# Momentum of neutral particles in particle colliders

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)

• Much better to write $Br = p/q$ because it is the momentum that matter and in the relativistic regime that is no longer exactly $mv$. – dmckee Jul 8 at 15:34

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.

• Thanks this is a great answer. To be clear though, neutral particles are not considered when jet clustering? To assign an observed particle to a jet under anti-kt we must be able to calculate its distance from other particles according to $d = min(1/p_{T1}^2, 1/p_{T2}^2) R_{angular sep}^2$ which is only possible if we have $p_{T1}$ and $p_{T2}$. – Clumsy cat Jul 7 at 13:34
• see the example i edited in. neutrons would give up energy in the calorimeter and be counted, pi0 have given gammas that are counted, only neutrinos will be missing and they will be modeled in the monte carlo. – anna v Jul 7 at 13:51
• So we estimate a mass and use that to deduce the energy? This seems reasonable, but I wonder how accurate it is. I had a look at my Monte Carlo (showering with pythia) and I am seeing some pions at the end of hadronisation that reach the tracker and even get out to the calorimeter. It's pretty common in my b-jets, so they possibly don't decay as fast as you think? – Clumsy cat Jul 7 at 22:59
• @Clumsycat Are they neutral pions?In general it is only charged hadrons that live long enough to be seen ( i.e. for their decay to start with a previous charged track, a neutral will appear without a beginning track from the vertex) at our energies in the tracking detector of colliders hyperphysics.phy-astr.gsu.edu/hbase/Particles/hadron.html – anna v Jul 8 at 5:24