QCD Constituent Counting Rules for Neutral Vector Mesons

QCD constituent counting rules define the scaling behavior of exclusive hadronic scattering and electromagnetic scattering amplitudes at high momentum transfer in terms of the total number of fundamental constituents in the initial and final states participating in the hard subprocess. The scaling laws reflect the twist of the leading Fock state for each hadron and hence the leading operator that creates the composite state from the vacuum. Thus, the constituent counting scaling laws can be used to identify the twist of exotic hadronic candidates such as tetraquarks and pentaquarks. Effective field theories must consistently implement the scaling rules in order to be consistent with the fundamental theory. Here we examine how one can apply constituent counting rules for the exclusive production of one or two neutral vector mesons $V^0$ in $e^+ e^-$ annihilation, processes in which the $V^0$ can couple via intermediate photons. In case of a (narrow) real $V^0$, the photon virtuality is fixed to a precise value $s_1 = m_{V^0}^2$, in effect treating the $V^0$ as a single fundamental particle. Each real $V^0$ thus contributes to the constituent counting rules with $N_{V_0} = 1$. In effect, the leading operator underlying the $V^0$ has twist 1. Thus, in the specific physical case of single or double on-shell $V^0$ production via intermediate photons, the predicted scaling from counting rules coincides with Vector Meson Dominance (VMD), an effective theory that treats $V^0$ as an elementary field. However, the VMD prediction fails in the general case where the $V^0$ is not coupled through an elementary photon field, and then the leading-twist interpolating operator has twist $N_{V_0} = 2$. Analogous effects appear in $pp$ scattering processes.Comment: 15 page

QCD Compositeness as Revealed in Exclusive Vector Boson Reactions through Double-Photon Annihilation: e+e−→γγ∗→γV0e^+ e^- \to \gamma \gamma^\ast \to \gamma V^0 and e+e−→γ∗γ∗→V0V0e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0 V^0

We study the exclusive double-photon annihilation processes, $e^+ e^- \to \gamma \gamma^\ast\to \gamma V^0$ and $e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg \Lambda_{\rm QCD}^2$. We show how the differential cross sections $\frac{d\sigma}{dt}$, as predicted by QCD, have additional falloff in the momentum transfer squared $t$ due to the QCD compositeness of the hadrons, consistent with the leading-twist fixed-$\theta_{\rm CM}$ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to \gamma^\ast \to q \bar q,$ these total cross sections $\sigma(e^+ e^- \to \gamma V^0)$ and $\sigma(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$\theta_{\rm CM}$ angular domains, scale as $1/s$, and thus contribute to the leading-twist scaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results to exclusive double-electroweak vector-boson annihilation processes accompanied by the forward production of hadrons, such as $e^+ e^- \to Z^0 V^0$ and $e^+ e^- \to W^-\rho^+$. These results can also be applied to the exclusive production of exotic hadrons such as tetraquarks, where the cross-section scaling behavior can reveal their multiquark nature.Comment: 10 page

Phase Structure of the Interacting Vector Boson Model

The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a dynamical group possesses a rich algebraic structure of physical interesting subgroups that define its distinct exactly solvable dynamical limits. The classical images corresponding to different dynamical symmetries are obtained by means of the coherent state method. The phase structure of the IVBM is investigated and the following basic phase shapes, connected to a specific geometric configurations of the ground state, are determined: spherical, $U_{p}(3)\otimes U_{n}(3)$, $\gamma-$unstable, O(6), and axially deformed shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions between different phase shapes, corresponding to the different dynamical symmetries and mixed symmetry case, are investigated.Comment: 9 pages, 10 figure

Arbitrage-Free Bond Pricing with Dynamic Macroeconomic Models

We examine the relationship between monetary-policy-induced changes in short interest rates and yields on long-maturity default-free bonds. The volatility of the long end of the term structure and its relationship with monetary policy are puzzling from the perspective of simple structural macroeconomic models. We explore whether richer models of risk premiums, specifically stochastic volatility models combined with Epstein-Zin recursive utility, can account for such patterns. We study the properties of the yield curve when inflation is an exogenous process and compare this to the yield curve when inflation is endogenous and determined through an interest-rate/Taylor rule. When inflation is exogenous, it is difficult to match the shape of the historical average yield curve. Capturing its upward slope is especially difficult as the nominal pricing kernel with exogenous inflation does not exhibit any negative autocorrelation - a necessary condition for an upward sloping yield curve as shown in Backus and Zin (1994). Endogenizing inflation provides a substantially better fit of the historical yield curve as the Taylor rule provides additional flexibility in introducing negative autocorrelation into the nominal pricing kernel. Additionally, endogenous inflation provides for a flatter term structure of yield volatilities which better fits historical bond data.

Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

Arbitrage-free bond pricing with dynamic macroeconomic models

The authors examine the relationship between changes in short-term interest rates induced by monetary policy and the yields on long-maturity default-free bonds. The volatility of the long end of the term structure and its relationship with monetary policy are puzzling from the perspective of simple structural macroeconomic models. The authors explore whether richer models of risk premiums, specifically stochastic volatility models combined with Epstein-Zin recursive utility, can account for such patterns. They study the properties of the yield curve when inflation is an exogenous process and compare this with the yield curve when inflation is endogenous and determined through an interest rate (Taylor) rule. When inflation is exogenous, it is difficult to match the shape of the historical average yield curve. Capturing its upward slope is especially difficult because the nominal pricing kernel with exogenous inflation does not exhibit any negative autocorrelation-a necessary condition for an upward-sloping yield curve, as shown in Backus and Zin. Endogenizing inflation provides a substantially better fit of the historical yield curve because the Taylor rule provides additional flexibility in introducing negative autocorrelation into the nominal pricing kernel. Additionally, endogenous inflation provides for a flatter term structure of yield volatilities, which better fits historical bond data.Bonds - Prices ; Macroeconomics