MIT Center for Theoretical Physics — a Leinweber Institute Publications

Likelihood-based inference in particle physics, and in the physical sciences more broadly, relies on the assumption that the model accurately describes the data. When the model is misspecified, though, standard confidence intervals shrink to zero width with increasing data, producing overconfident and potentially misleading constraints. We propose the well-tempered likelihood, which divides the likelihood-ratio test statistic by a goodness-of-fit (GOF) statistic evaluated at the best-fit point. Under correct specification, the GOF is $\mathcal{O}(1)$ and standard inference is recovered. Under misspecification, both the likelihood and the GOF scale as $\mathcal{O}(N)$ for $N$ data points, so their ratio remains $\mathcal{O}(1)$ and the resulting well-tempered confidence interval self-limits at a floor determined by the model’s inadequacy, essentially reducing the effective sample size. In other words, \textit{all models are correct, as long as your dataset is small enough}. We present binned and unbinned formulations of the well-tempered likelihood—the latter based on a classifier two-sample test—and demonstrate our method on a Gaussian example and on a measurement of the strong coupling constant using synthetic electron-positron collisions.

We explore the potential of multiple possible future 10 TeV wakefield colliders to measure electroweak couplings of the Higgs boson. We find that the beam-beam interactions are not an impediment to high precision measurements of the Higgs couplings, provided that the luminosity spectra can be measured or calculated to high accuracy. In addition to $e^+ e^-$ colliders, we also assess the effectiveness of alternatives such as $e^- e^-$ colliders or $γγ$ colliders, which by-pass the positron acceleration challenge for wakefield colliders. We find that a 10 $\text{ab}^{-1}$ dataset at a $γγ$ collider yields qualitatively similar sensitivity to 10 $\text{ab}^{-1}$ at a muon collider and 1 $\text{ab}^{-1}$ at an $e^+e^-$ wakefield collider.

We present new \compass high-statistics measurements of the peripheral production of $ηπ^-$ and $η^\prime π^-$ pairs in the reactions $π^- p \to η^{(\prime)}π^- p$. For the first time, we perform an unbinned analysis of the high-mass region of the $ηπ^-$ and $η^\primeπ^-$ systems, which allows us to disentangle the exchange mechanisms governing their production. We report the first observation in high-energy scattering of an exotic Reggeon with high significance exceeding $5\,σ$ for both channels, which is, most likely, related to the exotic $π_1(1600)$.8

Relativistic quantum field theory is the structure on which the Standard Model and beyond-Standard Model physics are built. One of its most striking predictions is the Unruh effect: an accelerating observer measures the Minkowski vacuum as a thermal bath at a fixed temperature. Despite decades of theoretical interest, this effect has never been directly observed. We propose to use the high acceleration gradients provided by wakefield accelerators, coupled with a forward laboratory-frequency ~THz detector array, to measure the resulting forward-beamed radiation, and outline the unique signature provided by quantum detailed balance to extract the signal from backgrounds. While challenging, such a measurement appears within reach of present-day accelerator and detector technologies.

Hydrodynamics is a macroscopic theory of long-wavelength dynamics around local thermal equilibrium. We develop attractodynamics, the analogous construction around a far-from-equilibrium attractor. Dynamics near a far-from-equilibrium attractor retains some non-hydrodynamic microscopic information, which attractodynamics systematically organizes. We move towards this general structure by starting in 0+1D, and consider a model for which an anisotropic far-from-equilibrium attractor solution is exactly known. This setting provides a clean benchmark in which the ideal attractodynamic equations and a leading transient residual extension can be compared directly with the full kinetic evolution. The resulting hierarchy gives an improvable description of near-attractor dynamics: the ideal theory captures evolution close to the attracting manifold, while retaining the leading off-attractor moments extends the regime of agreement until the finite truncation breaks down. This example identifies the ingredients needed for local 3+1D attractodynamics and for macroscopic attractodynamic theories not derived from an underlying kinetic description.

The worldsheet description of string amplitudes can be reinterpreted as a baby universe field theory. Under this reinterpretation, we determine the $α$-states of a topological string theory: the Hurwitz worldsheet. We find that their relation to the Hartle–Hawking state encodes foundational results in the asymptotic representation theory of the symmetric group. In the holographic dual, our results characterize the pseudorandom nature of an ensemble of cluster-decomposing correlators.

We study the algebra of observables of a semiclassical observer in de Sitter space. When operators are time-evolved by a scrambling time, out-of-time-ordered correlation functions (OTOCs) receive corrections due to shockwave scattering near the cosmological horizon. When the observer’s clock is treated classically, we show that the time advance effect implies the breakdown of the KMS condition for vacuum correlators of matter operators. When the observer’s clock is quantized, this implies that the Hartle-Hawking state is not a trace on the resulting crossed-product algebra. We conjecture that the observer’s algebra has a trivial commutant. When the time separation between operators exceeds the scrambling time, the OTOC decays to zero and a free product algebra emerges. We illustrate this using classical solutions of de Sitter JT gravity with shocks. We comment on how our results pose a challenge for observer-centric static patch holography.

The Standard Model prediction for the rare $K_L\toμ^+μ^-$ decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the $u$, $d$ and $s$ quarks, provided terms falling as the inverse square of the omitted charm quark mass, $1/m_c^2$ are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancelation, this three-flavor theory contains additional low-energy constants that depend on $m_c$. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with $u$ and $d$ quark masses that are heavier than physical.

Diffraction is characterized by forward scattering and a large rapidity gap. Ordinary hard scattering also produces gapped events and presents a significant background to identification of diffractively produced events. We present a fully differential factorization of gapped hard $ep$ scattering. We find that the unpolarized azimuthally-dependent structure functions $F_{3,4}^{\rm gap}$ and the longitudinal $F_L^{\rm gap}$ vanish at leading power for hard scattering. Azimuthal dependence is thus a pure diffractive signature. This is borne out in Monte Carlo simulations.

We use effective field theory techniques to factorize elastic, single, and double diffractive forward $pp$ scattering in the Regge limit $|t|\ll s$, where $t$ is the squared momentum transfer. These processes involve a large rapidity gap and comprise about half the total $pp$ cross section. We explain why the diffractive PDFs appearing in $ep$ diffraction do not appear as universal hadronic functions for $pp$ diffraction. For $|t|\sim Λ_{\rm QCD}^2$, we show that the hadronic functions in $ep$ and $pp$ diffraction differ, and hence are non-universal. In general, we prove that rapidity anomalous dimensions are universal between diffractive $ep$ and $pp$ processes, and that color-singlet (Pomeron) evolution equations can be determined at the amplitude level.

The measurement of the sum of neutrino masses is among the primary promises of precision cosmology, achievable by combining complementary early- and late-Universe probes. However, these datasets currently exhibit mild-to-strong disagreements within $Λ$CDM and its simplest extensions, giving rise to multiple tensions, including the Hubble tension, the preference for “negative” neutrino mass, and indications of evolving dark energy. It has recently been shown that these tensions can be alleviated by adopting a higher value of the optical depth to reionization parameter, $τ$, when large-scale cosmic microwave background (CMB) polarization data are ignored. We extend this proposal and show that an especially high prior on $τ= 0.11 \pm 0.006$ simultaneously addresses all three of these tensions, significantly reducing the need for new physics beyond $Λ$CDM. We determine the “concordance” value of $τ$ by requiring physical neutrino mass and consistency of the Hubble constant, $H_0$, inferred from the CMB and that preferred by the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) and full-shape measurements. Within this high-$τ$ Universe, we obtain the first $2σ$ detection of a positive neutrino mass, $Σm_ν = 0.10^{+0.04}_{-0.05}$~eV at 68% C.L., while restoring cosmological concordance between datasets within $Λ$CDM. In particular, low-redshift distance predictions are consistent with DESI BAO observations and the inferred dark-energy equation-of-state parameters are consistent with a cosmological constant, both with and without supernovae data. The concordance power of our $τ$ prior further motivates new measurements of $τ$, e.g., through large angular scale CMB polarization observations with the \textit{LiteBIRD}, CLASS, or proposed PICO experiments. (Abridged)

We compute the galaxy power spectrum at two-loop order in cosmological perturbation theory (effective field theory, EFT). We derive galaxy bias operators through the fifth order and obtain two-loop renormalization conditions for the their bias coefficients. We compute the two-loop integrals using a renormalization scheme consistent with the CLASS-PT code, allowing for an easy interface of our new computations with standard tools used in the one-loop galaxy power spectrum and bispectrum analyses. We also derive the relevant higher-derivative and stochastic contributions, and implement IR resummation using time-sliced perturbation theory. Having identified the redundant operators, we find that the two-loop galaxy power spectrum requires 21 additional EFT parameters per galaxy sample. We compare our computation with the galaxy-galaxy and galaxy-matter power spectra from the PT Challenge N-body simulation at $z=0.61$ and find a per mille-level agreement up to $k=0.85~h$Mpc$^{-1}$. We show that even with conservative priors on all EFT parameters, the two-loop model produces an unbiased measurement of the mass fluctuation amplitude $σ_8$ with three times narrower error-bars than the linear theory model. The improvement over the one-loop model is $\simeq 40\%$. This suggests significant gains in the two-loop EFT analyses of galaxy clustering and galaxy–lensing two-point functions ($2\times2$ pt) from CMB lensing maps and imaging surveys like Euclid, LSST, and Roman. In addition, our two-loop computation offers a probe of new physics scenarios that modify the shape of the matter power spectrum at wavenumbers $(0.4-0.8)~h$Mpc$^{-1}$ such as the presence of ultra-light axion dark matter sub-components with masses $m_a\sim 10^{-24}$ eV.

We present a field-level perturbative forward model for the Lyman-alpha (Lya) forest flux decrement. We validate it on two simulation suites: large-volume AbacusSummit N-body simulations with the Lya forest painted onto the dark matter field, and the Sherwood hydrodynamic simulations. Across the redshift range of the simulations (z=2.0-3.2), the 3D and 1D power spectra of the model match the simulated Lya fields at the 1% (5%) level up to k <= 0.3 (1.0) h/Mpc, with similar performance for the cross-correlation with massive dark matter halos. The counts-in-cells statistic shows excellent agreement down to cell radii of 2 Mpc/h. Leveraging cosmic variance cancellation, the model enables precision measurements of Lya bias parameters and robustly detects the full set of quadratic line-of-sight bias operators, consistent with the notion of naturalness in effective field theory (EFT). We quantify the stochasticity of the Lya forest (the analog to the one-halo term), and find it to be white (scale- and orientation-independent) on large scales, matching EFT predictions. We further find that phenomenological flux power spectrum models, based on modulations of the linear-theory power spectrum, fail at the field level even on quasi-linear scales. For the currently observing Dark Energy Spectroscopic Instrument (DESI), we generate large-scale clustering mocks of the Lya forest to validate cosmological parameter inference pipelines. Looking ahead to its successor, DESI-II, we produce large-volume mocks of representative samples of Lyman-break galaxies (LBGs) and Lya emitters (LAEs), calibrated on Astrid hydrodynamic simulations and matched to observations at z=3, enabling joint analyses of Lya forest and high-redshift galaxy data.

We review the concepts of interpretability and explainability as they apply to machine learning in physics. We define interpretability as concerning the structural transparency of a model (the ability to understand or approximate its inner workings) and explainability as concerning the scientific content of a model (the ability to map it onto domain knowledge). We discuss the trade-offs each entails (interpretability vs. expressivity; explainability vs. adaptability), the contexts in which each is needed, and the intrinsic and post-hoc tools available for achieving them. Throughout, we emphasize that machine-learned models are subject to the same scientific questions as classical models, differing only in scale, and that interpretability and explainability are best understood as deliberate modeling choices rather than inherent properties. We also emphasize the importance of task specification and intervention plans as a core aspect of model design.

We introduce a procedure called random dimension reduction that simultaneously reduces the dimensions of many, potentially distinct quantum states while preserving properties invariant under the tensor power action of an isometry. This provides a black-box method to replace the dimension with the maximum rank in the sample complexity of learning symmetric properties, even those depending on multiple input states. We show that dimension reduction followed by full state tomography yields improved upper bounds for estimating distances, fidelities, and relative entropies between pairs of states. We also give an efficient quantum circuit implementation of the procedure using the Schur transform. Expressing the action of our procedure through the Choi-Jamiolkowski isomorphism reveals an intimate connection with the recently introduced random purification channel by Tang, Wright, and Zhandry. This perspective also completes an end-to-end analysis of sample-optimal tomography without requiring a reference to the Schur transform or Schur polynomials. Finally, we prove that there does not exist a random purification channel that simultaneously purifies copies of multiple, potentially different input states. Hence, random dimension reduction is related to, but distinct from, random purification.

We introduce the \emph{Centauric 1-jettiness}, $τ_1^C$, a generalized event shape for Deep Inelastic Scattering (DIS) with adjustable beam and jet reference vectors and thus beam and jet regions. We demonstrate that a specific choice of weights allows this observable to exactly reproduce the geometric boundaries of the Centauro jet algorithm in the Breit frame. Within the framework of Soft-Collinear Effective Theory (SCET), we derive a factorized cross section in the small-$τ_1^C$ region in terms of known perturbative ingredients. This allows the resummation of large logarithms to N$^3$LL accuracy, which we then match to fixed-order NLO QCD ($\mathcal{O}(α_s^2)$) predictions from \texttt{NLOJet++}. We establish that the soft measurement reduces to a rescaled hemisphere measurement, placing Centauric 1-jettiness in the same universality class, for the leading non-perturbative corrections, as DIS thrust and jet mass. As a consequence, the leading non-perturbative shift depends on the same universal first-moment-shift parameter $Ω_1$ and scales exactly as $1/R$ with the jet radius, thanks to the boost invariance of the Centauro algorithm along the photon axis in the Breit frame, a scaling that we test using \textsc{Pythia} simulations. These results open new strategies for determining the strong coupling from DIS event shapes, with $R$ providing a handle to break the degeneracy between $α_s$ and the universal non-perturbative shift parameter $Ω_1$.

We study two-point functions of half-BPS operators in maximally supersymmetric Yang-Mills theory continued to $d=4-2\,\varepsilon$ dimensions. Using supersymmetric localization on $S^d$, we derive perturbative matrix-model expressions for the $\varepsilon$-expansion of these correlators and obtain all-loop results at leading order in $\varepsilon$ in the planar limit, with extensions to finite-$N$ corrections and higher-charge operators. We compare the localization results with direct perturbative computations in flat space. At order $\varepsilon$ the two descriptions agree perfectly, while at higher orders our construction fails to reproduce the perturbative data due to the breaking of conformal symmetry away from four dimensions. Nevertheless, in the case of the dimension-two operator we conjecture an all-loop formula at order $\varepsilon^2$ by exploiting the precise form of the mismatch.

A principal lesson from recreating droplets of quark-gluon plasma (QGP) in heavy ion collisions is that it is a strongly coupled liquid, not a plasma of partons. The energy density and pressure of quarks and gluons confined within a proton are comparable to those of QGP at or just above the QCD transition temperature. Given this similarity between protons and QGP, we propose that the investigation of correlations between nearby partons within a proton must be a central goal for the future Electron-Ion Collider (EIC). Here, we ask how EIC measurements can discern such short-range correlations (SRCs) of quark pairs. Doing so would characterize the strongly coupled interior of a proton, augmenting the one-parton-at-a-time understanding of protons via (generalized) parton distribution functions, and could at the same time yield a key ingredient for the microscopic understanding of the liquid nature of QGP. Motivated by the experiments that have been used to demonstrate the existence of SRCs between nucleon pairs within a nucleus, we propose using EIC observables involving measurements of a jet and a pion, together with the scattered electron, to seek and quantify the possible existence of SRCs between quark pairs within a nucleon. The pronounced isospin dependence observed in the dominance of $np$ SRCs over $pp$ or $nn$ SRCs has played a central role in establishing the importance of SRCs among nucleons in nuclei. Analogously, the QCD attraction in the $ud$ diquark channel can make the $ud$ SRC stronger than the $uu$ and $dd$ SRCs, allowing a first observation of partonic SRCs.

Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicating that the formal inverse problem in the latter is not a concern at this volume. We further extend the framework to higher dimensions and obtain the first 3D image of the pion directly from lattice QCD.

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.