Determination of the strong coupling constant, as

The strong coupling constant as
Each of the four fundamental forces in nature is characterised by a coupling constant, which determines the strength of the force. The weakest force is the gravitational force having the coupling constant G. The coupling constant of the electromagnetic force is named a and the coupling constant for the strong force is as. These coupling constants, which determine the strength of the different forces and processes are some of the most fundamental parameters in Nature.

2-jet events
The dominant process in e+e- annihilations to hadrons at high energies is the formation of two back-to-back jets of particles. This is due to the production of the Z particle which subsequently decays into a quark and an antiquark. The quarks rapidly move away from each other, but at distances of the order of or larger than 1 fm (1 fm = 10-15 m) the strong force prevents individual quarks from separating further. Instead new pairs of quarks and antiquarks are created. This process finally gives rise to a spray of particles, mainly mesons moving away in the direction of the original quark and antiquark.

3-jet events
Sometimes a high energy gluon is emitted by one of the quarks. Also the emitted gluon will give rise to a spray or jet of particles. This leads to the formation of a clear 3-jet event.

Three-jet events demonstrate the existence of the gluon

4-jet events
Both quarks can emit a high energy gluon resulting in 4-jet events. The probability that this will happen is relatively small.

The existence of the multi-jet events is a manifestation of the gluon and the strong force at work. The proportion of these events directly depend on the strong coupling constant as.

Determine the number of jets in the quark events. Determine the proportion of multi jet events. Use the ratio of number of three jet events with the number of two jet events to determine the strong coupling constant - one of the most fundamental parameters describing the strong interaction.

In approximately 70% of all e+e- collisions at a collision energy of 91 GeV, there are two or more jets produced. Two-jet events are due to two quarks (a quark and an antiquark) and three-jet events are due to two quarks and a gluon, where one of the quarks has radiated a gluon. Gluon radiation involves the strong force and the probability to produce an additional gluon is proportional to the strong coupling constant (as). Hence, if we count the number of two- and three-jet events, we can determine

as = k N3-jets / N2-jets

The determination of the number of particle jets in the events depends on the reconstruction program and in particular a parameter which determines the grouping of the particles into jets.
The number of two- and three-jet events dependens on this resolution parameter (d) of the clustering routine meaning that the constant, k, will have different values for different values of d. The dependence of k of d can be seen in the plot below


Figure 1, k as a function of d.


In the data available on these pages, d=5 GeV/c. In order to perform this experiment, you have to count the number of three-jet events and the number of two-jet events, decide the ratio, look up the constant k and find out the strong coupling constant. The RELATIVE error in as, i.e. Das/as could be estimated by

squareroot( 0.01 + 1/N3-jets + 1/N2-jets )
where 0.01 is the contribution from the uncertainty in k and the other factors are the contribution from the uncertainty in 3-jet and 2jet events.

For further reading, please refer to:
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and also:
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