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Chiral leptoquarks and vector currents 
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#1
Jul1314, 03:44 PM

PF Gold
P: 2,892

In a comment http://motls.blogspot.com.es/2014/07...ent1479399237 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? 


#2
Jul1414, 12:52 AM

P: 842




#3
Jul1414, 10:53 AM

PF Gold
P: 2,892

Or I could imagine they are different of zero but they do not couple to electromagnetism, ie that their EM charge is zero. 


#4
Jul1414, 11:59 AM

P: 842

Chiral leptoquarks and vector currents
##\chi^{\dagger}_{\dot a} \bar\sigma^{\mu \dot a a} \chi_a## This is a fine vector current; it transforms like a 4vector 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. 


#5
Jul1414, 01:50 PM

PF Gold
P: 2,892




#6
Jul1614, 07:11 AM

PF Gold
P: 2,892

Ok I think that the point is that really is not a "vectorlike" current, but a "pure VA" 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 VA 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. 


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