Center for Theoretical Physics Publications

In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry \(A_{TU,T}^{\cos(\phi _S - \hat{\phi}_{S_h})}\) from polarized semi-inclusive hadron-in-jet production in polarized \(pp\) collisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry, \(A_{TU, L}^{\cos(\phi _q - \phi _{S})}\) from polarized exclusive hadron-in-jet production in polarized \(ep\) collisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements.

We study the possibility that dark matter re-enters kinetic equilibrium with a radiation bath after kinetic decoupling, a scenario we dub kinetic recoupling. This naturally occurs, for instance, with certain types of resonantly-enhanced interactions, or as the result of a phase transition. While late kinetic decoupling damps structure on small scales below a cutoff, kinetic recoupling produces more complex changes in the power spectrum that depend on the nature and extent of the recoupling period. We explore the features that kinetic recoupling imprints upon the matter power spectrum, and discuss how such features can be traced to dark matter microphysics with future observations.

We derive the finite-temperature quantum-tunneling rate from first principles. The decay rate depends on both real- and imaginary-time; we demonstrate that the relevant instantons should therefore be defined on a Keldysh-Schwinger contour, and how the familiar Euclidean-time result arises from it in the limit of large physical times. We generalize previous results for excited initial states, and identify distinct behavior in the high- and low-temperature limits, incorporating effects from background fields. We construct a consistent perturbative scheme that incorporates large finite-temperature effects.

We review and update constraints on the Early Dark Energy (EDE) model from cosmological data sets, in particular Planck PR3 and PR4 cosmic microwave background (CMB) data and large-scale structure (LSS) data sets including galaxy clustering and weak lensing data from the Dark Energy Survey, Subaru Hyper Suprime-Cam, and KiDS+VIKING-450, as well as BOSS/eBOSS galaxy clustering and Lyman-\(\alpha\) forest data. We detail the fit to CMB data, and perform the first analyses of EDE using the CAMSPEC and Hillipop likelihoods for Planck CMB data, rather than Plik, both of which yield a tighter upper bound on the allowed EDE fraction than that found with Plik. We then supplement CMB data with large-scale structure data in a series of new analyses. All these analyses are concordant in their Bayesian preference for \(\Lambda\)CDM over EDE, as indicated by marginalized posterior distributions. We perform a series of tests of the impact of priors in these results, and compare with frequentist analyses based on the profile likelihood, finding qualitative agreement with the Bayesian results. All these tests suggest prior volume effects are not a determining factor in analyses of EDE. This work provides both a review of existing constraints and several new analyses.

We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.

We describe a realistic mechanism whereby black holes with significant QCD color charge could have formed during the early universe. Primordial black holes (PBHs) could make up a significant fraction of the dark matter if they formed well before the QCD confinement transition. Such PBHs would form by absorbing unconfined quarks and gluons, and hence could acquire a net color charge. We estimate the number of PBHs per Hubble volume with near-extremal color charge for various scenarios, and discuss possible phenomenological implications.

We analyze the internal symmetries and their anomalies in the Kitaev spin-\(S\) models. Importantly, these models have a lattice version of a \(\mathbb{Z}_2\) 1-form symmetry, denoted by \(\mathbb{Z}_2^{[1]}\). There is also an ordinary 0-form \(\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T\) symmetry, where \(\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\) are \(\pi\) spin rotations around two orthogonal axes, and \(\mathbb{Z}_2^T\) is the time reversal symmetry. The anomalies associated with the full \(\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T\times\mathbb{Z}_2^{[1]}\) symmetry are classified by \(\mathbb{Z}_2^{17}\). We find that for \(S\in\mathbb{Z}\) the model is anomaly-free, while for \(S\in\mathbb{Z}+\frac{1}{2}\) there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these anomalies apply to not only the Kitaev spin-\(S\) models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, these consequences apply even if the perturbations break the 1-form symmetry. A notable consequence is that there must be a deconfined fermionic excitation carrying no fractional quantum number under the \(\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T\) symmetry if \(S\in\mathbb{Z}+\frac{1}{2}\).

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.