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Spontaneous symmetry breaking, an insight.

March 25, 2010

Mohan, mdashf

The Nobel committee decided to award the 2008 Nobel Prize to the Japanese Physicists, Yoichiro Nambu, Kobayashi and Masukawa for their theoretical works leading to our understanding of a phenomena called spontaneous symmetry breaking.
Nambu immigrated to the US and became a naturalized citizen while Kobayashi and Masukawa retained their Japanese citizenship. Nambu had corroborated the idea of spontaneous symmetry breaking from the theory of superconductivity to particle physics. But Kobayashi and Masukawa along with Cabibbo had formulated this in terms of a model of quark interaction leading to several measurable angles.

These angles represent “mixing” or rotation of meson systems from one type of eigen-states to another. A meson is a “bound” state of 2 different types of quarks and an eigen-state is a complex number function or wave function amplitude with a definite value for the physical properties of the quark or meson system. eg the meson can be either measured in a flavor eigen-state or a mass eigen-state. In the former it’s flavor [quark content] is definitely known and in the latter its mass can be measured definitely.

A transformation or rotation or mixing between these two states is caused by an interaction or force in this case the weak-force. This force was thought to be symmetrical under a reversal in charge and parity [CP] of the wave-function state.

But its found that this symmetry is broken or that such a symmetry of CP does not exist. This is called CP violation. While Kobayashi and Masukawa had proposed such a violation or symmetry breaking through their mathematical work, the experimental evidence was found in the K-meson system [or Kaons]. The Belle and BaBar experiments found the evidence in the B-mesons.

A spontaneous symmetry breaking is akin to the symmetry breaking in the following situation. If you hold a sharpened pencil on a plain surface and release your hand, for a very small time, howsoever small, the pencil stands on the plain upright, and then falls in a specific direction.

Before the pencil falls, it stands upright because of the symmetrical situation provided by Gravity. No particular direction is chosen over another. But when the pencil falls it takes a particular direction and obviously the symmetry of the situation is lost.

If we “look” a little deeper into this its easy to find the reason. While the gravity is symmetrical, the fluctuation which may be present in the air which is much smaller in scale compared to the gravity can push the pencil in a particular direction.

While the air fluctuation is not a part of gravity we can’t measure the gravity precisely enough. A little fluctuation in that force can cause a spontaneous loss of symmetry in the so called ground state or minimum energy configuration.

In the realm of subatomic particles and their interaction fluctuations are present as higher order [lower in strength] perturbations of the force field and provide an asymmetry or a loss of symmetry.

While in idea this sounds like a simple explanation the physicist’s job is to measure the forces and the underlying processes so precisely as to measure this asymmetry. Particle Physics experiments measuring such processes do exactly that.

Furthermore it can be understood that spontaneous symmetry breaking is not a phenomenon confined to only CP violation type asymmetries. If there is an asymmetry in any process it can come because of presence of an additional small component of a force.

An experimentalist should try to measure any type of asymmetry and small forces that may occur in a particle production process. One such measurement which the author has tried to perform is the so called KS0-KL0 asymmetry or the asymmetry in the production of KS0 and KL0 from a D0 meson.

This process does not involve a significant CP violation but a significant interference between Cabibbo-Favored and Suppressed amplitudes.

This process may be akin to a process of spontaneous symmetry breaking.

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