science

Pati–Salam model

Pati–Salam model is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pati–Salam model rather than just read about it. In short: In physics, the Pati–Salam model is a Grand Unified Theory (GUT) proposed in 1974 by Jogesh Pati and Abdus Salam. Like other GUTs, its goal is to explain the seeming arbitrariness and complexity of the Standard Model in terms of a simpler, more fundamental theory that unifies, what are in the Standard Model, disparate particles and forces.

Key takeaways

Pati–Salam model belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Pati–Salam model to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Pati–Salam model from memory before moving on to harder problems.

Reference excerpt

In physics, the Pati–Salam model is a Grand Unified Theory (GUT) proposed in 1974 by Jogesh Pati and Abdus Salam. Like other GUTs, its goal is to explain the seeming arbitrariness and complexity of the Standard Model in terms of a simpler, more fundamental theory that unifies, what are in the Standard Model, disparate particles and forces. The Pati–Salam unification is based on there being four quark color charges, dubbed red, green, blue and violet (or originally lilac), instead of the conventional three, with the new "violet" quark being identified with the leptons. 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 and right-handed neutrinos. Originally the fourth color was labelled "lilac" to alliterate with "lepton". Pati–Salam is an alternative to the Georgi–Glashow SU(5) unification also proposed in 1974. Both can be embedded within an SO(10) unification model.

Core theory The Pati–Salam model states that the gauge group is either SU(4) × SU(2)L × SU(2)R or (SU(4) × SU(2)L × SU(2)R)/Z2 and the fermions form three families, each consisting of the representations (4, 2, 1) and (4, 1, 2). This needs some explanation. The center of SU(4) × SU(2)L × SU(2)R is Z4 × Z2L × Z2R. The Z2 in the quotient refers to the two element subgroup generated by the element of the center corresponding to the two element of Z4 and the 1 elements of Z2L and Z2R. This includes the right-handed neutrino. See neutrino oscillations. There is also a (4, 1, 2) and/or a (4, 1, 2) scalar field called the Higgs field which acquires a non-zero vacuum expectation value (VEV). This results in a spontaneous symmetry breaking from SU(4) × SU(2)L × SU(2)R to (SU(3) × SU(2) × U(1)Y)/Z3 or from (SU(4) × SU(2)L × SU(2)R)/Z2 to (SU(3) × SU(2) × U(1)Y)/Z6 and also,

(4, 2, 1) → (3, 2)⁠1/6⁠ ⊕ (1, 2)− ⁠1/2⁠ (q & l) (4, 1, 2) → (3, 1)⁠1/3⁠ ⊕ (3, 1)− ⁠2/3⁠ ⊕ (1, 1)1 ⊕ (1, 1)0 (d c, uc, ec & νc) (6, 1, 1) → (3, 1)− ⁠1/3⁠ ⊕ (3, 1)⁠1/3⁠ (1, 3, 1) → (1, 3)0 (1, 1, 3) → (1, 1)1 ⊕ (1, 1)0 ⊕ (1, 1)−1 See restricted representation. Calling the representations things like (4, 1, 2) and (6, 1, 1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young diagrams or by Dynkin diagrams with numbers on their vertices, but still, it is standard among GUT theorists. The weak hypercharge, Y, is the sum of the two matrices:

( 1 3 0 0 0 0 1 3 0 0 0 0 1 3 0 0 0 0 − 1 ) ∈ SU ( 4 ) , ( 1 0 0 − 1 ) ∈ SU ( 2 ) R {\displaystyle {\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}}\in {\text{SU}}(4),\qquad {\begin{pmatrix}1&0\\0&-1\end{pmatrix}}\in {\text{SU}}(2)_{\text{R}}}

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Pati–Salam model

Start with the simplest possible case. Write down what Pati–Salam model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pati–Salam model before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pati–Salam model ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pati–Salam model

In research: Pati–Salam model appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Pati–Salam model in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Pati–Salam model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Abdus Salam, Grand Unified Theory, so understanding it makes those chapters shorter.
In everyday life: Look for Pati–Salam model outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Pati–Salam model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pati–Salam model means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Pati–Salam model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pati–Salam model in simple terms?

Why does Pati–Salam model matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pati–Salam model?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pati–Salam model.