1. Proton structure at low Q2
Wei Zhu
East Chin Normal University

2. Our collaboration
E (East China-Normal University)^2 +
I (Institute of Modern-Physics)^1
C (Collaboration)
=EIC

3. First part (15 min.)
Why we study the proton structure at low Q^2?

4. Second part (10 min.)
Using a simple model we explain and predict many aspects about un-polarized and polarized proton structure, which can be tested in

5. First part
GeV
2 GeV
3_12

6. EIC@HIAF is essentially a lower energy EIC
The proton structure at lower Q^2 is an important subject for

7. Two faces of the proton At rest At infinite momentum frame
Only 1 GeV^2 gap
We lack a “bridge”
Q^2~0 GeV^2
Q^2>1GeV^2
At rest
At infinite momentum frame At

8. A naive idea

9. PDF

10. A pioneer work
G. Parisi and R. Petronzio, Phys. Lett. B62, 331 (1976); V.A. Novikov, M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, JETP Lett., 24, 341 (1976); M. Gluck, E. Reya, Nucl. Phys. B 130, 76 (1977).

12. DGLAP

13. DGLAP Resummation

14. Evolution of second moment

15. Reya
for Q2 ~1 GeV^2 one can obtain a reasonable agreement with the experimental result that at low values of Q^2 about 50% of the nucleon momentum is carried by gluons.
\mu^2=0.064GeV^2.
However, such natural inputs fail due to overly steep behavior of the predicted parton distributions at small x.

16. Experiments at Q^2<1GeV^2

17. Smaller x

18. JLab larger x
Partonic scaling +Hadron resonance

19. Parton correlations at low Q^2 and full x

20. The leading (twist-2) term corresponds to scattering from a single free parton,
The higher twist terms correspond to multi-quark and quark-gluon interactions
Only a little of higher twist can been calculated perturbatively in terms of quark and gluon degrees

21. Q^2<1GeV^2
DGLAP ? ??

22. Recombination of two initial partons
L. V. Gribov, E. M. Levin and M. G. Ryskin, Phys. Rep. 100 (1983) 1.
H. Mueller and J. Qiu, Nucl. Phys. B 268 (1986) 427.
W. Zhu, Nucl. Phys. B 551 (1999) 245.
W. Zhu and J. H. Ruan, Nucl. Phys. B 559 (1999) 378.
W. Zhu and Z. Q. Shen, HEP & NP 29 (2005) 109.

23. Why is ZRS correction at low Q^2?
1. Parton fusion (gluon+gluon, quark+quark, quark+gluon) in a full x range.
2. Naturally connecting with DGLAP equation.
3. Parton number at low Q^2<< that at high Q^2.

25. ??

26. Stricken quark must be on mass shell26

28. Backward component
Forward component

29. Factorization Coefficient function Universal parton distribution γT*
PQCD
γT* 29

30. Breaking factorization

31. Vector meson dominance (VMD) model31

33. Our model A simple bridge from Q^2~ 0 to >1GeV^2
VMD part is irrelevant to the definition of PDF!
It does not participate the PDF evolution but
contributes to F_2

34. A. D. Martin, M. G. Ryskin arXiv:hep-ph/9802366v2
Christer Friberg arXiv:hep-ph/ v1
B.Badelek, M.Krawczyk, J.Kwiecinski, A. M. Stasto arXiv:hep-ph/ v2

35. What is new? ZRS correction is new
It provides an smooth connection between perturbative partonic picture
and nonperturbative hadronic picture.
Some quantitative predictions become possible.

36. If we haven’t ZRS corrections
We can’t put starting point of QCD evolution down to \mu^2=0.064GeV^2.
We haven’t simplest input.
Input contains uncertainly gluon distribution.
We can’t separate asymmetry light sea.
We haven’t quark saturation.
We don’t know the contribution of gluon
to proton spin……
7. I haven’t this ppt.

37. Our motivation

38. Two possible results 1. ? is small.
All higher order corrections are almost absorbed into the free parameters.
We have a useful bridge between Q^2=0 and 1 GeV^2.
? is large.
It provides an important information about higher order QCD effects.

39. Second part (A short review within 10 min.)
Database of PDF in proton and nuclei.
Dynamic prediction of gluon distribution in proton and nuclei.
Dynamic determination of asymmetric light sea in proton.
Quark saturation in proton and nuclei.
A larger glounic helicity and the origin of proton spin .
Quark-hadron duality.
Generalized Gerasimov-Drell-Hearn sum rule

40. 1. PDF database in nucleon and nuclei with minimum free parameters
Explanation

43. Free parameters 4

44. Comparing with GRV (Gluck-Reya-Vogt)
Free parameters 16

45. Prediction

47. Dynamic predictions of gluon distribution in proton and nuclei

48. 2. Dynamic prediction of gluon distribution in nuclei

50. 3. Dynamic determination of asymmetric light sea in proton
The symmetric and asymmetric sea quarks have not yet completely separated from experiments.
The reason is that the solutions of QCD evolution equation depend on the initial parton distributions, which are fixed at an arbitrary scale Q_0^2 1~ GeV^2, where the asymmetric sea always mixes with the symmetric sea since the gluons are already produced.

53. Prediction

58. at low Q^2 4.
Explanation

59. 5. Quark saturation in proton and nuclei
Prediction

61. Quark saturation

62. Saturation in Nuclear Shadowing

65. 6. Polarized parton distributions
Explanation

68. A larger glounic helicity
Prediction

69. Predictive behavior of g_1^p at small x

70. Our prediction

76. 7. Simple parameterization of the GDH sum rule

79. 8. Quark-hadron duality
Explanation

82. Conclusions

83. One small step for a man, one giant leap for mankind
Armstrong’s famous comment when he first stepped down in the lunar surface-1969
One small step for a man, one
giant leap for mankind
I wish that from Q^2=0 to 1 GeV^2
is such a step in the proton structure.