Center for Theoretical Physics Publications

We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the \(U(1)_\text{A}\) axial symmetry because of the ABJ anomaly, for every rational angle \(2\pi p/N\), we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic \(U(1)\) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra over TQFT coefficients. They act invertibly on all local operators as axial rotations, but non-invertibly on the 't Hooft lines. These non-invertible symmetries lead to selection rules, which are consistent with the scattering amplitudes in QED. We further generalize our construction to QCD, and show that the coupling \(\pi^0 F\wedge F\) in the effective pion Lagrangian is necessary to match these non-invertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.

Machine learning offers an exciting opportunity to improve the calibration of nearly all reconstructed objects in high-energy physics detectors. However, machine learning approaches often depend on the spectra of examples used during training, an issue known as prior dependence. This is an undesirable property of a calibration, which needs to be applicable in a variety of environments. The purpose of this paper is to explicitly highlight the prior dependence of some machine learning-based calibration strategies. We demonstrate how some recent proposals for both simulation-based and data-based calibrations inherit properties of the sample used for training, which can result in biases for downstream analyses. In the case of simulation-based calibration, we argue that our recently proposed Gaussian Ansatz approach can avoid some of the pitfalls of prior dependence, whereas prior-independent data-based calibration remains an open problem.

Primordial black holes (PBHs) provide an exciting prospect for accounting for dark matter. In this paper, we consider inflationary models that incorporate realistic features from high-energy physics -- including multiple interacting scalar fields and nonminimal couplings to the spacetime Ricci scalar -- that could produce PBHs with masses in the range required to address the present-day dark matter abundance. Such models are consistent with supersymmetric constructions, and only incorporate operators in the effective action that would be expected from generic effective field theory considerations. The models feature potentials with smooth large-field plateaus together with small-field features that can induce a brief phase of ultra-slow-roll evolution. Inflationary dynamics within this family of models yield predictions for observables in close agreement with recent measurements, such as the spectral index of primordial curvature perturbations and the ratio of power spectra for tensor to scalar perturbations. As in previous studies of PBH formation resulting from a period of ultra-slow-roll inflation, we find that at least one dimensionless parameter must be highly fine-tuned to produce PBHs in the relevant mass-range for dark matter. Nonetheless, we find that the models described here yield accurate predictions for a significant number of observable quantities using a smaller number of relevant free parameters.

Many transport coefficients of the quark-gluon plasma and nuclear structure functions can be written as gauge invariant correlation functions of non-Abelian field strengths dressed with Wilson lines. We discuss the applicability of axial gauge \(n\cdot A=0\) to calculate them. In particular, we address issues that appear when one attempts to trivialize the Wilson lines in the correlation functions by gauge-fixing. We find it is always impossible to completely remove the gauge fields \(n\cdot A\) in Wilson lines that extend to infinity in the \(n\)-direction by means of gauge transformations. We show how the obstruction appears in an explicit example of a perturbative calculation, and we also explain it more generally from the perspective of the path integral that defines the theory. Our results explain why the two correlators that define the heavy quark and quarkonium transport coefficients, which are seemingly equal in axial gauge, are actually different physical quantities of the quark-gluon plasma and have different values. Furthermore, our findings provide insights into the difference between two inequivalent gluon parton distribution functions.

We study quark and gluon jets separately using public collider data from the CMS experiment. Our analysis is based on 2.3/fb of proton-proton collisions at 7 TeV, collected at the Large Hadron Collider in 2011. We define two non-overlapping samples via a pseudorapidity cut -- central jets with |eta| < 0.65 and forward jets with |eta| > 0.65 -- and employ jet topic modeling to extract individual distributions for the maximally separable categories. Under certain assumptions, such as sample independence and mutual irreducibility, these categories correspond to "quark" and "gluon" jets, as given by a recently proposed operational definition. We consider a number of different methods for extracting reducibility factors from the central and forward datasets, from which the fractions of quark jets in each sample can be determined. The greatest stability and robustness to statistical uncertainties is achieved by a novel method based on parametrizing the endpoints of a receiver operating characteristic (ROC) curve. To mitigate detector effects, which would otherwise induce unphysical differences between central and forward jets, we use the OmniFold method to perform central value unfolding. As a demonstration of the power of this method, we extract the intrinsic dimensionality of the quark and gluon jet samples, which exhibit Casimir scaling, as expected from the strongly-ordered limit. To our knowledge, this work is the first application of full phase space unfolding to real collider data, and one of the first applications of topic modeling to extract separate quark and gluon distributions at the LHC.

Calibration is a common experimental physics problem, whose goal is to infer the value and uncertainty of an unobservable quantity Z given a measured quantity X. Additionally, one would like to quantify the extent to which X and Z are correlated. In this paper, we present a machine learning framework for performing frequentist maximum likelihood inference with Gaussian uncertainty estimation, which also quantifies the mutual information between the unobservable and measured quantities. This framework uses the Donsker-Varadhan representation of the Kullback-Leibler divergence -- parametrized with a novel Gaussian Ansatz -- to enable a simultaneous extraction of the maximum likelihood values, uncertainties, and mutual information in a single training. We demonstrate our framework by extracting jet energy corrections and resolution factors from a simulation of the CMS detector at the Large Hadron Collider. By leveraging the high-dimensional feature space inside jets, we improve upon the nominal CMS jet resolution by upwards of 15%.

The microscopic dynamics of particle collisions is imprinted into the statistical properties of asymptotic energy flux, much like the dynamics of inflation is imprinted into the cosmic microwave background. This energy flux is characterized by correlation functions \(\langle \mathcal{E}(\vec n_1)\cdots \mathcal{E}(\vec n_k) \rangle\) of energy flow operators \( \mathcal{E}(\vec n)\). There has been significant recent progress in studying energy flux, including the calculation of multi-point correlation functions and their direct measurement inside high-energy jets at the Large Hadron Collider (LHC). In this paper, we build on these advances by defining a notion of "celestial non-gaussianity" as a ratio of the three-point function to a product of two-point functions. We show that this celestial non-gaussianity is under perturbative control within jets at the LHC, allowing us to cleanly access the non-gaussian interactions of quarks and gluons. We find good agreement between perturbative calculations of the non-gaussianity and a charged-particle-based analysis using CMS Open Data, and we observe a strong non-gaussianity peaked in the "flattened triangle" regime. The ability to robustly study three-point correlations is a significant step in advancing our understanding of jet substructure at the LHC. We anticipate that the celestial non-gaussianity, and its generalizations, will play an important role in the development of higher-order parton showers simulations and in the hunt for ever more subtle signals of potential new physics within jets.

Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called "thrust" in electron-positron collision events. We find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, but only after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.

In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of an estimator of a particular quantity is formally infinite, or in practice very large compared to the square of the mean, then that quantity can not be reliably estimated using the given sampling procedure. There are multiple scenarios in which this occurs, including in Lattice Quantum Chromodynamics, and a particularly simple example is given by the Gross-Neveu model where Monte Carlo calculations involve the introduction of auxiliary bosonic variables through a Hubbard-Stratonovich (HS) transformation. Here, it is shown that the variances of HS estimators for classes of operators involving fermion fields are divergent in this model and an even simpler zero-dimensional analogue. To correctly estimate these observables, two alternative sampling methods are proposed and numerically investigated.

We describe the dimensional reduction of the IIB B-fields in F-theory using a conjectured description of normalizable B-fields in terms of perverse sheaves. Computations are facilitated using the Decomposition Theorem. Many of our descriptions are new, and all our results are all consistent with known results in physics. We also conjecture a physical framework for normalizable B-fields and show consistency with mathematics. We dedicate this paper to Herb Clemens, in admiration for his myriad fundamental contributions to complex algebraic geometry, together with his more recent interest in F-theory in physics. This paper deals with three of Herb's interests: Hodge theory, topology of algebraic varieties, and F-theory, and so is a fitting way for us to express our appreciation for his contributions over a period of more than five decades.

A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entanglement grows linearly at a rate given by entanglement velocity, which is upper bounded by the growth of the light cone. We show that the unitary interactions achieving the maximal rate must remain unitary if we exchange the space and time directions -- a property known as dual unitarity. Our results are robust: approximate maximal entanglement velocity also implies approximate dual unitarity. We further show that maximal entanglement velocity is always accompanied by a specific dynamical pattern of entanglement, which yields simpler analyses of several known exactly solvable models.

We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, \(\mathbb{Z}_N\) gauge theories, and \(U(1)_N\) Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, \({\cal N}=1,\) and \({\cal N}=4\) super Yang-Mills theories.

We study Euclidean D3-branes wrapping divisors \(D\) in Calabi-Yau orientifold compactifications of type IIB string theory. Witten's counting of fermion zero modes in terms of the cohomology of the structure sheaf \(\mathcal{O}_D\) applies when \(D\) is smooth, but we argue that effective divisors of Calabi-Yau threefolds typically have singularities along rational curves. We generalize the counting of fermion zero modes to such singular divisors, in terms of the cohomology of the structure sheaf \(\mathcal{O}_{\overline{D}}\) of the normalization \(\overline{D}\) of \(D\). We establish this by detailing compactifications in which the singularities can be unwound by passing through flop transitions, giving a physical incarnation of the normalization process. Analytically continuing the superpotential through the flops, we find that singular divisors whose normalizations are rigid can contribute to the superpotential: specifically, \(h^{\bullet}_{+}(\mathcal{O}_{\overline{D}})=(1,0,0)\) and \(h^{\bullet}_{-}(\mathcal{O}_{\overline{D}})=(0,0,0)\) give a sufficient condition for a contribution. The examples that we present feature infinitely many isomorphic geometric phases, with corresponding infinite-order monodromy groups \(\Gamma\). We use the action of \(\Gamma\) on effective divisors to determine the exact effective cones, which have infinitely many generators. The resulting nonperturbative superpotentials are Jacobi theta functions, whose modular symmetries suggest the existence of strong-weak coupling dualities involving inversion of divisor volumes.

The CDF collaboration recently reported a new precise measurement of the \(W\) boson mass \(M_W\) with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters \(S\), \(T\) and \(U\). We show that the large \(M_W\) value can be accommodated in the fit by a large, nonzero value of \(U\), which is difficult to construct in explicit models. Assuming \(U = 0\), the electroweak fit strongly prefers large, positive values of \(T\). Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of \(T\) and \(S\) can be generated with a real SU(2)\(_L\) triplet scalar, the humble "swino," which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large \(M_W\) value, and several directions for further study.

We use string field theory to fix the normalization of the D-instanton corrections to the superpotential involving the moduli fields of type II string theory compactified on an orientifold of a Calabi-Yau threefold in the absence of fluxes. We focus on \(O(1)\) instantons whose only zero modes are the four bosonic modes associated with translation of the instanton in non-compact directions and a pair of fermionic zero modes associated with the two supercharges broken by the instanton. We work with a generic superconformal field theory and express our answer in terms of the spectrum of open strings on the instanton. We analyse the contribution of multi-instantons of this kind to the superpotential and argue that it vanishes when background fluxes are absent.

We review recent developments and outstanding questions regarding connecting the top-down UV complete physical framework of string theory with the observed physics of the Standard Model and beyond the Standard Model physics, emphasizing the global nonperturbative framework of F-theory and general lessons from UV physics. This paper, prepared for the TF01 conveners of the Snowmass 2022 process, provides a brief synopsis of this important area, focusing on ongoing developments and opportunities.

We introduce a freeze-out procedure to convert the critical fluctuations in a droplet of quark-gluon plasma (QGP) that has, as it expanded and cooled, passed close to a posited critical point on the phase diagram into cumulants of hadron multiplicities that can subsequently be measured. The procedure connects the out-of-equilibrium critical fluctuations described in concert with the hydrodynamic evolution of the droplet of QGP by extended hydrodynamics, known as Hydro+, with the subsequent kinetic description in terms of observable hadrons. We introduce a critical scalar isoscalar field sigma whose fluctuations cause correlations between observed hadrons due to the couplings of the sigma field to the hadrons via their masses. We match the QGP fluctuations obtained by solving the Hydro+ equations describing the evolution of critical fluctuations before freeze-out to the correlations of the sigma field. In turn, these are imprinted onto correlations and fluctuations in the multiplicity of hadrons, most importantly protons, after freeze-out via the generalization of the familiar half-century-old Cooper-Frye freeze-out prescription which we introduce. The proposed framework allows us to study the effects of critical slowing down and the consequent deviation of the observable predictions from equilibrium expectations quantitatively. We also quantify the suppression of cumulants due to conservation of baryon number. We demonstrate the procedure in practice by freezing out a Hydro+ simulation in an azimuthally symmetric and boost invariant background that includes radial flow discussed in arXiv:1908.08539.

It has been shown that a first order confinement phase transition can drastically change the relic dark matter abundance in confining dark sectors with only heavy dark quarks. We study the phenomenology of one such model with a Z' portal to Standard Model. We find that dark glueballs are long-lived in this setup and dilute the dark matter abundance after their decay to Standard Model. With this effect, the correct relic abundance is obtained with dark matter masses up to \(\mathcal{O}(10^6)\)~TeV. We find that while a part of the parameter space is already ruled out by direct detection and collider searches, there is still a broad space of viable scenarios that can be probed by future experiments.

We construct a class of pure quark and gluon observables by using the collinear drop grooming technique. The construction is based on linear combinations of multiple cumulative distributions of the jet mass in collinear drop, whose specific weights are fully predicted perturbatively. This yields observables which obtain their values purely from quarks (or purely from gluons) in a wide region of phase space. We demonstrate this by showing that these observables are effective in two phase space regions, one dominated by perturbative resummation and one dominated by nonperturbative effects. The nonperturbative effects are included using shape functions which only appear as a common factor in the linear combinations constructed. We test this construction using a numerical analysis with next-to-leading logarithmic resummation and various shape function models, as well as analyzing these observables with Pythia and Vincia. Choices for the collinear drop parameters are optimized for experimental use.

As particles traverse the quark-gluon plasma (QGP) formed during a heavy ion collision they undergo energy loss depending on the distance travelled. We study several temperature- and velocity-weighted path length distributions of non-interacting particles as they traverse the plasma using the Trajectum heavy ion code, including those of back-to-back path lengths. We use event-shape engineering (ESE) in combination with in-plane versus out-of-plane selection to accurately control these path lengths. Lastly, we show how soft observables depend on the different ESE classes.