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High-Energy Collisions in Space-Time Perspective

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

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High-Energy Collisions in Space-Time Perspective

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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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