LHC Science down to earth..

I've had a long read through a couple of particle physics books, in an attempt to fathom all this interest in the Higgs. Some thoughts, if you'll suffer it :

- it's actually the Higgs mechanism being sought, as up to a point the Higgs particle(s) are virtual.

- the expectation is of a single type of Higgs particle, with a particular rest mass below the energy equivalent of 1 Tera electronvolt.

- from special relativity any detected particle must have a specific relationship between it's momentum and energy ( assuming a given rest mass ). Because of the way this relationship appears when plotted in a certain way this is called the 'mass shell'.

- by colliding the beams of protons one can create energy 'bubbles' at the centre of the collision. Then analysing the products emerging one can hopefully deduce/refine a consistent set of points on a mass shell curve, and thus derive a rest mass estimate. However quantum mechanics adds a couple of curly bits ....

- firstly, there is an 'anarchic principle'. If one has given initial and final states ( particles going in and out from some region ), then any and all possible/legal ways to transition between must be included. These ways interfere with each other. That is, they can act together ( with the same sign ) or against each other ( with opposite sign ). The summation of these various transition modes yields numbers, that when squared give the probabilities of outcomes ie. fractions of observed events. These transitions may be infinite in number, are characterised by Feynman diagrams, and thus require some fancy maths to yield an answer.

- secondly, these transitions may involve 'virtual' particles. By definition these are never detected. A virtual particle is 'off mass shell' and thus can have any combination of momentum and energy. However all particles meeting at a vertex ( where lines intersect on a Feynman diagram ) still must collectively satisfy a host of conservation rules - mass/energy, momenta, charge and numerous quantum numbers. Via Heisenberg uncertainty ( as applied to energy ) there is an inverse quality to energy and time. Greater departures from the mass shell curve can only exist for shorter times, smaller departures for longer. So if I am an electron relatively far away from a proton, say, I can only be affected by low energy/momentum virtual photons : those that can exist for long enough to reach me, and not violate Heisenberg or be detected. If I am rather closer then I can be influenced by virtual photons with higher energy/momenta. This roughly explains why the electromagnetic force is greater as you get closer, and lesser with distance. Don't try this at home with quarks though. The strong force is more or less constant with separation, and the gluons have energy of self interactions and stuff .... see QCD lattice .... let's not go there. :-)

- thirdly, while not directly observable these virtual particles affect results. Or at least the assumption of their presence gives stunning concordance between theory and measurements. See the 'radiative corrections' to the magnetic moment of the electron. Or that some quarks and their properties were accurately predicted from such considerations - and then detected later! This is the equivalent of predicting an unknown planet by examining perturbations in the orbits of existing ones.

- fourthly, as one is summing transitions over a potentially infinite range of values then it is important that a finite answer is reached. One solution for the difficult sums ( those that become infinite ) has been a bit of a cheat, in my view. Two parts are defined to some finite measurable quantity. The first part is negatively infinite and the second is positively infinite. Neither are separately measurable. But when you add them together a finite number is reached which equals the observed quantity. This effectively comes down usually to matching the Feynman diagrams in particular groups. Personally I think this is trickery but it is a well recognised manouevre under the label of 'renormalisation'.

- this is where the Higgs seems to come in. If it exists then one can add it in to the diagrams and simplify the summations dramatically - this is the Higgs mechanism - and rely less on that renormalisation trickery. It ought to be involved with all particles with a non-zero rest mass. In fact the idea of 'rest mass' is a bit squirrely too. Given that Heisenberg says nothing can truly be at rest then perhaps one should say that rest mass refers to the energy axis intercept of the mass shell curve when you set momentum to zero.

- so I guess if they don't find evidence for the Higgs it will be disappointing on several levels. Obviously one can't then explain the mass values of known particles. But more deeply it embarrasses the whole program of using virtual particles in calculations, which has worked so well elsewhere, and I'd expect also prejudices an older problem - that of incorporating gravity too.

Cheers, Mike.

An article on today's NYTimes says "LHC fizzles". You can find a link to it in a LHC@home forum. The superconducting magnets are not working as expected. They were installed to give magnetic fields capable of curving the protons' trajectories into the 27 km tunnel which hosted the LEP collider, now shut, But protons are almost 2000 times heavier than electrons. CERN gambled on the superconducting technology in order to avoid to have to bore a new tunnel with a far larger radius. To gamble is to take risks,
Tullio

You are not missing much. They are not giving out any work and even the fora are quite silent,

LHC News Aug. 6th 2009