Taking a closer look at LHC - LHC p collisions

LHC p collisions

Taking a closer look at LHC

LHC works with proton (or lead nuclei) that are accelerated to speeds close to the speed of light. By letting very fast and energetic particles collide in the center of detectors, the scientists can extract information about matters smallest components. In such collisions are new particles created, which will provide information about the secrets of particle physics. In some sense the big accelerators can be said to be today's "super microscopes".

In the LHC proton bunches are accelerated (over a period of 25 minutes) to their peak 7-TeV energy, and finally circulated for 10 hours while collisions occur at the four intersection points.

Between each consecutive bunch there will be 7,5 m. So, with a circumference of 27 km there should be:

26659 / 7,5 ~ 3550 bunches.

To get a correct sequence of bunches injected into the ring and to be able to insert new bunches when non-useful ones are extracted it´s necessary to allow enough space for that.

The effective number of bunches per beam is 2808

For a more complete discussion click here....

The larger is the crossing angle, θ_c , the semaller is the area of overlap ant therefore smaller is the possibility of collision. It si worth noting that while σ_z is constant over the machine (~7,5 cm), σ_x varies and assumes its minimum in the Interaction Points.

For the calculation we take into account the fact that there are 1,15·10¹¹ protons per bunch (in LHC Run 3 -from 2022 to 2026- up to 1.8 × 10¹¹ protons per bunch are reached). In order to understand this value, it should be noted that 1 cm³ STP of hydrogen has ~10¹⁹ protons).

Each bunch gets squeezed down (using magnetics lenses) to 16 x16 μm section at an interaction point, where collisions take place.

The "volume occupied" for each proton in the inteaction point is:

(74800x16x16) / (1,15·10¹¹) ~ 10^-4 μm³

That’s much bigger than an atom!, so a collision is still rare.

But when done ...

A 7 TeV proton–proton collision in CMS yielding more than 100 charged particles.

(CERN COURIER, October 26, 2010)

The probability of one particular proton in a bunch coming from the left hitting a particular proton in a bunch coming from the right depends roughly on the rate of proton size (d² with d~1 fm) and the cross-sectional size of the bunch (σ², with σ =16 microns) in the interaction point.

Then:

Probability ≈ (d_proton)²/(σ²) ⇒ Probability ≈ (10^-15)²/(16·10^-6)² ≈ 4 ·10^-21

But with 1,15·10¹¹ protons/bunch a good number of interactions will be possible every crossing.

Now, the number of interactions will be:

Probability x N² (with N = number of protons per bunch)

So, (4·10^-21) x ( 1,15·10¹¹)² ⇒ ~ 50 interactions every crossing

But just a fraction of these interactions (~50 %) are inelastic scatterings that give rise to particles at sufficient high angles with respect to the beam axis.

Therefore, there are about 20 "effective" collisions every crossing.

With 11245 crosses per second we get:

11245 x 2808 = 31,6 millions crosses , the "average crossing rate".

(31,6·10⁶crosses/s) x (20 collisions/cross) ⇒ 600 millions collision/s

If we consider 3550 bunches: 11245 x 3550 = 40 millions crosses ⇒ 40 MHz

Every time two bunches of protons pass each other, some of the protons will collide at very high energy: primary vertices. At maximum Luminosity a lot of primary vertices are expected (pile-up vertices).

(About "pile-up" see more here...)

From these primary vertices secondary vertices are created and so on.

The less energetic primary vertices (generally no interesting) are not taking into account and only the most energetic primary vertix is considered.

In the harsh environment of the Large Hadron Collider at CERN efficient reconstruction of the signal primary vertex is crucial for many physics analyses. The track reconstruction algorithms are charged to carry out this selection.

Event with four Pile-up Vertices ATLAS April 24th - 2010.

AUTHORS

Xabier Cid Vidal, PhD in experimental Particle Physics for Santiago University (USC). Research Fellow in experimental Particle Physics at CERN from January 2013 to Decembre 2015. He was until 2022 linked to the Department of Particle Physics of the USC as a "Juan de La Cierva", "Ramon y Cajal" fellow (Spanish Postdoctoral Senior Grants), and Associate Professor. Since 2023 is Senior Lecturer in that Department.(ORCID).

Ramon Cid Manzano, until his retirement in 2020 was secondary school Physics Teacher at IES de SAR (Santiago - Spain), and part-time Lecturer (Profesor Asociado) in Faculty of Education at the University of Santiago (Spain). He has a Degree in Physics and a Degree in Chemistry, and he is PhD for Santiago University (USC) (ORCID).

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