The Higgs Particle
The Higgs Particle
The Large Hadron Collider (LHC) at CERN is becoming operational this month (September 2008). A prime objective of the biggest and most expensive scientific experiment in history is detection of the Higgs particle, speculated to be the generator of mass for elementary particles. This would, in fact, be the last missing piece of the Standard Model. The discovery might occur sometime during 2009 or 2010.
This Demonstration gives a highly simplified account of the proposed Higgs mechanism that might produce the neutral scalar Higgs boson . The motivation was a puzzle arising in a unification of electromagnetic and weak interactions as a SU(2)×U(1) "electroweak" gauge group mediated by four massless vector bosons, according to a theory developed by Sheldon Glashow, Steven Weinberg and Abdus Salam (they shared the 1979 Nobel Prize in Physics). Whereas electromagnetic interactions are carried by massless photons , weak interactions, such as radioactive decays, involve interchange of massive bosons, with masses of the order of 80 GeV. However, putting these masses in "by hand" would spoil the symmetry and gauge invariance of the theory. It is important to note that massless vector bosons have two possible transverse polarization states, such as the right- and left-handed polarizations of photons. Massive vector bosons have three polarization states, with a longitudinal mode added.
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Peter Higgs and several others proposed that all of space is permeated by an invisible Higgs field , with four scalar components (actually a doublet of complex scalars). The symmetry of the Higgs field is spontaneously broken when its (four-dimensional) potential energy surface is distorted into the shape of a "Mexican hat", of the form , with negative. The Higgs field thereby acquires a vacuum expectation value expressed by the parameter , estimated as 250 GeV. Three of the scalar components are thereby "gauged away"—more picturesquely described as being "eaten"—by three of the massless electroweak bosons, to turn into their third polarization states. This produces three massive vector bosons, designated , , and . The remaining electroweak boson remains massless. At the same time, the remaining Higgs field component turns into the putative massive Higgs boson .
ϕ=,,,
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2
ϕ
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ϕ
Vϕ=ϕ+
†
ϕ
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†
ϕ
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λϕ
†
ϕ
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v=
-λ
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+
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The neutral bosons and form linear combinations and =-sinB+cos, such that only the experiences the weak interaction while remains the massless photon. The weak mixing angle or Weinberg angle is estimated to have a value such that ≈0.223. The Higgs mechanism predicts the masses GeV and GeV (, the electron charge, represents the electromagnetic coupling constant with ). The Higgs mass is given by , with its value unknown, since the individual values of and are undetermined. Estimates which assume the validity of the Standard Model suggest a Higgs boson in the mass range 115-125 GeV.
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γ=cosB+sin
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sin
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M()=≈80.4
±
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2sin
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M()=≈91.2
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2sin
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cosθ
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α=≈
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4π
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137
M()=
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Supersymmetric extensions of the Standard Model predict multiplets of Higgs bosons. There is also the possibility that the Higgs particle does not even exist! Alternatives to the Higgs mechanism include theories proposing technicolor, composite and bosons, or a top-quark condensate. The next couple of years will be very exciting for particle physics.
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