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== | The '''Gell-Mann–Nishijima formula''' (sometimes known as the '''NNG formula''') relates the [[baryon number]] ''B'', the [[strangeness]] ''S'', the [[isospin]] ''I<sub>3</sub>'' of [[hadron]]s to the charge ''Q''. It was originally given by [[Kazuhiko Nishijima]] and [[Tadao Nakano]] in 1953,<ref> | ||
{{cite journal | |||
|last=Nakano |first=T | |||
|last2=Nishijima |first2=N | |||
|year=1953 | |||
|title=Charge Independence for V-particles |journal=[[Progress of Theoretical Physics]] | |||
|volume=10 |issue=5 |pages=581 | |||
|doi=10.1143/PTP.10.581 | |||
|bibcode = 1953PThPh..10..581N }}</ref> and led to the proposal of [[strangeness]] as a concept, which Nishijima originally called "eta-charge" after the [[eta meson]].<ref> | |||
{{cite journal | |||
|last=Nishijima |first=K | |||
|year=1955 | |||
|title=Charge Independence Theory of V Particles | |||
|journal=[[Progress of Theoretical Physics]] | |||
|volume=13 |issue=3 |pages=285 | |||
|doi=10.1143/PTP.13.285 | |||
|bibcode = 1955PThPh..13..285N }}</ref> [[Murray Gell-Mann]] proposed the formula independently in 1956.<ref> | |||
{{cite journal | |||
|last=Gell-Mann |first=M | |||
|year=1956 | |||
|title=The Interpretation of the New Particles as Displaced Charged Multiplets | |||
|journal=[[Il Nuovo Cimento]] | |||
|volume=4 | |||
|issue=S2 |pages=848 | |||
|doi=10.1007/BF02748000 | |||
}}</ref> The modern version of the formula relates all [[flavour quantum numbers]] (isospin up and down, strangeness, [[charm (quantum number)|charm]], [[bottomness]], and [[topness]]) with the baryon number and the electric charge. | |||
==Formula== | |||
The original form of the Gell-Mann–Nishijima formula is: | |||
:<math> Q = I_3 + \frac{1}{2} (B+S).\ </math> | |||
This equation was originally based on empirical experiments. It is now understood as a result of the [[quark model]]. In particular, the [[electric charge]] ''Q'' of a particle is related to its [[isospin]] ''I<sub>3</sub>'' and its [[hypercharge]] ''Y'' via the relation: | |||
:<math> Q = I_3 + \frac{1}{2} Y.\ </math> | |||
Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form: | |||
:<math> Q = I_3 + \frac{1}{2} (B+S+C+B^\prime+T) </math> | |||
where ''Q'' is the [[electric charge|charge]], ''I''<sub>3</sub> the 3rd-component of the [[isospin]], ''B'' the [[baryon number]], and ''S'', ''C'', ''B′'', ''T'' are the [[strangeness]], [[charm (quantum number)|charm]], [[bottomness]] and [[topness]] numbers. | |||
Expressed in terms of quark content, these would become: | |||
:<math> Q = \frac{2}{3}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) + \left(n_\text{c} - n_\bar{\text{c}}\right) + \left(n_\text{t} - n_\bar{\text{t}}\right)\right] - \frac{1}{3}\left[\left(n_\text{d} - n_\bar{\text{d}}\right) + \left(n_\text{s} - n_\bar{\text{s}}\right) + \left(n_\text{b} - n_\bar{\text{b}}\right)\right]</math> | |||
:<math> B = \frac{1}{3}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) + \left(n_\text{c} - n_\bar{\text{c}}\right) + \left(n_\text{t} - n_\bar{\text{t}}\right) + \left(n_\text{d} - n_\bar{\text{d}}\right) + \left(n_\text{s} - n_\bar{\text{s}}\right) + \left(n_\text{b} - n_\bar{\text{b}}\right)\right]</math> | |||
:<math>I_3=\frac{1}{2}[(n_\text{u}-n_\bar{\text{u}})-(n_\text{d}-n_\bar{\text{d}})]</math> | |||
:<math>S=-\left(n_\text{s}-n_\bar{\text{s}}\right); </math> <math>C=+\left(n_\text{c}-n_\bar{\text{c}}\right); </math> <math>B^\prime=-\left(n_\text{b}-n_\bar{\text{b}}\right); </math> <math>T=+\left(n_\text{t}-n_\bar{\text{t}}\right)</math> | |||
By convention, the flavor quantum numbers (strangeness, charm, bottomness, and topness) carry the same sign as the electric charge of the particle. So, since the strange and bottom quarks have a negative charge, they have flavor quantum numbers equal to −1. And since the charm and top quarks have positive electric charge, their flavor quantum numbers are +1. | |||
== References == | |||
{{reflist}} | |||
==Further reading== | |||
*{{cite book | |||
|last=Griffiths |first=DJ | |||
|year=2008 | |||
|title=Introduction to Elementary Particles | |||
|edition=2nd | |||
|publisher=Wiley-VCH | |||
|isbn=978-3-527-40601-2 | |||
}} | |||
{{DEFAULTSORT:Gell-Mann-Nishijima Formula}} | |||
[[Category:Particle physics]] | |||
Revision as of 06:17, 7 July 2013
The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number B, the strangeness S, the isospin I3 of hadrons to the charge Q. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953,[1] and led to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge" after the eta meson.[2] Murray Gell-Mann proposed the formula independently in 1956.[3] The modern version of the formula relates all flavour quantum numbers (isospin up and down, strangeness, charm, bottomness, and topness) with the baryon number and the electric charge.
Formula
The original form of the Gell-Mann–Nishijima formula is:
This equation was originally based on empirical experiments. It is now understood as a result of the quark model. In particular, the electric charge Q of a particle is related to its isospin I3 and its hypercharge Y via the relation:
Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form:
where Q is the charge, I3 the 3rd-component of the isospin, B the baryon number, and S, C, B′, T are the strangeness, charm, bottomness and topness numbers.
Expressed in terms of quark content, these would become:
![{\displaystyle Q={\frac {2}{3}}\left[\left(n_{\text{u}}-n_{\bar {\text{u}}}\right)+\left(n_{\text{c}}-n_{\bar {\text{c}}}\right)+\left(n_{\text{t}}-n_{\bar {\text{t}}}\right)\right]-{\frac {1}{3}}\left[\left(n_{\text{d}}-n_{\bar {\text{d}}}\right)+\left(n_{\text{s}}-n_{\bar {\text{s}}}\right)+\left(n_{\text{b}}-n_{\bar {\text{b}}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdae7ce1b32af903a4100f614f9ec77fdb5b7f9f)
![{\displaystyle B={\frac {1}{3}}\left[\left(n_{\text{u}}-n_{\bar {\text{u}}}\right)+\left(n_{\text{c}}-n_{\bar {\text{c}}}\right)+\left(n_{\text{t}}-n_{\bar {\text{t}}}\right)+\left(n_{\text{d}}-n_{\bar {\text{d}}}\right)+\left(n_{\text{s}}-n_{\bar {\text{s}}}\right)+\left(n_{\text{b}}-n_{\bar {\text{b}}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1e79046985eb27cdbf52575498735dfc97ba9e7)
![{\displaystyle I_{3}={\frac {1}{2}}[(n_{\text{u}}-n_{\bar {\text{u}}})-(n_{\text{d}}-n_{\bar {\text{d}}})]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd9119f54b7cc21af268e110ae32f9b8bd098ce0)
By convention, the flavor quantum numbers (strangeness, charm, bottomness, and topness) carry the same sign as the electric charge of the particle. So, since the strange and bottom quarks have a negative charge, they have flavor quantum numbers equal to −1. And since the charm and top quarks have positive electric charge, their flavor quantum numbers are +1.
References
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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
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One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang