Information on the absorption of hadrons

General information

When traversing the material in the detector, hadrons (e.g. pions, kaons and protons) are subject to hadronic interactions with the nuclei in the material. Thereby the particles generate a shower of secondary particles which are subsequently absorbed in the detector material. In case a hadronic interaction occurs in the tracking system the particle is lost for reconstruction. Please keep in mind that photons and leptons are not subject to these nuclear interactions. The distance that a hadron can travel before an nuclear interaction occurs is called the hadronic interaction length. Also keep in mind that the hadronic interaction length is different from the radiation length. The radiation length determines:

  • electrons: energy loss by bremsstrahlung
  • photons: conversions (), also named pair production
  • hadrons: multiple scattering
So for a hadron, the radiation length is a measure for the number of scatters that it receives, while the hadronic interaction length is a measure for the probability that it is absorbed in the material. At this point it is also worth mentioning that below 0.1-1.0 GeV/c (depending on the mass of the hadron) the energy loss due to ionisation rises asympotically and the particle can be stopped in the material. The energy loss follows the famous Bethe-Bloch curve and the distance that the particle can travel before losing all its energy is determined by the Bragg peak. However, in most high-energy physics experiment the absorption of hadrons due to ionisations is neglible.

The hadronic (nuclear) interaction length for different materials is given in the PDG and is obtained from a simulation of 200 GeV/c neutrons using the MARS15 code. For example, the nuclear interaction length for aluminum is 397.0 mm. This means that for a 397.0 mm thick piece aluminium a hadron has a 1/e=37% probability of traversing without having an interaction with a nucleus. In the LHCb software the hadronic interaction lenght (called absorption length) is stored inside the Material class. For elements this uses the following formula to approximate the hadronic interaction length,

where is the number of nucleons, is the density of the material and is a constant. For aluminium this gives an absorption length of 388.8 mm. In fact this number is not used in the LHCb simulation (Geant). The Geant simulation models hadronic interactions of course in much more detail. A nice study is done by Silvia Miglioranzi and Gloria Corti where they count the number of particles passing through 1 mm and 5 cm thick blocks of aluminium:

It can be seen in this study that in the range 5-100 GeV/c protons can have up to 60% shorter interaction lengths, pions can have up to 20% shorter interactions lengths, while kaons have on average 20% longer interaction length. Especially for kaons and protons there are also large differences between particles and anti-particles.

Material scan (as seen by simulation)

The amount of material or distance () that a particle has to traverse in the tracking system can be given in terms of hadronic interaction lengths (). In LHCb, up to the last tracking station a particle traverses on average about 20% of an interaction length. The figures below are obtained by calculating the material intersections for straight lines starting at the origin of the LHCb coordinate system using the TransportSvc and the hadronic interaction length stored in the Material class. The peak at pseudorapidity comes from the 25 mrad conical beam pipe inside RICH1.

Distance in hadronic interaction length: phi versus eta Distance in hadronic interaction length versus eta

Study in Gauss/Geant4

The vertices in Gauss are classified into different vertex types. See the doxygen documentation of the MCVertex class. For hadrons, the main types are:

  • Unknown: These are typically hadronic interactions that are not (yet) recognized when converting from the Geant4 vertex type.
  • Decayed: Normal decays in flight of the particles. This is always the last vertex of a MCParticle as the original particles ceases to exist.
  • HadronicInteraction: A vertex due to a hadronic interaction. In most cases (>95%) this is a inelastic collision which means the original particle ceases to exists. Many secondary particles are produced in the resulting shower.
  • GenericInteraction: These are hadronic interactions in the calorimeters. In the calorimeters there are too many secondary particles created to be simulated individually. Only the secondary particles that emerge from the shower are simulated. This type is introduced to connect these particles to the original mother particle.
  • DeltaRay: An electron is emitted by the particle when traversing the detector. These vertices do not desctruct the original particle.

These two plots show the z position of end-vertex for the different vertex types:

pionZvtx.png kaonZvtx.png

Below is a table with the fraction of particles (kaons and pions) from a which have an end-vertex before z=9410 mm. The fiducial cuts are and .

  Unknown Decayed Hadronic Generic
pi+- 1.2 +- 0.1 % 4.0 +- 0.2 % 22.8 +- 0.4 % 0.0 +- 0.0 %
pi+ 1.3 +- 0.1 % 4.3 +- 0.3 % 22.0 +- 0.5 % 0.0 +- 0.0 %
pi- 1.1 +- 0.1 % 3.7 +- 0.2 % 23.6 +- 0.5 % 0.0 +- 0.0 %
pi+- (fiducial cuts) 0.0 +- 0.0 % 1.3 +- 0.1 % 15.0 +- 0.4 % 0.0 +- 0.0 %
pi+ (fiducial cuts) 0.0 +- 0.0 % 1.4 +- 0.2 % 14.7 +- 0.6 % 0.0 +- 0.0 %
pi- (fiducial cuts) 0.0 +- 0.0 % 1.2 +- 0.2 % 15.4 +- 0.6 % 0.0 +- 0.0 %
K+- 0.1 +- 0.0 % 11.7 +- 0.3 % 15.2 +- 0.3 % 0.0 +- 0.0 %
K+ 0.1 +- 0.0 % 12.0 +- 0.4 % 13.9 +- 0.4 % 0.0 +- 0.0 %
K- 0.1 +- 0.0 % 11.3 +- 0.4 % 16.5 +- 0.5 % 0.0 +- 0.0 %
K+- (fiducial cuts) 0.0 +- 0.0 % 7.9 +- 0.3 % 12.7 +- 0.3 % 0.0 +- 0.0 %
K+ (fiducial cuts) 0.0 +- 0.0 % 7.8 +- 0.4 % 11.5 +- 0.5 % 0.0 +- 0.0 %
K- (fiducial cuts) 0.0 +- 0.0 % 7.9 +- 0.4 % 13.7 +- 0.5 % 0.0 +- 0.0 %

These two plots show the fractional loss from hadronic interactions and decays versus momentum. The particle is required to be in the eta range as defined above and the z positon of the end vertex is < 9410 mm.

pionLossVsP.png kaonLossVsP.png

A small part of the particles that have a hadronic interaction before z=9410 mm can still be reconstructed. The figures below show the reconstructed B mass for all events (left), for events where the pion has a hadronic interaction (middle) and for events where the kaon has a hadronic interaction. Only a small fraction can be recovered.

mass.png massPionHadronic.png massKaonHadronic.png
 

-- JeroenVanTilburg - 08-Aug-2011

Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng absLength_0_11900.png r1 manage 11.5 K 2011-08-08 - 15:25 JeroenVanTilburg Absorption length versus eta z=[0,11900]
PNGpng absLength_0_11900_2d.png r1 manage 60.8 K 2011-08-08 - 15:25 JeroenVanTilburg Absorption length z=[0,11900]: phi versus eta
PNGpng absLength_0_770.png r1 manage 10.8 K 2011-08-08 - 15:29 JeroenVanTilburg Absorption length versus eta z=[0,770]
PNGpng absLength_0_770_2d.png r1 manage 63.6 K 2011-08-08 - 15:25 JeroenVanTilburg Absorption length z=[0,770]: phi versus eta
PNGpng absLength_0_9410.png r1 manage 11.5 K 2011-08-08 - 12:46 JeroenVanTilburg Absorption length versus eta z=[0,9410]
PNGpng absLength_0_9410_2d.png r1 manage 66.6 K 2011-08-08 - 12:47 JeroenVanTilburg Absorption length z=[0,9410]: phi versus eta
PNGpng absLength_2270_2700.png r1 manage 11.9 K 2011-08-08 - 15:30 JeroenVanTilburg Absorption length versus eta z=[2270,2700]
PNGpng absLength_2270_2700_2d.png r1 manage 31.6 K 2011-08-08 - 15:26 JeroenVanTilburg Absorption length z=[2270,2700]: phi versus eta
PNGpng absLength_2700_7500.png r1 manage 11.4 K 2011-08-08 - 15:31 JeroenVanTilburg Absorption length versus eta z=[2700,7500]
PNGpng absLength_2700_7500_2d.png r1 manage 16.5 K 2011-08-08 - 15:27 JeroenVanTilburg Absorption length z=[2700,7500]: phi versus eta
PNGpng absLength_7500_9410.png r1 manage 12.2 K 2011-08-08 - 15:31 JeroenVanTilburg Absorption length versus eta z=[7500,9410]
PNGpng absLength_7500_9410_2d.png r1 manage 60.4 K 2011-08-08 - 15:28 JeroenVanTilburg Absorption length z=[7500,9410]: phi versus eta
PNGpng absLength_770_2270.png r2 r1 manage 9.0 K 2011-08-09 - 08:49 JeroenVanTilburg Absorption length versus eta z=[770,2270]
PNGpng absLength_770_2270_2d.png r2 r1 manage 21.1 K 2011-08-09 - 08:49 JeroenVanTilburg Absorption length z=[770,2270]: phi versus eta
PNGpng absLength_9410_11900.png r1 manage 12.0 K 2011-08-08 - 15:32 JeroenVanTilburg Absorption length versus eta z=[9410,11900]
PNGpng absLength_9410_11900_2d.png r1 manage 24.8 K 2011-08-08 - 15:28 JeroenVanTilburg Absorption length z=[9410,11900]: phi versus eta
PNGpng kaonLossVsP.png r2 r1 manage 10.3 K 2011-08-30 - 11:06 JeroenVanTilburg Fractional loss of kaons
PNGpng kaonZvtx.png r1 manage 10.3 K 2011-08-30 - 10:37 JeroenVanTilburg z of end-vertex kaon
PNGpng mass.png r1 manage 12.8 K 2011-08-30 - 10:38 JeroenVanTilburg Reconstructed mass
PNGpng massKaonHadronic.png r1 manage 11.2 K 2011-08-30 - 10:39 JeroenVanTilburg Reconstructed mass where kaon decayed hadronically
PNGpng massPionHadronic.png r1 manage 11.6 K 2011-08-30 - 10:39 JeroenVanTilburg Reconstructed mass where pion decayed hadronically
PNGpng pionLossVsP.png r2 r1 manage 10.4 K 2011-08-30 - 11:06 JeroenVanTilburg Fractional loss of pions
PNGpng pionZvtx.png r1 manage 10.2 K 2011-08-30 - 10:36 JeroenVanTilburg z of end-vertex pion
Edit | Attach | Watch | Print version | History: r9 < r8 < r7 < r6 < r5 | Backlinks | Raw View | WYSIWYG | More topic actions
Topic revision: r9 - 2018-01-15 - LuciaGrillo
 
    • Cern Search Icon Cern Search
    • TWiki Search Icon TWiki Search
    • Google Search Icon Google Search

    LHCb All webs login

This site is powered by the TWiki collaboration platform Powered by PerlCopyright & 2008-2018 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding TWiki? Send feedback