Register to reply 
Chiral leptoquarks and vector currents 
Share this thread: 
#1
Jul1314, 03:44 PM

PF Gold
P: 2,902

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: 860




#3
Jul1414, 10:53 AM

PF Gold
P: 2,902

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: 860

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: 2,902




#6
Jul1614, 07:11 AM

PF Gold
P: 2,902

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. 


Register to reply 
Related Discussions  
Magnetic vector potential for antiparallel currents  Advanced Physics Homework  3  
Chiral currents of a Dirac plane wave  Advanced Physics Homework  0  
Vector and Axial vector currents  Advanced Physics Homework  1  
Currents in two same direction, they attract ?currents are going in opposite repel?  General Physics  10  
Vector currents, vector fields and bosons  Quantum Physics  2 