Emergence of ghost in once-subtracted on-shell unitarization in glueball-glueball scattering

Abstract

We investigate the scattering of two scalar glueballs in pure YM theory, using the well known dilaton potential. We perform the calculations considering a glueball mass of about $m_G\approx 1.7$ GeV, as predicted by lattice QCD. We begin with the tree-level theory, but the question about the presence of a bound state needs a deeper study to be answered. Thus we unitarize the theory through a self energy loop function consisting of a single subtraction at the single glueball resonance pole. We show that this choice is inconsistent as it leads to the emergence of a ghost-like state with negative norm. This problem is related with the sign of the coefficient in the first order term of the expansion of the reverse unitarized amplitude. We briefly discuss the solution which consists of an additional subtraction in the loop function, as presented in Eur.Phys.J.C 82 (2022) 5, 487.

References in corpus (14)

• Light scalar at LHC: the Higgs or the dilaton?
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• Numerical Evidence for the Observation of a Scalar Glueball
• The glueball spectrum of SU(3) gauge theory in 3+1 dimension
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Dilaton, winding modes and cosmological solutions
• Scalar Glueball in Radiative $J/\psi$ Decay on Lattice
• A chiral covariant approach to $\rho \rho$ scattering
• Bound states and glueballs in three-dimensional Ising systems
• Dark matter scattering cross section and dynamics in dark Yang-Mills theory
• Extremal statistics of entanglement eigenvalues can track the many-body localized to ergodic transition
• Glueball-glueball scattering and the glueballonium
• Magnetic order in lightly doped cuprates: Coherent vs. incoherent hole quasiparticles and non-magnetic impurities
• The Inflationary Role of the Dilaton in String Cosmology