MIT Center for Theoretical Physics — a Leinweber Institute Publications

As the field examines a future muon collider as a possible successor to the LHC, we must consider how to fully utilize not only the high-energy particle collisions, but also any lower-energy staging facilities necessary in the R&D process. An economical and efficient possibility is to use the accelerated muon beam from either the full experiment or from cooling and acceleration tests in beam-dump experiments.Beam-dump experiments are complementary to the main collider as they achieve sensitivity to very small couplings with minimal instrumentation. We demonstrate the utility of muon beam-dump experiments for new physics searches at energies from 10 GeV to 5 TeV. We find that, even at low energies like those accessible at staging or demonstrator facilities, it is possible to probe new regions of parameter space for a variety of generic BSM models, including muonphilic, leptophilic, \(L_\mu - L_\tau\), and dark photon scenarios. Such experiments could therefore provide opportunities for discovery of new physics well before the completion of the full multi-TeV collider.

We study the azimuthal angle dependence of the energy-energy correlators \(\langle \mathcal{E}(\hat{n}_1)\mathcal{E}(\hat{n}_2)\rangle\) in the back-to-back region for \(e^+e^-\) annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers \(\mathbb{S}_i\) in the back-to-back limit \(\langle \mathcal{E}_{\mathbb{S}_1}(\hat{n}_1)\mathcal{E}_{\mathbb{S}_2}(\hat{n}_2)\rangle\). We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.

We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities we explore its formulation in terms of a \(U(1)\) gauge theory coupled to elasticity, that at low energies reduces to a Lifshitz theory augmented with a Berry phase term encoding the vortex dynamics in the presence of a superflow. Utilizing elasticity- and Lifshitz-gauge theory dualities, we derive dual formulations of the vortex lattice in terms of a traceless symmetric scalar-charge theory and demonstrate low-energy equivalence of our dual gauge theory to its elasticity-gauge theory dual. We further discuss a multipole symmetry of the vortex lattice and its dual gauge theory's multipole one-form symmetries. We also study its topological crystalline defects, where the multipole one-form symmetry plays a prominent role, organizing the defects, explaining their restricted mobility, and characterizing descendant vortex phases.

We study the generalized gluon distribution that governs the dynamics of quarkonium inside a non-Abelian thermal plasma characterizing its dissociation and recombination rates. This gluon distribution can be written in terms of a correlation function of two chromoelectric fields connected by an adjoint Wilson line. We formulate and calculate this object in \(\mathcal{N}=4\) supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence, allowing for a nonzero center-of-mass velocity \(v\) of the heavy quark pair relative to the medium. The effect of a moving medium on the dynamics of the heavy quark pair is described by the simple substitution \(T \to \sqrt{\gamma} \, T\) in agreement with previous calculations of other observables at strong coupling, where \(T\) is the temperature of the plasma in its rest frame, and \(\gamma = (1 - v^2)^{-1/2}\) is the Lorentz boost factor. Such a velocity dependence can be important when the quarkonium momentum is larger than its mass. Contrary to general expectations for open quantum systems weakly coupled with large thermal environments, the contributions to the transition rates that are usually thought of as the leading ones in Markovian descriptions vanish in this strongly coupled plasma. This calls for new theoretical developments to assess the effects of strongly coupled non-Abelian plasmas on in-medium quarkonium dynamics. Finally, we compare our results with those from weakly coupled QCD, and find that the QCD result moves toward the \(\mathcal{N}=4\) strongly coupled result as the coupling constant is increased within the regime of applicability of perturbation theory. This behavior makes it even more pressing to develop a non-Markovian description of quarkonium in-medium dynamics.

The gravitational form factors of a hadron encode fundamental aspects of its structure, including the hadron's shape and size as defined from e.g., its energy density. This work presents a determination of the flavor decomposition of the gravitational form factors of the proton from lattice QCD, in the kinematic region \(0\leq -t\leq 2~\text{GeV}^2\). The decomposition of the form factors into up-, down-, strange-quark, and gluon contributions provides first-principles constraints on the role of each fundamental degree of freedom in generating key proton structure observables, such as its mechanical radius, mass radius, and \(D\)-term.

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width -- which govern the evolution of observables during training -- saturate at a depth of \(\sim 20\), rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep nonlinear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

The homogeneous precession domain (HPD) of superfluid \(^{3}\)He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling \(g_{aNN}\) competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a non-stationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching \(g_{aNN} \sim 10^{-12}\) GeV\(^{-1}\) across a decade in axion mass.

Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated collinear and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.

Axion dark matter (DM) produces echo images of bright radio sources via stimulated decay. These images appear as a faint radio line centered at half the axion mass, with the line width set by the DM velocity dispersion. Due to the kinematics of the decay, the echo can be emitted in the direction nearly opposite to the incoming source of stimulating radiation, meaning that axions effectively behave as imperfect monochromatic mirrors. We present an all-sky analysis of axion DM-induced echo images using extragalactic radio point sources, Galactic supernova remnants (SNRs), and Galactic synchrotron radiation (GSR) as sources of stimulating radiation. The aggregate signal strength is not significantly affected by unknown properties of individual sources of stimulating radiation, which we sample from an empirical distribution to generate an ensemble of realizations for the all-sky signal template. We perform forecasts for CHIME, HERA, CHORD, HIRAX, and BURSTT, finding that they can run as competitive axion experiments simultaneously with other objectives, requiring no new hardware.

In recent years, detailed studies of three-pion systems have become possible in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions in the chiral perturbation theory framework. In addition to being an interesting study of multi-meson dynamics in its own right, it provides a valuable handle on finite-volume effects and the pion mass dependence, thus complementing the lattice results. I present our derivation of the next-to-leading order amplitude for this process, as well as its conversion into the three-particle K-matrix, which enables direct comparison to the lattice. Our results significantly improve the agreement between theory and lattice, which was poor when only leading-order effects were taken into account.

The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from Fourier analysis on Banach spaces, and as such are not especially transparent to an audience of physicists. In this article, I present a construction of modular flow that differs from existing treatments. The main pedagogical contribution is that I start with thermal physics via the KMS condition, and derive the modular operator as the only operator that could generate a thermal arrow of time, rather than starting with the modular operator as the fundamental object of the theory. The main technical contribution is a new proof of the fundamental theorem stating that modular flow is a symmetry. The new proof circumvents the delicate issues of Fourier analysis that appear in previous treatments, but is still mathematically rigorous.

Decades of analytic and computational work have demonstrated that a charge immersed in a hot plasma is screened. For both Abelian and non-Abelian interactions, the characteristic screening length \(1/m_D\) is set by the so-called Debye mass \(m_D \sim g_s T\), proportional to the plasma temperature \(T\) and the dimensionless gauge coupling \(g_s\). One of the most interesting naturally occurring examples is the quark-gluon plasma (QGP) that filled the early universe prior to the QCD confinement phase transition at \(t_{\rm QCD} \sim 10^{-5}\,{\rm s}\). During this early epoch, regimes of strong spacetime curvature are of significant cosmological interest, such as near primordial black holes (PBHs). However, the typical description of Debye screening only applies within Minkowski spacetime, and is therefore insufficient to describe the dynamics of charged plasmas near PBHs or other primordial features. We construct an effective field theory for soft modes of the gauge field \(A_\mu^a\) to give a full description of Debye screening in non-Abelian plasmas within arbitrary curved spacetimes, recovering a temperature-dependent Debye mass that exhibits gravitational redshift. We then apply our results to some scenarios of cosmological interest: an expanding FLRW universe and the vicinity of a PBH immersed in a hot QGP.

We derive an effective field theory (EFT) for cosmological Lyman alpha forest fluctuations valid for the power spectrum at the one-loop order. The ``bottom-up'' EFT expansion at the level of the transmitted flux is identical to the line-of-sight dependent bias model first derived by Desjacques et al. We confirm this result by a ``top-down'' derivation based on the exponential map of the optical depth field. Specifically, we show that the combination of the exponential map and conditions of renormalizability generates the same EFT expansion as the ``bottom-up'' approach. In passing, we point out inconsistencies of the tree-level perturbative expansion of the exponential map without counterterms. To facilitate practical applications, we generalize the FFTLog method for efficient calculations of one-loop integrals from new line-of-sight dependent operators. Finally, we compare the one-loop EFT model against data from the Sherwood hydrodynamic simulation. The theory fits the data with sub percent accuracy up to \(k= \) 3 \(h\)Mpc\(^{-1}\) at \(z= 2.8\) for both 3D and 1D correlations. Our model can be readily used for cosmological full-shape analyses of Lyman alpha forest data.

We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear (i.e., dipolar), quadratic and exponential modulations. We present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls to spatially modulated symmetry defects, and develop several tools for characterizing and classifying modulated SPT phases. A salient feature of modulated symmetries is that they are generically only present for open chains, and are broken upon the imposition of periodic boundary conditions. Nevertheless, we show that SPT order is present even with periodic boundary conditions, a phenomenon we understand within the context of an object we dub a ``bundle symmetry''. In addition, we show that modulated SPT phases can avoid a certain no-go theorem, leading to an unusual algebraic structure in their matrix product state descriptions.

We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much simpler ones which share interestingly rigid structures. By performing a systematic search over some of these structures, we are able to discover more than 300 novel entropy inequalities for six parties, thereby demonstrating that these recastings provide a fruitful generating technique for uncovering new holographic entropy inequalities. In attempting to interpret the corresponding sign-definite quantities as correlation measures, we also obtain a no-go result: the superbalance property of holographic entropy inequalities turns out to preclude them from being monotonic under partial tracing. In the process, we also comment on the geometrical significance of multipartite information quantities and present various structural relations amongst them.

We explore a self-interacting neutrino cosmology in which neutrinos experience a delayed onset of free-streaming. We use the effective field theory of large-scale structure (LSS) to model matter distribution on mildly non-linear scales within the self-interacting neutrino cosmology for the first time. We perform the first combined likelihood analysis of BOSS full-shape galaxy clustering, weak lensing, and Lyman-\(\alpha\) forest measurements, together with the cosmic microwave background (CMB) data from Planck. We find that the full data set strongly favors presence of a flavor-universal neutrino self-interaction, with a characteristic energy scale of order \(10\) MeV. The preference is at the \(>5\sigma\) level and is primarily driven by the Lyman-\(\alpha\) forest measurements and, to a lesser extent, the weak lensing data from DES. The self-interacting neutrino model reduces both the Hubble tension and the \(S_8\) tension between different cosmological data sets, but it does not fully resolve either. Finally, we note a preference for a non-zero sum of neutrino masses at the level of \(\sim 0.3\) eV under this model, consistent with previous bounds. These results call for further investigation in several directions, and may have significant implications for neutrino physics and for future new-physics searches with galaxy surveys.

We derive model-independent quantization conditions on the axion couplings (sometimes known as the anomaly coefficients) to the Standard Model gauge group \([SU(3)\times SU(2)\times U(1)_Y]/\mathbb{Z}_q\) with \(q=1,2,3,6\). Using these quantization conditions, we prove that any QCD axion model to the right of the \(E/N=8/3\) line on the \(g_{a\gamma\gamma}\)-\(m_a\) plot must necessarily face the axion domain wall problem in a post-inflationary scenario. We further demonstrate the higher-group and non-invertible global symmetries in the Standard Model coupled to a single axion. These generalized global symmetries lead to universal bounds on the axion string tension and the monopole mass. If axion were discovered in the future, our quantization conditions could be used to constrain the global form of the Standard Model gauge group.

The 3.5 keV line is a purported emission line observed in galaxies, galaxy clusters, and the Milky Way whose origin is inconsistent with known atomic transitions and has previously been suggested to arise from dark matter decay. We systematically re-examine the bulk of the evidence for the 3.5 keV line, attempting to reproduce six previous analyses that found evidence for the line. Surprisingly, we only reproduce one of the analyses; in the other five we find no significant evidence for a 3.5 keV line when following the described analysis procedures on the original data sets. For example, previous results claimed 4\(\sigma\) evidence for a 3.5 keV line from the Perseus cluster; we dispute this claim, finding no evidence for a 3.5 keV line. We find evidence for background mismodeling in multiple analyses. We show that analyzing these data in narrower energy windows diminishes the effects of mismodeling but returns no evidence for a 3.5 keV line. We conclude that there is little robust evidence for the existence of the 3.5 keV line. Some of the discrepancy of our results from those of the original works may be due to the earlier reliance on local optimizers, which we demonstrate can lead to incorrect results. For ease of reproducibility, all code and data are publicly available.

Consider the \(n!\) different unitary matrices that permute \(n\)\(d\)-dimensional quantum systems. If \(d\geq n\) then they are linearly independent. This paper discusses a sense in which they are approximately orthogonal (with respect to the Hilbert-Schmidt inner product) if \(d\gg n^2\), or, in a different sense, if \(d\gg n\). Previous work had shown pairwise approximate orthogonality of these matrices, but here we show a more collective statement, quantified in terms of the operator norm distance of the Gram matrix to the identity matrix. This simple point has several applications in quantum information and random matrix theory: (1) showing that random maximally entangled states resemble fully random states, (2) showing that Boson sampling output probabilities resemble those from Gaussian matrices, (3) improving the Eggeling-Werner scheme for multipartite data hiding, (4) proving that the product test of Harrow-Montanaro cannot be performed using LOCC without a large number of copies of the state to be tested, (5) proving that the purity of a quantum state also cannot be efficiently tested using LOCC, and (6, published separately) helping prove that poly-size random quantum circuits are poly-designs.

The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in terms of the concepts of the other. In this paper we explore the possibility of finding a Bayesian significance for the frequentist's main object of interest, the \(p\)-value, which is the probability assigned to the proposition -- which we call the {\it extremity proposition}-- that a measurement will result in a value that is at least as extreme as the value that was actually obtained. To make contact with the frequentist language, the Bayesian can choose to update probabilities based on the {\it extremity proposition}, which is weaker than the standard Bayesian update proposition, which uses the actual observed value. We then show that the posterior probability (or probability density) of a theory is equal to the prior probability (or probability density) multiplied by the ratio of the \(p\)-value for the data obtained, given that theory, to the mean \(p\)-value -- averaged over all theories weighted by their prior probabilities. Thus, we provide frequentist answers to Bayesian questions. Our result is generic -- it does not rely on restrictive assumptions about the situation under consideration or specific properties of the likelihoods or the priors.