According to the usual application of the sequential-suppression picture to the dynamics of heavy quarkonia in the hot medium formed in ultrarelativistic nuclear collisions, quark-antiquark pairs created in a given bound or unbound state remain in that same state as the medium evolves. We argue that this scenario implicitly assumes an adiabatic evolution of the quarkonia, and we show that the validity of the adiabaticity assumption is questionable.PACS numbers: 25.75. Nq, 12.38.Mh, 14.40.Pq More than 25 years ago, finite-temperature gaugetheory studies on the lattice of the screening of static (color) charges prompted Matsui and Satz to suggest that in a quark-gluon plasma (QGP) the formation of bound charmonia may be prevented [1]. It was quickly realized that the various cc or bb states might in fact be dissociated at different temperatures [2,3]. Over the years, paralleling progress in theoretical studies of quarkonia properties (see Refs. [4,5] for recent reviews), this led to the "sequential-suppression" picture of heavy quarkonia as QGP thermometer [6]. According to the latter, a given state will be totally suppressed above a threshold temperature-which might actually be smaller than the transition temperature to a QGP. This prediction is supported by several approaches. First, spectral functions are extracted from lattice-QCD computations of correlators of quantum numbers for heavy quark-antiquark pairs [7][8][9][10]. The disappearance of a peak in the spectral function then signals the suppression of a state. Alternatively, one resorts to an effective in-medium quark-antiquark (QQ) potential-either derived from lattice-QCD computations of spatial correlators [1][2][3][11][12][13][14][15] or derived within finite-temperature field theory [16-18]-, which then enters a Schrödinger or Bethe-Salpeter equation, whose bound states model the quarkonia in the medium. The suppression of a given state takes place when it is no longer bound by the potential, although the precise criterion for dissociation might be open to discussion [19].In either description, the in-medium bound states of heavy quark-antiquark pairs are, be it explicitly stated or not, eigenstates of a Hamiltonian. Note that as the effective potential might actually possess an imaginary part [15][16][17], these eigenstates are not necessarily stable, but might have only a finite lifetime. That notwithstanding, the generally accepted picture is that of a temperature-dependent suppression pattern, in which at a given energy density of the medium some states survive, while more excited ones are not bound and thus do not form.This picture is seemingly supported by experimental measurements in ultrarelativistic nucleus-nucleus collisions. At the SPS, the NA50 collaboration reported that the anomalous suppression of the ψ ′ in Pb-Pb collisions sets in at a smaller average in-medium path crossed by the cc pair than for the J/ψ [20]. At the much higher LHC energy, the CMS collaboration studied bottomonia and observed yields consistent with the idea that...
