No Radial Excitations in Low Energy QCD. I. Diquarks and Classification of Mesons

We propose a new schematic model for mesons in which the building blocks are quarks and flavor-antisymmetric diquarks. The outcome is a new classification of the entire meson spectrum into quark-antiquark and diquark-antidiquark states which does not give rise to a radial quantum number: all mesons which have so far been believed to be radially excited are orbitally excited diquark-antidiquark states; similarly, there are no radially excited baryons. Further, mesons that were previously viewed as "exotic" are no longer exotic as they are now naturally integrated into the classification as diquark-antidiquark states. The classification also leads to the introduction of isorons (iso-hadrons), which are analogs of atomic isotopes, and their magic quantum numbers, which are analogs of the magic numbers of the nuclear shell model. The magic quantum numbers of isorons match the quantum numbers expected for low-lying glueballs in lattice QCD. We observe that interquark forces in mesons behave substantially differently from those in baryons: qualitatively, they are color-magnetic in mesons but color-electrostatic in baryons. We comment on potential models and the hydrogen atom. The implications of our results for confinement, asymptotic freedom, and a new set of relations between two fundamental properties of hadrons - their size and their energy - are discussed in our companion paper [arXiv:0910.2231].Comment: 40 pages, references added, minor revisions, to appear in Eur. Phys. J.

Unification Scale, Proton Decay, And Manifolds Of G_2 Holonomy

Models of particle physics based on manifolds of $G_2$ holonomy are in most respects much more complicated than other string-derived models, but as we show here they do have one simplification: threshold corrections to grand unification are particularly simple. We compute these corrections, getting completely explicit results in some simple cases. We estimate the relation between Newton's constant, the GUT scale, and the value of $\alpha_{GUT}$, and explore the implications for proton decay. In the case of proton decay, there is an interesting mechanism which (relative to four-dimensional SUSY GUT's) enhances the gauge boson contribution to $p\to\pi^0e^+_L$ compared to other modes such as $p\to \pi^0e^+_R$ or $p\to \pi^+\bar\nu_R$. Because of numerical uncertainties, we do not know whether to intepret this as an enhancement of the $p\to \pi^0e^+_L$ mode or a suppression of the others.Comment: 40 p

Group-Theoretical Derivation of Angular Momentum Eigenvalues in Spaces of Arbitrary Dimensions

The spectrum of the square of the angular momentum in arbitrary dimensions is derived using only group theoretical techniques. This is accomplished by application of the Lie algebra of the noncompact group O(2,1).Comment: 4 pages; to appear in Journal of Mathematical Physic

Quantum Mechanical Derivation of the Wallis Formula for π\pi

A famous pre-Newtonian formula for $\pi$ is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.Comment: 4 pages; to appear in J. Math. Phys.; v2: minor typo fixe

No Radial Excitations in Low Energy QCD. II. The Shrinking Radius of Hadrons

We discuss the implications of our prior results obtained in our companion paper (Eur. Phys. J. C (2013). doi:10.1140/epjc/s10052-013-2298-9). Inescapably, they lead to three laws governing the size of hadrons, including in particular protons and neutrons that make up the bulk of ordinary matter: (a) there are no radial excitations in low-energy QCD; (b) the size of a hadron is largest in its ground state; (c) the hadron’s size shrinks when its orbital excitation increases. The second and third laws follow from the first law. It follows that the path from confinement to asymptotic freedom is a Regge trajectory. It also follows that the top quark is a free, albeit short-lived, quark

On Baryon Number Non-Conservation in Two-Dimensional O(2N+1) QCD

We construct a classical dynamical system whose phase space is a certain infinite dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N + 1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models

Schwinger Pair Creation of Kaluza-Klein Particles: Pair Creation Without Tunneling

We study Schwinger pair creation of charged Kaluza-Klein (KK) particles from a static KK electric field. We find that the gravitational backreaction of the electric field on the geometry—which is incorporated via the electric KK-Melvin solution—prevents the electrostatic potential from overcoming the rest mass of the KK particles, thus impeding the tunneling mechanism which is often thought of as responsible for the pair creation. However, we find that pair creation still occurs with a finite rate formally similar to the classic Schwinger result, but via an apparently different mechanism, involving a combination of the Unruh effect and vacuum polarization due to the E-field

On a generalization of Lie(kk): a CataLAnKe theorem

We define a generalization of the free Lie algebra based on an $n$-ary commutator and call it the free LAnKe. We show that the action of the symmetric group $S_{2n-1}$ on the multilinear component with $2n-1$ generators is given by the representation $S^{2^{n-1}1}$, whose dimension is the $n$th Catalan number. An application involving Specht modules of staircase shape is presented. We also introduce a conjecture that extends the relation between the Whitehouse representation and Lie($k$).Comment: 14 page