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Can someone provide an expanded explanation on the statement that the Higgs field is already 3/4 detected?

Link to ref (@nic, sorry I left it off, do a quick search on Higgs to find the right location on page)

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from which source? Link please! – Nic May 26 '11 at 11:12 – Kostya Jul 4 '12 at 10:23
up vote 4 down vote accepted

The link you provided is a page of G t'Gooft on an official site and is quite interesting reading.

the statement you are wondering about is:

consider the scientific facts concerning the Standard Model. Fact is that the W+, W‾ and the Z boson each carry three spin degrees of freedom, whereas the Yang-Mills field quanta, which describe their interactions correctly in great detail, each carry only two. Those remaining modes come from the Higgs field. What this means is that three quarters of the field of the Higgs have already been found. The fourth is still missing, and if you calculate its properties, it is also clear why it is missing: it is hiding in the form of a particle that is difficult to detect.

He is stating that the Higgs' existence is based on the very strong verification of the Standard Model. There is strong experimental verification of the existence of W+ W- and Z The construction of the theory is such that since the gauge bosons exist one has 3/4 of the data needed to confirm the model, of which the existence of the Higgs is 1/4, counting up dimensions, of the necessary evidence/prediction. He is equating the existence of the Higgs to the validity of the SM in this statement.

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Nice answer and also clearification of the question itself. As you said, he links to the predictive power of the standard model. But isn't there any degree of freedom left which could explain why interactions look like given by SM but explains masses of particles differently? Greets – Robert Filter May 27 '11 at 6:26
@Robert Filter if you read the link of t'Hooft you will see that he himself considers more complicated models as far as the Higgs goes. At the moment string theories incorporate the SM as a package that discriminates physically possible modelling. I do not know if there exist string theories with alternate SM solutions. The SM is really a shorthand for a plethora of real data and the most economic way to assure that your higher theory is not contradicted by real data is to include the SM. If the Higgs is elusive, other avenues will be explored. – anna v May 27 '11 at 7:02

The Higgs field in the Standard Model is a scalar field that is a complex $SU(2)$ doublet, so it has 4 real scalar degrees of freedom. Electroweak symmetry breaking converts 3 of these 4 scalar degrees of freedom into longitudinal modes of 3 gauge bosons, which then become massive. These 3 massive gauge bosons all have been observed in collider experiments at CERN ($W^\pm$, $Z$ bosons). So we know for sure that they exist. The fourth degree of freedom - the Higgs particle - has not been observed.

In this sense it is true that 3/4 of the Higgs field have been observed, but it is not true that 3/4 of the Higgs particle have been observed, since the latter is precisely the missing quarter.

This statement reminds me a bit about a joke on the "early evidence for supersymmetry": nearly half of the particles of the minimal supersymmetric Standard Model have been observed already ;-)

Update after July 4th 2012: now all 4/4 are discovered - congrats to CMS and ATLAS!

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