J/Psi Production from Electromagnetic Fragmentation in Z decay

The rate for $Z^{0}\to J/ \psi + \ell^{+}\ell^{-}$ is suprisingly large with about one event for every million $Z^{0}$ decays. The reason for this is that there is a fragmentation contribution that is not suppressed by a factor of $M^{2}_{\psi}/M^{2}_{Z}$. In the fragmentation limit $M_{Z}\to\infty$ with $E_{\psi}/M_{Z}$ fixed, the differential decay rate for $Z^{0}\to J/ \psi + \ell^{+}\ell^{-}$ factors into electromagnetic decay rates and universal fragmentation functions. The fragmentation functions for lepton fragmentation and photon fragmentation into $J/\psi$ are calculated to lowest order in $\alpha$. The fragmentation approximation to the rate is shown to match the full calculation for $E_{\psi}$ greater than about $3 M_{\psi}$.Comment: 16 pages and 8 figure

QCD evolution of naive-time-reversal-odd fragmentation functions

We study QCD evolution equations of the first transverse-momentum-moment of the naive-time-reversal-odd fragmentation functions - the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.Comment: 8 pages,4 figure

The minimum mass for star formation, and the origin of binary brown dwarfs

Our first aim is to calculate the minimum mass for Primary Fragmentation in a variety of potential star-formation scenarios, i.e. (i) hierarchical fragmentation of a 3-D medium; (ii) one-shot, 2-D fragmentation of a shock-compressed layer; (iii) fragmentation of a circumstellar disc. Our second aim is to evaluate the role of H2 dissociation in facilitating Secondary Fragmentation and thereby producing close, low-mass binaries. Results: (i)For contemporary, local star formation, the minimum mass for Primary Fragmentation is in the range 0.001-0.004Msun, irrespective of the scenario considered. (ii)Circumstellar discs are only able to radiate fast enough to undergo Primary Fragmentation in their cool outer parts (R>100AU). Therefore brown dwarfs (BDs) should have difficulty forming by Primary Fragmentation at R<30AU, explaining the Brown Dwarf Desert.Conversely, Primary Fragmentation at R>100AU could be the source of brown dwarfs in wide orbits, and could explain why massive discs with Rd>100AU are rarely seen.(iii)H2 dissociation can lead to collapse and Secondary Fragmentation, thereby converting primary fragments into close, low-mass binaries, with semi-major axes a~5AU(Msystem/0.1Msun), in good agreement with observation; in this case, the minimum mass for Primary Fragmentation becomes a minimum system mass, rather than a minimum stellar mass.(iv)Any primary fragment can undergo Secondary Fragmentation, producing a close low-mass binary, provided only that the fragment is spinning. Secondary Fragmentation is therefore most likely in fragments formed in the outer parts of discs, and this could explain why a BD in a wide orbit about a Sun-like star has a greater likelihood of having a BD companion than a BD in the field -as seems to be observed.Comment: 15 pages, A&A accepte

General Fragmentation Trees

We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes

Non-Symbolic Fragmentation

This paper reports on the use of non-symbolic fragmentation of data for securing communications. Non-symbolic fragmentation, or NSF, relies on breaking up data into non-symbolic fragments, which are (usually irregularly-sized) chunks whose boundaries do not necessarily coincide with the boundaries of the symbols making up the data. For example, ASCII data is broken up into fragments which may include 8-bit fragments but also include many other sized fragments. Fragments are then separated with a form of path diversity. The secrecy of the transmission relies on the secrecy of one or more of a number of things: the ordering of the fragments, the sizes of the fragments, and the use of path diversity. Once NSF is in place, it can help secure many forms of communication, and is useful for exchanging sensitive information, and for commercial transactions. A sample implementation is described with an evaluation of the technology