Proton structure at low Q2 Wei Zhu East Chin Normal University

Our collaboration E (East China-Normal University)^2 + I (Institute of Modern-Physics)^1 C (Collaboration) =EIC 2012-2015

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

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 EIC@HIAF.

First part EIC@HIAF 3+12 GeV 2 GeV 3_12

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

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

A naive idea

PDF

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).

DGLAP

DGLAP Resummation

Evolution of second moment

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.

Experiments at Q^2<1GeV^2

Smaller x

JLab larger x Partonic scaling +Hadron resonance

Parton correlations at low Q^2 and full x

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

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

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.

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.

??

Stricken quark must be on mass shell 26

Backward component Forward component

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

Breaking factorization

Vector meson dominance (VMD) model 31

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

A. D. Martin, M. G. Ryskin arXiv:hep-ph/9802366v2 Christer Friberg arXiv:hep-ph/0005048v1 B.Badelek, M.Krawczyk, J.Kwiecinski, A. M. Stasto arXiv:hep-ph/0001161v2

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.

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.

Our motivation

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.

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

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

Free parameters 4

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

Prediction

Dynamic predictions of gluon distribution in proton and nuclei

2. Dynamic prediction of gluon distribution in nuclei

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.

Prediction

at low Q^2 4. Explanation

5. Quark saturation in proton and nuclei Prediction

Quark saturation

Saturation in Nuclear Shadowing

6. Polarized parton distributions Explanation

A larger glounic helicity Prediction

Predictive behavior of g_1^p at small x

Our prediction

7. Simple parameterization of the GDH sum rule

8. Quark-hadron duality Explanation

Conclusions

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.