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Advancements in Low-x Physics: Models, Saturation, and Equilibrium

Explore the complexities of Low-x physics, from soft processes to hard processes, introducing tQCD perturbation theory and discussing the phenomenon of equilibrium. Delve into various models and classifications for a thorough understanding. Discover the implications of VHM and the multiperipheral model, shedding light on the critical Pomeron and resonance decay mechanisms. Unravel the concepts of Renormalons and Saturation, highlighting the classical dynamics at play. This comprehensive guide provides insights into cutting-edge research and predictions in the field of Low-x physics.

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Advancements in Low-x Physics: Models, Saturation, and Equilibrium

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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

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  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

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  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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