How bright is the LHC?

The LHCb Collaboration has published the results of a luminosity calibration with a precision of 1.12%. This is the most precise luminosity measurement achieved so far at a bunched-beam hadron collider.

The absolute luminosity at a particle collider is not only an important figure of merit for the machine, it is also a necessity for determining the absolute cross-sections for reaction processes. Specifically, the number of interactions, N, measured in an experiment depends on the value of cross-section σ and luminosity L, N = σL, so the precision obtained in measuring a given cross-section depends critically on the precision with which the luminosity is known. The luminosity itself depends on the number of particles in each collider beam and on the size of overlap of both beams at the collision point. At the LHC, dedicated instruments measure the beam currents, and hence the number of particles in each colliding beam, while the experiments measure the size of overlap of the beams at the collision point.

A standard method to determine the overlap of the beams is the van der Meer scan, invented in 1968 by Simon van der Meer to measure luminosity in CERN’s Intersecting Storage Rings, the world’s first hadron collider. This technique, which involves scanning the beams across each other and monitoring the interaction rate, has been used by all of the four large LHC experiments. However, LHCb physicists proposed an alternative method in 2005 – the beam-gas imaging (BGI) method – which they successfully applied for the first time in 2009. This takes advantage of the excellent precision of LHCb’s Vertex Locator, a detector that is placed around the proton–proton collision point. The BGI method is based on reconstructing the vertices of “beam-gas” interactions, i.e. interactions between beam particles and residual gas nuclei in the beam pipe to measure the angles, positions and shapes of the individual beams without displacing them.

To date, LHCb is the only experiment capable of using the BGI method. The technique involves calibrating the luminosity during special measurement periods at the LHC, and then tracking relative changes through changes in the counting rate in different sub-detectors. However, the vacuum pressure in the LHC is so low that for the technique to work with high precision, the beam–gas collision rate was increased by injecting neon gas into the LHC beam pipe during the luminosity calibration periods. This allowed the LHCb physicists to obtain precise images of the shapes of the individual beams, as illustrated in the left and middle graphs of the figure, which unravelled subtle but important features of the distributions of beam particles. By combining the beam–gas data with the measured distribution of beam–beam interactions, which provides the shape of the luminous region (the right graph in the figure), an accurate calibration of the luminosity was achieved.

The beam–gas data also revealed that a small fraction of the beam’s charge is spread outside of the expected (i.e. “nominal”) bunch locations. Because only collisions of protons located in the nominal bunches are included in physics measurements, it was important to measure which fraction of the total beam current measured with the LHC’s current monitors participated in the collisions, i.e. contributed to the luminosity. Only LHCb could measure this fraction with sufficient precision, so the results of LHCb’s measurements of the fraction of charge outside the nominal bunch locations – the so-called “ghost” charge – were also used by the ALICE, ATLAS and CMS experiments.

For proton–proton interactions at 8 TeV, a relative precision of the luminosity calibration of 1.47% was obtained using van der Meer scans and 1.43% using beam–gas imaging, resulting in a combined precision of 1.12%. The BGI method has proved to be so successful that it will now be used to measure beam sizes as part of monitoring and studying the LHC beams. Dedicated equipment will be installed in a modified region of the LHC ring near Point 4. This system, dubbed the Beam-Gas Vertexing system (BGV), is being developed by a collaboration from CERN, EPFL and RTWH Aachen. It includes a gas-injection system and a scintillating-fibre tracker telescope, which are expected to be commissioned with beam in 2015.