Question

Within three years after it begins operation, the proton beam at the Large Hadron Collider at CERN is expected to reach a luminosity of \(10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) (this means that in a \(1-\mathrm{cm}^{2}\) area, \(10^{34}\) protons encounter each other every second). The cross section for collisions, which could lead to direct evidence of the Higgs boson, is approximately \(1 \mathrm{pb}\) (picobarn). [These numbers were obtained from "Introduction to LHC physics," by G. Polesello, Journal of Physics: Conference Series \(53(2006), 107-116 .]\) If the accelerator runs without interruption, approximately how many of these Higgs events can one expect in one year at the LHC?

Short answer

Answer: Approximately 315,360 Higgs events.

Step-by-step solution

Find the number of collisions per second

To find out the number of collisions per second, we should multiply the luminosity by the cross-section. The luminosity is \(10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) and the cross-section is given as 1 pb. We should convert picobarns (pb) to square centimeters (cm²) for consistency. One picobarn is equal to \(10^{-36}\mathrm{~cm}^2\). Number of collisions per second = Luminosity × Cross-section = \(10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) × \(1 \mathrm{pb}\) = \(10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) × \(10^{-36} \mathrm{~cm}^{2}\) = \(10^{34-36} \mathrm{~s}^{-1}\)

Calculate the number of seconds in a year

As there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year, the number of seconds in a year can be calculated as follows: Number of seconds in a year = 60 seconds/minute × 60 minutes/hour × 24 hours/day × 365 days/year = 31,536,000 seconds/year

Determine the number of Higgs events in a year

We can now multiply the number of collisions per second with the number of seconds in a year to find out the number of Higgs events in a year. Number of Higgs events in a year = Number of collisions per second × Number of seconds in a year = \(10^{-2} \mathrm{~s}^{-1}\) × 31,536,000 seconds/year = 315,360 Higgs events/year Approximately, 315,360 Higgs events can be expected in one year at the LHC if it runs without any interruptions.

Key concepts

Large Hadron Collider

The Large Hadron Collider (LHC) at CERN is the world's largest and most powerful particle accelerator. It consists of a 27-kilometer ring of superconducting magnets and a number of accelerating structures to boost the energy of particles along the way.

Inside the LHC, two high-energy particle beams travel at close to the speed of light before they are made to collide. The LHC is designed to collide protons with protons, as these are among the simplest particles with an internal structure, allowing physicists to test the predictions of different theories of particle physics and high-energy physics.

Since its start, the LHC has been at the forefront of scientific discovery, including the detection of the Higgs boson in 2012, a fundamental particle associated with the Higgs field, which gives other particles their mass. The LHC enables physicists to recreate the conditions just after the Big Bang in an attempt to answer fundamental questions of science and the universe itself.

proton-proton luminosity

Luminosity is a critical factor in the operation of particle colliders like the LHC. It is a measure of the number of collisions that occur in a certain amount of time and a given cross-sectional area.

For proton-proton collisions, the luminosity indicates how many protons pass through a specific area, usually a square centimeter, every second. High luminosity is vital because it increases the chances of observing rare processes, such as the creation of Higgs bosons. A higher proton-proton luminosity means that more collisions are happening, which leads to more data and better statistics for experiments.

In the context of the LHC, having a luminosity of \(10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) is exceptionally high. This enables the detection of events with very small probabilities. Understanding luminosity helps us appreciate the challenges and engineering marvels behind measuring and detecting particles as elusive as the Higgs boson.

cross-section calculation

A cross-section is a probability measure that represents the likelihood of a specific type of particle collision occurring. In the context of particle physics, it's analogous to the effective area that one particle presents to another for a specified interaction.

In cross-section calculations, one commonly used unit is the barn, which is \(10^{-24} \mathrm{~cm}^2\). A picobarn (pb) is one-trillionth of a barn, or \(10^{-36} \mathrm{~cm}^2\). The cross-section value helps scientists predict how many collisions will result in the occurrence of a particular event, like the production of a Higgs boson.

By multiplying the cross-section with the luminosity, scientists can estimate the number of interactions that lead to the desired outcome. This is a fundamental calculation in particle physics that underpins experimental predictions for particle collision outcomes.