# Do any good theories exist on why the weak interaction is so profoundly chiral?

I find the profound asymmetry in the sensitivity of left and right chiral particles to be one of the most remarkable analytical observations captured in the Standard Model. Yet for some, I've not found much in the way of discussions that worry about why of such as truly remarkable fact is true. I can't help but be reminded a wee bit of views on the motions of planets before Newton... you know, "it be Angels that do push them around, ask ye not why!"

Seriously, I know the Standard Model has a lot of givens in it... but surely someone has mulled over why the universe might exhibit such a non-intuitive and thus interesting asymmetry? And perhaps even developed some solid speculations or full theories on why such in-your-face chiral asymmetries exist in nature?

Do such theories exist, or is this asymmetry truly just a "given" and nothing more?

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surely someone has mulled over why the universe might exhibit such a non-intuitive and thus interesting asymmetry?

Oh yes, definitely. I have for one (though I haven't made a significant contribution to the question)! :)

There are a number of "left-right symmetric" models out there which usually involve a group like $SU(2)_L \times SU(2)_R$ where the $SU(2)_R$ gets spontaneously broken by a Higgs mechanism. You'll find a number of highly cited papers in InspireHEP.

I've always thought these models sounded very interesting but haven't yet had the opportunity to work on them! If you find anything good let me know. :)

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thanks, that's nicely to the central point of my question: Is there a good thread I can pick up on to understand this more in the context of some interesting form of symmetry breaking? Very likely Lubos's excellent-as-usual answer says something similar, but you kind of nailed it where I was coming from. –  Terry Bollinger Mar 22 '13 at 12:36

Surely someone has mulled over why the universe might exhibit such a non-intuitive and thus interesting asymmetry?

As always, when it comes to valid and important physical theories, the reason why the Universe has non-intuitive features is simply that the intuition is wrong. Arguments based on wrong intuition are irrational and unscientific.

Rationally speaking, there doesn't exist any reason why the laws of Nature should be left-right-symmetric. In particular, spin-1/2 fermionic fields may naturally come in elementary pieces which are 2-component spinors. 2-component spinors inherently allow a left-right asymmetry and because the left-handed and right-handed components of the Dirac 4-spinors may have different charges under the gauge groups, this asymmetry is translated to the interactions, too.

It would be unusual and somewhat unlikely if all the 2-component spinor fields could be combined into 4-spinors in which the pairs of 2-component spinor fields have the same charges under all the gauge groups. The minimal building blocks are the 2-component spinors and as long as we combine them and their charges in a way that is free of gauge anomalies, it's a valid theory. The left-right-symmetric theories form a small (but not infinitely small) fraction of the allowed theories.

The more right way to formulate your question would be to ask Why have we created the intuition that the world should be left-right-symmetric. The reason is that the world is approximately left-right-symmetric. That's because at long distances i.e. low energies, all the forces – specifically the weak force – that make the physics left-right-asymmetric disappear because they're caused by massive messengers (W-bosons and Z-bosons).

The only unbroken group at low energies – and therefore the only long-range force (except for gravity) – is electromagnetism and its $U(1)$ group. Under that group, there is a pairing of the 2-component spinors and physics is left-right-symmetric. This is no accident. The electromagnetic $U(1)$, the unbroken group, is defined as the group under which the vacuum condensate is neutral. Because it's neutral but it's still able to convert the two 2-component spinors in the massive Dirac 4-component spinors into each other (it's what the mass term does), it implies that these two 2-component spinors must have the same charges under this electromagnetic $U(1)$.

The previous sentence doesn't hold for neutrinos because they're probably strictly neutral particles described by Majorana fermions whose "number of degrees of freedom" is exactly the same as for a 2-component Weyl fermion.

One may also obtain left-right-symmetric models by breaking a symmetry in a more fundamental left-right-symmetric model. However, there's really no known valid argument indicating that the starting point should be left-right-symmetric.

In fact, I updated the answer by adding this paragraph. There exists an anthropic reason why the world should better violate similar discrete symmetries. The laws of Nature allows both matter and antimatter. Their properties are always related by the CPT symmetry. But if there were also an exact C symmetry or CP symmetry, the matter and antimatter in the early Universe would be balanced and they would pretty much exactly annihilate with each other. Because some matter is left, the symmetry couldn't be exact. Andrei Sakharov actually formulated the necessary Sakharov conditions for baryogenesis. $B$, $C+CP$ violation, and interactions away from thermal equilibrium. I realize that $P$ violation isn't really there but it's pretty close to $C$ violation which is found in the list. The list is enough to say that violations of discrete symmetries are necessary for life to exist.

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+1 for "The more right way to formulate your question would be to ask Why have we created the intuition that the world should be left-right-symmetric." –  Michael Brown Mar 22 '13 at 6:21
@Lubos: Then, how does nature decide whether to couple to the right-handed sector or to the left-handed sector? Is that arbitrary? –  Siva Mar 22 '13 at 6:46
@Siva It's entirely a matter of convention - the same as whether you talk about particle and antiparticles. You can write every field as a left handed field. For example if you take the right hand electron field and conjugate it you get a left hand positron field. The physical fact is that the weak interaction does not couple to every field. Nevertheless the Higgs mechanism lets the fields that feel the weak force to interact with the ones that don't in a specific way (the gauge invariant Yukawas). As a result things get mixed up at low energies and you get massive particles. –  Michael Brown Mar 22 '13 at 11:18
Dear @Siva, Michael's answer is great but I may have understood your question differently. Nature doesn't decide "whether". In general, both left-handed and right-handed sectors are coupled to gauge fields. Just the charges - and representations under the gauge group - are different for the left-handed and right-handed spinors. Our Universe has some particular assignment of the charges which is, except for some conditions that must be obeyed, random, and there's no reason why it should respect a pairing of the Weyl spinors. –  Luboš Motl Mar 22 '13 at 14:06
If you were asking about the left-right asymmetry of amino acids and life etc., it just happens that they are also chiral and prefer the left-handed forms. The P violation in Nature actually gives these forms a slightly lower - preferred - energy but the difference is so low that it's generally believed that it's an accident that life is composed of left-handed molecules and not their images. At any rate, (animals and) people had to learn to distinguish left and right and invented the (random) words and adjectives they may learn from others, too. –  Luboš Motl Mar 22 '13 at 14:07