Landau-Pomeranchuk-Migdal (LPM)
Goals
- To measure the LPM suppression at high energies:
The quantum correction to LPM
The possible compensation of
LPM at high energy
Proposed setup
- The figure (not to scale) shows the 4 drift chambers, the Lead glass detectors, the MBPL magnet and the target. Look here for coordinates.
Photon energy resolution
Photon energy resolution
Papers of relevance
- Compensation paper by J.S. Bell
- See also the explanations of LPM
Team and affiliations
- Sergio Ballestrero, INFN, Firenze, Italy
- Cristina Biino, INFN, Torino, Italy
- Per B. Cristensen, IFA, Århus University, Denmark
- Henrik Dahl Hansen, IFA, Århus University, Denmark
- Tjeerd Ketel, NIKHEF, Amsterdam, Holland
- Alessio Mangiarotti, INFN, Firenze, Italy
- Pietro Sona, INFN, Firenze, Italy
- Ulrik I. Uggerhøj, IFA, Århus University, Denmark
- Gökhan Unel, Northwestern University, Chicago, USA
- Mayda Velasco, Northwestern University, Chicago, USA
- Zeblon Z. Vilakazi, Univ. of Cape Town, South Africa
Measurement program
- To minimize systematic effects of photon pile-up, foils of
Z = 6, 29, 71, 74 and 77 will be used.
- Two different eff. radiation lengths for each foil: 1% and 5%.
- Each foil: 4 hrs ? total: 32 (40) hrs.
- Calibration of Lead Glass and tagging system:
- 10, 35, 70, 110, 150, 180, 225 and 280 GeV electrons.
- Each energy: 30 min. incl. switchover ? total: 4hrs.
- Calibration of drift chambers by sliced scintillators.
- Can be done partly in parallel with energy calibration
Schedule
- Experiment: Week 36:
- Start: 04.09.01 at 8 am. (MD 8-16)
- End: 10.09.01 at 8 am.
- Total beam time: 136 hrs.
-
SPS schedule
Status of LPM test
Current Status
- Target foils have been received and checked
- DAQ is being tested and is ready. Two systems are working.
- Detectors have been shipped to CERN:
15.06.01. and the rest: 13.08.01.
To be done during week 34
- H2 beamline status: MBPL magnet for tagging system has been installed
LPM - a classical viewpoint
- If the multiple Coulomb scattering angle in the formation zone exceeds the radiation emission cone, the radiation intensity diminishes.
- In other words, the LPM effect appears when:
?f > ?1/? i.e. ?f = 2?2c/? > ?/4? ·X0 = ?1/?
which gives the LPM energy:
ELPM = X0mc2/8?a0= 3.8 TeV/cm·X0[cm]
Quantum correction
- At high energies, there is an important correction to the classical LPM effect due to the recoil imparted by the photon:
?f > ?1/? i.e. ?f = 2?2c/?* > ?/4? ·X0 = ?1/?
which gives the LPM energy:
where as in the classical case:
ELPM = X0mc2/8?a0= 3.8 TeV/cm·X0[cm]
Compensation?
- By use of Lienards formula for the total radiated intensity, John S. Bell was able to conclude that any change in the effective radiation length at high electron energies must be a quantum effect. He speculated about a possible compensation of the LPM effect at high photon energies which would leave the radiation length unchanged.
- See J.S. Bell, Nucl. Phys. 8, p. 613 (1958)
Formation length, ?f
-
- Synchrotron radiation
-
- Photon wavelength
-
- Longitudinal momentum transfer
Multiple Coulomb scattering
- After the passage of a foil of thickness, x, and radiation length, X0, the RMS scattering angle is appr. given as
?=13.6 MeV/cp? ·sqrt(x/X0)
- Conversely, the thickness required to scatter 1/? is given as
Radiation emission cone
- As a consequence of the Lorentz boost, the dipole radiation which in the rest system is radiated as sin2?, is transformed into a forward cone with opening angle 1/?.
- In this cone, over the formation length, the scattering amplitudes can interfere - constructively as in crystals or destructively as is the usual case for the LPM effect.
Synchrotron radiation - ?f
- The figure shows the trajectory of an electron in a magnetic field as in a synchrotron. If the detector does not resolve below the radiation emission cone, 1/?, there is no
Photon wavelength - ?f
- The figure shows the emission of a photon by an electron. As the velocity of the electron, v=?c, is slightly smaller than that of the photon, c, the electron ‘lacks behind’. Once the distance becomes one wavelength of the photon, it is ‘formed’.
Longitudinal momentum transfer - ?f
- Calculating the minimum longitudinal momentum transfer to the nucleus and using the uncertainty relation, Ter-Mikaelian concluded to the surprise of Landau that it takes a certain distance to create a photon:
q||=p1-p2-??/c and ?f=?/q||
?f=2E(E-??)/??mc2 ·?c ? 2?2c/?
Other experiments
LPM at SLAC
- Experiments performed at SLAC (E-146) in the laboratory with Ee = 25 GeV.
S. Klein, Rev. Mod. Phys. 71, p. 1501 (1999)
P.L. Anthony et al., Phys. Rev. D 56, p.1373 (1997)
P.L. Anthony et al., Phys. Rev. Lett. 75, p. 1949 (1995)
LPM at CERN
- Experiments performed at CERN (PS188, WA64) in the laboratory with Ee = 5-20 GeV in crystals.
J.F. Bak et al., Nucl. Phys. B 302, p. 525 (1988)
LPM at Serpukhov
- Experiments performed at Serpukhov in the laboratory with Ee = 40 GeV.
A.A. Varfolomev et al., JETP 42, p. 218 (1976)
LPM from cosmic rays
P.H. Fowler et al., Phil. Mag. 4, p. 1030 (1959)
A.A. Varfolomev et al., JETP 11, p. 23 (1960)
News
- Zeblon starts GEANT simulation
- List of targets and radiation lengths
GEANT Simulation - Input
- Coordinates for the centre of each detector in m, (x,y,z) z is in the beam direction, y vertical, x horizontal.
- DC1 : (0,0,0)
- DC2 : (0,0,61.039)
- DC3 : (0.055,0,64.728)
- DC4 : (0.120,0,80.7)
- Each DC has 0.15 sensitive area in x and y and X0 = 1.09e-3 in z.
- LG1 : (0,0,80.35)
- LG2 : (-0.09,0,80.35)
- LG3 : (-0.09,0.09,80.35)
- LG4 : (0,0.09,80.35)
- Each LG is 0.70 m long (25 X0), 0.09 m in x and y.
- The targets are put between DC2 and DC3 at: (0,0,61.100)
- The MBPL magnet, 2 m in z, Bl = 4.058 Tm, centre at (0,0,63.0).
- BEATCH (beam line layout).
Targets
Total price: 1086.80 GBP More information from the periodic table
Thickness accuracy quoted: ?10 %
Carbon density quoted: 1.76 g/cm3
Radiation lengths
Table of calculated radiation lengths
Atom and electron densities
LPM papers
- According to this paper by Baier and Katkov, there is no compensation at high energy.