No, they don´t want to find God. They want to find the unbreakable particle. For long, the elementar particles were believed to be electrons, neutrons and protons. With better mass accelerators, they could break up neutrons and protons and see, that they are in turn made up with three different particles. Now we see, that those quarks (which make up protons, eleectrons and neutrons) are in turn again made up by different particles. That bugs those scientists and they want to get to the particle, that is elementary. Many other things hang on this, like the electronic elementary charge.
The bonding forces inside a proton or neutron are so strong, that it is impossible to seperate them long enough for study. You can´t even see or detect them directly.
I would guess, that photons are special concerning their double properties as wave and particles. You must not forget, that Einstein´s Theroy, that things get heavier, the faster they go has been proven correct. With light speed as limiting factor. You get infinitesmal heavy at lightspeed.
I admit it is a long time, i had Physics, but as far as I know, photons don´t have a charge. Or the lightwaves would bend in every electric field.
The E=mc2 formula gives us the information, which amount of energy we have to pour in to create matter and how much energy we get out when destroying matter.