1. Sigma meson cloud and Proton’s light flavor sea quarks Peking University, China ( 北京大学 ) Feng Huang ( 黄 峰） Feng Huang ( 黄 峰） Supervisor: Bo-Qiang Ma （马伯强）

2. outline Introduction Introduction Meson cloud model Meson cloud model Adding sigma meson in this model Adding sigma meson in this model Summary Summary

3. Introduction Gottfried sum rule (GSR) Gottfried sum rule (GSR) NMC results in 1994 (first in 1991) NMC results in 1994 (first in 1991) imply imply

4. Light flavor sea quarks in proton

5. Explanations for this asymmetry Chiral quark model Chiral quark model Meson cloud model Meson cloud model (directly including mesons) Lattice gauge approach Lattice gauge approach Instanton induced interaction Instanton induced interaction Statistical model Statistical model Chiral quark soliton model Chiral quark soliton model (not directly including mesons)

6. Meson cloud model The nucleon was viewed as a bare nucleon plus a series of baryon-meson Fock states which result from the fluctuation of nucleon to baryon plus meson then the physical proton wave function is The nucleon was viewed as a bare nucleon plus a series of baryon-meson Fock states which result from the fluctuation of nucleon to baryon plus meson then the physical proton wave function is

7. So the quark distribution functions q(x) in the proton is the splitting function is

8. We use time-ordered perturbation theory in the infinite momentum frame to calculate this function

9. the quark distribution functions of Pi meson with the splitting function convolution

10. In a full calculation, we should include all kinds of mesons and baryons. While the probability of baryon-meson fluctuation should decrease with the invariant mass of the baryon-meson Fock state increasing, we can neglect the effects of Fock states with higher invariant mass In a full calculation, we should include all kinds of mesons and baryons. While the probability of baryon-meson fluctuation should decrease with the invariant mass of the baryon-meson Fock state increasing, we can neglect the effects of Fock states with higher invariant mass Pion, the lightest meson, plays the dominant role. Difference between u_bar and d_bar in virtual pion clouds can provide the large light flavor asymmetry in proton naturally Pion, the lightest meson, plays the dominant role. Difference between u_bar and d_bar in virtual pion clouds can provide the large light flavor asymmetry in proton naturally

11. Pi mesonic contribution

12. Problem in description for The dominant role is played by the pion, while it provides the ratio either increases monotonically with x or turns back towards unity too slowly. The dominant role is played by the pion, while it provides the ratio either increases monotonically with x or turns back towards unity too slowly.

13. Flavor symmetric sea contribution bare nucleon sea quarks bare nucleon sea quarks (M. Alberg, E. M. Henley, Nucl. Phys. A663 (2000) 301) isoscalar meson, such as omega, sigmaisoscalar meson, such as omega, sigma (M. Alberg, E. M. Henley, G. A. Miller, Phys. Lett. B471 (2000) 396)

14. Using different bare sea quarks Comparison of a harder bare nucleon sea quarks (thick solid line) with a traditional bare sea quarks (dashed line). Comparison of a harder bare nucleon sea quarks (thick solid line) with a traditional bare sea quarks (dashed line). The thin solid line is only Pi contribution to the ratio The thin solid line is only Pi contribution to the ratio

15. Adding sigma meson in this model Sigma meson Sigma meson a) isoscalar scalar meson a) isoscalar scalar meson b) chiral partner of Pi b) chiral partner of Pi c) not well established in experiment c) not well established in experiment

16. The splitting function

17. the quark distribution functions of sigma meson We assume the valence and sea quark distribution of mesons related here are the same. We assume the valence and sea quark distribution of mesons related here are the same.

18. Adding sigma effects here Our calculations illustrate that the larger value of tends to give small values of the ratio and decreasing causes the maximum value of the ratio to be large and to appear at higher value of x Our calculations illustrate that the larger value of tends to give small values of the ratio and decreasing causes the maximum value of the ratio to be large and to appear at higher value of x

19. Together with omega meson compare pion+omega (dashed curve, Alberg- Henley ’ s work) to pion+omega+sigma. compare pion+omega (dashed curve, Alberg- Henley ’ s work) to pion+omega+sigma.

20. Parameters related omega meson Lambda_omega as 1.5GeV could cover over the sigma contribution Lambda_omega as 1.5GeV could cover over the sigma contribution we present the number of the related mesons in the proton with the different cutoff values we present the number of the related mesons in the proton with the different cutoff values

21. Parameters and meson numbers in the proton The larger cutoff value leads to a large meson number in proton The larger cutoff value leads to a large meson number in proton A reasonable picture of proton favors smaller cutoff of omega A reasonable picture of proton favors smaller cutoff of omega

22. Summary The inclusion of the sigma meson cloud effects has an improvement of the description for light flavor sea quarks in the proton The inclusion of the sigma meson cloud effects has an improvement of the description for light flavor sea quarks in the proton We also provides a picture of a reasonable small n_omega with a smaller cutoff in the proton. We also provides a picture of a reasonable small n_omega with a smaller cutoff in the proton. Sigma meson may play an important role in meson cloud model Sigma meson may play an important role in meson cloud model