Automated Search for Conserved Quantities in Particle Reactions

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Automated Search for Conserved Quantities in
Particle Reactions

• Oliver Schulte
• School of Computing Science
• Simon Fraser University
• oschulte_at_cs.sfu.ca

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Outline

• Whats this about?
• Finding conserved quantities in particle
  reactions
• Algorithm
• Data
• Findings
• Introducing extra particles to fit the data better

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CS Goals

• Basic research (good enough) Write programs
  that match the theories from physics.
• Previous work
• Kobacas, Valdes-Perez on discovering selection
  rules.
• Valdes-Perez, Zytkow on (re)discovering particle
  substructure (Physical Review E, 1996)
• Practical use (icing on the cake) analyze data
  to help with new discoveries.

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The Goal Find Absolutely Conserved Quantities

• Omnes (1971), Introduction to Particle Physics.
• The method of assigning quantum numbers is
  rather lengthy so that we give the procedure in
  detail, once and for all.
• Want a program for assigning quantum numbers.

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Basic Principle Disallow as much as you can

• Leon Cooper (1970).
• In the analysis of events among these new
  particles, where the forces are unknown and the
  dynamical analysis, if they were known, is almost
  impossibly difficult, one has tried by observing
  what does not happen to find selection rules,
  quantum numbers, and thus the symmetries of the
  interactions that are relevant.
• Kenneth Ford (1965).
• Everything that can happen without violating a
  conservation law does happen.

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How much can we rule out?
Hypothetical Scenario
observed reactions
not yet observed reactions
?- ? ?- n ?- ? m- nm m- ? e- nm ne n ?
e- ne pp p ? p p ?
n ? e- ne
p p ? p p ? ?
cant rule out
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The Vector Representation for Reactions

• Fix n particles.
• Reaction ? n-vector list net occurrence of each
  particle.

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Conserved Quantities in Vector Space
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Conserved Quantities are in the Null Space of
Observed Reactions

• Let q be the vector for a quantum number, r for a
  reaction.
• Then q is conserved in r ? q ? r 0.
• Let Q be a matrix of quantities. Then Qr 0 ? r
  is allowed by Q.
• So if r1, , rk are allowed, so is any linear
  combination .

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Maximally strict selection rules basis for
nullspace of observations

• Defn A list of selection rules Q is maximally
  strict ? nullspace(Q) span(R).
• Proposition Q is maximally strict ? span(Q)
  R?.

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System for Finding a Maximally Strict Set of
Selection Rules

• Read in Observed Reactions

from database
Convert to list of vectors R
using conversion utility
Compute basis Q for nullspace R?
Maple function nullspace
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The Data Particles

• Particles from Review of Particle Physics
• Total 193 particles
• Separate entries for particle and anti-particles
• e.g., p, p 2 entries
• One entry for same type, different masses
• e.g., just one entry for S(1385), S(1670)

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The Data Reactions

• At least one decay for each particle with a
  decay mode.
• Particle utility converts to vector
  representation.

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Why Decays?

• Wanted linearly independent reactions.
• Proposition Decays of distinct particles are
  linearly independent.

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independent quantities ? unstable particles

• Defn. A particle is stable if it has no decay
  mode, e.g.,

• Proposition Fix n particles, allowed reactions R.
• dim(R?) ? n - unstable particles
• independent conserved quantities ? stable
  particles

• e.g. n 193 particles, 11 stable ? ? 11
  conserved quantities
• because of antiparticles, can be improved to ? 6
  conserved quantities

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Finding 1

• Baryon, E. Charge, Muon, Electron, Tau is
  basis for nullspace of possible reactions.

1. Output of Program is equivalent classifier to
   standard rules.
2. All absolutely conserved quantum numbers are
   linear combinations of Baryon, E. Charge,
   Muon, Electron, Tau e.g., Lepton Muon
   Electron Tau

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Finding 2

• Program matches particle-antiparticle pairings.
• There is an analytic explanation.

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Finding 3

• Different runs seem to produce version of the
  lepton family lawse.g., - Muon, - Electron,
  -Tau.
• No analytic explanation.

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More Particles can lead to stricter Conservation
Principles

• Well-known example if ?e ?e, then n n ? p
  p e- e- should be possible.(Williams
  Ch.12.2).

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When do more particles lead to stricter
Conservation Principles?

• Theorem An extra particle yields stricter
  selection rules for a set of reactions R ?there
  is a reaction r such that
• r is a linear combination of R
• but only with fractional coefficients.

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Hidden Particles, Finding 1

• The standard selection rules are maximally
  strict with respect to transitions among
  nonneutrinos.

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Critical Reaction for ?e ? ?e Discovered by
Computer
Finding if ?e ?e , then the process ? ?0 ? p
e- cannot be ruled out with selection rules.
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Conclusions

• Program computes maximally strict set of
  selection rules.
• Good match with Baryon, E. Charge, Muon,
  Electron, Tau
• Classifies reactions as possible or impossible in
  exact agreement.
• Reproduces particle-antiparticle pairings
• Extra particle Computes a critical experiment to
  test if ?e ?e .

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Further Work

• Search for partially conserved quantities like
  strangeness.
• Historical Analysis of Data (R. Coleman).
• Pitch looking for coauthor/proofreader for
  interdisciplinary or physics publication.