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Observables in Particle Physics: New Results and Challenges in High-Energy Collisions

Delve into the latest findings and current problems in particle and astroparticle physics and cosmology, exploring the structure of nucleons, collision geometry, and the behavior of observables. Discover the significance of various theoretical concepts and experimental data in understanding high-energy collisions in a space-time perspective.

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Observables in Particle Physics: New Results and Challenges in High-Energy Collisions

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  1. XXIX-th International Workshop on High Energy Physics NEW RESULTS and ACTUAL PROBLEMS in PARTICLE & ASTROPARTICLE PHYSICS and COSMOLOGY June 26-28, 2013, Protvino High-Energy Collisions in Space-Time Perspective V. A. Petrov Division of Theoretical Physics Institute for High Energy Physics

  2. What are observables in particle physics? • S-matrix ( W. Heisenberg, 1943) Ψ (x) S+S = 1 • “The Lagrangean Field Theory is dead and should be buried, with all the proper honors of course.” ( L. Landau, 1960) S

  3. “Elastic” Observables t =- p* 2(1- cosθ*) 1΄ 1 s = (E*1+E*2) 2 2΄ 2 σ p + p → everything = σtot σ p + p →p + p = σel dσ p + p →p + p /dt S

  4. Transverse Space • Moving nucleon’s spatial structure Vacuum fluctuations: Gluons, quark-antiquarks Gluo Valence core

  5. Collision Geometry b1  b b2 b = b1 + b2 + <b2> = <b21 >+ <b22 > + <2>

  6. Nucleon’s valence size • <b21 > = ? • Often: <b21 > = 2/3 r2p • rp = “protons charge radius”  0.88 fm r2p = -6 dF(q2)/dq2q = 0 • r2n = “neutron charge radius”   0.115 fm2 • Correct option: • <b21 > = 2/3 (r2p - r2n )  0.44 fm2 = 11 GeV-2

  7. Overlaps • <b2> = <b21 >+ <b22 > + <2> • <b2>critical = <b21 >+ <b22 > = 2 11 GeV-2 • Relation to observables d/dt  eBt 2B(s)  <b2> • B(s) critical  11 GeV-2

  8. Experiment B = b = 11 GeV-2 at scritical  110-120 GeV2

  9. Proton-proton total cross-section S critical = 10.5 11.0 GeV

  10. Hypothesis: • total cross sections start to grow when valence cores of the colliding hadrons cease to overlap. Cross-check: p collisions B critical  9.1 GeV-2 Happens at p lab  40-50 GeV

  11. Experiment The growth starts at Plab = 40-45 GeV

  12. Where is “true asymptotics”? Natural criterium: B >> B critical LHC (7 TeV) : B =20 GeV-2 = 1.8 B critical B = 5 B critical corresponds to the energy 50-100 TeV

  13. Cross-sections vs Energy

  14. Angular Distribution of Elastically Scattered Protons

  15. Where are other minimae? • Optical analogy ( Fraunhoffer diffraction) d/dt  {J1( Rq)/q}2 q2 = -t Minimae are situated at (non-zero)zeroes of the Bessel function x 1,2,… LHC: -t1 = 0.5 GeV2 = x21/R2 The next minimum should be at • t2 = -t1 (x2/x1)2  1.7 GeV2 ABSENT!

  16. Longitudinal Does the interaction region shrinks in the longitudinal direction? <x||> = <-id/dp||> = 2p*<d/dt>, p*   s/2 T = |T|exp(i  (s,t)) d/dt  |T|2 Can be the scattering phase observed?

  17. Regge poles T = (e -i/2s/s0)(t) (t)  (0) + (0) t <x||> =  s/2 (0)ln(s/s0)  40-50000 fm at  s = 7 TeV 0.5 Angstrem  atomic Bohr radius

  18. Is there any relation to observables? • Fluctuations < x||> = p* /  <t2> - <t>2   s B/2 = 7000  20/2 = 70000 GeV-1 = 14 000 fm Longitudinal range grows with energy enormously.

  19. Where is QCD? • Can we calculate Regge trajectories perurbatively ? • Naïve expectation: (t) =  g2n  n(t) (0) =  g2n  n(0)  (0) =  g2n  n(0) Renormalization group: (0) does not depend on g2  (0)  exp(1/0 g2)

  20. TIME?! • Interaction time grows with energy proportionally

  21. CONCLUSION There remains much to be said in C-major (Arnold Schoenberg)

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