Center for Theoretical Physics Publications

We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution operators grow linearly with time, at least initially, for both the one- and two-qubit cases. The precursor operators display switchback-effect-like behavior provided we choose our cost factors so that the resulting complexity geometry is negatively curved.

We introduce a model for heavy ion collisions named Trajectum, which includes an expanded initial stage with a variable free streaming velocity \(v_{\rm fs}\) and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian Emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in [1] to perform a detailed comparison to experimental data from PbPb and \(p\)Pb collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

We present a technique for translating a black-box machine-learned classifier operating on a high-dimensional input space into a small set of human-interpretable observables that can be combined to make the same classification decisions. We iteratively select these observables from a large space of high-level discriminants by finding those with the highest decision similarity relative to the black box, quantified via a metric we introduce that evaluates the relative ordering of pairs of inputs. Successive iterations focus only on the subset of input pairs that are misordered by the current set of observables. This method enables simplification of the machine-learning strategy, interpretation of the results in terms of well-understood physical concepts, validation of the physical model, and the potential for new insights into the nature of the problem itself. As a demonstration, we apply our approach to the benchmark task of jet classification in collider physics, where a convolutional neural network acting on calorimeter jet images outperforms a set of six well-known jet substructure observables. Our method maps the convolutional neural network into a set of observables called energy flow polynomials, and it closes the performance gap by identifying a class of observables with an interesting physical interpretation that has been previously overlooked in the jet substructure literature.

Guided by the naturalness criterion for an exponentially small cosmological constant, we present a string theory motivated 4-dimensional \(\mathcal{N}=1\) non-linear supergravity model (or its linear version with a nilpotent superfield) with spontaneous supersymmetry breaking. The model encompasses the minimal supersymmetric standard model, the racetrack K\"ahler uplift, and the KKLT anti-\(\rm D3\)-branes, and use the nilpotent superfield to project out the undesirable interaction terms as well as the unwanted degrees of freedom to end up with the standard model (not the supersymmetric version) of strong and electroweak interactions.

We study the multifield dynamics of axion models nonminimally coupled to gravity. As usual, we consider a canonical \(U(1)\) symmetry-breaking model in which the axion is the phase of a complex scalar field. If the complex scalar field has a nonminimal coupling to gravity, then the (oft-forgotten) radial component can drive a phase of inflation prior to an inflationary phase driven by the axion field. In this setup, the mass of the axion field is dependent on the radial field because of the nonminimal coupling, and the axion remains extremely light during the phase of radial inflation. As the radial field approaches the minimum of its potential, there is a transition to natural inflation in the angular direction. In the language of multifield inflation, this system exhibits ultra-light isocurvature perturbations, which are converted to adiabatic perturbations at a fast turn, namely the onset of axion inflation. For models wherein the CMB pivot scale exited the horizon during radial inflation, this acts to suppresses the tensor-to-scalar ratio \(r\), without generating CMB non-Gaussianity or observable isocurvature perturbations. Finally, we note that the interaction strength between axion and gauge fields is suppressed during the radial phase relative to its value during the axion inflation phase by several orders of magnitude. This decouples the constraints on the inflationary production of gauge fields (e.g., from primordial black holes) from the constraints on their production during (p)reheating.

We present a framework to simulate the dynamics of hard probes such as heavy quarks or jets in a hot, strongly-coupled quark-gluon plasma (QGP) on a quantum computer. Hard probes in the QGP can be treated as open quantum systems governed in the Markovian limit by the Lindblad equation. However, due to large computational costs, most current phenomenological calculations of hard probes evolving in the QGP use semiclassical approximations of the quantum evolution. Quantum computation can mitigate these costs, and offers the potential for a fully quantum treatment with exponential speedup over classical techniques. We report a simplified demonstration of our framework on IBM Q quantum devices, and apply the Random Identity Insertion Method (RIIM) to account for CNOT depolarization noise, in addition to measurement error mitigation. Our work demonstrates the feasibility of simulating open quantum systems on current and near-term quantum devices, which is of broad relevance to applications in nuclear physics, quantum information, and other fields.

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than \(2\) GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

We present exoplanets as new targets to discover Dark Matter (DM). Throughout the Milky Way, DM can scatter, become captured, deposit annihilation energy, and increase the heat flow within exoplanets. We estimate upcoming infrared telescope sensitivity to this scenario, finding actionable discovery or exclusion searches. We find that DM with masses above about an MeV can be probed with exoplanets, with DM-proton and DM-electron scattering cross sections down to about \(10^{-37}\)cm\(^2\), stronger than existing limits by up to six orders of magnitude. Supporting evidence of a DM origin can be identified through DM-induced exoplanet heating correlated with Galactic position, and hence DM density. This provides new motivation to measure the temperature of the billions of brown dwarfs, rogue planets, and gas giants peppered throughout our Galaxy.

I develop an Effective Field Theory (EFT) framework to compute jet substructure observables for heavy ion collision experiments. I consider dijet events that accompany the formation of a weakly coupled Quark Gluon Plasma(QGP) medium in a heavy ion collision and look at the simultaneous measurement of jet mass along with the transverse momentum imbalance between the jets accounting for both vacuum and medium evolution. The jets are groomed using a suitable grooming algorithm in order to mitigate effects of soft contamination from Multi-parton interactions as well as the QGP medium. This has the great advantage that we do not have to keep track of the evolution of the QGP medium into subsequent soft hadrons since these are groomed away from the final jet. Treating the energetic jet as an open quantum system interacting with a QGP bath, I write down a factorization formula within the SCET(Soft Collinear Effective Theory) framework, in which the forward scattering regime accounts for the interaction of the medium with the jet. This leads me to a Lindblad type master equation for the evolution of the reduced density matrix of the jet in the Markovian approximation. The resulting solution allows a resummation of large logarithms that arise due to the final state measurements imposed while simultaneously summing over multiple interactions of the jet with the medium. I find that the the decoherence between the hard interaction that creates the jet and the subsequent medium interactions leads to \(\ physical\) Infra-Red(IR) collinear divergences that are otherwise absent in pure vacuum evolution. I show that these IR divergences are completely regulated by the medium induced gluon mass and highlight the need to develop a multi-scale EFT approach in the future to resum the new logarithms that arise from these divergences.

The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of \(m_{\pi}\sim 450\) MeV and a kaon mass of \(m_{K}\sim 596\) MeV. The two-baryon systems that are analyzed range from strangeness \(S=0\) to \(S=-4\) and include the spin-singlet and triplet \(NN\), \(\Sigma N\) (\(I=3/2\)), and \(\Xi\Xi\) states, the spin-singlet \(\Sigma\Sigma\) (\(I=2\)) and \(\Xi\Sigma\) (\(I=3/2\)) states, and the spin-triplet \(\Xi N\) (\(I=0\)) state. The \(s\)-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using L\"uscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet \(\Sigma N\) and \(\Xi\Xi\) channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for \(SU(3)\) flavor-symmetry breaking, are constrained. The \(SU(3)\) symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the \(SU(6)\) spin-flavor symmetry, predicted at large \(N_c\). A remnant of an accidental \(SU(16)\) symmetry found previously at a larger pion mass is further observed. The \(SU(6)\)-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading \(SU(3)\) flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.

In this paper we study the chaos exponent, the exponential growth rate of the out-of-time-ordered four point functions, in a two coupled SYK models which exhibits a first order phase transition between the high temperature black hole phase and the low temperature gapped phase interpreted as a traversable wormhole. We see that as the temperature decreases the chaos exponent exhibits a discontinuous fall-off from the value of order the universal bound \(2\pi/\beta\) at the critical temperature of the phase transition, which is consistent with the expected relation between black holes and strong chaos. Interestingly, the chaos exponent is small but non-zero even in the wormhole phase. This is surprising but consistent with the observation on the decay rate of the two point function [arXiv:2003.03916], and we found the chaos exponent and the decay rate indeed obey the same temperature dependence in this regime. We also studied the chaos exponent of a closely related model with single SYK term, and found that the chaos exponent of this model is always greater than that of the two coupled model in the entire parameter space.

We explore the feasibility of determining Mellin moments of the pion's light cone distribution amplitude using the heavy quark operator product expansion (HOPE) method. As the first step of a proof of principle study we pursue a determination of the second Mellin moment. We discuss our choice of kinematics which allows us to successfully extract the moment at low pion momentum. We describe the numerical simulation, and describe the data analysis, which leads us to a preliminary determination of the second Mellin moment in the continuum limit in the quenched approximation as \(\langle\xi^2\rangle=0.19(7)\) in the \(\bar{\text{MS}}\) scheme at 2 GeV.

Motivated by recent applications of the open quantum system formalism to understand quarkonium transport in the quark-gluon plasma, we develop a set of coupled Boltzmann equations for open heavy quark-antiquark pairs and quarkonia. Our approach keeps track of the correlation between the heavy quark-antiquark pair from quarkonium dissociation and thus is able to account for both uncorrelated and correlated recombination. By solving the coupled Boltzmann equations for current heavy ion collision experiments, we find correlated recombination is crucial to describe the data of bottomonia nuclear modification factors. To further test the importance of correlated recombination in experiments, we propose a new observable: \(\frac{R_{AA}[\chi_b(1P)]}{R_{AA}[\Upsilon(2S)]}\). Future measurements of this ratio will help distinguish calculations with and without correlated recombination.

The fraction of the longitudinal momentum of \({}^3\text{He}\) that is carried by the isovector combination of \(u\) and \(d\) quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to \(m_\pi\sim 800\) MeV, extrapolated to the physical quark masses. This constraint is consistent with, and significantly more precise than, determinations from global nuclear parton distribution function fits. Including the lattice QCD determination of the momentum fraction in the nNNPDF global fitting framework results in the uncertainty on the isovector momentum fraction ratio being reduced by a factor of 2.5, and thereby enables a more precise extraction of the \(u\) and \(d\) parton distributions in \({}^3\text{He}\).

Kirkwood discovered in 1933, and Dirac discovered in 1945, a representation of quantum states that has undergone a renaissance recently. The Kirkwood-Dirac (KD) distribution has been employed to study nonclassicality across quantum physics, from metrology to chaos to the foundations of quantum theory. The KD distribution is a quasiprobability distribution, a quantum generalization of a probability distribution, which can behave nonclassically by having negative or nonreal elements. Negative KD elements signify quantum information scrambling and potential metrological quantum advantages. Nonreal elements encode measurement disturbance and thermodynamic nonclassicality. KD distributions' nonclassicality has been believed to follow necessarily from noncommutation of operators. We show that noncommutation does not suffice. We prove sufficient conditions for the KD distribution to be nonclassical (equivalently, necessary conditions for it to be classical). We also quantify the KD nonclassicality achievable under various conditions. This work resolves long-standing questions about nonclassicality and may be used to engineer quantum advantages.

Jet modification in heavy-ion collisions is an important probe of the nature and structure of the quark-gluon plasma (QGP) produced in these collisions and also encodes information about how the wakes that jets excite in a droplet of QGP form and relax. However, in experiment, one cannot know what a particular jet in a heavy ion collision would have looked like without quenching, making it difficult to interpret measurements in terms of individual jet modification. The goal of this Monte Carlo study is to gain insight into the modification of jet observables using the hybrid strong/weak coupling model of jet quenching as a test bed. In this Monte Carlo study (but not in experiment) it is possible to watch \(\textit{the same jet}\) as it evolves in vacuum or in QGP. We use this ability to disentangle the effects of modification of individual jets in heavy ion collisions vs. the effects of differing selection bias on the distribution of two observables: fractional energy loss and groomed \(\Delta R\). We find that in the hybrid model the distribution of groomed \(\Delta R\) appears to be unmodified in a sample of jets selected after quenching, as in heavy ion collisions, and confirm that this lack of modification arises because of a selection bias toward jets that lose only a small fraction of their energy. If instead we select jets in a way that avoids this bias, and then follow these selected jets as they are quenched, we show that there is, in fact, a substantial modification of the \(\Delta R\) of individual jets. We show that this jet modification is principally due to the incorporation of particles coming from the wake that the parton shower excites in the plasma as a component of what an experimentalist reconstructs as a jet. The effects we discuss are substantial in magnitude, suggesting that our qualitative conclusions are more general than the Monte Carlo study in which we obtain them.

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear reactions in astrophysics, dark matter direct detection experiments, and experimental searches for violations of the symmetries of the Standard Model, including searches for additional CP violation in the hadronic and leptonic sectors, baryon-number violation, and lepton-number or flavor violation. Similarly, important inputs to neutrino experiments seeking to determine the neutrino-mass hierarchy and oscillation parameters, as well as other electroweak and beyond-Standard-Model processes can be determined. The phenomenological implications of existing studies of electroweak and beyond-Standard-Model matrix elements in light nuclear systems are discussed, and future prospects for the field toward precision studies of these matrix elements are outlined.

Whether quark- and gluon-initiated jets are modified differently by the quark-gluon plasma produced in heavy-ion collisions is a long-standing question that has thus far eluded a definitive experimental answer. A crucial complication for quark-gluon discrimination in both proton-proton and heavy-ion collisions is that all measurements necessarily average over the (unknown) quark-gluon composition of a jet sample. In the heavy-ion context, the simultaneous modification of both the fractions and substructure of quark and gluon jets by the quark-gluon plasma further obscures the interpretation. Here, we demonstrate a fully data-driven method for separating quark and gluon contributions to jet observables using a statistical technique called topic modeling. Assuming that jet distributions are a mixture of underlying "quark-like" and "gluon-like" distributions, we show how to extract quark and gluon jet fractions and constituent multiplicity distributions as a function of the jet transverse momentum. This proof-of-concept study is based on proton-proton and heavy-ion collision events from the Monte Carlo event generator Jewel with statistics accessible in Run 4 of the Large Hadron Collider. These results suggest the potential for an experimental determination of quark and gluon jet modifications.

We develop a universal approximation for the Renyi entropies of a pure state at late times in a non-integrable many-body system, which macroscopically resembles an equilibrium density matrix. The resulting expressions are fully determined by properties of the associated equilibrium density matrix, and are hence independent of the details of the initial state, while also being manifestly consistent with unitary time-evolution. For equilibrated pure states in gravity systems, such as those involving black holes, this approximation gives a prescription for calculating entanglement entropies using Euclidean path integrals which is consistent with unitarity and hence can be used to address the information loss paradox of Hawking. Applied to recent models of evaporating black holes and eternal black holes coupled to baths, it provides a derivation of replica wormholes, and elucidates their mathematical and physical origins. In particular, it shows that replica wormholes can arise in a system with a fixed Hamiltonian, without the need for ensemble averages.