Explaining the naturalness problem April 27, 2007Posted by dorigo in internet, news, physics, science.
I just read the insightful slides presented by Michelangelo Mangano at IFAE 2007 last month, in his plenary talk titled “Stato e prospettive della Fisica delle Particelle” (Status and prospects of Particle Physics). His slides are in English, and you are well advised to have a look at them.
Michelangelo points out from the outset what are the possible outcomes of the searches for the Higgs boson at the LHC. He foresees a situation when:
- the SM Higgs is found, it is light, and everything goes well. In that case, a pressing question to answer will be the one of the naturalness (see below).
- the SM Higgs is not found below 0.8-1 TeV of mass. If that happens, it may be because of either:
- cross section below SM predictions, and that is New Physics;
- Visible branching ratios below SM values, and that is also New Physics;
- H exists but has a mass above 800 GeV, and that, too, means New Physics.
Talking about the naturalness problem, Michelangelo puts things in a way even me and you can understand. He basically says: radiative corrections to the Higgs mass amount to a sum of different terms whose value gets multiplied by the square of the energy at which the Standard Model breaks down. If that energy scale is as large as the Planck mass (the scale at which quantum gravity enters the game), then one has to hypothesize that the several correction terms cancel out to a part in 10^34 (a hundred billionths of a billionth of a billionth of a billionth), if one is to make the Higgs mass smaller than a lead brick.
To see how likely that is (and here is the part where you get to touch things with your hand), he proposes you to do the following experiment: ask 10 friends to tell you a random number of their liking between -1 and +1, but make it a irrational number. Then, add the ten numbers. How likely is it that you come up with a number as small as 10^-32 ?
I happen to know the answer: it is the hell of a small chance.
Michelangelo’s point is that you would rightly conclude that your friends played you a trick, and agreed in advance on the numbers they’d give you!
And that is what theorists think too: theorists feel that the accurate cancellation of Higgs mass corrections cannot be an accident.
The naturalness problem thus becomes the basis to discuss what solutions appear to make things more credible. All these solution have a thing in common: they tie the Higgs mass to some symmetry that protects it against the quadratic divergence drawn by the Planck mass scale.
If you read this post up to here, you are strongly advised to jump to his talk… No point for me to report more of it, adding to it my own fallacies.