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Why magnetic monopole has't been shown in the particle physics's Standard Model context?

+ 4 like - 0 dislike
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For various reasons, experts, since [Dirac](http://rspa.royalsocietypublishing.org/content/133/821/60), believe that a [unified field theory must have a magnetic monopole](https://cds.cern.ch/record/246430?ln=en). For example, [Polyakov](https://cds.cern.ch/record/246430?ln=en) said: "I am quite certain that magnetic monopoles really exist. How, when and if they will be found is another matter."

Strangely, thinking that **so many elementary particles in the Standard Model, we don't have any particle carry any U(1) magnetic monopole charge** --- which should exist for a compact Abelian U(1) gauge theory. For examples, quarks and leptons, they can carry various charges of the electric U(1)$_{em}$ and the weak charge SU(2)$_{weak}$; and the quarks also carry the strong charge, the SU(3)$_{strong}$ colors. Again, we still don't have any elementary particles carrying the U(1) magnetic monopole charge.

>For a theoretical purpose, **is it possible to have an elementary particle like quarks and leptons in the Standard Model attached a U(1) magnetic monopole?** 

>If yes, how could we **make the Standard Model becomes consistent under the U(1) magnetic monopole attached** to some known quarks or leptons?

>If no, is that the no-go reason due to (1) the fact of the [gauge-gravity anomaly-cancelation](https://en.wikipedia.org/wiki/Anomaly_(physics)#Gauge_anomalies) in Standard model, such as a simple version of the [Green–Schwarz mechanism
 for the Standard model](https://en.wikipedia.org/wiki/Green%E2%80%93Schwarz_mechanism)? Or, is the no-go that due to the fact that the **U(1) magnetic monopole is actually a topological charge, so it cannot be locally gauge-invariant, and it can not be created by a local operator**? Or something else?

The known anomaly cancellation for the Standard model is described, for example, in Peskin and Schroeder Chap 20.2:

asked Nov 20, 2016 in Theoretical Physics by wonderich (1,400 points) [ no revision ]

Just a comment:

Due to the Dirac quantization condition $ eq=2\pi$ you can not have both, particles with electric charge $e$ and particles with the magnetic charge $q$ of masses around the electroweak scale. Having the conventional standard model where the electrically charged particles are fundamental, the magnetically charged particles have to be assumed very massive.

On the other hand mathematically, a standard model including a magnetoweak symmetry group where the magnetically charged particles take to role of the electrically charged particles and the electrically charged particles are (with current technology) unobservably heavy is possible too in principle.

Thanks Dilaton for the nice comment. btw, we also know that there are objects called dyons that contains both electric charge and magnetic monopole. And we also know that the Witten effect at the nonzero theta term, gives rises to such dyons as fundamental particles. I wonder that does your comment hold to be true in this setting, too? Thank you again!

@Idear, interesting! Can you point to a reference that explains how dyons are created by the Witten effect? At what energy scale is this expected to happen?

As in our univers conventional QED is weakly coupled and an assumed quantum magneto dynamics would therefore be strongly coupled, I could imagine that both coupling constants run to the effect that they would meet at a higher than EW energy scale. And this would then also be the parameter space where the dyons can live (?)...

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