MIT Center for Theoretical Physics — a Leinweber Institute Publications

We present precision measurements of the bias parameters of the one-loop power spectrum model of the Lyman-$\alpha$ (Ly-$\alpha$) forest, derived within the effective field theory (EFT) of large-scale structure. We fit our model to the three-dimensional flux power spectrum measured from the ${\mathrm{ACCEL}}^2$ hydrodynamic simulations. The EFT model fits the data with an accuracy of below 2% up to $k=2h{\mathrm{Mpc}}^{-1}$. Further, we analytically derive how nonlinearities in the three-dimensional clustering of the Ly-$\alpha$ forest introduce biases in measurements of the baryon acoustic oscillations (BAOs) scaling parameters in radial and transverse directions. From our EFT parameter measurements, we obtain a theoretical error budget of $\Delta {\alpha }_{\parallel }=-0.2\%$ ($\Delta {\alpha }_{\perp }=-0.3\%$) for the radial (transverse) parameters at redshift $z=2.0$. This corresponds to a shift of $-0.3\%$ (0.1%) for the isotropic (anisotropic) distance measurements. We provide an estimate for the shift of the BAO peak for Ly-$\alpha$ -quasar cross-correlation measurements assuming analytical and simulation-based scaling relations for the nonlinear quasar bias parameters resulting in a shift of $-0.2\%$ ($-0.1\%$) for the radial (transverse) dilation parameters, respectively. This analysis emphasizes the robustness of Ly-$\alpha$ forest BAO measurements to the theory modeling. We provide informative priors and an error budget for measuring the BAO feature—a key science driver of the currently observing Dark Energy Spectroscopic Instrument (DESI). Our work paves the way for full-shape cosmological analyses of Ly-$\alpha$ forest data from DESI and upcoming surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.

We analyze the computation of $n$-point correlation functions in de Sitter spacetime, including loop corrections, using the wavefunction of the universe approach. This method consists of two stages employing distinct Feynman rules. First, one must compute the wavefunction coefficients using interactions as vertices. Then, in the second stage, one computes correlation functions using wavefunction coefficients as vertices. For massless fields, loop corrections in the first stage are free of infrared (IR) divergences, which leads to the question of how this matches the well-known IR behavior of correlators obtained via other methods. By considering a scalar field with an arbitrary potential, we compute $n$-point correlation functions to first order in the potential but to all orders in loops. We find that, although loop integrals in the first stage are indeed IR convergent, the second procedure reintroduces the IR divergence. We discuss how this induces renormalization of the interaction potential such that the final result combining both steps exactly matches the form of $n$-point functions previously calculated with other methods.

Cosmological analyses of redshift space clustering data are primarily based on using luminous red'' galaxies (LRGs) and blue'' emission line galaxies (ELGs) to trace underlying dark matter. Using the large high-fidelity high-resolution MillenniumTNG (MTNG) and Astrid simulations, we study these galaxies with the effective field theory (EFT)-based field level forward model. We confirm that both red and blue galaxies can be accurately modeled with EFT at the field level and their parameters match those of the phenomenological halo-based models. Specifically, we consider the state of the art Halo Occupation Distribution (HOD) and High Mass Quenched (HMQ) models for the red and blue galaxies, respectively. Our results explicitly confirm the validity of the halo-based models on large scales beyond the two-point statistics. In addition, we validate the field-level HOD/HMQ-based priors for EFT full-shape analysis. We find that the local bias parameters of the ELGs are in tension with the predictions of the LRG-like HOD models and present a simple analytic argument explaining this phenomenology. We also confirm that ELGs exhibit weaker non-linear redshift-space distortions (fingers-of-God''), suggesting that a significant fraction of their data should be perturbative. We find that the response of EFT parameters to galaxy selection is sensitive to assumptions about baryonic feedback, suggesting that a detailed understanding of feedback processes is necessary for robust predictions of EFT parameters. Finally, using neural density estimation based on paired HOD-EFT parameter samples, we obtain optimal HOD models that reproduce the clustering of Astrid and MTNG galaxies.

We supplement the string field theory action with boundary terms to make its variational principle well-posed. Central to our considerations is the violation of the stress-energy tensor conservation in non-compact CFTs due to the boundary terms. This manifests as the failure of the cyclicity of the BRST operator, which encodes the target space integration by parts identities at the level of the worldsheet. Using this failure, we argue that the free closed string field theory action admits a well-posed variational principle upon including an additional boundary contribution. We explicitly work out the resulting action up to the massless level and show that it is related to the expansion of the low-energy effective string action endowed with the Gibbons-Hawking-York term on a flat background. We also discuss the structure of the boundary terms in the interacting theory.

We provide state-of-the-art precision QCD predictions for the fiducial W and Z boson transverse momentum spectra at the LHC at N${}^{}$LL${}^{}$ and approximate N${}^{}$LL in resummed perturbation theory, matched to available $O\left({\alpha }_s^3\right)$ fixed-order results. Our predictions consistently combine all information from across the spectrum in a unified way, ranging from the nonperturbative region of small transverse momenta to the fixed-order tail, with an emphasis on estimating the magnitude of residual perturbative uncertainties, and in particular of those related to the matching. Parametric uncertainties related to the strong coupling, the collinear PDFs, and the nonperturbative transverse momentum-dependent (TMD) dynamics are studied in detail. To assess the latter, we explicitly demonstrate how the full complexity of flavor and Bjorken x-dependent TMD dynamics can be captured by a single, effective nonperturbative function for the resonant production of any given vector boson at a given collider. We point out that the cumulative $p_T^Z$ cross section at the level of precision enabled by our predictions provides strong constraining power for PDF determinations at full N${}^3$LO.

Collider experiments involving nuclei provide a direct means of studying exotic states of nuclear matter. Recent measurements of energy correlators in both proton-nucleus (p-A) and nucleus-nucleus (A-A) collisions reveal sizable modifications, attributable to nuclear effects, compared to proton-proton (p-p) collisions. Energy correlators, and their associated light-ray operator product expansion (OPE), allow scaling behaviors of the measured spectrum to be directly mapped to properties of the underlying quantum field theory. Here, we demonstrate for the first time how this mapping occurs in nuclear collisions, and highlight how the light-ray OPE characterizes leading nuclear effects. We show that the leading modification to the energy correlator distribution is characterized by an enhancement of the expectation value of twist-4 light-ray operators, resulting in a scaling for the ratio of the two-point correlator in nuclear matter to that in vacuum of $\sim 1+a{\theta }^2$ up to quantum corrections. We verify that this leading twist-4 correction accurately describes recent A-A and p-A data, and is thus sufficient to capture the scaling behavior within the angular range measured for jet radii used in nuclear experiments. Our light-ray OPE based approach lays the groundwork for a rigorous characterization of nuclear modification to energy correlator observables.

Inclusive hadronic observables are ubiquitous in particle and nuclear physics.Computation of these observables using lattice QCD is challenging due the presence of a difficult inverse problem.As a stepping stone to more complicated observables, we report on progress to compute the smeared $R$~ratio with staggered quarks using the spectral reconstruction algorithm of Hansen, Lupo, and Tantalo.We compare staggered-quark results on two ensembles to domain-wall results on a single ensemble and to the Bernecker-Meyer parameterization.This work utilizes two ensembles generated by the MILC collaboration using highly improved staggered quarks and one ensemble generated by the RBC/UKQCD collaboration using domain-wall quarks.Possible strategies for controlling opposite-parity effects associated with staggered quarks are discussed.

Lattice ℤ${}_3$ theories with complex actions share many key features with finite- density QCD including a sign problem and $CK$ symmetry. Complex ℤ${}_3$ spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ${}_3$ spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ${}_3$ models in dimensions one through four. Chiral ℤ${}_3$ spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ${}_3$ analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ${}_N$ models, SU(N) models and nonzero temperature.

We study the detectability of GeV-band gamma-ray polarization with the AMS-02 experiment and a proposed successor, from Galactic and extragalactic sources. Characterizing gamma-ray polarization in this energy range could shed light on gamma-ray emission mechanisms in the sources; physics beyond the Standard Model, such as the presence of axion-like particles (ALPs), could also induce a distinctive energy-dependent polarization signal due to propagation effects in magnetic fields. We present estimates for the minimum detectable polarization from bright sources and the forecast reach for axion-like particles (ALPs). We show that for an example bright extragalactic source (NGC1275), AMS-02 will only have sensitivity to ALP-induced polarization from currently open parameter space if the B-field configuration is unusually favorable to a signal. However, a successor experiment such as AMS-100 would be expected to probe new parameter space even for pessimistic B-field models, with prospects to measure the energy-dependence of such a signal. For Galactic sources, polarization measurements could provide a unique test of scenarios where ALPs induce energy-dependent features in the photon intensity. However, in the absence of a bright transient source (such as a Galactic supernova), the parameter space that would be probed by this approach with ten years of AMS-100 data is already nominally excluded by other experiments, although this conflict may be avoided in specific ALP models.

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.