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SU ( 5 ) is the simplest GUT.
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SU and 5
Historically, the first true GUT which was based on the simple Lie group SU ( 5 ), was proposed by Howard Georgi and Sheldon Glashow in 1974.
The fact that all currently known ( 2009 ) matter particles fit nicely into three copies of the smallest group representations of SU ( 5 ) and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.
Schematic representation of fermions and bosons in SU ( 5 ) GUT showing 5 + 10 split in the multiplets.
The two smallest irreducible representations of SU ( 5 ) are 5 and 10.
Here, the unification of matter is even more complete, since the irreducible spinor representation 16 contains both the and 10 of SU ( 5 ) and a right-handed neutrino, and thus the complete particle content of one generation of the extended standard model with neutrino masses.
Since different standard model fermions are grouped together in larger representations, GUTs specifically predict relations among the fermion masses, such as between the electron and the down quark, the muon and the strange quark, and the tau lepton and the bottom quark for SU ( 5 ) and SO ( 10 ).
The boson matrix for SO ( 10 ) is found by taking the 15x15 matrix from the 10 + 5 representation of SU ( 5 ) and adding an extra row and column for the right handed neutrino.
The renormalization group running of the three gauge couplings in the Standard Model has been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU ( 5 ) or SO ( 10 ) GUTs, which are precisely the GUT groups which lead to a simple fermion unification.
* Georgi – Glashow model — SU ( 5 )
* Flipped SU ( 5 ) — SU ( 5 ) × U ( 1 )
They are the minimal left-right model, SU ( 5 ), flipped SU ( 5 ) and the Pati-Salam model.
This experimental limit on the proton's lifetime pretty much rules out minimal SU ( 5 ).
Image: Proton_decay2. svg | Dimension 6 proton decay mediated by the X boson in SU ( 5 ) GUT
Image: proton decay3. svg | Dimension 6 proton decay mediated by the X boson in flipped SU ( 5 ) GUT
Image: proton decay4. svg | Dimension 6 proton decay mediated by the triplet Higgs and the anti-triplet Higgs in SU ( 5 ) GUT
SU and is
Mathematically, the unification is accomplished under an SU ( 2 ) × U ( 1 ) gauge group.
While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU ( 3 ) and SU ( 2 ) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U ( 1 ) which in principle allows for arbitrary charge assignments.
It turns out that including left and right-handed 4x4 quaternion matrices is equivalent to including a single right-multiplication by a unit quaternion which adds an extra SU ( 2 ) and so has an extra neutral boson and two more charged bosons.
Some GUT theories like SU ( 5 ) and SO ( 10 ) suffer from what is called the doublet-triplet problem.
As an approach to the unification of the forces, it is straightforward to apply the Kaluza – Klein theory in an attempt to unify gravity with the strong and electroweak forces by using the symmetry group of the Standard Model, SU ( 3 ) × SU ( 2 ) × U ( 1 ).
For example, the Lie algebra of SU ( n ) is written as.
* The group U ( 1 )× SU ( 2 )× SU ( 3 ) is a Lie group of dimension 1 + 3 + 8 = 12 that is the gauge group of the Standard Model in particle physics.
It is the study of the SU ( 3 ) Yang – Mills theory of color-charged fermions ( the quarks ).
QCD is a gauge theory of the SU ( 3 ) gauge group obtained by taking the color charge to define a local symmetry.
If one considers a version of QCD with N < sub > f </ sub > flavors of massless quarks, then there is a global ( chiral ) flavor symmetry group SU < sub > L </ sub >( N < sub > f </ sub >) × SU < sub > R </ sub >( N < sub > f </ sub >) × U < sub > B </ sub >( 1 ) × U < sub > A </ sub >( 1 ).
The chiral symmetry is spontaneously broken by the QCD vacuum to the vector ( L + R ) SU < sub > V </ sub >( N < sub > f </ sub >) with the formation of a chiral condensate.
SU and simplest
The simplest case, SU ( 1 ), is the trivial group, having only a single element.
SU and GUT
The Flipped SU ( 5 ) model is a Grand Unified Theory ( GUT ) theory first contemplated by Stephen Barr in 1982, and by Dimitri Nanopoulos and others in 1984.
Flipped SU ( 5 ) is not a fully unified model, because the U ( 1 ) y factor of the SM gauge group is within the U ( 1 ) factor of the GUT group.
Cryptons arising in the hidden sector of a superstring-derived flipped SU ( 5 ) GUT model have been shown to be metastable with a lifetime exceeding the age of the universe.
If the hypercharge is contained within SU ( 5 ), this is the conventional Georgi-Glashow model, with the 16 as the matter fields, the 10 as the electroweak Higgs field and the 24 within the 45 as the GUT Higgs field.
When this Higgs field acquires a GUT scale VEV, we have a symmetry breaking to Z < sub > 2 </ sub > ⋊ × SU ( 2 )< sub > L </ sub > × SU ( 2 )< sub > R </ sub >/ Z < sub > 2 </ sub >, i. e. the Pati-Salam model with a Z < sub > 2 </ sub > left-right symmetry.
The Yukawa coupling causes 5 and a SU ( 5 )- rep of fermions to pair up and acquire GUT scale masses for each generation.
SU and .
The corresponding gauge bosons are the three W bosons of weak isospin from SU ( 2 ) (,, and ), and the B < sup > 0 </ sup > boson of weak hypercharge from U ( 1 ), respectively, all of which are massless.
For example N = 4 Super Yang Mills Theory requires an SU ( N ) gauge group.
Unitary matrices of determinant 1 form a closed connected subgroup of dimension n < sup > 2 </ sup > − 1 denoted SU ( n ), the special unitary group.
He formulated the quark model of hadronic resonances, and identified the SU ( 3 ) flavor symmetry of the light quarks, extending isospin to include strangeness, which he also discovered.
5 and is
Subject to the limitations hereinafter provided, the Secretary of the Treasury is authorized and directed to pay, as prescribed by Section 8 of this Title, an amount not exceeding the principal of each award, plus accrued interests on such awards as bear interest, certified pursuant to Section 5 of this Title, in accordance with the award.
A typical `` sonogram '' of a human eye, together with a description of the anatomical parts, is shown in Fig. 5.
The following summary, based on Figures 5 and 6, is an example of one way of interpreting the 42 figures constructed from onset ages and completion ages of individual children with respect to the appropriate mean age for each growth center.
For example, the marksman gets 5 shots, but we take his score to be the number of shots before his first bull's-eye, that is, 0, 1, 2, 3, 4 ( or 5, if he gets no bull's-eye ).
The number of successes on each shot is a value of a random variable that has values 0 or 1, and there are 5 such random variables here.
It will be seen that where the scope is similar, the Athabascan ratios come out somewhat higher ( as indeed they ought to with a total ratio of 2.8 as against 3.5 or 4: 5 ) except for verbs, where alone the Athabascan ratio is lower.
If the force required to remove the coatings is plotted against film thickness, a graph as illustrated schematically in Fig. 5 may characteristically result.
Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).
The set of equations ( 5 ), ( 6 ), and the starting equation ( 7 ) is of a recursive type well suited to programming on the digital computer.
As a result, it is not easy to find a stock priced as the Morton issue was priced ( at roughly 10 times 1960 earnings, to yield a little over 5 per cent on the 64-cent anticipated dividend ).
Now, in 1961, the Catholic population of England is still quite small ( ten per cent, or 5 million ) ; ;
The importance of this 5 can largely be explained by the natural mathematical properties of the middle number and its special relationship to all the rest of the numbers -- quite apart from any numerological considerations, which is to say, any symbolic meaning arbitrarily assigned to it.
If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.
Made of gold-plated britannium on a black metal base, it is 13. 5 in ( 34 cm ) tall, weighs 8. 5 lb ( 3. 85 kg ) and depicts a knight rendered in Art Deco style holding a crusader's sword standing on a reel of film with five spokes.
It is a slab of white marble long, wide, and thick, on which are 5 groups of markings.
In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line.
In contrast, the largest North American community north of the circle, Sisimiut ( Greenland ), has approximately 5, 000 inhabitants, while between Canada and the USA, Barrow, Alaska is the largest settlement with circa 4, 000 inhabitants.
An Oligocene ( 34 – 23 Mya ) pollen is known for Asteraceae and Goodeniaceae, and seeds from Oligocene and Miocene ( 23 – 5. 3 Mya ) are known for Menyanthaceae and Campanulaceae respectively.
Argon has approximately the same solubility in water as oxygen and is 2. 5 times more soluble in water than nitrogen.
Because of weak bonding between the layers, gray arsenic is brittle and has a relatively low Mohs hardness of 3. 5.
0.167 seconds.