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The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order., Comment: 48 pages + references, 10 figures; v2: JHEP version; v3: fix references

We calculate the post-recombination contribution to the Cosmic Microwave Background (CMB) spectral distortion due to general exotic energy injections, including dark matter (DM) decaying or annihilating to Standard Model particles. Upon subtracting the background distortion that would be present even without such energy injections, we find residual distortions that are still potentially large enough to be detectable by future experiments such as PIXIE. The distortions also have a high-energy spectral feature that is a unique signature of the injection of high-energy particles. We present a calculation of the global ionization history in the presence of decaying dark matter with sub-keV masses, and also show that previous calculations of the global ionization history in the presence of energy injection are not significantly modified by these additional spectral distortions. Our improved treatment of low-energy electrons allows us to extend calculations of the CMB anisotropy constraints for decaying DM down to arbitrarily low masses. We also recast these bounds as constraints on the coupling of axion-like particles to photons., Comment: 23 pages, 16 figures

Decaying or annihilating dark matter and other exotic energy injections can modify the spectrum of the universe's photon bath, resulting in e.g. new contributions to spectral distortions of the cosmic microwave background blackbody spectrum and modifications to the temperature and ionization history of the universe. Here, we present an improved version of the $\texttt{DarkHistory}$ code, which is now capable of consistently calculating the spectrum of low-energy photons by properly treating the interactions of these photons with the levels of hydrogen atoms. Other changes to the code include a more detailed treatment of energy deposition by low-energy electrons, and spectral distortions from heating of the intergalactic medium. All of the improvements we have made to $\texttt{DarkHistory}$ are publicly available., Comment: 29 pages, 12 figures

Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of $2\to 2$ scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to $\mathcal{O}(\epsilon)$ in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e.~the terms $\sim \alpha_s^{k+1}n_f^k$ for any $k$, where $n_f$ is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit., Comment: 29 pages, 5 figures

The Beam Energy Scan Theory (BEST) Collaboration was formed with the goal of providing a theoretical framework for analyzing data from the Beam Energy Scan (BES) program at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory. The physics goal of the BES program is the search for a conjectured QCD critical point as well as for manifestations of the chiral magnetic effect. We describe progress that has been made over the previous five years. This includes studies of the equation of state and equilibrium susceptibilities, the development of suitable initial state models, progress in constructing a hydrodynamic framework that includes fluctuations and anomalous transport effects, as well as the development of freezeout prescriptions and hadronic transport models. Finally, we address the challenge of integrating these components into a complete analysis framework. This document describes the collective effort of the BEST Collaboration and its collaborators around the world., Comment: 103 pages

We carry out a detailed study of the confinement phase transition in a dark sector with a $SU(N)$ gauge group and a single generation of dark heavy quark. We focus on heavy enough quarks such that their abundance freezes out before the phase transition and the phase transition is of first-order. We find that during this phase transition the quarks are trapped inside contracting pockets of the deconfined phase and are compressed enough to interact at a significant rate, giving rise to a second stage of annihilation that can dramatically change the resulting dark matter abundance. As a result, the dark matter can be heavier than the often-quoted unitarity bound of $\sim100~$TeV. Our findings are almost completely independent of the details of the portal between the dark sector and the Standard Model. We comment briefly on possible signals of such a sector. Our main findings are summarized in a companion letter, while here we provide further details on different parts of the calculation., Comment: 38+30 pages, 14 figures

We study the effect of a first-order phase transition in a confining $SU(N)$ dark sector with heavy dark quarks. The baryons of this sector are the dark matter candidate. During the confinement phase transition the heavy quarks are trapped inside isolated, contracting pockets of the deconfined phase, giving rise to a second stage of annihilation that dramatically suppresses the dark quark abundance. The surviving abundance is determined by the local accidental asymmetry in each pocket. The correct dark matter abundance is obtained for $\mathcal{O}(1-100)$ PeV dark quarks, above the usual unitarity bound., Comment: 5 pages, 3 figures, comments are welcomed

We derive new constraints on models of decaying and annihilating dark matter (DM) by requiring that the energy injected into the intergalactic medium (IGM) not overheat it at late times, when measurements of the Lyman-$\alpha$ forest constrain the IGM temperature. We improve upon previous analyses by using the recently developed $\texttt{DarkHistory}$ code package, which self-consistently takes into account additional photoionization and photoheating processes due to reionization and DM sources. Our constraints are robust to the uncertainties of reionization and competitive with leading limits on sub-GeV DM that decays preferentially to electrons., Comment: 5+7 pages, 7 figures. v2 updates p-wave constraints, fixes typo in Eq. (4), fixes minor Fig. 1 error, and includes pion and muon constraints in new section of Appendix

Upcoming experimental programs will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any critical fluctuations must be out-of-equilibrium: because of critical slowing down, the fluctuations cannot stay in equilibrium as the droplet of QGP produced in a collision expands and cools. Furthermore, their out-of-equilibrium dynamics must also influence the hydrodynamic evolution of the cooling droplet. The recently developed Hydro+ formalism allows for a consistent description of both the hydrodynamics and the out-of-equilibrium fluctuations, including the feedback between them. We shall explicitly demonstrate how this works, setting up a Hydro+ simulation in a simplified setting: a rapidity-independent fireball undergoing radial flow with an equation of state in which we imagine a critical point close to the $\mu_B=0$ axis of the phase diagram. Within this setup, we show that we can quantitatively capture non-equilibrium phenomena, including critical fluctuations over a range of scales and memory effects. Furthermore, we illustrate the interplay between the dynamics of the fluctuations and the hydrodynamic flow of the fireball: as the fluid cools and flows, the dynamical fluctuations lag relative to how they would evolve if they stayed in equilibrium; there is then a backreaction on the flow itself due to the out-of-equilibrium fluctuations; and, in addition, the radial flow transports fluctuations outwards by advection. Within our model, we find that the backreaction from the out-of-equilibrium fluctuations does not yield dramatically large effects in the hydrodynamic variables. Further work will be needed in order to check this quantitative conclusion in other settings but, if it persists, this will considerably simplify future modelling., Comment: 40 pages, 9 figures

We present a new public Python package, DarkHistory, for computing the effects of dark matter annihilation and decay on the temperature and ionization history of the early universe. DarkHistory simultaneously solves for the evolution of the free electron fraction and gas temperature, and for the cooling of annihilation/decay products and the secondary particles produced in the process. Consequently, we can self-consistently include the effects of both astrophysical and exotic sources of heating and ionization, and automatically take into account backreaction, where modifications to the ionization/temperature history in turn modify the energy-loss processes for injected particles. We present a number of worked examples, demonstrating how to use the code in a range of different configurations, in particular for arbitrary dark matter masses and annihilation/decay final states. Possible applications of DarkHistory include mapping out the effects of dark matter annihilation/decay on the global 21cm signal and the epoch of reionization, as well as the effects of exotic energy injections other than dark matter annihilation/decay. The code is available at https://github.com/hongwanliu/DarkHistory with documentation at https://darkhistory.readthedocs.io . Data files required to run the code can be downloaded at https://doi.org/10.7910/DVN/DUOUWA ., Comment: 40 pages, 17 figures

A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real time dynamics of a scalar {\phi}^4 theory with weak and strong couplings., Comment: 12 pages, 5 figures

We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first example where a fermionic sign problem is solved in a quantum field theory by using the holomorphic gradient flow approach, a generalization of the Lefschetz thimble method., Comment: 6 pages, 5 figures

A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lefschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible., Comment: 12 pages, 6 figures, 1 table

A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models., Comment: 10 pages, 3 figures

We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such manifolds that interpolate between the tangent space at one critical point, where the sign problem is milder compared to the real plane but in some cases still severe, and the union of relevant thimbles, where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling. We exemplify this approach using a simple 0 + 1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefshetz thimbles was elusive., Comment: 12 pages, 7 figures, figure added, corrected typos