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

2、 Beijing, 2015.1.9-11,I. IntroductionII. Parton distribution functionIII. Numerical results IV. Summary,2,3,3,Introduction,Gottifried sum rule (GSR):,4,4,Introduction,Introduction,Ge

3、neralized parton distribution function:,Zero-th order moments, Dirac form factor, Pauli Form factor:,First moments:,Forward limit:,5,6,Theoretical research:Parameterization method:M. Guidal, M.V. Polyakov, A.V. Radyus

4、hkin, M. Vanderhaegen, Phys. Rev. D72(2005)054013Quark models:Bag model: X. Ji, W. Melnitchouk, X. Song, Phys. Rev. D56(1997)5511Cloudy bag mode: B. Pasquini, S.Boffi, Nucl.Phys.A782(2007)86Constituent quark model:

5、S. Scopetta, V. Vento, Phys. Rev. D69(2004)094004Light-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)074009NJL m

6、odel: 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)203Experiments:ZEUS and H1: 10^(-4) < x < 0.02

7、EIC: Up to x = 0.3HERMES: 0.02 < x < 0.3JLab 12 GeV: 0.1 < x < 0.7COMPASS: 0.006 < x < 0.3,Introduction,7,7,Dbar-ubar asymmetry,Relativistic Lagrangian:,Heavy baryon Lagrangian:,Z,8,Dbar-ubar asymme

8、try,The convolution form:,Y is the light-cone fraction of the proton’s momentum (p) carried by pion (k).,Tree level contribution is zero,i,i,9,Strange form factor,P. Wang, D. B. Leinweber and A. W. Thomas, Phys. Rev. D

9、89, 033008 (2014),10,Off-shell contribution:,On-shell (nucleon pole) contribution:,Pion momentum distribution in nucleon:,Dbar-ubar asymmetry,11,Dbar-ubar asymmetry,End-point singularity at y=1:,On-shell (Delta pole) con

10、tribution:,Delta intermediate state:,12,Dbar-ubar asymmetry,In the HB limit:,f (y) (m << M) = f (y),~,Off-shell contribution:,Bubble diagram:,13,Dbar-ubar asymmetry,LNA behavior:,Sullivan approach (on-shell compon

11、ent):,14,Dbar-ubar asymmetry,General regulator:,,,,15,Dbar-ubar asymmetry,==> infinity,Non-analytic term with DR:,First term:,Second term:,Third term:,LNA is the same as that with form factor at finite .,Same as

12、that with form factor when,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 :,0.26,18,18,Numerical results,I

13、nput: valence quark distribution function in pion [Gluck, 99],For µ ranging between 0.1 and 1 GeV, ? is fixed by matching the dbar-ubar integral extracted from the E866 Drell-Yan data over the measured x range:,19,

14、Y.Salamu, W.Melnitchouk,C.R.Ji,P.Wang, arXiv:1409.5885[hep-ph],Numerical results,20,Numerical results,HB limit is comparable with the relativistic case.,21,Numerical results,22,Y.Salamu, W.Melnitchouk,C.R.Ji,P.Wang,arXi

15、v:1409.5885[hep-ph],Numerical results,23,----------------------------------------------------------------------Report of Referee A -- LW14228/Salamu----------------------------------------------------------------------

16、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 interest

17、ing, 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 res

18、ults are sound. In summary, I recommend publication of this manuscript.----------------------------------------------------------------------Report of Referee B -- LW14228/Salamu---------------------------------------

19、-------------------------------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 asse

20、sses 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 stro

21、ng 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 th

22、em 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 relev

23、ant LECs, or reformulate correctly what they are doing.----------------------------------------------------------------------Report of Referee C -- LW14228/Salamu-------------------------------------------------------

24、---------------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 t

25、o 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 taki

26、ng 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 present

27、s 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 th

28、e 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 int

29、egrated 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 expe

30、riment 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 SeaQu

31、est 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

32、 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,