Positronium Decay : Gauge Invariance and Analyticity

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity). A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wavefunction are removed. Non-factorizable amplitudes are naturally introduced. Their dynamics is described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those non-factorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of order alpha^3. Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.Comment: 34 pages, 13 figure

Energy Spectra and Energy Correlations in the Decay H→ZZ→μ+μ−μ+μ−H\to ZZ\to \mu^+\mu^-\mu^+\mu^-

It is shown that in the sequential decay $H\to ZZ\to (f_1\bar{f_1})+ (f_2\bar{f_2})$, the energy distribution of the final state particles provides a simple and powerful test of the $HZZ$ vertex. For a standard Higgs boson, the energy spectrum of any final fermion, in the rest frame of $H$, is predicted to be $d\Gamma /dx\sim 1+\beta^4-2(x-1)^2$, with $\beta = \sqrt{1-4m^2_Z/m^2_H}$ and $1-\beta \le x=4E/m_H\le 1+\beta$. By contrast, the spectrum for a pseudoscalar Higgs is $d\Gamma /dx \sim \beta^2+(x-1)^2$. There are characteristic energy correlations between $f_1$ and $f_2$ and between $f_1$ and $\bar{f_2}$. These considerations are applied to the ``gold--plated'' reaction $H\to ZZ\to \mu^+\mu^-\mu^+\mu^-$, including possible effects of CP--violation in the $HZZ$ coupling. Our formalism also yields the energy spectra and correlations of leptons in the decay $H\to W^+W^-\to l^+\nu_ll^- \bar{\nu_l}$.Comment: 14 pages + 4 figure

Some fixed point theorems for nonconvex spaces

We give a theorem for nonconvex topological vector spaces which yields the classical fixed point theorems of Ky Fan, Kim, Kaczynski, Kelly and Namioka as immediate consequences, and prove a new fixed point theorem for set-valued maps on arbitrary topological vector spaces

Transverse sacralization of lumbar vertebrae: prevalence according to Castellvi classification

Background: Sacralization of L5 is a congenital anomaly, in which the lumbar vertebra, mainly its transverse process, gets fused or semi-fused with the sacrum or the ilium or to both. This fusion can occur in one or both sides of the body. Sacralization leads to fusion of the L5 (fifth lumbar vertebra) and S1 (first sacral vertebra) and the inter-vertebral disc between them may be narrow. Sacralization of lumbar vertebra may be asymptomatic but is not always clinically insignificant. While sacralization may not affect at all, it can cause problems in some cases. Sacralization may be at times associated with problems in biomechanics and affect the ways of movement and posture control. Sacralization may also be an important consideration in disc surgeries. This study has been carried out to find out prevalence of sacralisation of transverse process of fifth lumbar vertebrae.Methods: The present study of transverse sacralisation of fifth lumbar vertebra was carried out on 35 randomly selected patients. The sample consisted of patients undergoing CT scan for abdominal complains. Bone window of all patients were evaluated to look for lumbosacral transitional vertebra.Results: The prevalence of transverse sacralization of lumbar vertebra turned out to be 25.7% out of which Castellvi type IIb was found to be most common, accounting for 33.3% cases. 5.7% comprised the group of normal variant (Castellvi’s type I) and 68.6% were normal. Conclusions: It is important to determine lumbosacral transitional vertebra as it can affect spinal movement and put excess stress on the lumbar vertebrae and in between disc. Moreover it can have a bearing on counting of vertebral levels specially during planning of spinal surgey.

Tau Polarization in Λb→Xcτνˉ \Lambda_b \to X_c \tau \bar{\nu} and B→XcτνˉB \to X_c \tau \bar{\nu}

We discuss the longitudinal and transverse $\tau$-polarization in inclusive decays of hadrons containing $b$-quarks. The calculation is performed by means of an OPE in HQET. Some mathematical difficulties in calculating transverse polarizations are explained. Numerical results are presented for longitudinal and for transverse polarizations, both in and perpendicular to the decay plane.Comment: LATEX, 20 pages, 5 Postscript figure

Trends in the epidemiology of larynx and lung cancer in south-east England, 1985–2004

We analysed data on 8987 larynx and 174060 lung cancer patients diagnosed between 1985 and 2004, of which 17.3% of larynx and 35.5% of lung cancers were in females. The age-standardised rates for each cancer declined in both sexes, but since the 1990s, the rates in females over 70 years of age have been diverging

On V_ud determination from kaon decays

The pion beta decay pi^+ -> pi^0 e^+ nu proceeds through pure weak vector hadronic currents and, therefore, the theoretical prediction for it is more reliable than for the processes with axial-vector current contribution. For example, recently the pion beta decay has been used for V_ud determination. The main aim of this letter is to point that kaon beta decay K^0 -> K^+(pi^+ pi^0) e^- nu-bar analogously can be used for this purpose.Comment: 3 pages, no figures, one reference adde

On impact parameter dependence of low-x structure functions

We consider impact parameter dependence of the polarized and unpolarized structure functions. Unitarity does not allow factorization of the structure functions over the Bjorken x and the impact parameter b variables. On the basis of the particular geometrical model approach we conclude that spin of constituent quark may have a significant orbital angular momentum component which can manifest itself through the peripherality of the spin dependent structure functions.Comment: 5 pages, 1 figur

Alien chromosome segment from Aegilops speltoides and Dasypyrum villosum increases drought tolerance in wheat via profuse and deep root system

BackgroundRecurrent drought associated with climate change is a major constraint to wheat (Triticum aestivum L.) productivity. This study aimed to (i) quantify the effects of addition/substitution/translocation of chromosome segments from wild relatives of wheat on the root, physiological and yield traits of hexaploid wheat under drought, and (ii) understand the mechanism(s) associated with drought tolerance or susceptibility in wheat-alien chromosome lines.MethodsA set of 48 wheat-alien chromosome lines (addition/substitution/translocation lines) with Chinese Spring background were used. Seedling root traits were studied on solid agar medium. To understand the influence of drought on the root system of adult plants, these 48 lines were grown in 150-cm columns for 65 d under full irrigation or withholding water for 58 d. To quantify the effect of drought on physiological and yield traits, the 48 lines were grown in pots under full irrigation until anthesis; after that, half of the plants were drought stressed by withholding water for 16 d before recording physiological and yield-associated traits.ResultsThe alien chromosome lines exhibited altered root architecture and decreased photochemical efficiency and seed yield and its components under drought. The wheat-alien chromosome lines T5DS5S#3L (TA5088) with a chromosome segment from Aegilops speltoides (5S) and T5DL(.)5V#3S (TA5638) with a chromosome segment from Dasypyrum villosum (5V) were identified as drought tolerant, and the drought tolerance mechanism was associated with a deep, thin and profuse root system.ConclusionsThe two germplasm lines (TA5088 and TA5638) could be used in wheat breeding programs to improve drought tolerance in wheat and understand the underlying molecular genetic mechanisms of root architecture and drought tolerance