Higgs-Boson/Gravition Existence

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How will the LHC prove the existence of these two particles? How is it possible to prove they exist, and what means will they use to find out?
 
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Basically, you take physics models with and without the respective particle, and calculate expected experimental outcomes. Then, you compare the calculations to the actual outcome of the experiment. Since you already mentioned the name of the current main experiment, I don't really know how to explain "what means they use". There is a lot of computer simulation (both for the predictions and for the simulation of the experimental setup) and a lot of statistical data analysis techniques involved.
 
The energy signature of the Higgs is thought to be in a certain MEv range which the LHC can reach. They will search in the collision debris for a particle with the properties of the Higgs. There is no quantum theory of Gravity so the graviton does not have any theoretical basis at present.
 
cosmik debris said:
The energy signature of the Higgs is thought to be in a certain MEv range which the LHC can reach. They will search in the collision debris for a particle with the properties of the Higgs...
They actually search for combinations of particles the Higgs could decay into. It doesn't live long enough to be observed directly.

The hard part is that the same combinations of decay particles can also occur as the results of other, already known SM interactions. Therefore, as Timo says, they have to measure the actual occurrence rates very accurately and compare these with models that do or don't incorporate the Higgs, and if so assume different masses for it. The marginal difference in occurrence rates is not large, this is why they are having to collect so much data to clearly identify which predicition the facts actually match.

The MeV range is actually GeV, incidentally.
 
cosmik debris said:
There is no quantum theory of Gravity so the graviton does not have any theoretical basis at present.

This actually isn't true at all. We know that in any quantized theory of gravity, we require things to reduce to GR in the appropriate non-quantum limit. From what we know about gravitational waves in GR (of which the graviton is the quantization), we know the graviton must be a massless, spin 2 particle. Of course one can argue for other theories of gravity which have more exotic gravitational wave spectra, but that's not really the point; in these theories too you can make similar statements.

It's rather analogous to classical EM and QED. Before we had a theory of QED, it did not at all mean that we knew nothing about the photon. Based on the non-quantum limit you can make general statements about what the quantized theory must do.

But, it's completely ridiculous to expect to observe individual gravitons. The gravitational wave astronomers have been trying for decades and still haven't made any detections of the WAVES. A naive calculation shows that there's something like 10^30 gravitons in one of these (extremely feeble) gravitational waves, which basically shows that detecting the individual graviton is hopeless.
 
AdrianTheRock said:
They actually search for combinations of particles the Higgs could decay into. It doesn't live long enough to be observed directly.
...
The MeV range is actually GeV, incidentally.

Thanks for the correction, and yes GeV is what I meant.
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...

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