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W 2 = 2 [ E 1 E 2 + ( p 1 c ) ( p 2 c ) ] + ( m 1 c 2 ) 2 + ( m 2 c 2 ) 2 ,

where E 1 and E 2 are the total energies of the incoming particles (1 and 2), p 1 and p 2 are the magnitudes of their momenta, and m 1 and m 2 are their rest masses.

Creating a new particle

The mass of the upsilon ( ϒ ) meson ( b b ) is created in a symmetric electron-positron collider. What beam energy is required?

Strategy

The Particle Data Group has stated that the rest mass energy of this meson is approximately 10.58 GeV. The above expression for the center-of-mass energy can be simplified because a symmetric collider implies p 1 = p 2 . Also, the rest masses of the colliding electrons and positrons are identical ( m e c 2 = 0.511 MeV ) and much smaller than the mass of the energy particle created. Thus, the center-of-mass energy ( W ) can be expressed completely in terms of the beam energy, E beam = E 1 = E 2 .

Solution

Based on the above assumptions, we have

W 2 2 [ E 1 E 2 + E 1 E 2 ] = 4 E 1 E 2 = 4 E 1 2 .

The beam energy is therefore

E beam E 1 = W 2 .

The rest mass energy of the particle created in the collision is equal to the center-of-mass energy, so

E beam 10.58 GeV 2 = 5.29 GeV .

Significance

Given the energy scale of this problem, the rest mass energy of the upsilon ( ϒ ) meson is due almost entirely due to the initial kinetic energies of the electron and positrons. This meson is highly unstable and quickly decays to lighter and more stable particles. The existence of the upsilon ( ϒ ) particle appears as a dramatic increase of such events at 5.29 GeV.

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Check Your Understanding Why is a symmetric collider “symmetric?”

The colliding particles have identical mass but opposite vector momenta.

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Higher beam energies require larger accelerators, so modern colliding beam machines are very large. The LHC, for example, is 17 miles in circumference ( [link] ). (In the 1940s, Enrico Fermi envisioned an accelerator that encircled all of Earth!) An important scientific challenge of the twenty-first century is to reduce the size of particle accelerators.

Particle detectors

The purpose of a particle detector    is to accurately measure the outcome of collisions created by a particle accelerator. The detectors are multipurpose. In other words, the detector is divided into many subdetectors, each designed to measure a different aspect of the collision event. For example, one detector might be designed to measure photons and another might be designed to measure muons. To illustrate how subdetectors contribute to an understanding of an entire collision event, we describe the subdetectors of the Compact Muon Solenoid (CMS), which was used to discover the Higgs Boson at the LHC ( [link] ).

Figure shows a transverse slice through CMS. A section of it is expanded. At the center is a silicon tracker. The layers, moving outward from the center are labeled: Electromagnetic calorimeter at less than 1 m from center, Hadron Calorimeter at roughly 1.5 m to 2 m from center, Superconducting solenoid at roughly 2.5 m to 3.5 m from center and Iron return yoke interspersed with Muon chambers at roughly 3.5 m to just over 7m from center. Two lines from the center to the electromagnetic calorimeter are labeled Photon and Electron. Two lines form the center to the Hadron Calorimeter are labeled Neutral Haron example neutron and Charged Haron example Pion. A line labeled Muon extends from the center to the outermost layer. Within the second layer is a small circle labeled 4T. Within the last layer is a small circle labeled 2T.
Compact Muon Solenoid detector. The detector consists of several layers, each responsible for measuring different types of particles. (credit: David Barney/CERN)

The beam pipe of the detector is out of (and into) the page at the left. Particles produced by pp collisions (the “collision fragments”) stream out of the detector in all directions. These particles encounter multiple layers of subdetectors. A subdetector is a particle detector within a larger system of detectors designed to measure certain types of particles. There are several main types of subdetectors. Tracking devices determine the path and therefore momentum of a particle; calorimeters measure a particle’s energy; and particle-identification detectors determine a particle’s identity (mass).

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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