Chiral leptoquarks and vector currents

In summary: Or we could recast the question in terms of representation theory. Usual electromagnetism, as well as color, needs only to use the real representations for quarks and leptons. While there is not an apriori reason for this, one feels a bit uneasy about calling electromagnetism to a theory with complex U(1) representations.
  • #1
arivero
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In a comment http://motls.blogspot.com.es/2014/07/cms-sees-650-gev-leptoquarks.html#comment-1479399237 to Motl's blog, there are some reference to "chiral leptoquarks".

I am guessing that this is an object which is not a Dirac fermion, ie it only exists one of the two chiral components of it.

If it is so, can this fermion have QCD and fermion electromagnetic vertices? Because if it is, say, charge -1/3 spin +1/2 and it emits a photon, it should change to spin -1/2 and still have the same charge, shouldn't it?
 
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  • #2
arivero said:
If it is so, can this fermion have QCD and fermion electromagnetic vertices?

Why not? The Standard Model, for example, is a chiral gauge theory. Before electroweak symmetry breaking, left- and right-handed quarks are separate, and both have strong and EM interactions. A vector current like ##\bar \psi \gamma^\mu \psi## doesn't change the chirality of the fermion, so there is no problem with a chiral fermion having vector current interactions.
 
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  • #3
The_Duck;4796933A said:
vector current like ##\bar \psi \gamma^\mu \psi##

But is it really a vector current? Two of the four components of this ## \psi ## do not exist, they are zero.

Or I could imagine they are different of zero but they do not couple to electromagnetism, ie that their EM charge is zero.
 
  • #4
arivero said:
But is it really a vector current? Two of the four components of this ## \psi ## do not exist, they are zero.

Sure; maybe you would prefer to write the vector current out of a two-component Weyl spinor ##\chi## where it would look like

##\chi^{\dagger}_{\dot a} \bar\sigma^{\mu \dot a a} \chi_a##

This is a fine vector current; it transforms like a 4-vector and you can write down a theory in which it is coupled to a gauge field:

##\mathcal L = \chi^{\dagger}_{\dot a} \bar\sigma^{\mu \dot a a} (\partial_\mu - i g A_\mu) \chi_a + \cdots##

You just have to be careful that any anomalies cancel.
 
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  • #5
The_Duck said:
it transforms like a 4-vector and you can write down a theory in which it is coupled to a gauge field

But the Langrangian is not parity invariant anymore, isn't it? Because if I get a electromagnetic lagrangian which is not parity invariant, I feel myself a bit dirty :shy:
 
  • #6
Ok I think that the point is that really is not a "vector-like" current, but a "pure V-A" one. This is, while being true that you can build a current V= ##\bar \psi \gamma^\mu \psi##, you can also build an "axial" current A= ##\bar \psi \gamma^\mu \gamma^5 \psi##. In electromagnetism, the combinations V+A and V-A are both of them different of zero. In this theory with a chiral fermion, one of the combinations, say V+A, is zero.

Or we could recast the question in terms of representation theory. Usual electromagnetism, as well as color, needs only to use the real representations for quarks and leptons. While there is not an apriori reason for this, one feels a bit uneasy about calling electromagnetism to a theory with complex U(1) representations.
 

1. What are chiral leptoquarks?

Chiral leptoquarks are hypothetical particles that are predicted by some theories beyond the Standard Model of particle physics. They are thought to be bosons that have both lepton and quark properties, and they come in left-handed and right-handed versions.

2. How are chiral leptoquarks different from regular leptoquarks?

Regular leptoquarks are predicted by some theories to have both lepton and quark properties, but they do not distinguish between left-handed and right-handed versions. Chiral leptoquarks, on the other hand, come in both left-handed and right-handed versions and interact differently with particles of different chirality.

3. What are vector currents in relation to chiral leptoquarks?

Vector currents are a type of interaction between particles that is described by the Standard Model. Chiral leptoquarks are predicted to have a strong coupling to vector currents, meaning they can interact with particles in a way that is similar to the interactions between the W and Z bosons and fermions in the Standard Model.

4. How are chiral leptoquarks relevant to current research in particle physics?

Chiral leptoquarks are currently being studied as a potential explanation for some anomalies observed in experiments at the Large Hadron Collider. They also play a role in theories attempting to explain the matter-antimatter asymmetry in the universe and the hierarchy problem in the Standard Model.

5. Are there any experiments planned to detect chiral leptoquarks?

There are currently no specific experiments designed to detect chiral leptoquarks, but they may be indirectly observed through their effects on other particles in high energy collisions. Future experiments at the Large Hadron Collider and other high energy facilities may also provide more evidence for their existence.

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