We discuss the anharmonic oscillator in quantum mechanics using exact WKB methods in a ‘t Hooft-like double scaling limit where classical behavior is expected to dominate. We compute the tunneling action in this double scaling limit, and compare it to the transition amplitude from the vacuum to a highly excited state. Our results, exact in the semiclassical limit, show that the two expressions coincide, apart from an irreducible and surprising instanton contribution. The semiclassical limit of the anharmonic oscillator betrays its quantum origin as a rule showing that the quantum theory is intrinsically gapped from classical behavior. Besides an example of a resurgent connection between perturbative and nonperturbative physics, this may provide a way to study transition amplitudes from tunnelling actions, and vice versa.
Dr. Fatma Aslan, Jefferson National Laboratory and UConn
Hadron structure-oriented approach to TMD phenomenology
We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to TMD phenomenology applied to Drell-Yan like processes. We compare and contrast general features of our methodology with other common practices and emphasize the improvements derived from our approach that we view as essential for applications where extracting details of nonperturbative transverse hadron structure is a major goal. These include the HSO’s preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear PDFs, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions.
Fully Consistent NLO Calculation of Forward Single-Inclusive Hadron Production in Proton-Nucleus Collisions
We study the single-inclusive particle production from proton-nucleus collisions in the dilute-dense framework of the color glass condensate (CGC) at next-to-leading order (NLO) accuracy. In this regime, the cross section factorizes into hard impact factors and dipole-target scattering amplitude describing the eikonal interaction of the partons in the target color field. For the first time, we combine the NLO impact factors with the dipole amplitude evolved consistently using the NLO Balitsky-Kovchegov (BK) equation with the initial conditions fitted to HERA structure function data.
The resulting neutral pion cross section with all parton channels included are qualitatively consistent with the recent LHCb measurement. In particular, the NLO evolution coupled to the leading order impact factor is shown to produce a large Cronin peak that is not visible in the data, demonstrating the importance of consistently including NLO corrections to all the ingredients. Furthermore, the transverse momentum spectrum is found to be sensitive to the resummation scheme and the running coupling prescription in the BK evolution. This demonstrates how additional constraints for the initial condition of the BK evolution can be obtained from global analyses including both the HERA and LHC data. In light of the upcoming upgrades to the LHC, the dependence of our results on rapidity will also be discussed.
Scattering amplitudes are the arena where quantum field theory meets particle experiments, for example at the Large Hadron Collider where the copious scattering of quarks and gluons in quantum chromodynamics (QCD) produces Higgs bosons and many backgrounds to searches for new physics. Particle scattering in QCD and other gauge theories is far simpler than standard perturbative approaches would suggest. Modern approaches based on unitarity and bootstrapping dramatically simplify many computations previously done with Feynman diagrams. Even so, the final results are often highly intricate, multivariate mathematical functions, which are difficult to describe, let alone compute. In many cases, the functions have a “genetic code” underlying them, called the symbol, which reveals much of their structure. The symbol is a linear combination of words, sequences of letters analogous to sequences of DNA base pairs. Understanding the alphabet, and then reading the code, exposes the physics and mathematics underlying the scattering process, including new symmetries. For example, the two scattering amplitudes that are known to the highest orders in perturbation theory (8 loops) are related to each other by a mysterious antipodal duality, which involves reading the code backwards as well as forwards. A third scattering amplitude, which contains both of these as limits, has an antipodal self-duality which “explains” the other duality. However, we still don’t know `who ordered’ antipodal (self-)duality, or what it really means.
Daniel Norman, Department of Physics, University of Connecticut
The Complex Analytic Properties of Bandwidth Limited Signals and their Application to Conformal Cosmology and Signal Processing
Conformal gravity is an alternative theory of gravity derived from the conformally invariant Weyl squared action as opposed to the standard Einstein-Hilbert action. The general equations of conformal gravity were applied to the cosmological scale to create a theory of Conformal Cosmology where the geometry of space-time is described by first order fluctuations on a conformal-to-flat background of constant negative curvature. The differential equations of this cosmological model have solutions in terms of Legendre functions with complex degree and order. In order to calculate the multipole expansion of Cosmic Background Radiation (CMB) anisotropy within this model, it is necessary to integrate the Legendre function solutions with respect to their complex degree. An analytic method for solving this integration problem was developed which makes use of the fact that the Legendre functions are Bandwidth Limit Signals (BLS’s) which are functions with a finite domain in frequency space. A general analysis of the properties of BLS’s in the complex plane was done which has yielded new theorems and expansion formulas applicable to all BLS’s as well as to other related families of complex functions. These results have both specific applications to Conformal Cosmology as well as broader applications to the field of signal processing. The methods of complex integration developed in this work, initially for the purpose of computing the CMB anisotropy in Conformal Cosmology, have been used to provide a novel solution to the infamous Borweinn integral as well as a novel proof of the Nyquist-Shannon sampling theorem.