MIT Center for Theoretical Physics — a Leinweber Institute Publications

The theoretical description of observables at collider experiments relies on factorization theorems separating perturbative dynamics from universal non-perturbative matrix elements. Despite significant recent progress in extending these factorization theorems to increasingly differential jet substructure observables, the focus has been primarily on infrared safe observables sensitive only to correlations in the energy of final state hadrons. However, significant information about the dynamics of the underlying collision is encoded in how energy is correlated between hadrons of different quantum numbers. In this paper we extend the class of calculable correlations by deriving factorization theorems for a broad class of correlations, \(\langle \mathcal{E}_{R_1}(n_1) \cdots \mathcal{E}_{R_k}(n_k) \rangle\), between the energy flux carried by hadrons specified by quantum numbers, \(R_1, \cdots, R_k\). We show that these factorization theorems involve moments of a new class of universal non-perturbative functions, the “joint track functions”, which extend the track function formalism to describe the fraction of energy carried by hadrons of multiple quantum numbers arising from the fragmentation of quarks or gluons. We study the general properties of these functions, and then apply this to the specific case of joint track functions for positive and negative electromagnetic charges. We extract these from parton shower Monte Carlo programs and use them to calculate correlations in electromagnetically charged energy flux. We additionally propose and study a C-odd \(\mathcal{E}_{\mathcal{Q}}\) detector, which results in a qualitatively distinct scaling behavior compared to the standard energy correlators. Our formalism significantly extends the class of observables that can be computed at hadron colliders, with a wide range of applications from particle to nuclear physics.

The confining transition from asymptotically free partons to hadrons remains one of the most mysterious aspects of Quantum Chromodynamics. With the wealth of high quality jet substructure data we can hope to gain new experimental insights into the details of its dynamics. Jet substructure has traditionally focused on correlations, \(\langle \mathcal{E}(n_1) \mathcal{E}(n_2) \cdots \mathcal{E}(n_k) \rangle\), in the energy flux of hadrons. However, significantly more information about the confinement transition is encoded in how energy is correlated between hadrons with different quantum numbers, for example electric charge. In this Letter we develop the field theoretic formalism to compute general correlations, \(\langle \mathcal{E}_{R_1}(n_1) \mathcal{E}_{R_2}(n_2) \cdots\mathcal{E}_{R_k}(n_k) \rangle\), between the energy flux carried by hadrons with quantum numbers \(R_i\), by introducing new universal non-perturbative functions, which we term joint track functions. Using this formalism we show that the strong interactions introduce enhanced small angle correlations between opposite-sign hadrons, relative to like-sign hadrons, identifiable as an enhanced scaling of \(\langle \mathcal{E}_+(n_1) \mathcal{E}_-(n_2) \rangle\) relative to \(\langle \mathcal{E}_+(n_1) \mathcal{E}_+(n_2) \rangle\). We are also able to compute the scaling of a \(C\)-odd three-point function, \(\langle \mathcal{E}_\mathcal{Q}(n_1) \mathcal{E}_\mathcal{Q}(n_2) \mathcal{E}_\mathcal{Q}(n_3) \rangle\). Our results greatly extend the class of systematically computable jet substructure observables, pushing perturbation theory deeper into the parton to hadron transition, and providing new observables to understand the dynamics of confinement.

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program.

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of \(n\)-pion correlation functions for \(n \in \{ 1, \dots, N\}\) using a single \(N \times N\) matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 \(\pi^+\)s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass \(m_\pi = 170\) MeV and spacetime volumes of \((4.4^3\times 8.8)\ {\rm fm}^4\) and \((5.8^3\times 11.6)\ {\rm fm}^4\). We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential \(\mu_I\sim 1.5 m_\pi\), signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit (\(c_s^2\leq 1/3\)) over a wide range of chemical potential before falling towards the asymptotic expectation at \(\mu_I\sim 15 m_\pi\). These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

A lattice QCD computation of the coupled channel \(\pi\Sigma\unicode{x2013}\bar{K}N\) scattering amplitudes in the \(\Lambda(1405)\) region is detailed. Results are obtained using a single ensemble of gauge field configurations with \(N_{\rm f} = 2+1\) dynamical quark flavors and \(m_{\pi} \approx 200\) MeV and \(m_K\approx487\) MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering \(K\)-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the \(\pi\Sigma\) threshold and a resonance pole just below the \(\bar{K}N\) threshold.

This work presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice Quantum Chromodynamics (QCD). This is the first lattice QCD calculation of the kernel at quark masses corresponding to a close-to-physical value of the pion mass, with next-to-next-leading logarithmic matching to TMDs from the corresponding lattice-calculable distributions, and includes a complete analysis of systematic uncertainties arising from operator mixing. The kernel is extracted at transverse momentum scales \(240\,\text{MeV}\lesssim q_{T}\lesssim 1.6\,\text{GeV}\) with a precision sufficient to begin to discriminate between different phenomenological models in the non-perturbative region.

Suppression of open heavy flavors and quarkonia in heavy-ion collisions is among the most informative probes of the quark-gluon plasma. Interpreting the full wealth of data obtained from the collision events requires a precise understanding of the evolution of heavy quarks and quarkonia as they propagate through the nearly thermal and strongly coupled plasma. Systematic theoretical studies of quarkonium time evolution in the QGP in the regime where the temperature of the QGP is much smaller than the inverse of quarkonium size have only been carried out in the past few years. Such calculations require the evaluation of a gauge-invariant correlator of chromoelectric fields dressed with Wilson lines, which is similar to, but different from, the correlation used to define the well-known arXiv:hep-ph/0605199 heavy quark diffusion coefficient. The origin of this difference has been explained in arXiv:2107.03945, arXiv:2205.04477, arXiv:2306.13127. Here we show the results of the calculation of the analogous correlator in strongly coupled \(\mathcal{N}=4\) SYM using the AdS/CFT correspondence at a finite temperature arXiv:2304.03298. While it resembles the open heavy quark case, it has some crucial differences that highlight the relevance of quantum color correlations. We will also discuss the results for the quarkonium transport coefficients obtained from this correlator, thereby establishing the first analytic results at strong coupling in this context. We find that they vanish in the strong coupling limit for an \(\mathcal{N}=4\) SYM plasma with a large number of colors.

We present an estimate of the yield of hard probes expected for collisions of the isobars \(^{96}_{44}\)Ru and \(^{96}_{40}\)Zr at collision energies reachable at RHIC and the LHC\@. These yields are proportional to the number of binary nucleon-nucleon interactions, which is characteristically different due to the presence of the large neutron skin in \(^{96}_{40}\)Zr. This provides an independent opportunity to measure the difference between the neutron skin of \(^{96}_{44}\)Ru and \(^{96}_{40}\)Zr, which can provide an important constraint on the Equation of State of cold neutron-rich matter.

The two gravitational form factors of the pion, \(A^{\pi}(t)\) and \(D^{\pi}(t)\), are computed as functions of the momentum transfer squared \(t\) in the kinematic region \(0\leq -t< 2~\text{GeV}^2\) on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass \(m_{\pi}\approx 170~\text{MeV}\) and \(N_f=2+1\) quark flavors. The flavor decomposition of these form factors into gluon, up/down light-quark, and strange quark contributions is presented in the \(\overline{\text{MS}}\) scheme at energy scale \(\mu=2~\text{GeV}\), with renormalization factors computed non-perturbatively via the RI-MOM scheme. Using monopole and (modified) \(z\)-expansion fits to the gravitational form factors, we obtain estimates for the pion momentum fraction and \(D\)-term that are consistent with the momentum fraction sum rule and the next-to-leading order chiral perturbation theory prediction for \(D^{\pi}(0)\).

Holography on cutoff surfaces can appear to be in tension with causality. For example, as argued by Omiya and Wei [arxiv:2107.01219], double holography seemingly allows for superluminal signalling. In this paper we argue that the brane description of double holography should be treated as an effective theory and demonstrate that causality violations due to faster-than-light communication are not visible above the associated cutoff length scale. This suggests that end-of-the-world brane models are consistent with causality and that the apparent superluminal signalling is a UV effect. Moreover, we argue that short distance non-localities generically give rise to apparent faster-than-light propagation of signals in Anti-de Sitter space. Nonetheless, superluminal signalling indicates that the causal structure on holographic cutoff surfaces needs to be modified. We propose and study three different candidate regions that might replace the domain of dependence in the brane EFT of the Karch-Randall model. These regions are defined by unitarity on the brane, through bulk entanglement wedges and through the nice slice criterion, respectively. In all dimensions, these candidate regions exclude those parts of the domain of dependence which are affected by superluminal signalling. While all three definitions agree in two dimensions, they are different in higher dimensions.

Both parameters in the Higgs field’s potential, its mass and quartic coupling, appear fine-tuned to near-critical values, which gives rise to the hierarchy problem and the metastability of the electroweak vacuum. Whereas such behavior appears puzzling in the context of particle physics, it is a common feature of dynamical systems, which has led to the suggestion that the parameters of the Higgs potential could be set through some dynamical process. In this article, we discuss how this notion could be extended to physics beyond the Standard Model (SM). We first review in which sense the SM Higgs parameters can be understood as near-critical and show that this notion can be extrapolated in a unique way for a generic class of SM extensions. Our main result is a prediction for the parameters of such models in terms of their corresponding Standard Model effective field theory Wilson coefficients and corresponding matching scale. For generic models, our result suggests that the scale of new (bosonic) physics lies close to the instability scale. We explore the potentially observable consequences of this connection, and illustrate aspects of our analysis with a concrete example. Lastly, we discuss implications of our results for several mechanisms of dynamical vacuum selection associated with various Beyond-Standard-Model (BSM) constructions.

This letter presents the first lattice QCD computation of the coupled channel \(\pi\Sigma\unicode{x2013}\bar{K}N\) scattering amplitudes at energies near \(1405\,{\rm MeV}\). These amplitudes contain the resonance \(\Lambda(1405)\) with strangeness \(S=-1\) and isospin, spin, and parity quantum numbers \(I(J^P)=0(1/2^-)\). However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to \(m_\pi\approx200\) MeV and \(m_K\approx487\) MeV, this study finds the amplitudes exhibit a virtual bound state below the \(\pi\Sigma\) threshold in addition to the established resonance pole just below the \(\bar{K}N\) threshold. Several parametrizations of the two-channel \(K\)-matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by \(SU(3)\) chiral symmetry and unitarity.

We use the quantum spectral curve to compute the Hagedorn temperature for ABJM theory in terms of the interpolating function \(h(\lambda)\). At weak coupling we compute this temperature up to eight-loop order, showing that it matches the known tree-level and two-loop results. At strong coupling we compute the dependence numerically, showing that it is consistent with expectations from supergravity and the plane-wave limit for the four leading terms in the strong coupling expansion, up to an overall shift of the zero-point energy for type IIA string theory on AdS\(_4\times \mathbb{C}\textrm{P}^3\). We conjecture an analytic form for this shift to leading order that is consistent with our numerical results.

The dynamics of open quantum systems can be simulated by unraveling it into an ensemble of pure state trajectories undergoing non-unitary monitored evolution, which has recently been shown to undergo measurement-induced entanglement phase transition. Here, we show that, for an arbitrary decoherence channel, one can optimize the unraveling scheme to lower the threshold for entanglement phase transition, thereby enabling efficient classical simulation of the open dynamics for a broader range of decoherence rates. Taking noisy random unitary circuits as a paradigmatic example, we analytically derive the optimum unraveling basis that on average minimizes the threshold. Moreover, we present a heuristic algorithm that adaptively optimizes the unraveling basis for given noise channels, also significantly extending the simulatable regime. When applied to noisy Hamiltonian dynamics, the heuristic approach indeed extends the regime of efficient classical simulation based on matrix product states beyond conventional quantum trajectory methods. Finally, we assess the possibility of using a quasi-local unraveling, which involves multiple qubits and time steps, to efficiently simulate open systems with an arbitrarily small but finite decoherence rate.

Recent open quantum system studies showed that quarkonium time evolution inside the quark-gluon plasma is determined by transport coefficients that are defined in terms of a gauge invariant correlator of two chromoelectric field operators connected by an adjoint Wilson line. We study the Euclidean version of the correlator for quarkonium evolution and discuss the extraction of the transport coefficients from this Euclidean correlator, highlighting its difference from other problems that also require reconstructing a spectral function, such as the calculation of the heavy quark diffusion coefficient. Along the way, we explain why the transport coefficient \(\gamma_{\rm adj}\) differs from \(\gamma_{\rm fund}\) at finite temperature at \(\mathcal{O}(g^4)\), in spite of the fact that their corresponding spectral functions differ only by a temperature-independent term at the same order. We then discuss how to evaluate the Euclidean correlator via lattice QCD methods, with a focus on reducing the uncertainty caused by infrared renormalons in determining the renormalization factor nonperturbatively.

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure, where “local” parameters impact individual events and “global” parameters influence the entire dataset. We introduce practical approaches for optimal dataset-wide probabilistic inference in cases where the likelihood is intractable, but simulations can be realized via forward modeling. We construct neural estimators for the likelihood(-ratio) or posterior and show that explicitly accounting for the model’s hierarchical structure can lead to tighter parameter constraints. We ground our discussion using case studies from the physical sciences, focusing on examples from particle physics (particle collider data) and astrophysics (strong gravitational lensing observations).

Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry’s conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity — generated by the Fibonacci word and its generalizations — for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems.

Using the supergravity dual and the plane-wave limit as a guide, we conjecture the asymptotic large coupling form of the Hagedorn temperature for planar \(\mathcal{N}=4\) super Yang-Mills to order \(1/\sqrt{\lambda}\). This is two orders beyond the presently known behavior. Using the quantum spectral curve procedure of Harmark and Wilhelm, we show that our conjectured form is in excellent agreement with the numerical results.

Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. This geometry is relevant for the hyperbolic string tadpole vertex describing the one-loop quantum corrections of closed string field theory. We argue that the Lamé equation, upon fixing its accessory parameter via Polyakov conjecture, provides the input for the characterization. The explicit expressions for the Weil-Petersson metric as well as the local coordinates and the associated vertex region for the tadpole vertex are given in terms of classical torus conformal blocks. The relevance of this vertex for vacuum shift computations in string theory is highlighted.

We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy eigenstates of the full system and products of energy eigenstates of two extensive subsystems, using a family of spin chains in (1+1) dimensions as an illustration. The magnitudes of the coefficients relating the two bases have a simple universal form as a function of \(\omega\), the energy difference between the full system eigenstate and the product of eigenstates. This form explains the exponential decay with time of the probability for a product of eigenstates to return to itself during thermalization. We also find certain new statistical properties of the coefficients. While it is generally expected that the coefficients are uncorrelated random variables, we point out that correlations implied by unitarity are important for understanding the transition probability between two products of eigenstates, and the evolution of operator expectation values during thermalization. Moreover, we find that there are additional correlations resulting from locality, which lead to a slower growth of the second Renyi entropy than the one predicted by an uncorrelated random variable approximation.