Should I capitalize the "G" in "God Particle" when referring to the Higgs Boson particle?

If you want to avoid a debate then the answer is clear call it by a name not associated with religion like the Higgs boson.

Seeing as there is also an effectively limitless number of these "god particles" (if the theory is right) then a title of "The God Particle" seems to be incorrect.

In this case god serves as an adjective to the noun particle. It could be interchanged with any other adjective such as hot or cold. God is not serving as a title here but rather as descriptor of its role. The capitalization of it would serve only to inflame and confuse the issue.

If you want to call it the God particle, then you'll need to capitalize it, since that's how it's recognized. If you don't want to capitalize "God" in the name of the particle, I would suggest that you use one of its other names (e.g. Higgs boson or champagne bottle boson)

That said, I don't believe you will get into any religious confusion by going with the flow on this term. Unless your writings are aimed toward uninformed individuals, no one will blink. And if you are writing to such people, just explain the name.

My first choice is to use Higgs boson and avoid God particle altogether as many physicists feel it's lazy and sensationalist. From a 2009 competition announced in the Guardian looking for a new name:

But back to the physicist in Manchester. He paused. He sighed. And then he said: "I really, really don't like it. It sends out all the wrong messages. It overstates the case. It makes us look arrogant. It's rubbish." He then added: "If you walked down the corridor here, poked your head into people's offices and asked that question, you would likely be struck by flying books."

Today it's the 80th birthday of Peter Higgs, the Edinburgh-based physicist whose work pointed to the existence of the particle in the early 1960s. In previous interviews, I've asked him what he makes of the name, God particle. He hates it. He worries it might offend people who are religious, but I think he hates it for other reasons too.

But if you feel you really must use it, then capitalise God but not particle. The Guardian newspaper style guide agrees:

God particle, Higgs boson, Large Hadron Collider

As it happens, Peter Higgs isn't even keen on Higgs boson. From the same competition article:

The particle became known as the Higgs boson in 1972 after Ben Lee, a former head of theoretical physics at Fermilab, used the name to describe the idea. Even Higgs often distances himself from the name, referring to it as the "so-called Higgs boson".

For physicists, the name seems to have stuck, but not for the media.

The competition winning entry was the champagne bottle boson:

"The bottom of a champagne bottle is in the shape of the Higgs potential, and is often used as an illustration in physics lectures. So it's not an embarrassingly grandiose name, it is memorable, and has some physics connection too," the judges' spokesman said.

The so-called "wine bottle potential" is also called the "Mexican hat potential" and is a critical aspect of the Higgs mechanism.