Dalitz diagram

A Dalitz plot of Monte Carlo generated decays, using a ComPWA model. Optimized parameters for different resonances were determined with Geneva .

{\ displaystyle J / \ psi \ rightarrow \ gamma \ pi \ pi}

The Dalitz diagram (after Richard Dalitz , who introduced this method in 1953 to study the decay of K mesons ) is a scatter diagram that is often used in particle physics . The successive values of kinematic variables of a scattering or decay experiment are entered as points in an xy diagram. The point density then shows how often certain kinematic configurations of the end products occur.

For three-body decays

The kinematics of a three-body decay can be fully described with only two variables. In conventional Dalitz diagrams, the axes indicate the squares of the invariant masses of two pairs of decay products. ${\ displaystyle m_ {ij}}$

Disintegrates z. B. Particle A in three particles 1, 2 and 3, so can in a Dalitz diagram for this decay

on the x-axis ${\ displaystyle m_ {12} ^ {2} = (p_ {1} + p_ {2}) ^ {2}}$
on the y-axis ${\ displaystyle m_ {23} ^ {2} = (p_ {2} + p_ {3}) ^ {2}}$

be applied; with it

are the four pulses ${\ displaystyle p_ {i}}$
the squares each stand for the Minkowski products with themselves.

If a decay is a pure three-body decay, in which the mother particle decays directly into three particles, the distribution in the Dalitz diagram is uniform if there are no correlations in the angular distributions of the decay products.

However, three-body disintegrations are often dominated by resonances in which the mother particle first disintegrates into two product particles, one of which immediately further disintegrates into two end products. In this case, the Dalitz diagram shows a non-uniform distribution with increased point density in the area of the mass of the resonant decay.

In this way, the Dalitz diagram is an excellent tool for studying the dynamics of three-body decays.

For four-body decays

Dalitz diagram for four particles

The Dalitz diagram can also be applied to four-body decays.

A specific form of four-particle Dalitz diagrams (for non- relativistic kinematics) using a tetrahedral coordinate system was first developed to analyze four-particle atomic fragmentation processes, e.g. B. Double ionization of helium by ion impact. In this case, the Dalitz coordinates of the two electrons emitted, the recoil ion and the scattered projectile are plotted.

literature

RH Dalitz: Decay of τ-Mesons of Known Charge. In: Physical Review. 94, 1954, p. 1046, doi : 10.1103 / PhysRev.94.1046 .
Dalitz, Philosophical Magazine Vol. 44, 1953, p. 1068
E. Fabri, Nuovo Cimento Vol. 11, 1954, p. 479
M. Schulz et al. J. Phys. B Vol. 40, p 3091 2007
M. Schulz, Phys. Rev. A Vol. 79, p. 042708 (2009)

Web links

Bock in Briefbook Particle Detectors on Dalitz Plots with an example

Individual evidence

↑ ComPWA: A common amplitude analysis framework for PANDA M Michel et al. 2014 J. Phys .: Conf. Ser. 513 022025
↑ Schulz et al., 2007, 2009

[MMICHELPWA-1] ComPWA: A common amplitude analysis framework for PANDA M Michel et al. 2014 J. Phys .: Conf. Ser. 513 022025

[Schulzetal-2] Schulz et al., 2007, 2009