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I am looking into events within bubble chamber images and have come across a stumbling block. It relates to finding masses of neutral particles within bubble chamber images, specifically the mass of the neutral lambda baryon, with an accepted mass of ~1.116 GeV/c^2.

We are looking into lambda baryon decays into a proton and a negative pion, and have been unsuccessful in finding a method of calculating the lambda's mass. Our supervisor referred us to a method called the "Manchester Alpha Parameter", which involves finding the angles at which the decay products are emitted. However, we can find no mention of this method anywhere online.

I have tried to find other ways of calculating the mass, but they all make comments on the proton's curvature being too small to take reliable measurements from. Are there any methods that I could look into where (by only having access to bubble chamber event images and crude measurement tools i.e. rulers, protractors, etc) we could recover an acceptable mass value for the lambda baryons?

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  • $\begingroup$ Welcome SatinArmchair to Physics SE. Your question is not completely clear. Do you know how to measure the momentum of a particle in your images? Do you know how to calculate the invariant mass of two particles, given their momenta and rest masses? What are the sources that "all make comments on the proton's curvature being too small"? Protons from lambda decays might sometimes have too small curvature to be measured, but usually they won't. $\endgroup$ Dec 12, 2022 at 17:22
  • $\begingroup$ And then the ionisation and length of path can give the energy of the proton., example fig3 here in emulsion, cloudylabs.fr/wp/converting-stopping-power you have to find the curves for the bubble chamber $\endgroup$
    – anna v
    Dec 12, 2022 at 20:04
  • $\begingroup$ We know how to measure the momentum of particles in our images, we have done successful analyses of charged particles' properties (i.e charged sigma baryons). The sources are example questions such as dzre.com/alex/HonorsPhysics/Notes/Week6/bchb.pdf . In our case, the curvature for protons are too small to measure accurately with our tools. The centre of mass energies involved for the incident kaons (which interact with protons at rest producing lambdas) are low. @annav that was something I have been looking into but am unable to find the same graphs for liquid H bubble chambers $\endgroup$ Dec 13, 2022 at 9:18
  • $\begingroup$ have a look www2.physics.ox.ac.uk/sites/default/files/Passage.pdf on figure 2, it has the scale for protons too $\endgroup$
    – anna v
    Dec 13, 2022 at 11:43

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The answer is in the source you provided in a comment: PHY 4822L (Advanced Laboratory): Analysis of a bubble chamber picture. From page 4:

$$p_+\sin{θ}_+ = p_- \sin{θ_-}\qquad\qquad\qquad(2)$$ $$p_0 = p_+\cos{θ_+} + p_-\cos{θ_-}\qquad\qquad(3)$$ $$…$$ Note that there is a redundancy here. That is, if $p_+$, $p_-$, $θ_+$, and $θ_-$ are all known, equation (2) is not needed to find $m_0$. In our two-dimensional case we have two equations (2 and 3), and only one unknown quantity $m_0$, and the system is over-determined. This is fortunate, because sometimes (as here) one of the four measured quantities will have a large experimental error. When this is the case, it is usually advantageous to use only three of the variables and to use equation (2) to calculate the fourth. Alternatively, one may use the over-determination to "fit'' $m_0$, which allows to determine it more precisely.

I have highlighted the most relevant phrase. You don't need to measure the proton momentum – you can calculate it using transverse momentum conservation, i.e. Equation (2).

I believe the "Manchester Alpha Parameter" is $$\alpha =\frac{p_+\cos{θ}_+ - p_- \cos{θ_-}}{p_+\cos{θ}_+ + p_- \cos{θ_-}}$$ from page 5 of "The Early Times of Strange Particles Physics", (Peyrou 1989, CERN/EF 89-1).

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