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“Low-x” Physics J.Manjavidze & A.Sissakian

“Low-x” Physics J.Manjavidze & A.Sissakian. Introduction Models for soft processes Hard processes Saturation Equilibrium “tQCD” -- new type perturbation theory Conclusions. ISMD-02, Alushta, Crimea. Introduction (1). “Low-x” problem in pQCD transverse dimension:

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“Low-x” Physics J.Manjavidze & A.Sissakian

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  1. “Low-x” PhysicsJ.Manjavidze & A.Sissakian • Introduction • Models for soft processes • Hard processes • Saturation • Equilibrium • “tQCD” -- new type perturbation theory • Conclusions ISMD-02, Alushta, Crimea

  2. Introduction (1) “Low-x” problem in pQCD transverse dimension: expansion parameters: DIS structure function in LLA: Froissart limit: Screening effects are essential! L.V.Gribov,E.M.Levin and M.G.Ryskin, Phys. Rep., 100 (1983) 1;... ISMD-02, Alushta, Crimea

  3. Introduction (2) VHM and the “low-x” problem Very High Multiplicity: - mean multiplicity multiplicity is not too high: inelasticity coefficient for VHM processes is large: J.Manjavidze, El. Part. At. Nucl., 16 (1985) 101 J.Manjavidze and A.Sissakian, JINR Rap. Comm., 5/31 (1988) 5 ISMD-02, Alushta, Crimea

  4. Introduction (3) Phenomenology of VHM processes Generating function inverse problem: equation “of state”: asymptotic estimation: “chemical potential”: ISMD-02, Alushta, Crimea

  5. Introduction (5) VHM: definition “Big partition function” Statement: at , is the leftist singularity of J.Manjavidze and A.Sissakian, JINR Rap. Comm., 5/31 (1988) 5 ISMD-02, Alushta, Crimea

  6. Introduction (6) Classification of asymptotics -- multiperipheral models: -- (semi)hard processes: -- unstable vacuum (first order ph. tr.) Asymptotic classes: -- multiperipheral models -- (semi)hard processes -- unstable vacuum J.Manjavidze and A.Sissakian, Phys. Rep., 346 (2001) 1 ISMD-02, Alushta, Crimea

  7. Models Multiperipheral kinematics: longitudinal momenta: transverse momenta: Multiperipheral (Regge) anzats: the «superpropagator» The LLA of pQCD gives: E.Kuraev, L.Lipatov and V.Fadin, Sov. Phys. JETP, 44 (1976) 443 V.Fadin, talk at present Conference L.Lipatov, talk at present Conference ISMD-02, Alushta, Crimea

  8. VHM Solutions: Multiperipheral Model Critical Pomeron, • “Pomeron weak coupling model” leads to • “Pomeron strong coupling model” leads to Above-critical Pomeron, • Model may predict singularity at Dual resonance model. • Mass spectrum of resonances • Resonance decay onto hadrons is assumed Poissonian The model gives : Conclusion: MP kinematics predicts: J.Manjavidze and A.Sissakian, Phys. Rep., 346 (2001) 1 ISMD-02, Alushta, Crimea

  9. Range of validity of MPM Range of validity of the multiperipheral anzats • to produce the multiplicity one must use Pomerons • mean impact parameter • to exclude short distance interactions: J.Manjavidze, El. Part. At. Nucl., 16 (1985) 101 ISMD-02, Alushta, Crimea

  10. Hard processes Definitions • DIS kinematics: • structure function with gluons is • LLA describes Brownian motion over coordinate the time is The mobility must be high: Yu.L.Dokshitcer, D.L.Dyakonov and S.I.Troyan, Phys. Rep., 58 (1980) 271;... ISMD-02, Alushta, Crimea

  11. LLA in VHM kinematics • One may introduce The evolution (DGLAP) equation gives: Considering jets creation, probability to produce gluons in the gluon jet of the mass: In result: • The mobility depends on multiplicity: LLA has finite range of validity in the VHM region ISMD-02, Alushta, Crimea

  12. pQCD jets • Evolution equation: If then the solution: Introduction of infrared cut-off does not alter the estimation! Jet «generate» moving singularity at Conclusion: the tendency to weighting of pQCD jets in the VHM domain is predicted J.Manjavidze and A.Sissakian, Phys. Rep., 346 (2001) 1 ISMD-02, Alushta, Crimea

  13. Renormalons • «Renormalons» reflect an uncertainty to pQCD The infrared renormalon uncertainty indicates necessity to include the non-perturbative effects G.t’Hooft, «The why’s of subnucl. phys.» Erice, 1977; B.Lautrup, Phys.Lett., B69 (1978) 109 A.H.Mueller, Nucl.Phys., B250 ( 1985) 327, V.I.Zacharov, Nucl. Phys., B385 (1992) R.Akhouri and V.I.Zakharov, hep-ph/9610492, V.I.Zakhrov, hep-ph/9811294 ISMD-02, Alushta, Crimea

  14. ISMD-02, Alushta, Crimea

  15. Saturation: definitions • Saturation: the occupation number of «low-x» gluons can not be arbitrary large • Saturation scale: Number of gluons: becomes large in the weak coupling limit: The dynamics becomes essentially classical! D.Kharzeev, E.Levin and M.Martin, hep-ph/0111315; A.H.Mueller, hep-ph/0111244; L.McLeran and R.Venugopalan, Phys.Rev., D49 (1994) 2233; D50 (1994) 2225; Yu.Kovchegov, Phys.Rev., D54 (1996) 5463 NNN, present Conference ISMD-02, Alushta, Crimea

  16. ISMD-02, Alushta, Crimea

  17. ISMD-02, Alushta, Crimea

  18. ISMD-02, Alushta, Crimea

  19. ISMD-02, Alushta, Crimea

  20. Equilibrium • Statement: multiple production hadron final state in the deep VHM region is equilibrium. J.Manjavidze and A.Sissakian, Phys. Rep., 346 (2001) 1; See also: Proceedings of the Int. Workshops on «Very High Multiplicity Physics»Dubna, 2000, 2001, 2002. ISMD-02, Alushta, Crimea

  21. tQCD: references+idea • Vacuum expectation value N.N.Bogolyubov & S.Tyablikov, Zh. Eksp. Teor. Phys.,19 (1949) 256 R.Jackiw, C.Nohl and C.Rebbi, 1978; R.Jackiws, 1977 G.W.Mackey, 1969 N.P.Landsman & N.Linden, 1991; N.P.Landsman, 1991 C.J.Isham, 1984 Faddeev, in “Solitons” L.D.Faddeev & V.E.Korepin, Phys. Rep., 42 (1978) 1 (Gauge invariance) (Unitarity condition) (Time reversibility) ISMD-02, Alushta, Crimea

  22. tQCD: Dirac measure • Unitary definition of measure ISMD-02, Alushta, Crimea

  23. tQCD: YM theoryon manifold • Differential measure : • Perturbations generating operator • Interactions generating functional ISM D-02, Alushta, Crimea

  24. tQCD: generator of events J.Manjavidze, J.Math.Phys. 41 (2000) 5710; J.Manjavidze and A.Sissakian, J.Math.Phys. 42 (2001) 641, 42 (2001) 4158; Theor. Math. Phys.; 123 (2000) 776; 130 (2002) 153; Phys. Rep., 346 (2001) 1; hep-ph/0201182 ISM D-02, Alushta, Crimea

  25. Conclusions • It is impossible to consider the “low-x” domain without VHM effects. • tQCD --- presents expansion over inverse interaction constant: (i) no divergences (ii) no phenomenological dimensional constant of -type (iii) no “asymptotic freedom” (?) --- each order is gauge invariant (i) no Faddeev-Popov gauge fixing conditions • tQCD “works” at arbitrary distances • tQCD includes the pQCD as a “small distance” approximation • tQCD presents expansion over Plank constant ISMD-02, Alushta, Crimea

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