Is the1−+meson a hybrid?

Abstract

We calculate the vacuum to meson matrix elements of the dimension-4 operatorψγ 4 ← → D i ψ and dimension-5 operatorψε ijk γ j ψB k of the 1 −+ meson on the lattice and compare them to the corresponding matrix elements of the ordinary mesons to discern if it is a hybrid. For the charmoniums and strange quarkoniums, we find that the matrix elements of 1 −+ are comparable in size as compared to other known qq mesons. They are particularly similar to those of the 2 ++ meson, since their dimension-4 operators are in the same Lorentz multiplet. Based on these observations, we find no evidence to support the notion that the lowest 1 −+ mesons in the cc and ss regions are hybrids. As for the exotic quantum number is concerned, the non-relativistic reduction reveals that the leading terms in the dimension-4 and dimension-5 operators of 1 −+ are identical up to a proportional constant and it involves a center-of-mass momentum operator of the quark-antiquark pair. This explains why 1 −+ is an exotic quantum number in the constituent quark model where the center of mass of the qq is not a dynamical degree of freedom. Since QCD has gluon fields in the context of the flux-tube which is appropriate for heavy quarkoniums to allow the valence qq to recoil against them, it can accommodate such states as 1 −+ . By the same token, hadronic models with additional constituents besides the quarks can also accommodate the qq center-of-mass motion. To account for the quantum numbers of these qq mesons in QCD and hadron models in the non-relativistic case, the parity and total angular momentum should be modified to P = (−) L+l+1 and J = L + l + S, where L is the orbital angular momentum of the qq pair in the meson.

Analytical Black-Hole Binary Merger Waveforms

“…We note that this conclusion differs from previous treatments of QNMs in the geometric optics limit (e. g., Ref. [22]) that applied the result for expansion in empty space, k µ ∂ µ (dA 1/2 A) = 0 [23], which is not valid for these orbits and would lead one to conclude in our case that A = A p sech 1/2 [γ(t − t p )] rather than the correct result given in Eq. (4).…”

“…Merger amplitude.-The frequencies of the QNMs of a single perturbed black hole closely match the corresponding harmonics of the orbital frequency for a null geodesic circling the light ring, and the decay rate of the amplitude corresponds to the Lyapunov coefficient characterizing the rate of divergence of nearby null geodesics [21]. This correspondence is well motivated in the geometric optics limit where > − m 1 but provides accurate predictions even for small and m. The QNM family of exponentially decaying sinusoids can therefore be found by calculating the behavior at late times of a bundle of null geodesics, known as a null congruence, that has diverged from the light ring [22]. However, if we trace the behavior of the congruence back to the point where the bundle converges, which one would expect to be associated with the peak waveform amplitude, then we can predict the behavior of the amplitude at earlier times.…”

Hybrid Meson Interpretation of the Exotic Resonance π11600

“…This is not always true, we cannot understand the nature of a state by the appearance of its interpolation field. This is sufficiently illustrated by the strong projection on η and η′ produced with the glue interpolation field G μνGμν , it does not mean that they are glueballs [69] (ii) In the light sector, lattice authors report only results related to the j P g C g g = 1 +− TE-gluon since it has the best signal with the smallest statistical errors while the explicit masses of the j P g C g g = 1 −− TM-gluon are not yet published (iii) The lattice calculation sill uses an unrealistic mass of the π meson (~396 MeV) which is much greater than the observed one (~139 MeV). 23, the decay width is proportional to the parameter α s which is in turn correlated to the mass of the gluon m g , as mentioned above.…”

Flatness of minima in random inflationary landscapes

“…Since these theories describe physics at energy scales close to the inflationary scale, there is considerable interest in analyzing their dynamics. Considering random potentials with large-N fields has a considerable history [35][36][37][38][39][40][41][42][43][44][45][46][47]. As multi-field models have an almost infinite number of ways to inflate, the task of understanding how the potential energy driving inflation is distributed among all these fields becomes an incredibly difficult one.…”