Dbar-ubar asymmetry in the proton in chiral effective theory Ping Wang

1. Dbar-ubar asymmetry in the proton in chiral effective theory Ping Wang Institute of High Energy Physics, CAS Beijing, 2015.1.9-11 1

2. I. Introduction • II. Parton distribution function • III. Numerical results • IV. Summary

3. Introduction Gottifried sum rule (GSR): 3

4. Introduction 4

5. Introduction Generalized parton distribution function: Forward limit: Zero-th order moments, Dirac form factor, Pauli Form factor: First moments:

6. Introduction Theoretical research: Parameterization method: M. Guidal, M.V. Polyakov, A.V. Radyushkin, M. Vanderhaegen, Phys. Rev. D72(2005)054013 Quark models: Bag model: X. Ji, W. Melnitchouk, X. Song, Phys. Rev. D56(1997)5511 Cloudy bag mode: B. Pasquini, S.Boffi, Nucl.Phys.A782(2007)86 Constituent quark model: S. Scopetta, V. Vento, Phys. Rev. D69(2004)094004 Light-front bag model: H. Choi, C.R. Ji, L.S. Kisslinger, Phys. Rev. D64(2001)093006 Betha-Salpeter approach: B.C. Tiburzi, G.A. Miller, Phys. Rev. D65(2002)074009 NJL model: H. Mineo, S.N. Yang, C.Y. Cheung, W. Bentz, Phys. Rev. C72(2005)025202 Color glass condensate model: K. Goeke, V. Guzey, M. Siddidov, Eur. Phys. J. C56(2008)203 Experiments: ZEUS and H1: 10^(-4) < x < 0.02 EIC: Up to x = 0.3 HERMES: 0.02 < x < 0.3 JLab 12 GeV: 0.1 < x < 0.7 COMPASS: 0.006 < x < 0.3

7. Dbar-ubar asymmetry Relativistic Lagrangian: Z Heavy baryon Lagrangian: 7

8. Dbar-ubar asymmetry The convolution form: i i Y is the light-cone fraction of the proton’s momentum (p) carried by pion (k). Tree level contribution is zero

9. Strange form factor P. Wang, D. B. Leinweber and A. W. Thomas, Phys. Rev. D 89, 033008 (2014)

10. Dbar-ubar asymmetry Pion momentum distribution in nucleon: On-shell (nucleon pole) contribution: Off-shell contribution:

11. Dbar-ubar asymmetry Delta intermediate state: On-shell (Delta pole) contribution: End-point singularity at y=1:

12. Dbar-ubar asymmetry Off-shell contribution: Bubble diagram: In the HB limit: ~ f (y) (m << M) = f (y)

13. Dbar-ubar asymmetry LNA behavior: Sullivan approach (on-shell component):

14. Dbar-ubar asymmetry General regulator:

15. Dbar-ubar asymmetry Non-analytic term with DR: First term: Second term: Third term: ==> infinity Same as that with form factor when LNA is the same as that with form factor at finite .

16. Numerical results The constituent building blocks of the nucleon and the pion U and D [Gluck et at]:

17. Numerical results Pionic parton distribution function : 0.26

18. Numerical results Input: valence quark distribution function in pion [Gluck, 99] For µ ranging between 0.1 and 1 GeV, ᴧis fixed by matching the dbar-ubar integral extracted from the E866 Drell-Yan data over the measured x range: 18

19. Numerical results Y.Salamu, W.Melnitchouk,C.R.Ji,P.Wang, arXiv:1409.5885[hep-ph]

20. Numerical results HB limit is comparable with the relativistic case.

21. Numerical results

22. Numerical results Y.Salamu, W.Melnitchouk,C.R.Ji,P.Wang, arXiv:1409.5885[hep-ph]

23. -------------------------------------------------------------------------------------------------------------------------------------------- Report of Referee A -- LW14228/Salamu ---------------------------------------------------------------------- The authors applied a recently developed method (matching of non-local operators within Heavy Baryon Chiral Perturbation Theory) to calculate the $\bar d - \bar u$ asymmetry in the proton. The results are quite interesting, especially, the found cancellation of terms nicely explains the success of a simplified phenomenological description of this flavor asymmetry. The paper is clearly written, and as far as I can judge the obtained results are sound. In summary, I recommend publication of this manuscript. ---------------------------------------------------------------------- Report of Referee B -- LW14228/Salamu ---------------------------------------------------------------------- The paper is claimed to consider the light-quark flavor asymmetry in the framework chiral perturbation theory (chiPT). Unfortunately, this is not a rigorous chiPT calculation. It only assesses the leading non-analytic (LNA) terms. The pertinent low-energy constants (LECs) which come at lower-order in chiPT, and therefore are potentially more important, are omitted. The latter omission shows up in the strong cutoff dependence of the results. Basically one can get any size for the effects by varying the cutoffs. It is not written why these particular cutoffs are chosen, but certainly there is no justification for having them in the chiPT framework. Despite the very interesting topic, promising results and clearly written text, I do not recommend the publication of this manuscript. Not until the authors either discuss the role of the relevant LECs, or reformulate correctly what they are doing. ---------------------------------------------------------------------- Report of Referee C -- LW14228/Salamu ---------------------------------------------------------------------- The authors have presented an interesting analysis of the flavor asymmetry of the light-quark sea in the framework of chiral effective theory. They have identified and calculated the novel contributions to this flavor asymmetry at x=0 originating from the off-shell components and the bubble diagrams. They have found that the full calculations including various terms are surprisingly close to the simplest calculation taking into account only the on-shell pi-nucleon term. The authors have also calculated the x-dependence of the flavor asymmetry, and compared the relativistic versus non-relativistic heavy-baryon results. This paper presents new insights on an important topics in hadron physics. I recommend it be published in PRL. However, the following comments should be addressed by the authors:

24. Summary • ● We compute the dbar-ubar asymmetry in the proton within relativistic and heavy baryon effective field theory Including both nucleon and baryon intermediate states. • ● In addition to the distribution at nonzero x, we also estimate the correction to the integrated asymmetry arising at x = 0, which have not been accounted for in previous empirical analyses. • ● Without attempting to fine-tune the parameters, the overall agreement between the • calculation and experiment is very good. • ●As with all previous pion loop calculations, the apparent trend of the E866 data towards • negative dbar−ubar values for x > 0.3 is not reproduced in this analysis. The new • SeaQuest experiment at Fermilab is expected to provide new information on the shape • of dbar-ubar for x < 0.45. • ● The analysis described here can be applied to other nonperturbative quantities in the • proton, such as the flavor asymmetry of the polarized sea, the strange–antistrange asymmetry, transverse momentum dependent distributions and generalized parton distributions, etc.

25. The End 25

26. Numerical results y y