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q=q V +q sea q=q sea so: total sea (q+q): q sea = 2 q Kresimir Kumericki, Dieter Mueller, Nucl.Phys.B841:1-58,2010.

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Presentation on theme: "q=q V +q sea q=q sea so: total sea (q+q): q sea = 2 q Kresimir Kumericki, Dieter Mueller, Nucl.Phys.B841:1-58,2010."— Presentation transcript:

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2 q=q V +q sea q=q sea so: total sea (q+q): q sea = 2 q Kresimir Kumericki, Dieter Mueller, Nucl.Phys.B841:1-58,2010.

3 Belitsky A V, Mueller D and Kirchner A 2002 Nucl. Phys. B –392

4 H Im H Re H Im H Re HERMES x B =0.09,Q 2 =2.5 JLab (Hall A) x B =0.36,Q 2 =2.3 t (GeV 2 )

5 x b(GeV -1 ) H u (x,b ) y x z

6 VGG prediction Fit with 7 CFFs (boundaries 5xVGG CFFs) Fit with 7 CFFs (boundaries 3xVGG CFFs) Fit with ONLY H and H ~ t-dependence at fixed x B of H Im & H Im ~ Axial charge more concentrated than electromagnetic charge ?

7 In the non-perturbative regime the interaction of quarks and gluons is highly non-linear

8  (more data existing) L.O calculation with running  s calculation with k perp effects One example:

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10

11 ,

12 Regge theory: Exchange of families of mesons in the t-channel

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14 Regge theory: Exchange of families of mesons in the t-channel M(s,t) ~ s  (t) where  (t) (trajectory) is the relation between the spin and the (squared) mass of a family of particles M->s  (t)  tot ~1/s x Im(M(s,t=0))->s  (0)-1 [optical theorem]  tot d  /dt s t d  /dt~1/s 2 x |M(s,t)| 2 ->s  (t)-2 ->[e  (t)lns(s) ]

15 Each time a reaction proceeds via the exchange of a charged (meson) in the t-channel, the cross-section decreases (  (0)~0.5) However, when a reaction proceeds via the exchange of vacuum quantum numbers, the cross section doesn’t decrease (even slightly increases).

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17 However, in contrast with meson trajectories, there is no physical particles which has been identified very Conclusively for such trajectory. [QCD:glueballs] =>Introduction of a trajectory with intercept  (0) ~1 : the Pomeron [  (0) ~1.08] Each time a reaction proceeds via the exchange of a charged (meson) in the t-channel, the cross-section decreases (  (0)~0.5) However, when a reaction proceeds via the exchange of vaccuum quantum numbers, the cross section doesn’t decrease (even slightly increases).

18 The theory of Regge poles has been very popular a few decades ago because it could describe the main characteristics of numerous processes with a limited number of parameters Difficulty to connect Regge with quantum field theory (QCD) and the fundamental degrees of freedom (quarks, gluons)=> hadronic theory. However, relative loss of interest after: describe with precision the data and refine the theory means to go beyond the basic hypothesis and becomes very quickly complicated. For instance, other singularities than simple poles (cuts…) =>first approximation

19 ,

20 ,

21 , Q 2 >>

22 ,

23 Some signatures of the (asymptotic) « hard » processes:  L /  T ~Q 2  J  ~9/1/2/8  L ~1/Q 6  T ~1/Q 8  ~|xG(x)| 2 Q 2 dependence: W dependence: (for gluon handbag) Ratio of yields: (for gluon handbag) Saturation with hard scale of  P (0), b, … SCHC : checks with SDMEs

24 LO (w/o kperp effect) Handbag diagram calculation needs k perp effects to account for preasymptotic effects LO (with kperp effect) Same thing for 2-gluon exchange process

25 H1, ZEUS, Q 2 >>

26 H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS

27 H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS + « older » data from: E665, NMC, Cornell,…

28 H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS + « older » data from: E665, NMC, Cornell,…

29 Steepening W slope as a function of Q 2 indicates « hard » regime (reflects gluon distribution in the proton) W dependence

30 Two ways to set a « hard » scale: *large Q 2 *mass of produced VM W dependence Steepening W slope as a function of Q 2 indicates « hard » regime (reflects gluon distribution in the proton) Universality :  at large Q 2 +M 2 similar to J/ 

31  P (0) increases from “soft” (~1.1) to “hard” (~1.3) as a function of scale  2 =(Q 2 +M V 2 )/4. Hardening of W distributions with  2

32 Approaching handbag prediction of n=6 (Q 2 not asymptotic, fixed W vs fixed x B,  tot vs  L, Q 2 evolution of G(x)…) Q 2 dependence  L ~  /Q 6 => Fit with  ~1/(Q 2 +M V 2 ) n Q 2 >0 GeV 2 => n=2+/ Q 2 >10 GeV 2 => n=2.5+/ Q 2 >0 GeV 2 => n= / /  J  (S. Kananov) Q 2 dependence is damped at low Q 2 and steepens at large Q 2

33 t dependence b decreases from “soft” (~10 GeV -2 ) to “hard” (~4-5 GeV -2 ) as a function of scale  2 =(Q 2 +M V 2 )/4

34 Ratios  J  ~ 9/1/2/8 (SU(4) universality)    1/sqrt(2){|uu>-|dd>}  1/sqrt(2){|uu>+|dd>}   Ratio  =9

35 L/TL/TL/TL/T (almost) compatible with handbag prediction (damping at large Q 2 )

36 SDMEs HERMES H1 (almost) no SCHC violation

37 At high energy (W>5 GeV), the general features of the kinematics dependences and of the SDMEs are relatively/qualitatively well understood Good indications that the “hard”/pQCD regime is dominant for for  2 =(Q 2 +M V 2 )/4 ~ 3-5 GeV 2. Data are relatively well described by GPD/handbag approaches

38 H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS

39 Exclusive  0,   electroproduction on the CLAS6 on the CLAS6 S. Morrow et al., Eur.Phys.J.A39:5-31,2009 (  J. Santoro et al., Phys.Rev.C78:025210,2008 ( L. Morand et al., Eur.Phys.J.A24: ,2005 ( C. Hadjidakis et al., Phys.Lett.B605: ,2005 (  GeV) K. Lukashin et al., Phys.Rev.C63:065205,2001 ( GeV) } e1-b (1999) } e1-6 ( ) A. Fradi, Orsay Univ. PhD thesis (  GeV) } e1-dvcs (2005)

40 e1-6 experiment (E e =5.75 GeV) (October 2001 – January 2002)

41 ep  ep  + (  - ) Mm(epX) Mm(ep  + X) e p ++  - )

42 1) Ross-Stodolsky B-W for  0 (770), f 0 (980) and f 2 (1270) with variable skewedness parameter, 2)  ++ (1232)  +  - inv.mass spectrum and  +  - phase space. Background Subtraction

43    (  * p  p  0 ) vs W

44 L. Morand et al., Eur.Phys.J.A24: ,2005 ( C. Hadjidakis et al., Phys.Lett.B605: ,2005 (  GeV) K. Lukashin, Phys.Rev.C63:065205,2001 ( GeV) J. Santoro et al., Phys.Rev.C78:025210,2008 ( S. Morrow et al., Eur.Phys.J.A39:5-31,2009 (      A. Fradi, Orsay Univ. PhD thesis, 2009 ( 

45 GK  L LL ep->ep     

46 GPDs parametrization based on DDs (VGG/GK model) Strong power corrections… but seems to work at large W…

47 VGG GPD model +

48 GK GPD model

49 H, H, E, E (x,ξ,t) ~~ x+ξx-ξ t γ, π, ρ, ω… -2ξ x ξ-ξ-ξ +1 0 Quark distribution q q Distribution amplitude Antiquark distribution “ERBL” region“DGLAP” region W~1/  ERBLDGLAP

50 DDs + “meson exchange” DDs w/o “meson exchange” (VGG) “meson exchange”

51 VMs (  0,  ) the only exclusive process [with DVCS] measured over a W range of 2 orders of magnitude (  L,T, d  /dt, SDMEs,…) At high energy (W>5 GeV), transition from “soft” to “hard” (  2 scale) physics relatively well understood (further work needed for precision understanding/extractions) At low energy (W<5 GeV), large failure of “hard” approach. This is not understood. Is the GPD/handbag approach setting at much larger Q 2 or is the widely used GPD parametrisation in the valence region completely wrong ? A lot of new data expected soon from COMPASS (transv. target), HERA new analysis,…

52 Interpretation “a la Regge” : Laget model  *p  p  0  *p  p   *p  p  Free parameters: *Hadronic coupling constants: g MNN *Mass scales of EM FFs: (1+Q 2 /  2 ) -2

53 Regge/Laget  L (  * L p  p  L 0 ) Pomeron ,f 2

54 Comparison with   


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