# What will the Large Hadron Collider see?

The Large Hadron Collider (LHC) will start its first operation on September 10, 2008. The world of Particle Physics is all agog with excitement. What will the LHC see? I give below a list of possibilities.

Supersymmetry

All elementary particles, electrons, protons, neutrons, photons etc, are divided according to whether they follow Bose statistics (bosons) or Fermi statistics (fermions). Light particles, photons, are Bosons. Electrons are examples of fermions. In the 1980s some Physicists suggested that there might be an additional symmetry at higher energies than normally seen where all elementary particles follow a single symmetry. Bose and Fermi statistics are just the lower limits of this higher symmetry. This higher symmetry is known as supersymmetry. This has never been observed. The LHC experiment might tell us if there is supersymmetry.

What would be the consequence of seeing supersymmetry? It would imply that nature has produced many more elemenatry particles than observed today.

Higgs bosons

Higgs bosons are a standard ingredient in the standard model of elementary
particle Physics developed by Weinberg, Salam and Glashow in the late 1970s. The standard model is a combination of 2 relativistic quantum field theories, the electroweak theory and quantum chromodynamics. The electroweak theory of Weinberg, Salam and Glashow unites 2 forces, the weak nuclear force and the electromagnetic force. The quantum chromodynamics theory deals with the strong nuclear force. In order to understand the importance of the Higgs Bosons let us take a look at the Hamiltonian of the electroweak theory. Hamiltonian is roughly the energy of a system and governs the time evolution of a system. If the total Hamiltonian is H(total) and the weak nuclear force Hamiltonian is H(weak) and the electromagnetic Hamiltonian is H(electromagnetic) then we can write the total Hamiltonian as

H(total)=H(weak)+H(electromagnetic).

The H(total) is invariant under the SU(2) X U( 1) group. SU stands for special unitary group while U stands for unitary group. This formulation immediately raises a serious question. Why should we see today 2 separate forces, the weak force and the electromagnetic force, if H(total) is invariant under the combined SU(2) X U( 1) group? For example, currently H(electromagnetic) is found to be invariant under only U(1) group. If the equation given above is correct then we should see the combined electroweak force. It is at this point that three Physicists, including the English Physicist, Higgs, suggested adding a third term involving a scalar Boson now named Higgs boson. Then the H(total) equation changes to

H(total)=H(weak)+H(electromagnetic)+H(Higgs boson).

Now H(total) is not invariant under SU(2) X U(1) since the third term is not invariant. This explains why the symmetry is broken and we see 2 separate forces. The standard model is a well tested model except for the Higgs bosons which have not yet been observed. The LHC experiment might tell us if there are Higgs bosons. If no Higgs boson is found then Physicists will have to change the third term.

String theory

The string theory is touted by its adherents as an appealing candidate for a theory of all the forces of nature. The theory assumes that all elementary particles are composed of strings and are not point particles. This relativistic quantum field theory unites all 4 forces (electromagnetic, weak and strong nuclear force and gravity). It is also free from all infinities that are such a major pain in quantum field theories. The LHC might find evidence for strings.

New Dimensions

The string theory works best at dimensions higher than 4. Normally, it is assumed that we live in a 4-dimensional world (3 spatial and 1 time dimension). The LHC might find evidence for higher dimensions.

Wild Speculation

The LHC might find some exotic particle that has not yet been thought of by anyone..

Such a discovery would really set Particle Physics on fire.