Center for Theoretical Physics Publications

We present a new method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic in the upper half plane. A novel aspect of our method is rigorous bounding of systematic uncertainties, which are handled by constructing the full space of interpolating functions (at each point in the upper half-plane) consistent with the given Euclidean data and the constraints of analyticity. The resulting Green function in the upper half-plane has an appealing interpretation as a smeared spectral function.

We initiate the study of transverse momentum-dependent (TMD) fragmentation functions for heavy quarks, demonstrate their factorization in terms of novel nonperturbative matrix elements in heavy-quark effective theory (HQET), and prove new TMD sum rules that arise from heavy-quark spin symmetry. We discuss the phenomenology of heavy-quark TMD FFs at \(B\) factories and find that the Collins effect, in contrast to claims in the literature, is not parametrically suppressed by the heavy-quark mass. We further calculate all TMD parton distribution functions for the production of heavy quarks from polarized gluons within the nucleon and use our results to demonstrate the potential of the future EIC to resolve TMD heavy-quark fragmentation in semi-inclusive DIS, complementing the planned EIC program to use heavy quarks as probes of gluon distributions.

This manuscript concerns string one-loop corrections to the Kahler potential in 4d N=1 vacua of string theories, and it largely consists of two parts. In the first part, we compute the string one-loop correction to the dilaton kinetic term in heterotic string theories, and we show that the dilaton kinetic term is not renormalized at one-loop. We explain how this result can be reconciled with the well-known result on the string one-loop correction to the Kahler potential in heterotic string theories. In the second part, we study the dilaton dependence of the one-loop corrected Kahler potential in type II string theories. To do so, we compute the string one-loop correction to the kinetic action of the 4d-dilaton in type II string theories compactified on orientifolds of Calabi-Yau threefolds. We find that the string one-loop corrected 4d dilaton kinetic term in string-frame and Einstein-frame is determined by the Witten index and the new supersymmetric index of the string worldsheet CFT. Quite surprisingly, we find that in the vertex-frame, the open string contributions to the 4d dilaton kinetic term cancel, and the 4d dilaton kinetic term at string one-loop depends only on the Witten index of the closed string sector.

We present a class of exactly solvable 2D models whose ground states violate conventional beliefs about entanglement scaling in quantum matter. These beliefs are (i) that area law entanglement scaling originates from local correlations proximate to the boundary of the entanglement cut, and (ii) that ground state entanglement in 2D Hamiltonians cannot violate area law scaling by more than a multiplicative logarithmic factor. We explicitly present two classes of models defined by local, translation-invariant Hamiltonians, whose ground states can be exactly written as weighted superpositions of framed loop configurations. The first class of models exhibits area-law scaling, but of an intrinsically nonlocal origin so that the topological entanglement entropy scales with subsystem sizes. The second class of models has a rich ground state phase diagram that includes a phase exhibiting volume law entanglement.

Finite-volume pionless effective field theory (FVEFT\(_{ \pi\!/ }\)) at next-to-leading order (NLO) is used to analyze the two-nucleon lattice QCD spectrum of Ref.~\cite{Amarasinghe:2021lqa}, performed at quark masses corresponding to a pion mass of approximately \(800 \) MeV. Specifically, the effective theory is formulated in finite volume, and variational sets of wave functions are optimized using differential programming. Using these wave functions projected to the appropriate finite-volume symmetry group, variational bounds from FVEFT\(_{\pi\!/ }\) are obtained for the ground state, as well as excited states. By comparison with the lattice QCD GEVP spectrum, different low energy constants (LECs) are constrained. Relativistic corrections are incorporated, allowing for the extractions of NLO LECs, as well as the leading \(s\)-\(d\)-wave mixing term in the deuteron channel.

By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories.

Jet grooming is an important strategy for analyzing relativistic particle collisions in the presence of contaminating radiation. Most jet grooming techniques introduce hard cutoffs to remove soft radiation, leading to discontinuous behavior and associated experimental and theoretical challenges. In this paper, we introduce Pileup and Infrared Radiation Annihilation (PIRANHA), a paradigm for continuous jet grooming that overcomes the discontinuity and infrared sensitivity of hard-cutoff grooming procedures. We motivate PIRANHA from the perspective of optimal transport and the Energy Mover's Distance and review Apollonius Subtraction and Iterated Voronoi Subtraction as examples of PIRANHA-style grooming. We then introduce a new tree-based implementation of PIRANHA, Recursive Subtraction, with reduced computational costs. Finally, we demonstrate the performance of Recursive Subtraction in mitigating sensitivity to soft distortions from hadronization and detector effects, and additive contamination from pileup and the underlying event.

Generalizing the results of 1211.6077 and 1703.00905, we prove a formula for the pushforward of an arbitrary analytic function of the exceptional divisor class of a weighted blowup of an algebraic variety centered at a smooth complete intersection with normal crossing. We check this formula extensively by computing the generating function of intersection numbers of a weighted blowup of the generic SU(5) Tate model over arbitrary smooth base, and comparing the answer to known results. Motivated by applications to four-dimensional F-theory flux compactifications, we use our formula to compute the intersection pairing on the vertical part of the middle cohomology of elliptic Calabi-Yau 4-folds resolving the generic F\(_4\) and Sp(6) Tate models with non-minimal singularities. These resolutions lead to non-flat fibrations in which certain fibers contain 3-fold (divisor) components, whose physical interpretation in M/F-theory remains to be fully explored.

Emergent bulk properties of matter governed by the strong nuclear force give rise to physical phenomena across vastly different scales, ranging from the shape of atomic nuclei to the masses and radii of neutron stars. They can be accessed on Earth by measuring the spatial extent of the outer skin made of neutrons that characterises the surface of heavy nuclei. The isotope \(^{208}\)Pb, owing to its simple structure and neutron excess, has been in this context the target of many dedicated efforts. Here, we determine the neutron skin from measurements of particle distributions and their collective flow in \(^{208}\)Pb+\(^{208}\)Pb collisions at ultrarelativistic energy performed at the Large Hadron Collider, which are sensitive to the overall size of the colliding \(^{208}\)Pb ions. By means of state-of-the-art global analysis tools within the hydrodynamic model of heavy-ion collisions, we infer a neutron skin \(\Delta r_{np}=0.217\pm0.058\) fm, consistent with nuclear theory predictions, and competitive in accuracy with a recent determination from parity-violating asymmetries in polarised electron scattering. We establish thus a new experimental method to systematically measure neutron distributions in the ground state of atomic nuclei.

Right-handed neutrinos (RHN) destabilize the electroweak vacuum by increasing its decay rate. In the SM, the latter is dominated by physics at the RG scale at which \(\lambda\) reaches its minimum, \(\mu_*^{\text{SM}} \sim 10^{17}\) GeV. RHNs generically push \(\mu_*\) beyond the Planck scale, implying that gravitational effects need to be taken into account. In this work, we perform the first comprehensive study of electroweak vacuum metastability in the type-I seesaw mechanism including these effects. Our analysis covers both low- and high-scale seesaw models, with two as well as three RHNs and for multiple values of the Higgs' non-minimal coupling to gravity. We find that gravitational effects can significantly stabilize the vacuum, leading to weaker metastability bounds. We show that metastability sets the strongest bounds for low-scale seesaws with \(M_N>1\) TeV. For high-scale seesaws, we find upper bounds on the allowed masses for the RHNs, which are relevant for high-scale leptogenesis. We also point out that \(\text{Tr}(Y_\nu^\dagger Y_\nu)\), which is commonly used to express these metastability bounds, cannot be used for all of parameter space. Instead, we argue that bounds can always be expressed reliably through \(\text{Tr}(Y_\nu^\dagger Y_\nu\,Y_\nu^\dagger Y_\nu)\). Lastly, we use this insight to develop a new technique for an easier RG analysis applicable to scenarios with degenerate RHN masses.

We present an extended Bayesian analysis using Trajectum where the initial condition can now include binary scaling. For the far-from-equilibrium evolution before hydrodynamics we introduce an interpolation between free streaming and a holographically inspired evolution that exhibits fast hydrodynamization. We find strong evidence that binary scaling is incompatible with experimental data and find evidence that the holographic far-from-equilibrium evolution is preferred. We end with a discussion on several changes and improvements in the Bayesian framework.

Numerical computations in strongly-interacting quantum field theories are often performed using Monte-Carlo sampling methods. A key task in these calculations is to estimate the value of a given physical quantity from the distribution of stochastic samples that are generated using the Monte-Carlo method. Typically, the sample mean and sample variance are used to define the expectation values and uncertainties of computed quantities. However, the Monte-Carlo sample distribution contains more information than these basic properties and it is useful to investigate it more generally. In this work, the exact form of the probability distributions of two-point correlation functions at zero momentum in O(N) lattice field theories in the disordered phase and in infinite volume are determined. These distributions allow for a robust investigation of the efficacy of the Monte-Carlo sampling procedure and are shown also to allow for improved estimators of the target physical quantity to be constructed. The theoretical expectations are shown to agree with numerical calculations in the O(2) model.

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

Previous studies have shown that a gauge-invariant correlation function of two chromoelectric fields connected by a straight timelike adjoint Wilson line encodes crucial information about quark-gluon plasma (QGP) that determines the dynamics of small-sized quarkonium in the medium. Motivated by the successes of holographic calculations to describe strongly coupled QGP, we calculate the analog gauge-invariant correlation function in strongly coupled \(\mathcal{N}=4\) supersymmetric Yang-Mills theory at finite temperature by using the AdS/CFT correspondence. Our results indicate that the transition processes between bound and unbound quarkonium states are suppressed in strongly coupled plasmas, and moreover, the leading contributions to these transition processes vanish in both the quantum Brownian motion and quantum optical limits of open quantum system approaches to quarkonia.

Since diffusion models (DM) and the more recent Poisson flow generative models (PFGM) are inspired by physical processes, it is reasonable to ask: Can physical processes offer additional new generative models? We show that the answer is yes. We introduce a general family, Generative Models from Physical Processes (GenPhys), where we translate partial differential equations (PDEs) describing physical processes to generative models. We show that generative models can be constructed from s-generative PDEs (s for smooth). GenPhys subsume the two existing generative models (DM and PFGM) and even give rise to new families of generative models, e.g., "Yukawa Generative Models" inspired from weak interactions. On the other hand, some physical processes by default do not belong to the GenPhys family, e.g., the wave equation and the Schrödinger equation, but could be made into the GenPhys family with some modifications. Our goal with GenPhys is to explore and expand the design space of generative models.

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and optimization. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions with exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on the 2D \(J_1\)-\(J_2\) Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for both scientific simulations and machine learning applications.

The LUXE experiment is a new experiment in planning in Hamburg, which will study Quantum Electrodynamics at the strong-field frontier. LUXE intends to measure the positron production rate in this unprecedented regime by using, among others, a silicon tracking detector. The large number of expected positrons traversing the sensitive detector layers results in an extremely challenging combinatorial problem, which can become computationally expensive for classical computers. This paper investigates the potential future use of gate-based quantum computers for pattern recognition in track reconstruction. Approaches based on a quadratic unconstrained binary optimisation and a quantum graph neural network are investigated in classical simulations of quantum devices and compared with a classical track reconstruction algorithm. In addition, a proof-of-principle study is performed using quantum hardware.

In an important recent development, Anshu, Breuckmann, and Nirkhe [ABN22] resolved positively the so-called No Low-Energy Trivial State (NLTS) conjecture by Freedman and Hastings. The conjecture postulated the existence of linear-size local Hamiltonians on n qubit systems for which no near-ground state can be prepared by a shallow (sublogarithmic depth) circuit. The construction in [ABN22] is based on recently developed good quantum codes. Earlier results in this direction included the constructions of the so-called Combinatorial NLTS -- a weaker version of NLTS -- where a state is defined to have low energy if it violates at most a vanishing fraction of the Hamiltonian terms [AB22]. These constructions were also based on codes. In this paper we provide a "non-code" construction of a class of Hamiltonians satisfying the Combinatorial NLTS. The construction is inspired by one in [AB22], but our proof uses the complex solution space geometry of random K-SAT instead of properties of codes. Specifically, it is known that above a certain clause-to-variables density the set of satisfying assignments of random K-SAT exhibits an overlap gap property, which implies that it can be partitioned into exponentially many clusters each constituting at most an exponentially small fraction of the total set of satisfying solutions. We establish a certain robust version of this clustering property for the space of near-satisfying assignments and show that for our constructed Hamiltonians every combinatorial near-ground state induces a near-uniform distribution supported by this set. Standard arguments then are used to show that such distributions cannot be prepared by quantum circuits with depth o(log n). Since the clustering property is exhibited by many random structures, including proper coloring and maximum cut, we anticipate that our approach is extendable to these models as well.

We derive a factorization theorem that allows for resummation of small-\(x\) logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor \(W^{\mu\nu}\) in deep inelastic scattering, and leads to the definition of a new gauge invariant soft function \(S^{\mu\nu}\) that describes quark and gluon emission in the central region. This soft function provides a new framework for extending resummed calculations for coefficient functions to higher logarithmic orders. Our factorization also defines impact factors by universal collinear functions that are process independent, for instance being identical in small-\(x\) DIS and Drell-Yan.

The three-particle \(K\)-matrix, \(\mathcal{K}_{\mathrm{df},3}\), is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of \(\mathcal{K}_{\mathrm{df},3}\) is significantly improved with respect to leading order once NLO effects are incorporated.