical point. The enhanced density fluctuations lead to critical slowing down and rapid growth of transport coefficients including bulk viscosity. While this growth is regulated by finite-time effects, finite-size effects, and the breakdown of hydrodynamic scale separation, which bound the correlation length, we demonstrate that the QCD contribution to bulk viscosity can rival the electroweak contribution in realistic conditions. Thus, critical dynamics could leave observable imprints on the hydrodynamic evolution of neutron star mergers.

We consider the energy loss of a high-energy parton in the early anisotropic plasma in heavy-ion collisions. Working in the harmonic approximation, we compute the change in the mean energy of an emitted gluon in the presence of an anisotropic background, characterized by anisotropic jet quenching parameters $\hat q_{x}\neq \hat q_{y}$. Evaluating the resulting integrals numerically, we compare with isotropic media, and obtain a simple pocket formula to estimate the impact of anisotropy on the mean emitted gluon energy, which is generally small. We then combine our results with the values of the jet quenching parameter extracted from QCD kinetic theory simulations and show that the medium length dependence of this mean energy loss exhibits the characteristics of limiting attractors, which can be obtained by extrapolating to zero and infinite coupling. Our study thus relates energy loss of jet partons to universal dynamics of anisotropic plasmas.

Quark-gluon plasma (QGP) is a strongly coupled liquid when viewed at length scales of order the inverse of its temperature and longer. However, when it is probed at short enough length scales, asymptotic freedom mandates the presence of quark- and gluon-like quasiparticles. Partons in jets can trigger perturbative, high momentum-exchange $2\rightarrow2$ Molière scatterings off quasiparticles in the medium, making jets useful probes of the microscopic structure of QGP. Prior to this work, soft strongly coupled momentum-exchanges between jet partons and the QGP droplet produced in a heavy-ion collision, as well as the wakes that jets excite in the droplet, had been accounted for in the Hybrid Model of jet quenching. Here, we present a full calculation of Molière scattering off a QGP quasiparticle which results in the deflection of the jet parton and the excitation of a parton from the thermal medium that recoils after being kicked, and describe how it is implemented in the Hybrid Model. The scattered jet and recoil partons continue to propagate through the QGP, lose energy and momentum, excite wakes, and may further re-scatter. Using the Hybrid Model, we study how Molière scatterings impact jet shapes and fragmentation functions, the Soft Drop angle $R_g$, jet girth $g$, and observables that focus on the number and angular distribution of subjets within jets. We demonstrate that photon-tagged jets provide a particularly sensitive probe: selecting events by the photon energy mitigates the selection bias inherent in inclusive jet measurements and enhances sensitivity to rare large-angle scatterings. We find that Molière scatterings broaden both the $R_g$ and $g$ distributions when jets significantly softer than the photon are included. Our results point the way towards distinctive model-independent experimental signatures of hard scattering of jet partons off quasiparticles in QGP.

We present a combined analytical and numerical study of the effective action of field theory cosmic strings in the Abelian-Higgs model in flat space. Starting directly from the underlying solitonic field theory description, we provide a systematic derivation of the low energy effective action and present evidence for the absence of nontrivial curvature correction terms when only the translational Goldstone modes are retained. Using this framework, we extend the effective theory to include higher energy fluctuations of the soliton profile, which map to massive degrees of freedom propagating on the worldsheet. We show that the leading curvature contribution enters only through the coupling between these massive modes and the worldsheet Ricci scalar. We validate the resulting effective theory via lattice simulations of the full field theory equations of motion in flat space, implemented with Adaptive Mesh Refinement to capture the string dynamics across different scales. The numerical simulations confirm the dynamics obtained using the effective action in its validity range. Furthermore, they also demonstrate the existence of the predicted parametric instability of excited strings that drives the transfer of energy from massive excitations to the Goldstone sector.

Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of existing metrics. In particular, we show how ergodicity and chaos improve the robustness of Hamiltonian learning to small errors and furthermore demonstrate that this robustness can be used as a metric for such phenomena. We analytically and numerically show that our metrics not only distinguish between integrable and ergodic regimes in various spin chains but also quantify chaos and ergodicity, allowing us to locate regions of parameter space displaying maximal ergodicity and maximal sensitivity to local perturbations. Our approach not only provides conceptual ways to study quantum chaos and ergodicity but also presents viable experimental methods for quantum simulators.

The light-cone distribution amplitude (LCDA) is a fundamental non-perturbative quantity for understanding hadron structure and exclusive scattering processes. We report on our calculation of the pion and kaon LCDAs using the heavy-quark operator product expansion (HOPE) framework. This method employs an OPE analysis of hadronic amplitudes through the inclusion of a fictitious valence heavy quark. In these proceedings, we report progress on the determination of the first three nontrivial Mellin moments of the kaon LCDAs from dynamical lattice QCD calculations, and we summarize the recently published continuum-limit result for the pion fourth Mellin moment obtained in the quenched approximation, thereby demonstrating the feasibility of the HOPE method for accessing higher moments.

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor Quantum Chromodynamics (QCD) in four space-time dimensions. Variance reduction by factors of $10$-$60$ is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so that volume transfer can be utilized to minimize training costs.

We analyze the public DESI full-shape clustering data using simulation-based priors (SBPs). Our priors are obtained by fitting normalizing flows to the distribution of EFT parameters measured from field-level simulations, themselves generated using tailored halo occupation distribution (HOD) models for each tracer. Incorporating SBPs in a power spectrum analysis significantly enhances $Λ$CDM cosmological parameter constraints; in combination with BAO information from DESI DR2 and a BBN prior on the baryon density, we find the matter density parameter $Ω_m=0.2987\pm 0.0066$, the Hubble constant $H_0=68.80\pm 0.35\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, and the mass fluctuation amplitude $σ_8 = 0.766\pm 0.015$ (or the lensing parameter $S_8=0.764\pm 0.018$), which are $1\%$, $40\%$ and $50\%$ stronger than the baseline results, though with a notable downwards shift in $σ_8$. The SBPs also have a significant impact in extended models, with the dark energy figure-of-merit improving by $70\%$ ($20\%$) in a $w_0w_a$CDM analysis when combining with the CMB (and supernovae). In the SBP analysis, we do not find statistically significant evidence for dynamical dark energy: the equation of state parameters are consistent with a cosmological constant within $2.2σ$ ($1.4σ$) in analyses without (with) supernovae. The neutrino mass constraints are also enhanced, with the $95\%$ limits $M_ν<0.073\,\mathrm{eV}$ and $M_ν<0.090\,\mathrm{eV}$ in $Λ$CDM and $w_0w_a$CDM respectively. The latter is the strongest constraint obtained to date and reinforces the preference for the normal neutrino mass hierarchy, regardless of the background dynamics. While our results are sensitive to HOD modeling assumptions, they clearly demonstrate that the inclusion of small-scale information can significantly sharpen cosmological parameter constraints.