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In [[physics]], the '''Gell-Mann–Okubo mass formula''' provides a [[sum rule in quantum mechanics|sum rule]] for the masses of [[hadron]]s within a specific multiplet, determined by their [[isospin]] (''I'') and [[strangeness]] (or alternatively, [[hypercharge]])
:<math>M = a_0 + a_1 S + a_2 \left[ I \left( I + 1 \right)-\frac{1}{4} S^2 \right] ,</math>
where ''a''<sub>0</sub>, ''a''<sub>1</sub>, and ''a''<sub>2</sub> are [[free parameter]]s.


The rule was first formulated by [[Murray Gell-Mann]] in 1961<ref>
{{cite paper
|author=M. Gell-Mann
|year=1961
|title=The Eightfold Way: A Theory of Strong Interaction Symmetry
|publisher=[[California Institute of Technology]]
|series=Synchrotron Laboratory Report CTSL-20
|doi=10.2172/4008239
|osti=4008239
}}</ref> and independently proposed by [[Susumu Okubo]] in 1962.<ref>
{{cite journal
|author=S. Okubo
|year=1962
|title=Note on Unitary Symmetry in Strong Interactions
|journal=[[Progress of Theoretical Physics]]
|volume=27 |issue=5 |pages=949–966
|bibcode=1962PThPh..27..949O
|doi=10.1143/PTP.27.949
}}</ref><ref>
{{cite journal
|author=S. Okubo
|year=1962
|title=Note on Unitary Symmetry in Strong Interactions. II —Excited States of Baryons—
|journal=[[Progress of Theoretical Physics]]
|volume=28 |issue=1 |pages=24–32
|bibcode=1962PThPh..28...24O
|doi=10.1143/PTP.28.24
}}</ref> Isospin and hypercharge are generated by [[SU(3)]], which can be represented by [[Gell-Mann matrices|eight unitary and traceless matrices]] corresponding to the "components" of isospin and hypercharge. Six of the matrices correspond to flavor change, and the final two correspond to the third-component of isospin projection, and hypercharge.


==Theory==
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The mass formula was obtained by considering the [[Lie algebra representation|representations]] of the [[Lie algebra]] [[su(3)]]. In particular, the meson octet corresponds to the [[root system]] of the [[adjoint endomorphism|adjoint representation]]. However, the simplest, lowest-dimensional representation of su(3) is the [[fundamental representation]], which is three-dimensional, and is now understood to describe the approximate [[flavor symmetry]] of the three [[quark]]s ''u'', ''d'', and ''s''. Thus, the discovery of not only an su(3) symmetry, but also of this workable formula for the [[mass spectrum]] was one of the earliest indicators for the existence of quarks.
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This formula is ''phenomenological'', describing an approximate relation between meson and baryon masses, and may be superseded as theoretical work in [[quantum chromodynamics]] advances.
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==Baryons==
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{| class="wikitable" style="float:right; text-align:center; margin: 0em 0em 0em 1em;"
|+ Baryon properties<ref name=PDG>
{{cite journal
|author=J. Beringer ''et al.'' ([[Particle Data Group]])
|coauthors=<!-- -->
|year=2012
|title=Review of Particle Physics
|journal=[[Physical Review D]]
|volume=86 |issue=1 |page=010001
|bibcode=2012PhRvD..86a0001B
|doi=10.1103/PhysRevD.86.010001
|postscript=<!-- -->
}} and [http://pdg.lbl.gov/ 2013 partial update] for the 2014 edition.</ref>
|-
|rowspan="6"| Octet
|-
| Name || Symbol || [[Isospin]] || [[Strangeness]] || Mass (MeV/''c''<sup>2</sup>)
|-
| [[Nucleon]]s || N || {{frac|1|2}} || 0 || 939
|-
| [[Lambda baryon]]s || &Lambda; || 0 || &minus;1 || 1116
|-
| [[Sigma baryon]]s || &Sigma; || 1 || &minus;1 || 1193
|-
| [[Xi baryon]]s || &Xi; || {{frac|1|2}} || &minus;2 || 1318
|-
|rowspan="5"| Decuplet
|-
| [[Delta baryon]]s || &Delta; || {{frac|1|2}} || 0 || 1232
|-
| [[Sigma baryon]]s || &Sigma;<sup>*</sup> || 1 || &minus;1 || 1385
|-
| [[Xi baryon]]s || &Xi;<sup>*</sup> || {{frac|1|2}} || &minus;2 || 1533
|-
| [[Omega baryon]] || &Omega; || 0 || &minus;3 || 1672
|-
|}


Using the values of relevant ''I'' and ''S'' for baryons, the Gell-Mann–Okubo formula can be rewritten for the baryon octet,
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:<math>\frac{N + \Xi}{2} = \frac{3 \Lambda + \Sigma}{4} \, </math>
where ''N'', &Lambda;, &Sigma;, and &Xi; represent the average mass of corresponding baryons. Using the current mass of baryons,<ref name=PDG/> this yields:
:<math> \frac{N + \Xi}{2} = 1128.5~\mathrm{MeV}/c^2 </math>
and
:<math> \frac{3 \Lambda + \Sigma}{4} = 1135.25~\mathrm{MeV}/c^2</math>
meaning that the Gell-Man&ndash;Okubo formula reproduces the mass of octet baryons within ~0.5% of measured values.


For the baryon decuplet, the Gell-Mann–Okubo formula can be rewritten as the "equal-spacing" rule
I've yet to flip it, just not enough room where I fly indoors and I've but to identify exactly where the �A' button is to alter it from mode 1 to 2. The Syma UFO out of the box was straightforward to get flying.Must admit I have not utilized supplied charger as have other individuals already like the Eflite Celectra Charger that functions effectively for my many batteries. Syma X1 weighs 57.65 gm and battery and stock battery weigh ten.73 gm. Hence, with batteries X1 is 15% lighter than V949. The similar flip button works for X1 as <br><br>.
:<math>\Delta -\Sigma^* = \Sigma^* - \Xi^* = \Xi^* - \Omega = a_1 - 2a_2 \approx \, 147 ~\mathrm{MeV}/c^2</math>
where &Delta;, &Sigma;<sup>*</sup>, &Xi;<sup>*</sup>, and &Omega; represent the average mass of corresponding baryons.


The baryon decuplet formula famously allowed Gell-Mann to predict the mass of the then undiscovered &Omega;<sup>&minus;</sup>.<ref>
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{{cite conference
|last=Gell-Mann |first=M.
|year=1962
|title=Strange Particle Physics. Strong Interactions
|editor=J. Prentki
|booktitle=Proceedings of the International Conference on High-Energy Physics at CERN, Geneva,
1962
|page=805
}}</ref><ref>{{cite journal
|author=V. E. Barnes ''et al.''
  |year=1964
|title=Observation of a Hyperon with Strangeness Number Three
|url=http://teachers.web.cern.ch/teachers/archiv/HST2001/bubblechambers/omegaminus.pdf
|journal=[[Physical Review Letters]]
|volume=12 |issue=8 |page=204
|bibcode=1964PhRvL..12..204B
|doi=10.1103/PhysRevLett.12.204
}}</ref>


== Mesons ==
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The same mass relation can be found for the meson octet,
:<math>\frac{\frac{ K^- + \bar{K}^0 }{2} + \frac{ K^+ + K^0}{2}}{2} = \frac{3\eta + \pi}{4}</math>
Using the current mass of mesons,<ref name=PDG/> this yields
:<math> \frac{\frac{ K^- + \bar{K}^0 }{2} + \frac{ K^+ + K^0}{2}}{2} = 248~\mathrm{MeV}/c^2</math>
and
:<math> \frac{3\eta + \pi}{4} = 445~\mathrm{MeV}/c^2</math>


Because of this large discrepancy, several people attempted to find a way to understand the failure of the GMO formula in mesons, when it worked so well in baryons. In particular, people noticed that using the square of the average masses yielded much better results:<ref>
Give it some throttle, at the same time, twist, turn, or roll the X1 in your hand.X1 has a built-in security function that prevents the motors from engaging if the throttle is not Zero at the time the Tx is powered on. If the throttle is not Zero at the time the Tx is powered on, you will have to return throttle to zero ahead of the motors would spin up. "Arming the Tx" is an extension of that safety feature. On the other hand, the main gear of the X1 is smaller than the V949.
{{cite book
|author=D. J. Griffiths
|year=1987
|title=Introduction to Elementary Particles
|publisher=[[John Wiley & Sons]]
|isbn=0-471-60386-4
}}</ref>
:<math>\frac{ \left( \frac{ K^- + \bar{K}^0 }{2} \right)^2 + \left( \frac{ K^+ + K^0}{2} \right)^2}2 = \frac{3\eta^2 + \pi^2}{4}</math>
This now yields
:<math>\frac{ \left( \frac{ K^- + \bar{K}^0 }{2} \right)^2 + \left( \frac{ K^+ + K^0}{2} \right)^2}2 = 246\times10^3~\mathrm{MeV^2}/c^4</math>
and
:<math>\frac{3\eta^2 + \pi^2}{4} = 230\times10^3~\mathrm{MeV^2}/c^4</math>
which fall within 5% of each other.
 
For a while, the GMO formula involving the square of masses was simply an [[empirical relationship]], but later a justification for using the square of masses was found.<ref>
{{cite book
|author1=J. F. Donoghue
|author2=E. Golowich
|author3=B. R. Holstein
|year=1992
|title=Dynamics of the Standard Model
|pages=188–191
|publisher=[[Cambridge University Press]]
|isbn=978-0-521-47652-2
}}</ref><ref>
{{cite book
|author=S. Weinberg
|year=1996
|title=The Quantum Theory of Fields, Volume 2
|pages=225–233
|publisher=[[Cambridge University Press]]
|isbn=978-0-521-55002-4
}}</ref>
 
==See also==
*[[Gell-Mann–Nishijima formula]]
*[[Eightfold Way (physics)|Eightfold Way]]
*[[Quark model]]
*[[SU(3)]]
 
==References==
{{reflist}}
 
==Further reading==
The following book contains most (if not all) historical papers on the Eightfold Way and related topics, including the Gell-Mann&ndash;Okubo mass formula.
*{{cite book
|editor1=M. Gell-Mann
|editor2=Y. Ne'eman
|year=1964
|title=The Eightfold Way
|url=http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/THE%20EIGHTFOLD%20WAY.pdf
|publisher=[[W. A. Benjamin]]
|lccn=65013009
}}
 
{{DEFAULTSORT:Gell-Mann-Okubo mass formula}}
[[Category:Hadrons]]
[[Category:Quantum chromodynamics]]

Latest revision as of 16:22, 18 March 2014


It is accessible in 3 designs. By way of the use of of the 2. If you have any kind of inquiries relating to where and how you can use Syma X1 Assessment , you can http://tinyurl.com/kecvhhb make get in touch with with us at the internet page. I ordered a Wl v911, and http://tinyurl.com/kecvhhb this Syma X1. The V911 broke whiten two days, Its challenge was the tail motor burned out I have ordered replacements. If you have any inquiries with regards to particularly exactly where and also ideas on how to use ​Syma X1 Vs 1Sq , you are going to be able to make contact with us at our private net net page. Syma x1 rc quadcopter is a terrific tiny toy for significant boys and girls, but not for the little ones. The Syma X1 has four rotors - every single driven with a gear underneath the (very tiny!) motor - and a thin plastic body that comes in 3 varieties UFO, Bumblebee and X-Fighter. Flying the X1 was quick to get utilised to but Study THE Recommendations! The X1 quadcopter performs as nicely as I could ask of it, plus some. SYMA uses this word called, Eversion�



The Syma X1 4 Channel quadcopter brings a new element to radio manage helicopters and provides a totally various encounter of flying. Flying the Syma helicopter is basic and intuitive allowing the pilot to boost their abilities swiftly. Once you boost your capabilities sufficient there are settings constructed in that you can disable to advance your ability to fly the X1. With the use of 2.4ghz technology the Syma X1 radio method has the benefit of longer control distance, powerful anti-interference technologies, low power consumption, and rapid response occasions. With the setting on L� the X1 is much less responsive and inherently far more steady. With the setting on H� mode the X1 is awaken and a lot far more responsive. The Syma Helicopter brand is 1 that is pretty effectively recognized in the micro helicopter business. The Syma X1 comes in 3 flavors. For a handful of motives, SYMA produced this saying named, Eversi

I've but to flip it, just not enough space where I fly indoors and I've but to establish exactly where the �A' button is to alter it from mode 1 to two. The Syma UFO out of the box was easy to get flying.Should really admit I have not applied supplied charger as have other people currently like the Eflite Celectra Charger that performs appropriately for my many batteries. Syma X1 weighs 57.65 gm and battery and stock battery weigh 10.73 gm. Hence, with batteries X1 is 15% lighter than V949. The identical flip button performs for X1 a

By way of the use of of the two. If you have any type of inquiries with regards to where and how you can use Syma X1 Overview , you can make make contact with with us at the internet page. I ordered a Wl v911, and this Syma X1. The V911 broke whiten two days, Its issue was the tail motor burned out I have ordered replacements. If you have any inquiries with regards to specifically exactly where and also suggestions on how to use ​Syma X1 Vs 1Sq , you are going to be in a position to make contact with us at our private internet net web page. Syma x1 rc quadcopter is a terrific little toy for substantial boys and girls, but not for the modest ones. The Syma X1 has four rotors - every single driven with a gear underneath the (quite tiny!) motor - and a thin Syma X1 Helicopter plastic body that comes in 3 varieties http://tinyurl.com/kecvhhb UFO, Bumblebee and X-Fighter. Flying the X1 was easy to get utilised to but Study THE Recommendations! The X1 quadcopter functions as effectively as I could ask of it, plus some. SYMA utilizes this word named, Evers

.

Large TIP - Every time you crash your Syma X1 quad (which will be a lot), cheap ugg boots be positive to flip it over and make certain your battery is nonetheless intact. Then immediately review your props and your motors and make positive nothing is loose, bent or broken. With use of the newer 2.4GHz technology, the Syma X1 has the traits of longer control distance, strong anti-interference potential,compact power consumption, and fast response. Different handle selections for those piloting the X1: Up, Down, Left, Appropriate, Forward, Backward, Leftward flight, Rightward flight. Syma X1 4 Channel two.4Gh RC Quad Copter: Spacecraft Version. The Syma UFO has been obtainable for acquire in many on the internet and retail retailers considering the fact that March

.

I've yet to flip it, just not enough room where I fly indoors and I've but to identify exactly where the �A' button is to alter it from mode 1 to 2. The Syma UFO out of the box was straightforward to get flying.Must admit I have not utilized supplied charger as have other individuals already like the Eflite Celectra Charger that functions effectively for my many batteries. Syma X1 weighs 57.65 gm and battery and stock battery weigh ten.73 gm. Hence, with batteries X1 is 15% lighter than V949. The similar flip button works for X1 as

.

When you adored this article and you would like to receive more info regarding Syma X1 Review generously go to the web site. I ordered a Wl v911, and this Syma X1. The V911 broke whiten two days, Its issue was the tail motor burned out I have ordered replacements. The primary undesirable issue is the battery life, but it is quick to get them off the syma components store. I previously had a Syma 107g and decided to try a quadcopter. I believe this is due to the fact Syma X1 With Camera the 4 rotors are fixed and do not take fine adjustments for steering like the single blade copters do. As long as a thing doesn't physically break I am cheap ugg boots pretty certain it will last a extended time (there are no compact components or joints to worry about). The Syma Quad led on the board will then be a Strong on indicating the bind course of action is

.

A: If it has been correctly initialized, but the X1 still veers, there are two different scenarios. Verify for broken/frayed motor wire, especially if the X1 used to hover well, but doesn't immediately after a crash. A: Generally, that doesn't imply anything is wrong, specially when you only give it a tiny quantity of throttle, and the X1 has not begun to lift off. Or, you could attempt holding the X1 in your hand by grabbing it from the bottle and keep away from any spinning rotors. HeliPad, I ordered an X1 board and some motors, just recieved them last

.

Give it some throttle, at the same time, twist, turn, or roll the X1 in your hand.X1 has a built-in security function that prevents the motors from engaging if the throttle is not Zero at the time the Tx is powered on. If the throttle is not Zero at the time the Tx is powered on, you will have to return throttle to zero ahead of the motors would spin up. "Arming the Tx" is an extension of that safety feature. On the other hand, the main gear of the X1 is smaller than the V949.

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