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Concept# Quantum number

Summary

In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.
An important aspect of quantum mechanics is the quantization of many observable quantities of interest. In particular, this leads to quantum numbers that take values in discrete sets of integers or half-integers; although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, all range continuously. Quantum numbers often describe specifically the energy lev

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Angelo Esposito, Claudio Andrea Manzari

Ultraperipheral heavy ion collisions constitute an ideal setup to look for exotic hadrons because of their low event multiplicity and the possibility of an efficient background rejection. We propose to look for fourquark states produced by photon-photon fusion in these collisions at the center-of-mass energy per nucleon pair root s(NN) = 5.5 TeV. In particular, we focus on those states that would represent a definite smoking gun for the compact tetraquark model. We show that the X(6900), a likely cc (c) over bar(c) over bar compact state, is a perfect candidate for this search, and estimate a production cross section ranging from around 250 nb to 1150 nb, depending on its quantum numbers. Furthermore, we discuss the importance of ultraperipheral collisions to the search for the scalar and tensor partners of the X(3872) predicted by the diquarkonium model, and not yet observed. The completion of such a flavor-spin multiplet would speak strongly in favor of the compact tetraquark model.

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In composite Higgs models with partial compositeness, the small value of the observed Higgs mass implies the existence of light fermionic resonances, the top partners, whose quantum numbers are determined by the symmetry (and symmetry breaking) structure of the theory. Here we study light top partners with electric charge 8/3, which are predicted, for instance, in some of the most natural composite Higgs realizations. We recast data from two same sign lepton searches and from searches for microscopic blackholes into a bound on its mass, M-8/3 > 940 GeV. Furthermore, we compare potential reach of these searches with a specifically designed search for three same-sign leptons, both at 8 and 14TeV. We provide a simplified model, suitable for collider analysis.

Andrea Guerrieri, Aditya Hebbar

We bootstrap the S matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S matrices is strongly constrained by the existence of a UV completion. In the context of flux tube (FT) physics, this allows us to constrain several terms in the S matrix low energy expansion or-equivalently-on Wilson coefficients of several irrelevant operators showing up in the FT effective action. These bounds have direct implications for other physical quantities; for instance, they allow us to further bound the ground state energy as well as the level splitting of degenerate energy levels of large FTs. We find that the S matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass, and width are precisely those of the world-sheet axion proposed by Athenodorou, Bringoltz, and Teper and Dubovsky, Flauger, and Gorbenko. The general method proposed here should be extendable to massless S matrices in higher dimensions and should lead to new quantitative bounds on irrelevant operators in theories of Goldstones and, also, in gauge and gravity theories.

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