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1 Introduction Models for soft processes Hard processes Saturation Equilibrium “tQCD” -- new type perturbation theory Conclusions “Low-x” Physics “Low-x”

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Presentation on theme: "1 Introduction Models for soft processes Hard processes Saturation Equilibrium “tQCD” -- new type perturbation theory Conclusions “Low-x” Physics “Low-x”"— Presentation transcript:

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

2 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 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 4 Introduction (3) Phenomenology of VHM processes Generating function inverse problem: equation “of state”: asymptotic estimation: “chemical potential”: ISMD-02, Alushta, Crimea

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

6 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 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 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 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 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 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 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 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 14 ISMD-02, Alushta, Crimea

15 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 16 ISMD-02, Alushta, Crimea

17 17 ISMD-02, Alushta, Crimea

18 18 ISMD-02, Alushta, Crimea

19 19 ISMD-02, Alushta, Crimea

20 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 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 22 tQCD: Dirac measure Unitary definition of measure ISMD-02, Alushta, Crimea

23 23 tQCD: YM theory on manifold Differential measure : Perturbations generating operator Interactions generating functional ISM D-02, Alushta, Crimea

24 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 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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