Luminosity and timeline

5.2 Luminosity and timeline

As discussed in Chapter 3, the number of scattering events we expect is the product of the scattering cross section and the luminosity ( $L$ ) of the particle beams (Eq. 3.2.16). Cross sections are typically given in units of barn (b), where $1 b = 1 0^{- 28} m^{2}$ , and thus the luminosity often in inverse barns (b $^{- 1}$ ). For a circular collider, the instantaneous luminosity is given by [34]:

L = \frac{N_{1} N_{2} n_{b} f_{rev}}{A},

(5.2.1)

where $N_{1}$ and $N_{2}$ are the number of protons in each bunch, $n_{b}$ is the number of bunches, $f_{rev}$ is the revolution frequency of the beams, and $A$ is the effective beam overlap area at the interaction point. This is why the LHC design aims to maximize the number of protons per bunch, the number of bunches, and the frequency of bunches, while focusing and aligning the beams as much as possible at the interaction point. The instantaneous luminosity of pp collisions at the LHC has increased steadily from a peak of $2.1 \times 1 0^{32}$ $cm^{- 2} s^{- 1}$ in 2010 to around $2.5 \times 1 0^{34}$ $cm^{- 2} s^{- 1}$ in 2022–24 [36]. Higher luminosity also leads to a higher rate of simultaneous pp collisions during a single bunch crossing, called pileup, which results in background noise to the detectors. As shown in Figure 5.6, the average rate of pileup in CMS has ranged from $10$ in 2011 to around $57$ in 2024.

The total luminosity delivered by the LHC is the integral of the above over time, called the integrated luminosity, and is shown in Figure 5.7 along with the projection up to 2041.¹ So far, the LHC has delivered around 60 $fb^{- 1}$ of integrated luminosity at $7$ or $8 TeV$ COM to the CMS and ATLAS experiments in Run 1, 138 $fb^{- 1}$ at $13 TeV$ in Run 2, and is currently aiming for around 300 $fb^{- 1}$ at $13.6 TeV$ in Run 3. After this, (tentatively) between 2026 and 2030, the LHC will undergo a significant upgrade aiming to deliver an order of magnitude more luminosity in Runs 4–6, between $5$ – $7 \times 1 0^{34}$ $cm^{- 2} s^{- 1}$ instantaneously, integrated to around 3000 $fb^{- 1}$ ! This is called the High-Luminosity LHC (HL-LHC) upgrade [172] (see Figure 5.8), and is expected to allow access to rare processes such as Higgs boson pair production; however, it also entails major accelerator, detector, and computational challenges to effectively deliver and exploit the increased luminosity.

Figure 5.6. Mean number of interactions per crossing (pileup) in CMS between 2011–2024, reproduced from Ref. [36].

Figure 5.7. Integrated luminosity delivered by the LHC so far and the projection up to 2041, reproduced from Ref. [37].

Figure 5.8. The LHC / HL-LHC operation and upgrade plan, reproduced from Ref. [38].

¹Note that this projection has not been updated to reflect the decision made in September 2024 to extend Run 3 up to 2026 and delay the start of Run 4 to 2030.