Model Standardowy. Spis treści. Z Wikipedii. Skocz do: nawigacji, szukaj

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1 Model Standardowy Z Wikipedii Skocz do: nawigacji, szukaj Model Standardowy jest teorią fizyki cząstek podstawowych, zwanych teŝ cząstkami elementarnymi, które są podstawowymi składnikami kaŝdej materii. Opisuje trzy z czterech (z wyjątkiem grawitacji) oddziaływań podstawowych: oddziaływanie elektromagnetyczne, oddziaływanie słabe, oddziaływanie silne. Model Standardowy opiera się na koncepcji pola Yanga-Millsa. Model Standardowy jest jedną z najwaŝniejszych teorii współczesnej fizyki, jego podstawy teoretyczne zaczęto formułować w latach 70. XX wieku. W latach 80. potwierdzono większość jego przewidywań doświadczalnie, jednak do dziś nie zaobserwowano jeszcze jednej z cząstek przewidywanych przez model, zwanej bozonem Higgsa. Model Standardowy sformułowany jest w języku matematyki opisując relacjami matematycznymi zaleŝności między elementami tej teorii. Model Standardowy zawarł w sobie, rozbudował, bądź wyjaśnił wcześniejsze teorie, takie jak: teoria cząstek elementarnych (kształtująca się od początku XX wieku), mechanika kwantowa, chromodynamika kwantowa, teoria elektrosłaba (łącząca oddziaływania elektromagnetyczne i słabe jako róŝne przejawy tego samego oddziaływania). Spis treści [ukryj] 1 Opis wniosków wynikających z Modelu Standardowego o 1.1 Fermiony jako budulec materii o 1.2 Bozony jako nośniki oddziaływań o 1.3 Cząstka Higgsa o 1.4 Co dalej? 2 Zobacz teŝ 1

2 3 Linki zewnętrzne Opis wniosków wynikających z Modelu Standardowego [edytuj] W modelu standardowym funkcjonuje podział na dwie grupy cząstek: fermiony i bozony. Fermiony jako budulec materii [edytuj] Fermiony są podstawowymi elementami budującymi materię. Materię trwałą, która nas otacza, tworzą następujące cząstki: elektron, kwark górny (u) oraz kwark dolny (d). Dwa kwarki górne i jeden dolny (uud) tworzą proton, a jeden kwark górny i dwa dolne (udd) tworzą neutron. Wiązanie to znane jest jako oddziaływanie silne. Protony i neutrony, łącząc się, tworzą jądra atomowe. Do tej grupy cząstek naleŝy teŝ neutrino elektronowe. Opisane wyŝej cząstki (elektron, neutrino elektronowe, kwark dolny i górny) tworzą pierwszą z trzech grup cząstek zwanych generacjami. W kaŝdej generacji występują cztery cząstki odpowiadające cząstkom z pierwszej generacji (lecz o róŝnej masie). Drugą generację tworzą cząstki: mion, neutrino mionowe, kwark dziwny i kwark powabny, zaś trzecią: taon, neutrino taonowe, kwark denny i kwark szczytowy. W sumie model określa dwanaście podstawowych fermionów. Dwa pierwsze w kaŝdej grupie nazywamy leptonami, a dwa pozostałe kwarkami. Istnienie czwartej i następnych generacji nie jest zabronione przez Model. Jednak obserwacje średniego czasu Ŝycia cząstek wskazują, Ŝe istnieją tylko trzy komplety fermionów. Rozumowanie to opiera się na następującym fakcie: im więcej jest moŝliwych sposobów, na które moŝe się rozpaść cząstka, tym krócej ta cząstka Ŝyje. Większa ilość cząstek związana z istnieniem wyŝszych generacji dostarczyłaby nowych kanałów rozpadu. Obserwowane cząstki Ŝyją na tyle długo, Ŝe istnienie czwartej generacji wydaje się wykluczone, chyba Ŝe odpowiadające jej nowe neutrino miałoby masę większą od ok. 45 GeV/c 2 (połowa masy bozonu Z). Wtedy cząstka Z nie mogłaby się rozpadać na parę neutrino - antyneutrino czwartej generacji. Wszystkie znane neutrina mają masy mniejsze od kilku ev/c 2 i dlatego istnienie czwartej rodziny nie wydaje się naturalne. 2

3 Fermiony w Modelu Standardowym Fermion Symbol Ładunek elektryczny Ładunek słaby* Ładunek silny (kolor) Masa Generacja 1 Elektron e /2 0 0,511 MeV Neutrino elektronowe ν e 0 +1/2 0 < 50 ev Kwark górny u +2/3 +1/2 R/G/B ~ 5 MeV Kwark dolny d -1/3-1/2 R/G/B ~10 MeV Generacja 2 Mion µ / ,6 MeV Neutrino mionowe ν µ 0 +1/2 0 < 0,5 MeV Kwark powabny c +2/3 +1/2 R/G/B ~1,5 GeV Kwark dziwny s -1/3-1/2 R/G/B ~100 MeV Generacja 3 Taon τ /2 0 1,784 GeV Neutrino taonowe ν τ 0 +1/2 0 < 70 MeV Kwark szczytowy (prawdziwy) t +2/3 +1/2 R/G/B 178 GeV Kwark denny (piękny) b -1/3-1/2 R/G/B ~4,7 GeV 3

4 Bozony jako nośniki oddziaływań W Modelu Standardowym oddziaływania przenoszone są przez specjalne cząstki/pola (w mechanice klasycznej rolę medium stanowiło wyłącznie pole). Oddziaływanie polega na wytworzeniu lub pochłonięciu cząstki przenoszącej oddziaływanie. Oddziaływanie elektromagnetyczne przenoszone jest przez foton. Oddziaływanie to odbywa się poprzez wytworzenie lub pochłonięcie fotonu. Oddziaływanie słabe, powodujące między innymi rozpady beta, przenoszone jest przez bozony W + i W - oraz Z 0. Oddziaływanie silne, łączące kwarki w hadrony, przenoszone jest przez osiem rodzajów gluonów, sposób oddziaływania (rodzaj gluonu) oznaczany jest właściwością nazywaną kolorem gluonu. Cząstka Higgsa [edytuj] Model Standardowy przewiduje teŝ istnienie cząstki, która oddziałując z innymi cząstkami nadaje im masę - jest to bozon Higgsa. Jest to jedyna cząstka, której istnienia jak dotąd nie udało się potwierdzić doświadczalnie. Co dalej? [edytuj] Model Standardowy jest potwierdzony doświadczalnie, lecz nie jest w pełni satysfakcjonujący z teoretycznego punktu widzenia. Ma on bowiem 19 swobodnych parametrów, które naleŝy wyznaczyć doświadczalnie i nie ma teorii wyjaśniającej wartości tych parametrów. Nie wiemy takŝe, czy poprawny jest mechanizm Higgsa naruszenia symetrii. Nie wyjaśnia pierwszych chwil istnienia Wszechświata po Wielkim Wybuchu, w czasie których nastąpiła wielka ekspansja zwana inflacją. Nie wyjaśnia dlaczego Wszechświat zbudowany jest z materii, a nie ma w nim antymaterii. Obliczenia masy Wszechświata nie zgadzają się z obserwowaną ilością materii we Wszechświecie, brakującą materię nazywa się ciemną materią. Nie określa mas cząstek. 4

5 Fizycy budują nowe teorie próbujące rozszerzyć Model Standardowy np. Teorie wielkiej unifikacji, supersymetria, teorie strun. Następcą będzie być moŝe Minimalny Standardowy Model Supersymetryczny. Zobacz teŝ [edytuj] cząstki elementarne: kwarki, leptony, hadrony, mezony, bariony, gluony oddziaływania podstawowe: oddziaływanie elektromagnetyczne, oddziaływanie silne, oddziaływanie słabe, oddziaływanie grawitacyjne Teorie wielkiej unifikacji Linki zewnętrzne [edytuj] Przygoda z cząstkami Aneks do Podstaw fizyki (pliki 45...) Wykłady o cząstkach elementarnych Źródło: " Kategoria: Fizyka cząstek elementarnych Tę stronę ostatnio zmodyfikowano 05:19, 5 kwi Tekst udostępniany na licencji GNU Free Documentation License. (patrz: Prawa autorskie) Wikipedia jest zarejestrowanym znakiem towarowym Wikimedia Foundation. MoŜesz przekazać dary pienięŝne Fundacji Wikimedia. Zasady ochrony prywatności O Wikipedii Informacje 5

6 Standard Model From Wikipedia, the free encyclopedia Have questions? Find out how to ask questions and get answers. Jump to: navigation, search For the mathematical formulation of the Standard Model of particle physics, see Standard Model (mathematical formulation). For the standard model in cryptography, see Standard Model (cryptography). Quantum field theory Feynman diagram History of... [show]background [show]symmetries [show]tools [show]equations [show]standard model [show]incomplete theories 6

7 [show]scientists This box: view talk edit The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It unifies the electroweak theory and quantum chromodynamics into a structure denoted by the gauge groups SU(3) SU(2) U(1). It is a quantum field theory which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the eighteen numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles). Contents [hide] 1 Historical background 2 Overview o 2.1 Particles of matter o 2.2 Force-mediating particles o 2.3 The Higgs boson o 2.4 List of standard model fermions 3 Tests and predictions 4 Challenges to the standard model 5 See also 6 Notes 7 References o 7.1 Introductory textbooks o 7.2 Advanced textbooks o 7.3 Journal articles 7

8 8 External links Historical background The formulation of the unification of the electromagnetic and weak interactions in the Standard Model is due to Steven Weinberg, Abdus Salam and, subsequently, Sheldon Glashow. The unification model was initially proposed by Steven Weinberg in 1967, [1] and completed integrating it with the proposal by Peter Higgs of spontaneous symmetry breaking [2][3][4] which gives origin to the masses of all particles described in the model. After the discovery, made at CERN of the existence of neutral weak currents, [5][6][7][8] mediated by the Z boson, foreseen in the Standard Model, Glashow, Salam, and Weinberg received the Nobel Prize in physics in [edit] Overview In physics, the dynamics of both matter and energy in nature is presently best understood in terms of the kinematics and interactions of fundamental particles. To date, science has managed to reduce the laws which seem to govern the behavior and interaction of all types of matter and energy we are aware of, to a small core of fundamental laws and theories. A major goal of physics is to find the 'common ground' that would unite all of these into one integrated model of everything, in which all the other laws we know of would be special cases, and from which the behavior of all matter and energy can be derived (at least in principle). "Details can be worked out if the situation is simple enough for us to make an approximation, which is almost never, but often we can understand more or less what is happening." (Feynman's lectures on Physics, Vol ) The standard model is a grouping of two major theories quantum electroweak and quantum chromodynamics which provides an internally consistent theory describing interactions between all experimentally observed particles. Technically, quantum field theory provides the mathematical framework for the standard model. The standard model describes each type of particle in terms of a mathematical field. For a technical description of the fields and their interactions, see standard model (mathematical formulation). 8

9 For ease of description, the standard model can be divided into three parts covering particles of matter, force mediating particles, and the Higgs boson. [edit] Particles of matter v d e eµτeµτ [show] Particles in physics The matter particles described by the standard model all have an intrinsic property known as 'spin' whose value is determined to be ½, i.e. all matter particles are fermions. For this reason, they follow the Pauli exclusion principle in accordance with the spin-statistics theorem, and it is this which causes their 'material' quality. [citation needed] Apart from their antiparticle partners, a total of twelve different types of matter particles are known and accounted for by the standard model. Six of these are classified as quarks (up, down, charm, strange, top and bottom), and the other six as leptons (electron, muon, tau, and their corresponding neutrinos). Matter particles (as do mediating particles) also carry various charges which make them susceptible to the fundamental forces, which are in turn mediated as described in the next subsection. Each quark can carry any one of three color charges red, green or blue, enabling them to participate in strong interactions. The up-type quarks (up, charm, and top quarks) carry an electric charge of +2/3, and the down-type quarks (down, strange, and bottom) carry an electric charge of 1/3, enabling both types to participate in electromagnetic interactions. Leptons do not carry any color charge they are color neutral, preventing them from participating in strong interactions. Quarks Leptons Organization of Fermions Generation 1 Generation 2 Generation 3 Up u Charm c Top t Down d Strange s Bottom b Electron Neutrino The electron-type leptons (the electron, the muon, and the tau lepton) carry an electric charge of 1, enabling them to participate in electromagnetic interactions. νe Muon Neutrino νµ Tau Neutrino Electron e Muon µ Tau τ ντ 9

10 The neutrino-type leptons (the electron neutrino, the muon neutrino and the tau neutrino) carry no electric charge, preventing them from participating in electromagnetic interactions Both quarks and leptons carry a handful of flavor charges, including the weak isospin, enabling all particles to interact via the weak nuclear interaction. Pairs from each group (one up-type quark, one down-type quark, a down-type lepton and its corresponding neutrino) form what is known as a 'generation'. The corresponding particles between each generation are identical to each other, with the exception of their mass and a property known as their flavor. [edit] Force-mediating particles Summary of interactions between particles described by the Standard Model. Forces in physics are the ways that particles interact and influence each other. At a macro level, the electromagnetic force allows particles to interact with one another via magnetic fields, and the force of gravitation allows two particles with mass to attract one another in accordance with Newton's Law of Gravitation. The standard model explains such forces as resulting from matter particles exchanging other particles, known as 10

11 force-mediating particles. When a force-mediating particle is exchanged, at a macro level the effect is equivalent to a force influencing both of them, and the particle is therefore said to have mediated (i.e., been the agent of) that force. Force-mediating particles are believed to be the reason why the forces and interactions between particles observed in the laboratory and in the universe exist. The known force-mediating particles described by the Standard Model also all have spin (as do matter particles), but in their case, the value of the spin is 1, meaning that all force-mediating particles are bosons. As a result, they do not follow the Pauli Exclusion Principle. The different types of force mediating particles are described below. Photons mediate the electromagnetic force between electrically charged particles. The photon is massless and is well-described by the theory of quantum electrodynamics. The W +, W, and Z gauge bosons mediate the weak interactions between particles of different flavors (all quarks and leptons). They are massive, with the Z being more massive than the W ±. The weak interactions involving the W ± act on exclusively left-handed particles and right-handed antiparticles. Furthermore, the W ± carry an electric charge of +1 and 1 and couple to the electromagnetic interactions. The electrically neutral Z boson interacts with both left-handed particles and antiparticles. These three gauge bosons along with the photons are grouped together which collectively mediate the electroweak interactions. The eight gluons mediate the strong interactions between color charged particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and an anticolor charge (e.g., Red-anti-Green). [9] Because the gluon has an effective color charge, they can interact among themselves. The gluons and their interactions are described by the theory of quantum chromodynamics. The interactions between all the particles described by the Standard Model are summarized in the illustration immediately above and to the right. [edit] The Higgs boson Force Mediating Particles Electromagnetic Force Weak Nuclear Force Strong Nuclear Force W +, W, and Z Photon γ Gauge Bosons W+, W, Z Gluons g 11

12 Main article: Higgs boson The Higgs particle is a hypothetical massive scalar elementary particle predicted by the Standard Model, and the only fundamental particle predicted by that model which has not been directly observed as yet. This is partly because it requires an exceptionally large amount of energy to create and observe under laboratory circumstances. It has no intrinsic spin, and thus, (like the force-mediating particles, which also have integral spin) is also classified as a boson. The Higgs boson plays a unique role in the Standard Model, and a key role in explaining the origins of the mass of other elementary particles, in particular the difference between the massless photon and the very heavy W and Z bosons. Elementary particle masses, and the differences between electromagnetism (caused by the photon) and the weak force (caused by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter; thus, if it is proven to exist, the Higgs boson has an enormous effect on the world around us. In electroweak theory it generates the masses of the massive leptons (electron, muon and tau); and also of the quarks. As of 2007, no experiment has directly detected the existence of the Higgs boson, but there is some indirect evidence for it. It is hoped that upon the completion of the Large Hadron Collider, experiments conducted at CERN would bring experimental evidence confirming the existence of the particle. Science, a journal of original scientific research, has reported: "...experimenters may have already overlooked a Higgs particle, argues theorist Chien-Peng Yuan of Michigan State University in East Lansing and his colleagues. They considered the simplest possible supersymmetric theory. Ordinarily, theorists assume that the lightest of theory's five Higgses is the one that drags on the W and Z. Those interactions then feed back on Higgs and push its mass above 121 times the mass of the proton, the highest mass searched for at CERN's Large Electron-Positron (LEP) collider, which ran from 1989 to But it's possible that the lightest Higgs weighs as little as 65 times the mass of a proton and has been missed, Yuan and colleagues argue in a paper to be published in Physical Review Letters`." [10] List of standard model fermions This table is based in part on data gathered by the Particle Data Group (QuarksPDF (54.8 KiB)). 12

13 Electron Positron Fermion (left-handed) Symbol Left-handed fermions in the Standard Model Electric charge Generation 1 Weak isospin Weak hypercharge Color charge * 511 kev 511 kev Electron-neutrino < 2 ev **** Up quark ~ 3 MeV *** Up antiquark ~ 3 MeV *** Down quark ~ 6 MeV *** Down antiquark ~ 6 MeV *** Mass ** 13

14 Generation 2 Fermion (left-handed) Symbol Electric charge Weak isospin Weak hypercharge Color charge * Mass ** Muon 106 MeV Antimuon 106 MeV Muon-neutrino < 2 ev **** Charm quark ~ 1.3 GeV Charm antiquark ~ 1.3 GeV Strange quark ~ 100 MeV Strange antiquark ~ 100 MeV Generation 3 Fermion (left-handed) Symbol Electric charge Weak isospin Weak hypercharge Color charge * Mass ** Tau lepton 1.78 GeV Anti-tau lepton 1.78 GeV 14

15 Tau-neutrino < 2 ev **** Top quark Top antiquark Bottom quark Bottom antiquark Notes: 171 GeV 171 GeV ~ 4.2 GeV ~ 4.2 GeV * These are not ordinary abelian charges, which can be added together, but are labels of group representations of Lie groups. ** Mass is really a coupling between a left-handed fermion and a right-handed fermion. For example, the mass of an electron is really a coupling between a left-handed electron and a right-handed electron, which is the antiparticle of a left-handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left-handed electron antineutrino. *** The masses of baryons and hadrons and various cross-sections are the experimentally measured quantities. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD scale. **** The Standard Model assumes that neutrinos are massless. Despite it several contemporary experiments prove that neutrinos oscillate between their flavour states and it wouldn't happen if they were all massless. [11] It is straightforward to extend the model to fit these data but there is plenty of possibilities and the mass eigenstates are still an open question. See Neutrino#Mass. Log plot of masses in the Standard Model. 15

16 Tests and predictions This section needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (April 2008) The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision. The Large Electron-Positron Collider at CERN tested various predictions about the decay of Z bosons, and found them confirmed. To get an idea of the success of the Standard Model a comparison between the measured and the predicted values of some quantities are shown in the following table: Quantity Measured (GeV) SM prediction (GeV) Mass of W boson ± ± Mass of Z boson ± ± [edit] Challenges to the standard model Unsolved problems in physics: Parameters in the Standard Model: What gives rise to the Standard Model of particle physics? Why do its particle masses and coupling constants possess the values we have measured? Does the Higgs boson predicted by the model really exist? Why are there three generations of particles in the Standard Model? The Standard Model of particle physics has been empirically determined through experiments over the past fifty years. Currently the Standard Model predicts that there is one more particle to be discovered, the Higgs boson. One of the reasons for building the Large Hadron Collider is 16

17 that the increase in energy is expected to make the Higgs observable. However, as of 2007, there are only indirect experimental indications for the existence of the Higgs boson and it can not be claimed to be found. The Standard Model is as yet unable to explain gravity in terms of particles. There has been a great deal of both theoretical and experimental research exploring whether the Standard Model could be extended into a complete theory of everything. This area of research is often described by the term 'Beyond the Standard Model'. There are several facets of this question. For example, one line of inquiry attempts to explore why there are seemingly so many unrelated parameters of the theory 21 in all (18 parameters in the core theory, plus G, c and h; there are believed to be an additional 7 or 8 parameters required for the neutrino masses although neutrino masses are outside the standard model and the details are unclear). Research also focuses on the Hierarchy problem (why the weak scale and Planck scale are so disparate), and attempts to reconcile the emerging Standard Model of Cosmology with the Standard Model of particle physics. Many questions relate to the initial conditions that led to the presently observed Universe. Examples include: Why is there a matter/antimatter asymmetry? Why is the Universe isotropic and homogeneous at large distances? [edit] See also The theoretical formulation of the standard model Weak interactions, Fermi theory of beta decay and electroweak theory Strong interactions, flavour, quark model and quantum chromodynamics For open questions, see quark matter, CP violation and neutrino masses Beyond the Standard Model noncommutative standard model [edit] Notes 1. ^ S. Weinberg Phys. Rev.Lett (1967). 2. ^ P. W. Higgs Phys. Lett (1964), Broken Symmetries, Massless Particles and Gauge Fields 3. ^ P. W. Higgs Phys. Rev. Lett (1964), Broken Symmetries and the Masses of Gauge Bosons 4. ^ Peter Higgs: the man behind the boson. Physicsworld.com ( ). Retrieved on ^ F. J. Hasert et al. Phys. Lett. 46B 121 (1973). 6. ^ F. J. Hasert et al. Phys. Lett. 46B 138 (1973). 17

18 7. ^ F. J. Hasert et al. Nucl. Phys. B73 1(1974). 8. ^ The discovery of the weak neutral currents. CERN courier ( ). Retrieved on ^ Technically, there are nine such color-anticolor combinations. However there is one color symmetric combination that can be constructed out of a linear superposition of the nine combinations, reducing the count to eight. 10. ^ Higgs Hiding in Plain Sight?. ScienceNOW ( ). Retrieved on ^ Particle Data Group: Neutrino mass, mixing, and flavor change (2006v) [edit] References [edit] Introductory textbooks Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN D.A. Bromley (2000). Gauge Theory of Weak Interactions. Springer. ISBN Gordon L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN [edit] Advanced textbooks Cheng, Ta Pei; Li, Ling Fong. Gauge theory of elementary particle physics. Oxford University Press. ISBN introduction to all aspects of gauge theories and the Standard Model. Donoghue, J. F.; Golowich, E.; Holstein, B. R.. Dynamics of the Standard Model. Cambridge University Press. ISBN highlights dynamical and phenomenological aspects of the Standard Model. O'Raifeartaigh, L.. Group structure of gauge theories. Cambridge University Press. ISBN highlights group-theoretical aspects of the Standard Model. [edit] Journal articles 18

19 S.F. Novaes, Standard Model: An Introduction, hep-ph/ D.P. Roy, Basic Constituents of Matter and their Interactions A Progress Report, hep-ph/ Y. Hayato et al., Search for Proton Decay through p νk + in a Large Water Cherenkov Detector. Phys. Rev. Lett. 83, 1529 (1999). Ernest S. Abers and Benjamin W. Lee, Gauge theories. Physics Reports (Elsevier) C9, (1973). [edit] External links New Scientist story: Standard Model may be found incomplete The Universe Is A Strange Place, a lecture by Frank Wilczek Observation of the Top Quark at Fermilab PDF version of the Standard Model Lagrangian (after electroweak symmetry breaking, with no explicit Higgs boson) PDF, PostScript, and LaTeX version of the Standard Model Lagrangian with explicit Higgs terms The particle adventure. [show] v d e General subfields within physics Retrieved from " Categories: Fundamental physics concepts Particle physics Standard Model Hidden categories: All articles with unsourced statements Articles with unsourced statements since September 2007 Articles needing additional references from April 2008 This page was last modified on 16 May 2008, at 12:35. All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.) Wikipedia is a registered trademark of the Wikimedia Foundation, Inc., a U.S. registered 501(c)(3) tax-deductible nonprofit charity. Privacy policy About Wikipedia Disclaimers 19

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