Statistical approaches to lifetime measurements with restricted observation times

Abstract

Two generic methods based on frequentism and Bayesianism are presented in this work aiming to adequately estimate decay lifetimes from measured data, while accounting for restricted observation times in the measurements. All the experimental scenarios that can possibly arise from the observation constraints are treated systematically and formulas are derived. The methods are then tested against the decay data of bare isomeric 94m Ru 44+ , which were measured using isochronous mass spectrometry with a timing detector at the CSRe in Lanzhou, China. Applying both methods in three distinct scenarios yields six different but consistent lifetime estimates. The deduced values are all in good agreement with a prediction based on the neutral-atom value modified to take the absence of internal conversion into account. Potential applications of such methods are discussed.

Heavy quarkonium dissociation by thermal gluons at next-to-leading order in the Quark–Gluon Plasma

“…(10) would be ∝ 1/ω κ = 1/κ, causing an infrared divergence (from κ → 0) that manifests itself in the integration pc 0 dp as p → p c . In contrast, no divergence would occur if the initial state incident gluon is massless (the same is true for LO dissociation cross section [18]), as the denominator of C(p, κ) and D(p, κ) (see Eq. (12)) ∝ ω k = k must be larger than ǫ B in order to overcome the bound state binding energy.…”

“…While the derivation of the LO (gluo-dissociation) cross section involves only the singlet to octet transition vertex V SO [18], in deriving the NLO cross section, the octet to octet transition vertex V OO and the threegluon vertex V 3g will be also invoked.…”

“…with a temperature dependent potential parameterized in [30] V (r, which is a modification of the vacuum Cornell potential V (r, 0) = −α/r + σr by color screening [30], with the Debye screening mass m D /T = −4.058 + 6.32 · (T /T c − 0.885) 0.1035 (T c = 172.5 MeV) fitted to lattice data from [31,18]. With coupling strength α = 4/3α s = 0.471 of the Coulomb part, the string tension σ = 0.192 GeV 2 of the confining part, and heavy quark masses m c = 1.320 GeV, m b = 4.746 GeV, the vacuum masses of charmonia and bottomonia below threshold are well reproduced [30,18]. The temperature-dependent binding energy of the bound state is then obtained via ǫ B (T ) = 2m Q + σ/m D (T ) − E n,l (T ), whose zero point defines the dissociation temperature of the bound state under consideration [30,18].…”

“…These collisional processes generate inelastic widths that enter the transport equations describing the evolution (yields, momentum spectra) of the bound states in the QGP [3,4,5,6,7,8,9]. In this respect, the one that has been intensively studied in the past decades is the gluo-dissociation of heavy quarkonium g + Ψ → Q +Q (Ψ denotes a QQ bound state) [10,11,12,13,14,15,17,16,18], an analog of photo-dissociation of neutral atoms owing to dipole transition. In this process, an energetic thermal gluon from the medium is absorbed by the bound state, thereby the binding energy of the bound state is overcome, and the latter is dissociated into an unbound color octet (QQ) 8 .…”

“…In this process, an energetic thermal gluon from the medium is absorbed by the bound state, thereby the binding energy of the bound state is overcome, and the latter is dissociated into an unbound color octet (QQ) 8 . The cross section of this leading order (LO) scattering of thermal gluons off heavy quarkonium, when convoluted with the gluon distribution function, leads to a dissociation rate that decreases with increasing temperature, see e.g., [18], due to the fact that as the binding energy of the bound state gets lower, the peak of the LO cross section shifts toward smaller gluon energy corresponding to very small phase space [19].…”