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In [[physics]], the '''Pati–Salam model''' is a [[Grand Unification Theory]] (GUT) proposed in 1974 by nobel laureate [[Abdus Salam]] and [[Jogesh Pati]].  The unification is based on there being four [[quark]] [[color charge]]s, dubbed red, green, blue and violet (or lilac), instead of the conventional three, with the new "violet" quark being identified with the [[lepton]]s.  The model also has [[Left–right symmetry]] and predicts the existence of a high energy right handed [[weak interaction]] with heavy [[W' and Z' bosons]].


Originally the fourth color was labelled "'''l'''ilac" to alliterate with "'''l'''epton".  Pati-Salam is a mainstream theory and a viable alternative to the [[Georgi–Glashow model|Georgi–Glashow SU(5) unification]].  It can be embedded within an [[SO(10) (physics)|SO(10) unification model]] (as can [[SU(5)]]).
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On Sunday, we went to the Matisse exhibition at the Tate Modern (walking round the exhibit, talking, made me feel as though we were in a Woody Allen movie), and again his car had a parking ticket on it when we returned to it. This time, though, he didn�t hand it to me, although it�s sitting, accusingly, on my desk.<br><br>The whole phone, in fact, is a gleaming object of desire but it lacks standout new features other than the cameras, so you�ll miss out on gizmos such as the Samsung S5�s fingerprint scanner, or LG G3�s frankly frightening Quad HD screen.<br><br>99                  &#9733;&#9733;&#9733;&#9733;&#9733;Most of us who can be considered vaguely literate felt a faint anger when the term �selfie� passed from geek-speak into common parlance, especially after this year�s famous examples at the Oscars and Nelson Mandela�s funeral, where Barack Obama snuggled up to David Cameron. Huawei Ascend P7 �329.<br><br>And don�t say, �Don�t give me a hard time� when it�s you giving me a hard time. I did nothing today other than work hard and order dinner. 'Have a great life together, just leave me out of it. �You know I have no interest in her. I didn�t realise you had taken my keys back. I hope that was just a fit of pique. �<br>This came back the next morning, when he�d arrived at work. I love you and no one else. I have to work now, but I�ll see you tonight, as usual. My life is an open book to you.<br><br>Isobel and Dawn are in situ already, chilling the wine. Lots of books on Kindle. My Accessorize pink bikini. Wow, are we going to whip up some copy! What about the wedding proposal on the Pampelonne beach and me and Dawn can scatter white rose petals. Xxx� <br>The thing is, I�m not even sure David is still coming� Packing in tissue paper tonight: The Row sunglasses. My Dries negligee dress. 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Unless you�re the size of a Weight Watchers �before� picture, there�s only one reason for this to exist - a �group selfie� (ie, a group shot where one of you holds the camera) - hence �groufie�. Huawei is so proud of the word the company trademarked it in several countries to mark the launch of the P7.<br><br>In case you�re wondering what Huawei is, it�s one of those Chinese companies that only recently began hawking smartphones in the West, and shifts so many phones in the Far East it�s the third biggest phone company on Earth.<br><br>Upstage selfie-toting friends by turning you and your pals into a real 3D-model (warning: there�s a fair bit of work involved), ready to print off. 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==Core theory==
The Pati–Salam model states that the [[gauge group]] is either [[Special unitary group|SU(4) &times; SU(2)<sub>L</sub>&times; SU(2)<sub>R</sub>]] or [[Special unitary group|( SU(4) &times; SU(2)<sub>L</sub>&times; SU(2)<sub>R</sub> ) / '''Z'''<sub>2</sub>]] and the fermions form three families, each consisting of the [[Representations of Lie groups/algebras|representations]] [[Representations of Lie groups/algebras|(4,2,1)]] and <math>(\bar 4,1,2)</math>. This needs some explanation. The [[Center (group theory)|center]] of SU(4)&times; SU(2)<sub>L</sub>&times; SU(2)<sub>R</sub> is '''Z'''<sub>4</sub>&times; '''Z'''<sub>2L</sub>&times; '''Z'''<sub>2R</sub>. The '''Z'''<sub>2</sub> in the quotient refers to the two element subgroup generated by the element of the center corresponding to the 2 element of '''Z'''<sub>4</sub> and the 1 elements of '''Z'''<sub>2L</sub> and '''Z'''<sub>2R</sub>. This includes the right-handed neutrino, which is now likely believed to exist. See [[neutrino oscillation]]s. There is also a (4,1,2) and/or a <math>(\bar 4,1,2)</math> [[scalar field]] called the [[Higgs field]] which acquires a VEV. This results in a [[spontaneous symmetry breaking]] from <math>SU(4)\times SU(2)_L\times SU(2)_R</math> to <math>[SU(3)\times SU(2)\times U(1)_Y]/\mathbb{Z}_3</math> or from <math>[SU(4)\times SU(2)_L\times SU(2)_R]/\mathbb{Z}_2</math> to <math>[SU(3)\times SU(2)\times U(1)_Y]/\mathbb{Z}_6</math> and also,
:<math>(4,2,1)\rightarrow (3,2)_{\frac{1}{6}}\oplus (1,2)_{-\frac{1}{2}}</math> (q and l),
:<math>(\bar{4},1,2)\rightarrow (\bar{3},1)_{\frac{1}{3}}\oplus (\bar{3},1)_{-\frac{2}{3}}\oplus (1,1)_1\oplus (1,1)_0</math> (d<sup>c</sup>, u<sup>c</sup>, e<sup>c</sup> and &nu;<sup>c</sup>),
<math>(6,1,1)\rightarrow (3,1)_{-\frac{1}{3}}\oplus (\bar{3},1)_{\frac{1}{3}}</math>, <math>(1,3,1)\rightarrow (1,3)_0</math> and <math>(1,1,3)\rightarrow (1,1)_1\oplus (1,1)_0\oplus (1,1)_{-1}</math>. See [[restricted representation]]. Of course, calling the [[Representations of Lie groups/algebras|representations]] things like <math>(\bar{4},1,2)</math> and (6,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by [[Young tableau]]x or [[Dynkin diagram]]s with numbers on their vertices, but still, it is standard among GUT theorists.
 
The [[weak hypercharge]], Y, is the sum of <math>\begin{pmatrix}\frac{1}{3}&0&0&0\\0&\frac{1}{3}&0&0\\0&0&\frac{1}{3}&0\\0&0&0&-1\end{pmatrix}</math> of SU(4) and <math>\begin{pmatrix}1&0\\0&-1\end{pmatrix}</math> of SU(2)<sub>R</sub>
 
Actually, it is possible to extend the Pati-Salam group so that it has two [[connected space|connected component]]s. The relevant group is now the [[semidirect product]] <math>\{[SU(4)\times SU(2)_L\times SU(2)_R]/\mathbb{Z}_2\}\rtimes\mathbb{Z}_2</math>. The last '''Z'''<sub>2</sub> also needs explaining. It corresponds to an [[automorphism]] of the (unextended) Pati-Salam group which is the [[Function composition|composition]] of an [[Involution (mathematics)|involutive]] [[outer automorphism]] of SU(4) which isn't an [[inner automorphism]] with interchanging the left and right copies of SU(2). This explains the name left and right and is one of the main motivations for originally studying this model. This extra "[[left-right symmetry]]" restores the concept of [[parity (physics)|parity]] which had been shown not to hold at low energy scales for the [[weak interaction]]. In this extended model, <math>(4,2,1)\oplus(\bar{4},1,2)</math> is an irrep and so is <math>(4,1,2)\oplus(\bar{4},2,1)</math>. This is the simplest extension of the minimal [[left-right model]] unifying [[Quantum chromodynamics|QCD]] with [[B−L]].
 
Since the [[homotopy group]] <math>\pi_2\left(\frac{SU(4)\times SU(2)}{[SU(3)\times U(1)]/\mathbb{Z}_3}\right)=\mathbb{Z}</math>, this model predicts [[Magnetic monopole|monopoles]]. See [['t Hooft-Polyakov monopole]].
 
This model was invented by [[Jogesh Pati]] and [[Abdus Salam]].
 
This model doesn't predict gauge mediated [[proton decay]] (unless it is embedded within an even larger GUT group).
 
==Differences from the SU(5) unification==
As mentioned above, both the Pati-Salam and [[Georgi–Glashow model|Georgi–Glashow SU(5)]] unification models can be embedded in a [[SO(10) (physics)|SO(10) unification]]. The difference between the two models then lies in the way that the SO(10) symmetry is broken, generating different particles that may or may not be important at low scales and accessible by current experiments. If we look at the individual models, the most important difference is in the origin of the [[weak hypercharge]]. In the SU(5) model by itself there is no left-right symmetry (although there could be one in a larger unification in which the model is embedded), and the weak hypercharge is treated separately from the color charge. In the Pati–Salam model, part of the weak hypercharge (often called U(1)<sub>B-L</sub>) starts being unified with the color charge in the SU(4)<sub>C</sub> group, while the other part of the weak hypercharge is in the SU(2)<sub>R</sub>. When those two groups break then the two parts together eventually unify into the usual weak hypercharge U(1)<sub>Y</sub>.
 
==Minimal supersymmetric Pati-Salam==
 
===Spacetime===
The N=1 superspace extension of 3+1 Minkowski spacetime
 
===Spatial symmetry===
N=1 SUSY over 3+1 Minkowski spacetime with [[R-symmetry]]
 
===Gauge symmetry group===
[SU(4)&times; SU(2)<sub>L</sub> &times; SU(2)<sub>R</sub>]/'''Z'''<sub>2</sub>
 
===Global internal symmetry===
U(1)<sub>A</sub>
 
===Vector superfields===
Those associated with the SU(4)&times; SU(2)<sub>L</sub> &times; SU(2)<sub>R</sub>  gauge symmetry
 
===Chiral superfields===
As complex representations:
 
:{| class="wikitable"
!label!!description!!multiplicity!!SU(4)&times;SU(2)<sub>L</sub>&times; SU(2)<sub>R</sub> rep!!R!!A
|-
|<math>(4,1,2)_H</math>||GUT Higgs field||1||<math>(4,1,2)</math>||0||0
|-
|<math>(\bar{4},1,2)_H</math>||GUT Higgs field||1||<math>(\bar{4},1,2)</math>||0||0
|-
|<math>S</math>||singlet||1||<math>(1,1,1)</math>||2||0
|-
|<math>(1,2,2)_H</math>||electroweak Higgs field||1||<math>(1,2,2)</math>||0||0
|-
|<math>(6,1,1)_H</math>||no name||1||<math>(6,1,1)</math>||2||0
|-
|<math>(4,2,1)</math>||matter field||3||<math>(4,2,1)</math>||1||1
|-
|<math>(\bar{4},1,2)</math>||matter field||3||<math>(\bar{4},1,2)</math>||1||-1
|-
|<math>\phi</math>||sterile neutrino||3||<math>(1,1,1)</math>||1||1
|}
 
===Superpotential===
A generic invariant renormalizable superpotential is a (complex) <math>SU(4)\times SU(2)_L \times SU(2)_R</math> and U(1)<sub>R</sub> invariant cubic polynomial in the superfields. It is a linear combination of the following terms:
<math>
\begin{matrix}
S\\
S(4,1,2)_H (\bar{4},1,2)_H\\
S(1,2,2)_H (1,2,2)_H\\
(6,1,1)_H (4,1,2)_H (4,1,2)_H\\
(6,1,1)_H (\bar{4},1,2)_H (\bar{4},1,2)_H\\
(1,2,2)_H (4,2,1)_i (\bar{4},1,2)_j\\
(4,1,2)_H (\bar{4},1,2)_i \phi_j\\
\end{matrix}
</math>
 
<math>i</math> and <math>j</math> are the generation indices.
 
===Left-right extension===
We can extend this model to include [[left-right symmetry]]. For that, we need the additional chiral multiplets <math>(4,2,1)_H</math> and <math>(\bar{4},2,1)_H</math>
 
==Sources==
* Graham G. Ross, ''Grand Unified Theories'', Benjamin/Cummings, 1985, ISBN 0-8053-6968-6
* Anthony Zee, ''Quantum Field Theory in a Nutshell'', Princeton U. Press, Princeton, 2003, ISBN 0-691-01019-6
 
==References==
{{Reflist}}
*J. Pati and A. Salam, Phys. Rev. D10 (1974), 275. [http://www.hep.phys.soton.ac.uk/~belyaev/proj/lq/refs/pati_salam_p275_1.pdf Lepton number as the fourth "color"]
*{{Cite arXiv |author=[[John Baez|J.C. Baez]], J. Huerta |eprint=0904.1556 |title=The Algebra of Grand Unified Theories |year=2009 |class=hep-th }}
 
==External links==
*[http://www.scholarpedia.org/article/Pati-Salam_model Pati-Salam model on Scholarpedia]
* [http://adsabs.harvard.edu/abs/1985ZPhyC..27..321W Proton decay, annihilation or fusion?] by Wu, Dan-Di; Li, Tie-Zhong, ''Zeitschrift für Physik C'', Volume 27, Issue 2, pp.&nbsp;321–323 [http://www.springerlink.com/content/q544853j322w0356/ preview] Fusion of all three quarks is the only decay mechanism mediated by the [[Higgs particle]], not the [[gauge bosons]], in the [[Pati-Salam model]]
*[http://math.ucr.edu/~huerta/oral.pdf The Algebra of Grand Unified Theories] John Huerta. Slide show: contains an overview of Pati-Salam
*[http://math.ucr.edu/~huerta/guts/node18.html the Pati-Salam model] Motivation for the Pati–Salam model
 
{{DEFAULTSORT:Pati-Salam model}}
[[Category:Particle physics]]

Latest revision as of 04:34, 9 January 2015


He got back late, and looked so tired I said I�d order a Rasa curry, which I did. So, on Friday, I emailed him in the morning to say that I�d been worried by the fact that he�d read the address of my London flat on the internet. They wanted to phone us back, so I reminded David I�d lost my BlackBerry, and have no idea what the number of the Bat Phone is.

I keep conjuring up images of him in 1983, trying to reignite the passion.
I told him, before he started wriggling, that I think that memorable evening, when after our game of squash he had asked me to take his racquet home for him because he had a date, he had already started seeing the woman he would marry.

He bought me a bottle of prosecco, and some shopping. On Sunday, we went to the Matisse exhibition at the Tate Modern (walking round the exhibit, talking, made me feel as though we were in a Woody Allen movie), and again his car had a parking ticket on it when we returned to it. This time, though, he didn�t hand it to me, although it�s sitting, accusingly, on my desk.

The whole phone, in fact, is a gleaming object of desire but it lacks standout new features other than the cameras, so you�ll miss out on gizmos such as the Samsung S5�s fingerprint scanner, or LG G3�s frankly frightening Quad HD screen.

99 ★★★★★Most of us who can be considered vaguely literate felt a faint anger when the term �selfie� passed from geek-speak into common parlance, especially after this year�s famous examples at the Oscars and Nelson Mandela�s funeral, where Barack Obama snuggled up to David Cameron. Huawei Ascend P7 �329.

And don�t say, �Don�t give me a hard time� when it�s you giving me a hard time. I did nothing today other than work hard and order dinner. 'Have a great life together, just leave me out of it. �You know I have no interest in her. I didn�t realise you had taken my keys back. I hope that was just a fit of pique. �
This came back the next morning, when he�d arrived at work. I love you and no one else. I have to work now, but I�ll see you tonight, as usual. My life is an open book to you.

Isobel and Dawn are in situ already, chilling the wine. Lots of books on Kindle. My Accessorize pink bikini. Wow, are we going to whip up some copy! What about the wedding proposal on the Pampelonne beach and me and Dawn can scatter white rose petals. Xxx�
The thing is, I�m not even sure David is still coming� Packing in tissue paper tonight: The Row sunglasses. My Dries negligee dress. Isobel has just sent me a message�
�The cast of Liz Jones�s Diary are off to the South of France. Let�s get this show on the road!

She had written to him three times, about him giving her his car (His reply: �I will send you the log book�), and having found his bow tie (His reply: �I spent �75 on one last week.

The famous Oscars �selfie� taken by Bradley Cooper and featuring Angelina Jolie, Brad Pitt, Meryl Streep, Julia Roberts, Ellen DeGeneres, Jennifer Lawrence, Lupita Nyong�o, her brother Peter, Kevin Spacey, Jared Leto and Channing Tatum
But Huawei (pronounced like the reverse of a jubilant �Whahey�) needed to add to the language to sum up the purpose of its new Ascend P7�s stand-out feature - a forward-facing eight-megapixel camera, with the option for panoramic shots. By law, this is the only phone you�ll be taking �groufies� on - although as yet, the trademark doesn�t apply in the UK, so users of other phones can still use it for their own work. Unless you�re the size of a Weight Watchers �before� picture, there�s only one reason for this to exist - a �group selfie� (ie, a group shot where one of you holds the camera) - hence �groufie�. Huawei is so proud of the word the company trademarked it in several countries to mark the launch of the P7.

In case you�re wondering what Huawei is, it�s one of those Chinese companies that only recently began hawking smartphones in the West, and shifts so many phones in the Far East it�s the third biggest phone company on Earth.

Upstage selfie-toting friends by turning you and your pals into a real 3D-model (warning: there�s a fair bit of work involved), ready to print off. The app �walks� you round anything to capture it in 3D - now all you need is a few hundred quid for a 3D printer.

Huawei�s invention of the g-word, and the panoramic software to make it a reality, is down to a feeling that the endless Twitter parade of selfies (both celebrity and human), might be improved with a bit of context. And in action, it�s impressive too.

WOLFENSTEIN: THE NEW ORDER�40, PC, CONSOLES
The biggest surprise in Wolfensteing: The New Order is that it's the tense plotting that lifts this violent tale above its beige rivals
With an alternate-history plot hewn from the finest codswallop - a Nazi general uses high technology to summon an army of robots and zombies - the biggest surprise here is that it�s the tense plotting that lifts this violent tale above its beige rivals. ★★★★★

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