Timelapse

We discuss the existence, in an arbitrary frame, of a finite time for the transformation of an initial quantum state into another, e.g., in a decay. This leads to the introduction of a timelapse $\tau $ , by analogy with the lifetime of a particle. An argument based upon the Heisenberg uncertainty principle suggests the value of $\tau $ =1/M ₀. Consequences for the exponential decay formula and the modifications which $\tau $ introduces into the Breit-Wigner mass formula are described.     

Late-time tails of fields around Schwarzschild black hole surrounded by quintessence

The evolution of scalar, electromagnetic and gravitational fields around spherically symmetric black hole surrounded by quintessence are studied with special interest on the late-time behavior. In the ring down stage of evolution, we find in the evolution picture that the fields decay more slowly due to the presence of quintessence. As the quintessence parameter $\epsilon $ decreases, the decay of $\ell =0$ mode of scalar field gives up the power-law form of decay and relaxes to a constant residual field at asymptotically late times. The $\ell >0$ modes of scalar, electromagnetic and gravitational fields show a power-law decay for large values of $\epsilon $ , but for smaller values of $\epsilon $ they give way to an exponential decay.     

Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model

In this paper we study the decay to the equilibrium state for the solution of a generalized version of the Goldstein-Taylor system, posed in the one-dimensional torus ${\mathbb{T}}={\mathbb{R}}/{\mathbb{Z}}$ , by allowing that the nonnegative cross section σ can vanish in a subregion $X:=\{ x \in {\mathbb{T}}\, \vert\, \sigma(x)=0\}$ of the domain with meas?(X)≥0 with respect to the Lebesgue measure. We prove that the solution converges in time, with respect to the strong L ²-topology, to its unique equilibrium with an exponential rate whenever $\text{meas}\,({\mathbb{T}}\setminus X)\geq0$ and we give an optimal estimate of the spectral gap.     

Strong decays ofΨ(4.03) andΨ(4.16) as radial excitations of charmonium

Considering the signals detected at 4.03 and 4.16 GeV as radial excitations of charmonium, we study their relative decay rates intoD \(\bar D\) ,D \(\bar D^* \) ,D ^* \(\bar D\) ,D ^* \(\bar D^* \) . We point out that one can understand these two peaks as ac \(\bar c\) 3S?2D wave state system with a large mixing angle in a Coulomb+linear interquark potential. We also examine the possibility that these two signals are respectively 3S and 4S wave excitations by studying a logarithmic charmonium potential model. We show that both these interpretations lead to drastically different predictions for the Ψ (4.16) decay rates (eitherD \(\bar D^* \) +D ^* \(\bar D\) orD \(\bar D\) mode is strongly suppressed) which would be very instructive to test experimentally.     

Localizing fields on brane in magnetized background

In this work we will study the longitudinal polarisations of both leptons in the decay process ${\bar{B}} \to {\bar{K}}_{2}(1430) \ell^{+} \ell^{-}$ . This process has all the features of the related and well investigated process ${\bar{B}} \to {\bar{K}}^{*}(890) \ell^{+} \ell^{-}$ , with theoretically comparable branching ratios. The polarised differential decay rates as well as the single and double polarisation asymmetries are worked out, where the sensitivity of these to possible right-handed couplings for the related b→s radiative decay (and other BSM parameters) are also investigated.     

Ultraheavy Yukawa-bound states of fourth-generation at Large Hadron Collider

A study of bound states of the fourth-generation quarks in the range of 500?C700 GeV is presented, where the binding energies are expected to be mainly of Yukawa origin, with QCD subdominant. Near degeneracy of their masses exhibits a new ??isospin??. The production of a colour-octet, isosinglet vector meson via $q\bar q \to \omega_8$ is the most interesting. Its leading decay modes are $\pi_8^\pm W^\mp$ , $\pi_8^0Z^0$ , and constituent quark decay, with $q\bar q$ and $t\bar t'$ and $b\bar b'$ subdominant. The colour octet, isovector pseudoscalar ?? ₈ meson decays via constituent quark decay, or to Wg. This work calls for more detailed study of fourth-generation phenomena at LHC.     

Radiative open charm decay of the Y(3940) , Z(3930) , X(4160) resonances

We determine the radiative decay amplitudes for the decay into D^* and $ \bar{{D}}$ $ \gamma$ , or D ^* _s and $ \bar{{D}}_{s}^{}$ $ \gamma$ of some of the charmonium-like states classified as X , Y , Z resonances, plus some other hidden charm states which are dynamically generated from the interaction of vector mesons with charm. The mass distributions as a function of the $ \bar{{D}}$ $ \gamma$ or $ \bar{{D}}_{s}^{}$ $ \gamma$ invariant mass show a peculiar behavior as a consequence of the D ^* $ \bar{{D}}^{*}_{}$ nature of these states. The experimental search of these magnitudes can shed light on the nature of these states.     

Exponential Convergence to Equilibrium for the Homogeneous Boltzmann Equation for Hard Potentials Without Cut-Off

This paper deals with the long time behavior of solutions to the spatially homogeneous Boltzmann equation. The interactions considered are the so-called (non cut-off with a moderate angular singularity and non mollified) hard potentials. We prove an exponential in time convergence towards the equilibrium, improving results of Villani (Commun Math Phys 234(3): 455–490, 2003) where a polynomial decay to equilibrium is proven. The basis of the proof is the study of the linearized equation for which we prove a new spectral gap estimate in a \(L^1\) space with a polynomial weight by taking advantage of the theory of enlargement of the functional space for the semigroup decay developed by Gualdani et al. (http://hal.archives-ouvertes.fr/ccsd-00495786, 2013). We then get our final result by combining this new spectral gap estimate with bilinear estimates on the collisional operator that we establish.     

Hard bremsstrahlung photons in thet\bar t production anddecay: A background for the intermediate Higgs search

We discuss the radiation of hard photons in the $t\bar t$ production anddecay as a background for the intermediate Higgs search at LHC/SSC experiments. For the purpose of experimental simulation of this process we propose to use the approximate Monte Carlo algorithm together with any physics Monte Carlo not including QED corrections. We verify, by comparison with the exact matrix element Monte Carlo TOPKI, that this method can be used to generate single- and double-photon bremsstrahlung in the $t\bar t$ production process with a precision of 10% for experimental cuts. The predictions for the ψψl background from photons radiated in theproduction of $t\bar t$ pair and their cascadedecays, within simplified experimental cuts, are presented for the first time. We show that, even after additional cuts on the minimal lepton-photon mass, photons radiated in the productionand decay of a $t\bar t$ pair increase this background by a factor of 2 with respect to previous estimates from radiation in the $t\bar t$ production alone.     

On Energy-Momentum Transfer of Quantum Fields

We prove the following theorem on bounded operators in quantum field theory: if \({\|[B,B^*(x)]\|\leqslant{\rm const}D(x)}\) , then \({\|B^k_\pm(\nu)G(P^0)\|^2\leqslant{\rm const}\int D(x - y){\rm d}|\nu|(x){\rm d}|\nu|(y)}\) , where D(x) is a function weakly decaying in spacelike directions, \({B^k_\pm}\) are creation/annihilation parts of an appropriate time derivative of B, G is any positive, bounded, non-increasing function in \({L^2(\mathbb{R})}\) , and \({\nu}\) is any finite complex Borel measure; creation/annihilation operators may be also replaced by \({B^k_t}\) with \({\check{B^k_t}(p)=|p|^k\check{B}(p)}\) . We also use the notion of energy-momentum scaling degree of B with respect to a submanifold (Steinmann-type, but in momentum space, and applied to the norm of an operator). These two tools are applied to the analysis of singularities of \({\check{B}(p)G(P^0)}\) . We prove, among others, the following statement (modulo some more specific assumptions): outside p = 0 the only allowed contributions to this functional which are concentrated on a submanifold (including the trivial one—a single point) are Dirac measures on hypersurfaces (if the decay of D is not to slow).     

Mean L-shell x-ray fluorescence yields atZ=47, 60, and 63

MeanL-shell x-ray fluorescence yields \((\bar \omega _L )\) have been measured by observingK andL x-ray spectra emitted in the decay of¹⁰⁹Cd,¹⁴⁵Pm, and¹⁵³Gd with a high resolution Si(Li) x-ray detector. The results forZ=47, 60, and 63 are as follows: \(\bar \omega _L \) =0.0425±0.0064, 0.131±0.017, and 0.142±0.023, respectively. Additional values of \(\bar \omega _L \) from this laboratory atZ=55, 56, 57, 59, and 65 are also tabulated as are previous experimental values atZ=47, 60, and 63. For comparison, theoretical estimates of \(\bar \omega _L \) were computed using theoreticalL-subshell fluorescence and Coster-Kronig yields, together with subshell vacancy distributions calculated from the literature. The theoretical estimates atZ=47, 60, and 63, based on the subshell calculations of Chen, Crasemann, and Kostroun, agree well with experiment.     

Collider monojets ofW→τv origin

Within the standard model it is found that the most copious source of events with a single hadronic jet balanced by large missing transverse momentum \((\mathop {p_T }\limits^/ )\) is the decay process \(W \to \tau \bar v \to (n\pi )v\bar v\) . A detailed calculation of the monojet cross-section predicts a lower limit ofO(2) events with \(\mathop {p_T }\limits^/ > 35\) GeV per 100 nb^?1 of integrated luminosity at presently available \(\bar pp\) collider energies.     

Decay studies of K isomers in 254No

A detailed $ \gamma$ spectroscopic decay study of two K isomers in ²⁵⁴No was performed. In addition to the previously reported $ \gamma$ lines two new transitions of E = 778 , 856keV could be attributed to the decay pattern of ^254m1No ( T _1/2 = 275±7 ms). The population of an excited band built up on this isomer ( $\ensuremath K^{\pi} =8^{-}$ by the decay of ^254m2No ( T _1/2 = 198±13 μs) could be proven by measuring delayed $ \gamma$ - $ \gamma$ coincidences between transitions stemming from the decay of both isomeric states. The energies of the band members could be established up to $\ensuremath I^{\pi} = 15^{-}$ . A spontaneous fission branch of (2.0±1.2)×10^-4 was measured for ^254m1No , an upper limit of $ \le$ 1.2×10^-4 was estimated for ^254m2No . These values demonstrate the high stability of multi-quasiparticle configurations against spontaneous fission. Evidence for an $ \alpha$ decay branch of ^254m1No in the order of 1×10^-4 was found.     

Radiative neutralino decay in split supersymmetry

Radiative neutralino decay $\chi^{0}_{2}\longrightarrow\chi^{0}_{1}\gamma$ is studied in a Split Supersymmetric scenario, and compared with mSUGRA and MSSM. This one-loop process has a transition amplitude which is often quite small, but it has the advantage of providing a very clear and distinct signature: electromagnetic radiation plus missing energy. In Split Supersymmetry this radiative decay is in direct competition with the tree-level three-body decay $\chi^{0}_{2}\longrightarrow\chi^{0}_{1}f\bar{f}$ , and we obtain large values for the branching ratio $B(\chi^{0}_{2}\longrightarrow\chi^{0}_{1}\gamma)$ which can be close to unity in the region M ₂～M ₁, something already seen in the MSSM. Furthermore, the values for the radiative and the tree-level neutralino decay branching ratios have a strong dependence on the logarithm of the split supersymmetric scale $\widetilde{m}$ , which otherwise is very difficult to infer from experimental observables.     

Study of theJ/\Psi \to p\bar p\gamma and\Upsilon /(1S) \to p\bar p\gamma decays as possible tests of the proton wave function

Considering the proton either as a three-quark state with its wave function fulfilling QCD sum rules or as a quark-diquark state with wave function parametrizations that are shown to fitG _M ^P , we study the possibility of discriminating between these two competing pictures by comparing their respective predictions for \(J/\Psi \to p\bar p\gamma \) and \(\Upsilon (1S) \to p\bar p\gamma \) decays. ForJ/Ψ decay, thep \(\bar p\) invariantmass distributions derived from either model are found to be of about the same magnitude, but neither of them is able by itself to reproduce present-day data. Differences between the two pictures may eventually show up in the case of Υ(1S) decay, but the predicted counting rates are small. We also consider some other possible production mechanisms for \(p\bar p\gamma \) final states.     

Decay rate ratios of \varUpsilon (5S)\to B{\bar{B}} reactions

We calculate the decay rate ratios for OZI allowed decays of ?(5S) to two B mesons by using the decay amplitudes which incorporate the wave function of the ?(5S) state. We obtain the result that the branching ratio of the ?(5S) decay to $B_{s}^{*}{\bar{B}}_{s}^{*}$ is much larger than the branching ratio to $B_{s}{\bar{B}}_{s}^{*}$ or ${\bar{B}}_{s}B_{s}^{*}$ , in good agreement with the recent experimental results of CLEO and BELLE. This agreement with the experimental results is made possible since the nodes of the ?(5S) radial wave function induce the nodes of the decay amplitude. We find that the results for the ?(5S) decays to $B_{u}^{(*)}{\bar{B}}_{u}^{(*)}$ or $B_{d}^{(*)}{\bar{B}}_{d}^{(*)}$ pairs are sensitive to the parameter values used for the potential between heavy quarks.     

Reaction pp \rightarrow pp \pi \pi \pi as a background for hadronic decays of the \eta^{{\prime}}_{} meson

Isospin violating hadronic decays of the $ \eta$ and $ \eta{^\prime}$ mesons into 3 $ \pi$ mesons are driven by a term in the QCD Lagrangian proportional to the mass difference of the d and u quarks. The source giving large yield of the mesons for such decay studies are pp interactions close to the respective kinematical thresholds. The most important physics background for $ \eta$ , $ \eta{^\prime}$ $ \rightarrow$ $ \pi$ $ \pi$ $ \pi$ is coming from direct three-pion production reactions. In case of the $ \eta$ meson the background for the decays is relatively low ( $ \approx$ 10% . The purpose of this article is to provide an estimate of the direct pion production background for the $ \eta{^\prime}$ $ \rightarrow$ 3 $ \pi$ decays. Using the inclusive data from the COSY-11 experiment we have extracted the differential cross-section for the pp $ \rightarrow$ pp -multipion production reactions with the invariant mass of the pions equal to the $ \eta{^\prime}$ meson mass and estimated an upper limit for the signal to background ratio for studies of the $ \eta{^\prime}$ $ \rightarrow$ $ \pi^{+}_{}$ $ \pi^{-}_{}$ $ \pi^{0}_{}$ decay.     

Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

Polarization degrees of freedom in near-threshold photoproduction of \omega -mesons in the \pi^{0}_{} \gamma decay channel

We study polarization variables in the photoproduction of $ \omega$ -mesons with subsequent $ \omega$ → $ \gamma$ $ \pi^{0}_{}$ decay. Single and double polarization observables are calculated as a function of different final-state angles. Reaction models include pomeron (natural parity) and $ \pi^{0}_{}$ (unnatural parity) exchange in the t -channel. In addition, the contribution of s -channel resonances is considered. The sensitivity of the polarization observables to the reaction dynamics is discussed.