TITLE: Momentum of neutral particles in particle colliders
QUESTION [1 upvotes]: I understand that we can find a momentum (or a charge to momentum ratio anyhow) for a charged particle (charge $q$) in the LHC by using it's radius of curvature $r$ as
$$\frac{mv}{q} = Br$$
So that explains the momentum of charged particles.
For a neutral particles, however, we can see a topo-cluster of calorimeter cells, so the detector can determine $x,y,z$ and $E$. If the neutral particle interacts electromagnetically (for instance $\pi^0$) it will also leave a line in the tracker. Neither of these things seem to have enough information to calculate momentum, yet the most popular anti-kt jet clustering algorithm requires a momentum.
Are neutral particles clustered? Is there some way to estimate their transverse momentum?
(It seems like the answer to this ought to be in the particle flow algorithm, but I can't see it)

REPLY [1 votes]: First to be clear , neutral particles do not leave a track in the tracker ( and pios decay immediately,  as far as our detectors are concerned, go  into two gamma).
The LHC experiments  have a full set of detectors to catch by their interactions as many neutral particles as possible by the calorimetry. What is measured is energy deposited, but energy and momentum are connected if the mass of the particle is known, through the four vector. 

This is simple for the photons/gamma rays, as a particle that leaves no track in in the tracker but gives an electromagnetic jet in the electromagnetic calorimeter is a gamma.
There is the hadron calorimeter that can give total energy of jets , but it is not possible to separate the tracks coming from neutral particles, one is working  in a theory with jets generated attributed to quarks and gluons. If the jet is supposed to come from a gluon it still will have a mass defined in its four vector and, I suppose, that is the way  jet algorithms work.
In bubble chambers,some neutrons can be seen by their interaction, if you look at this site if you click on the link "do you want to see".
In general, specific models are used to fit the theory to the data, and in these models the masses are assumed and thus the momentum can be known, from the direction where the energy appeared in the calorimeter, and the four vector. Usually various hypothesis for the mass are tested, and the probability given , if it is a constrained fit.
Sometimes neutrals can be  found by their missing mass in the balance of energy and momentum for an event. That is how historically the netrino and the neutron were discovered.
Here is   an interesting four jet even in CMS, LHC.


-EVENTS-2019-004-1  -
Event display of a candidate ttt_t_ event with one of the top quark candidates producing a jet originating from a b quark (b jet), a muon and a neutrino (that the CMS experiment cannot directly detect). The additional jets could come from the other three top quarks. 

A possible explanation above.
One assumes that everything quantum mechanical happens at the vertex, one assume that all the energy of the jets is measured in the tracker and the calorimeters, and then one makes a four vector for each jet assuming the mass of t, that is a possible model.
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