There's still something that doesn't quite work with this argument as far as I can see. (I am a particle experimentalist and not a theorist, but hear me out. I'd be very interested to see if you have an argument for why the following idea doesn't work.) I understand that mass is necessary for flavour oscillations, but my issue is with the argument of SR banning any time dependence for massless particles. Sure there's no "Electric photon" or "Magnetic photon" as you say, but there IS a distinct, measurable, time dependent difference between, say, a horizontally and a vertically polarized photon. Say I have a circularly polarized photon fired at a horizontal filter. The probability of that photon passing the filter is dependent on the photon's time of flight before hitting it. It seems to me like I could experimentally measure a time dependent property of the photon: The same experiment performed at different times on an identically prepared photon yields different results. So how does this "mesh" with the SR argument? Perhaps you're being too general?

Many of the other replies are in the right spirit, but are also WRONG on an important point. Short answer: It's all about probability! Ok, to clarify. It is true that to create a particle you need a collision energy of at least its rest-mass energy. But this is _NOT_ the reason for the increase in energy! (At least not directly) Those who have said that the LHC was designed to find the Higgs, and operates above 1 TeV for the first time and then concluded that this means that the Higgs is heavier than 1 TeV are misguided. The Higgs is in fact likely between 110-165 GeV-ish in mass from previous experiments. So why the increase in energy? Well, we're producing an incredible number of collisions, but the vast majority of them don't produce a Higgs boson. It's just not that likely. When two particles collide, it is impossible to say exactly what particles will be created. You can only calculate the PROBABILITY of a certain particle being created. This is in precisely the same spirit as only being able to find the probability of a particle's position in elementary quantum mechanics. So to finally answer your question: When two particles collide, the PROBABILITY of the collision producing a Higgs boson (We call this the 'cross-section') increases with energy. We naturally combine this with a vast increase in the number of collisions per second. More collisions + higher probability per collision = much better chances of creating a bunch of Higgses.

You're missing a vital point. The exact same interactions can be achieved in proton-proton or proton-antiproton collisions. The Higgs, if it exists, can most certainly be produced in the LHC's proton-proton collisions, and high-energy cosmic ray particles can indeed produce collision energies higher than either the LHC or Tevatron can. The key point is that protons (or anti-protons) are NOT fundamental particles. As you probably know they are made up of quarks and gluons. What you may not know is that on the energy scales of these collisions it is not meaningful to say that a proton is made of 3 'normal matter' quarks (2 ups and 1 down). It contains these 3 so-called valence quarks as well as a 'sea' of gluons, other quarks, and - importantly - ANTI-quarks, all collectively referred to as 'partons'. When 2 protons collide in a high energy collision, what is REALLY colliding is either a pair of gluons (one from each), or a quark from one proton and a sea ANTI-quark from the other. The lesson to take away is that even in 'normal-matter' hadron collisions - in the LHC or from cosmic rays - it is still matter-antimatter annihilation at work. A last note: You may easily wonder WHY then the Tevatron collides protons and antiprotons while the LHC uses only protons. Since in the first case there are valence anti-quarks in one of the colliding particles, it is more likely that any given collision will give you the high-energy release wanted (not every collision does!). It is, however, much easier to produce protons than anti-protons! The LHC's approach is to simply produce many, many more collisions per second - easier to do with just protons. The result is more of the desired high-energy events per second than would be attainable with the limited supply of anti-protons.