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Register a new userGlueball Spectrum and Regge Trajectory from Supergravity
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Elena Caceres
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Brief review of the status of the glueball spectrum in the deformed conifold background. Talk based on work done with R. Hernandez and X. Amador.
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We calculate the mass of the lowest lying spin two glueball in N=1 super Yang-Mills from the dual Klebanov-Strassler background. We show that the Regge trajectory obtained is linear; the 0++, 1-- and 2++ states lie on a line of slope 0.23 -measured in units of the conifold deformation. We also compare mass ratios with lattice data and find agreement within one standard deviation.
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.
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.
The Regge limit of gauge-theory amplitudes and cross sections is a powerful theory tool for the study of fundamental interactions. It is a vast field of research, encompassing perturbative and non-perturbative dynamics, and ranging from purely theoretical developments to detailed phenomenological applications. It traces its origins to the proposal of Tullio Regge, almost sixty years ago, to study scattering phenomena in the complex angular momentum plane. In this very brief contribution, we look back to the early days of Regge theory, and follow a few of the many strands of its development, reaching to present day applications to scattering amplitudes in non-abelian gauge theories.
The lowest-lying glueballs are investigated in lattice QCD using $N_f=2$ clover Wilson fermion on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion mass of $m_pisim 938$ MeV and $650$ MeV. The quark mass dependence of the glueball masses have not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at $m_pisim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of $epsilon_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1GeV) and compatible with the expected masses of the flavor singlet $qbar{q}$ meson. This indicates that the operator $epsilon_{ijk}TrB_iD_jB_k$ and the topological charge density couple rather differently to the glueball states and $qbar{q}$ mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.
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