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Register a new userObservability of glueball spectrum in QCD and the width of $sigma$ resonance
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Authors
Marco Frasca
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We prove a theorem in QCD stating that in the limit of strong coupling, $gtoinfty$, the observed spectrum of glueballs in QCD is the same of a pure Yang-Mills theory, being mixing effects due to the next-to-leading order. A full effective theory for QCD is obtained and the width of the $sigma$ resonance decay is straightforwardly computed. This appears as the lowest glueball state. Vacuum gluon condensate is computed that consistently support studies on the identification of this meson as a glueball.
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Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the $sigma$ and $eta-eta$ mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant $Lambda$ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.
We present for the first time a determination of the energy dependence of the isoscalar $pipi$ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the $S$-wave phase-shift up to the $Koverline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_pi = 236, 391$ MeV and the resulting amplitudes are described in terms of a $sigma$ meson which evolves from a bound-state below $pipi$ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.
We use a variational technique to study heavy glueballs on gauge configurations generated with 2+1 flavours of ASQTAD improved staggered fermions. The variational technique includes glueball scattering states. The measurements were made using 2150 configurations at 0.092 fm with a pion mass of 360 MeV. We report masses for 10 glueball states. We discuss the prospects for unquenched lattice QCD calculations of the oddballs.
We discuss properties of non-Abelian gauge theories that change significantly across the lower edge of the conformal window. Their probes are the topological observables, the meson spectrum and the scalar glueball operator. The way these quantities change tells about the way conformal symmetry is lost.
It has been argued that the leading scalar-isoscalar WIMP-nucleus interactions receive parametrically enhanced contributions in the context of nuclear effective field theories. These contributions arise from meson-exchange currents (MECs) and potentially modify the impulse approximation estimates of these interactions by 10--60%. We point out that these MECs also contribute to the quark mass dependence of nuclear binding energies, that is, nuclear sigma-terms. In this work, we use recent lattice QCD calculations of the binding energies of the deuteron, He-3 and He-4 at pion masses near 500 MeV and 800 MeV, combined with the experimentally determined binding energies at the physical point, to provide approximate determinations of the sigma-terms for these light nuclei. For each nucleus, we find that the deviation of the corresponding nuclear sigma-term from the single-nucleon estimate is at the few percent level, in conflict with the conjectured enhancement. As a consequence, lattice QCD calculations currently indicate that the cross sections for scalar-isoscalar WIMP-nucleus interactions arising from fundamental WIMP interactions with quarks do not suffer from significant uncertainties due to enhanced meson-exchange currents.
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