Neutral Currents in BEBC -
The experiment WA21 (part 4)

Analysis of Events

Kinematics

The (anti-) neutrino proton scattering takes place in the laborarty frame, where the proton is at rest. We call these reactions semi-leptonic, since both leptons as well has hadrons (here: protons) are involved.

The (anti-) neutrino transfers energy (v) and momentum (Q2) to the struck quark. Typically, the quark is struck 'hard', that means with considerable momentum transfer. This is usually referred to as '(deep) inelastic scattering' DIS. In this case, the proton breaks up into particular current fragments (originating from the struck quark) and the target fragment(s) (consisting of the stripped proton system). The whole system is 'excited' and the deposited energy (EHad in the lab frame and W in the CMS) gives raise to the production of short lived primary and longer lived secondary particles, which are perhaps measurable. Of course, the production of any particles is limited by the initial energy available.

The proton does not only consist of the valence quarks, but the nucleon binding forces (facilitated by the strong interaction and mediated by gluons) carry a large portion of the proton's energy and momentum. In addition, we observe the creation/destruction of (virtual) quark/anti-quark pairs: the quark sea. Those pairs carry very little (relative) momentum, but also contribute to the scattering process.

The dimensionless Bjorken scaling variables xBj and yBj in addition with the momentum transfer Q2 span the phase-space of the reactions. The population of events in the available phase-space is an important characteristic of the scattering process and the underlying physics involved.

Scattering process in neutrino-proton CC reactions

Initial kinematic variables:

Kinematic variables after collision:

Scaling variables (ranging between 0 to 1):

Specific particle variables:

Current and target region:

Typically, the analysis of any deep inelastic scattering process follows this scheme:

  1. Analysis of the gross post-scattering kinematical variables and their distribution: Q2, W, EHad, xBj, yBj.
  2. Analysis of the multiplicities of the produced charged and neutral hadrons, perhaps in different parts of the phase-space.
  3. Analysis of particular produced particles (pions, kaons, ...) and their characteristics.
  4. Analysis of specific production channels in restricted areas of the phase-space.

One remaining problem is the identification of charged tracks:

Corrections

Only about 10% - 15% of the NC and in particular CC events can be 'fitted' with a kinematical hypothesis, which means the event is completely visible in BEBC -- except of the (anti-) neutrino in case of a NC interaction -- and has been measured correctly.

0-C fit of a NC (anti-) neutrino event with assigned final state reaction hypothesis (including the detected Λ0 and K0) and the calculated kinematical values

For the vast majority of events we need however to correct for unseen neutral particles in the bubble chamber, mainly γs, K0L,S, and neutrons. For events with an identified muon, usually the Heilmann correction is applied, with utilizes the proportionality between missing transverse and longitudinal momentum. However, this correction can only be applied for CC events and in addition underestimates systematically the values of W and EHad. Thus, often simple multiplicity depending correction factors are used, which are derived from a Monte Carlo calculation.

The difference between the true physical values and the estimated ones is called smearing and impacts significantly the analysis; in particular in specific regions of the phase space were corrections may become large. This results in systematic errors of the analysis, which needed to be considered and estimated as well.

Multiplicities

One fundamental analysis regarding a sample of events is to measure the number of primary produced charged tracks: the multiplicity of the event.

According to our current understanding any high energy event's multiplicities (as discrete values) can be well expressed by statistical approaches, in particular the Negative Binomial Distribution (NBD).

However, initially it was believed that the multiplicity follow a certain production model, known as KNO scaling which utilizes the Levy function. This approach was falsified by the NA9 collaboration, analyzing the particle generation in different kinematical regions with high statistics.

Measured NBD distribution of (anti-) neutrino NC events at different energies W

Of course, the multiplicity depends directly on the energy deposited in the hadronic systems. Thus, it makes sense to analyze the multiplicities with respect to the hadronic energy, the energy of the incident (anti-) neutrino, and in particular the CMS energy W. Now, one may refine the analysis, selecting particular particle species: π+, π-, K0, ....

Historical note:

This is the first NBD fit of multiplicities for the WA21 experiment. For my thesis, I programmed (from first principals) an NBD evaluation routine, which was used for the subsequent analyses.

Particle combinations

For the vast majority of events, the identification of short-lived particles can not be achieved directly, but rather a combinatorial procedure is applied, combing (the momentum of) any track (with the assigned particle hypothesis) with any other. As a result, the correct hypothesis shows up as a resonance upon a background of false combinations.

The combinatorial background (for high statistics) is typically described by a Breit-Wigner function and can be subtracted statistically. From here, the number of correct combinations can be estimated and thus the production rate (cross-section) is determined. Further, the fit allows the estimation of the mass M of the identified particle and it's decay width Γ.

A lot of major discoveries, in particular for charm particles, have been done with a careful analysis of hypothetic mass combinations. However, the more complex the initial situation is, the more likely false interpretations become. For any new particle discovery it is required that the signal provides a quality of at least eight sigma, or even ten sigma, or can be established by a different experiment.

Determination of the ρ0 meson in anti-neutrino NC events by means of the π+- combinations in the forward and backward hemisphere

Strangeness and Charm

Shortly before BEBC came into operation, the J/Ψ charmonium meson was independently detected by groups at SLAC and BNL. Later, some very beautiful D0 hadron decays have been photographed in BEBC itself, establishing the field of charm-spectroscopy. From the elementary particle theory's point of view, those discoveries finally replaced the GIM mechanism with the now adopted Quark-Parton-Model (QPM), our current Standardmodel of particle physics.

Apart from the spectacular charm events initially found in WA21, the intensive later search for charmed hadrons in particle combinations done by Jost Kern for this Phd thesis at the MPI Munich, did not show up new production channels. Unfortunately, pictures of BEBC' HiRes camera never were helpful to catch decays from charm events. The only other source of charm production, di-muon CC events, were never exploited seriously.

Lately, the production of events with strangeness gathered some excitements due to the potential discovery of the Θ+ build up from Penta-Quarks.

Production rates of the strange particles K0S and Λ0 in (anti-) neutrino NC reactions

In BEBC the identification of strange particles is facilitated

Exclusive Channels

Unlike the inclusive production of particles, some exclusive channels exist. For neutrino CC event the most dominant channel is the Δ++ (decaying into proton and a π+) resonance, which is also visible in NC events. However, for anti-neutrino/proton CC scattering, the so-called 1-prong channel is most important, where the anti-neutrino hits the quark inside the proton quasi-elastic, thus the proton stays intact as such (and typically is not visible in the bubble chamber); even if the transferred momentum Q2 is significant.

Relative production rate of 1-prong CC events as function of the incident anti-neutrino energy

In later periods of BEBC (after the IPF was installed) a particular 1-prong scan was facilitated for anti-neutrino CC events, which yielded a detection efficiency of about 50% according to Peter Schmid.

A more interesting channel is due to so-called diffractive scattering. It is assumed that the W+- acts as virtual (off-shell) ρ, π+-, the Z0 as ρ0 exchange meson respectively. Unlike elastic scattering, the reaction happens at very low Q2 and momentum transfer t to the proton. These interactions are of special interest, because they show a lot about the helicity of the involved particles, which is known for CC events in terms of the Partial Conserved Axial Vector Current (PCAC). Uli Katz from the MPI Munich did a careful analysis of these interactions, theoretical founded by Adler and Paschos.

Potential diffractive NC (anti-) neutrino ρ0 event

Continue with Extracting the Neutral Current Couplings