Exotics

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The Exotics group was 'founded' in 2003, after many experiments reported evidence for a narrow resonance around 1540 MeV. This resonance, dubbed , was consistent with predictions by Diakonov, Petrov and Polyakov of a five quark state (or pentaquark). In the spring of 2003, a preliminary search in the Hermes data collected on the polarized deuterium target from 1998 to 2000 indicated that we also might see something. This resulted in a Hermes publication claiming evidence (with 3.4 significance) for this Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \Theta^+} state.

Relevant Documents

Publications

Internal Notes

Other Documents

Analysis Status

Below are the track and event selection criteria which are currently considered 'standard cuts'. For comparisons between different analysis methods, try to stick as closely as possible to this set of criteria. If you want to study variations of these criteria, only change one at a time.

Run and Burst Selection

Track Selection

  • Selection of long tracks in fiducial volume.
  • The usual geometrical cuts for every track are applied.
  • Particle identification using RICH unfolding:
    The EVT method is used when more than 1 track in the corresponding detector half. DRT is used when only one.
  • The energy cuts are 1.<E<15. GeV for pions and 2.<E<15. GeV for protons.
  • Events with (at least) 1 pi+, 1 pi- and 1 proton(or anti-proton) are saved for the next step: Event reconstruction with Siguang's TMC.

Event Reconstruction

To take into account the effects of the transverse target and recoil magnet, a track correction method on top of the HRC tracking has to be used. Without a correction the resolution is 2 MeV (7 MeV) worse for the recoil (transverse target) magnet data. Michiel Demey developed an analytic method for a homogeneous transverse target field (tmagnet). A more general correction method which uses magnetic field swimming was developed by Siguang Wang, and is called SiguangTMC (sTMC). Other implementations of the more general method were developed by Alberto Martinez de la Ossa and by Wouter Deconinck. All of these methods take the track parameters at z = 0 cm determined by HRC without target magnetic field and assume that they are valid outside the target region (e.g. z = 134 cm, the transformation from z = 0 cm to z = 134 cm is then trivial). From there the track is reconstructed backwards (analytically with tmagnet, using a Runge-Kutta method in the general methods).

  • sTMC starts the reconstruction from HRC information provided in the uDST tables
  • The starting reconstruction point for all the particles is the following:
    • The momentum is set from uncorrected values in the corresponding g1Track entry.
    • The track position is set from its extrapolated coordinates (without any TMC) at z = 0 cm: rxOff and ryOff.
    • sTMC take these initial values and extrapolates the particle trajectories linearly downstream until the z position where the magnetic field is negligible (z = 134 cm)

Currently discussions are ongoing as to how the information provided by HTC can be used. The track parameters determined by HTC are only valid at the vertex of the track with the lepton beam. It is not easy nor useful to calculate the track parameters at z = 134 cm. The suggestion is to take the HTC vertex point as the starting point for a magnetic field swimming approach.

Event Selection

  • Loop over the tracks to find 's.
  • Every time a Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^-} is found, other loop begins to search for the Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^+} 's.
  • Having a Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^-\pi^+} pair, it tries to reconstruct the Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_S} :
    • sTMC traces back the two pions in the magnetic field and finds the point of closest approach (the decay point candidate):
      The ppDCA (Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^-\pi^+} Distance of Closest Approach) must be smaller than 1. cm.
    • The decay vertex of Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_S} must be downstream respect to the begin of the target cell (sanity check).
    • To safe space and computing time, this iterative process only keeps Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^-\pi^+} systems having an invariant mass between 0.39 and 0.61.
      (We only need this window to fit the Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_S} peak in a latter stage).
  • If a suitable is found. The algorithm continues searching for a proton or anti-proton in our selected set of tracks.
    When such a proton is found, it start the proton-Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_S} reconstruction:
    • sTMC finds the point of closest approach between the proton and the Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^-\pi^+} system (the Main interaction point candidate).
      The pkDCA (proton-Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_S} Distance of Closest Approach) must be smaller than 0.6 cm.
    • The decay vertex of must be downstream respect to its production point (exactly equal to the previously called Main interaction point).
      Besides, the distance between these two points must be greater than 7. cm.
    • The main interaction point must lie on the "target region window" : between 0. and 25. cm (for 06-07 data).
  • The current Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pi^-\pi^+} p combination is stored if it fulfills the cuts stated above.
  • The algorithm continues searching for all other possible combinations.
  • All events with at least one Theta candidate are retained, with plenty of additional information for the next analysis step.

Data analysis

At this stage, the information stored after the reconstruction is analyzed.

  1. Further cutting: All the cuts applied during the event selection and reconstruction stage can be further restrictive:
    • The Proton energy is constrained to be between 4. and 9. GeV.
  2. Sample selection cuts: From the whole reconstructed data sample, one can select a certain sub-sample for the analysis.
    (i.e.: proton or anti-proton selection, beam charge, experimental mode, target type, year, etc.).
  3. Sample dependent cuts: They usually comes from some data processing (i.e. the fitted parameters of a certain distribution), and thus, they depends on the sample being analyzed (different data samples lead to different fitted values):
    • Cut on Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_{s}} invariant mass: Only events falling within Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pm 2\sigma} from the fitted Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle K_{s}} peak are kept.
    • Cut on Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle \Lambda (1116)} invariant mass: This cut acts as a veto. We want to prevent any possible contribution coming from the production of this particle. Events falling within Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pm 2\sigma} from the fitted Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \Lambda(1116)} peak are thrown away.
    • Cut on vertex transverse position: The primary vertex reconstructed position must lay in the target cell region. In addition to the cut on z vertex, cuts on x and y vertex position are also applied. Only events within Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \pm 2\sigma} from the mean x and y vertex position are selected.

Upper limits

It's important to define upper limit and confidence interval precisely, because it tends to lead to confusion. The frequentist approach, which we use, tends to be more objective; the Bayesian approach is more intuitive but depends on prior PDFs. The (frequentist) confidence interval with Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle C.L. = \alpha} is the range of parameters (i.e. real cross sections) for which the experimental result (number of observed events) is contained in a interval given that particular parameter value (Neyman's construction). If we were to repeat the experiment a large number of times, the confidence interval would contain the real parameter value in a fraction Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle 1-\alpha} of the experiments (PDG Reviews, Statistics). This does NOT mean that there is a Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle 1-\alpha} probability that the cross section we calculate from the experimental result is the right one.

The problem now lies in determining the Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle 1-\alpha} intervals for a fixed parameter. For a particular cross section we expect a Poisson distribution for the number of events. When the number of events is large, this becomes a Gaussian distribution and the situation is easier. Also, when do you see a signal (Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle Poisson_{bg} + Poisson_{signal}} ) and when not (Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle Poisson_{bg}} )? When the number of events is small, Feldman and Cousins developed an approach that ties this all together <ref>Unified approach to the classical statistical analysis of small signals, Feldman and Cousins, (doi:10.1103/PhysRevD.57.3873).

However, what we measure in our experiment is not the number of events! It is the number of events after a <1% acceptance with an uncertainty, on top of a background with an uncertainty much larger than the signal itself. This means that the Poisson distribution is actually again a Gaussian distribution but now convoluted with a bunch of other things. CLAS has the same problem, so they figured out a way to deal with it (CLAS internal note 2008-20), but didn't use it in any of their papers yet.

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