1. Chung-Wen Kao Chung-Yuan Christian University
Kaon multiplicities of Semi-inclusive DIS and the fragmentation functions
Chung-Wen Kao
Chung-Yuan Christian University
QNP 2018 Tsukuba, Japan

2. Collaboration and Reference
In Collaboration with
Nam Seung-il (PKU, Korea) Dong-Jing Yang, Fu-Jiun Jiang (NTNU, Taiwan)
Wen-Chen Chang (AS, Taiwan)
This talk is based on the following works:
(1) Nam Seung-il, CWK, Phys. Rev .D85, (2012)
(2) Nam Seung-il, CWK, : Phys.Rev.D85, (2012)
(3) Dong Jing Yang, Fu-Jiun Jaing, CWK, Nam Seung-il:
Phys. Rev D87, (2013)
(4) Dong Jing Yang, Fu-Jiun Jaing, CWK, Nam Seung-il: arXiv
(5) Dong Jing Yang, Fu-Jiun Jaing, Wen-Chen Chang, CWK,
Nam Seung-il: Phys. Lett. B 755(2016) 393

3. How to extract Fragmentation functions?

5. SIDIS using deuteron target
Charge Conjugation of fragmentation functions
Why deuteron ?

6. SIDIS off deuteron target
p: proton, n: neutron

7. SIDIS using deuteron target
Assume PDFs are charge symmetric:

8. SIDIS using deuteron target
DQ>>DS

9. HERMES Data of Pion multiplicity

10. Kaon Multiplicity

11. HERMES Kaon Data
A. Airapetian et al. (HERMES Collaboration), Phys. Rev. D , (2014).

12. Pion and kaon multiplicities
For pion and kaon multiplicities of SIDIS off the deuteron target:
Combine the HERMES data of kaon and DSS07
Fragmentation functions, the strange quark PDF
was extracted.
Phys. Rev. D 89, (2014)

13. Phys.Lett. B755 (2016)

14. Constrains on A and B
Since S(x)>0, Q(x)>0, then S(x)/Q(x) is positive!
At fixed x and Q2 :
Note that the values of and are independent of x!

15. Choices of FFs

16. HKNS (LO)
HKNS (NLO)
DSS (LO)
DSS (NLO)
5.NJL-Jet Model
6.Nonlocal Chiral Quark Model
7.AKK08
8.SMKA 9.DSEHS

17. HKNS (LO)
HKNS (NLO)
DSS (LO)
DSS (NLO)
5.NJL-Jet Model
6.Nonlocal Chiral Quark Model
7.AKK08

18. NLO fitting of SIDIS

19. A game need two players….

20. COMPASS and HERMES The data pointes are taken at
different Q2 values compared
with HERMES data.
Phys.Lett. B767 (2017)

21. COMPASS and HERMES
HERMES
COMPASS

22. COMPASS and HERMES

23. DSS 2017 fragmentation functions
Phys.Rev. D95 (2017) no.9, , already have 27 citations.

24. DSS 2017 fragmentation functions

25. DSS 2017 fragmentation functions

26. DSS 2017 fragmentation functions

27. DSS 2017 fragmentation functions

28. DSS 2017 fragmentation functions

29. Our Puzzle over DSS17
If DSS17 can describe both of HERMES and COMPASS kaon multiplicities well, then the two sets of data surely are compatible.
However, the simple plot shows otherwise.
So what’s going on?
Maybe the difference of two sets of data is indeed due to the different Q2?

30. Test of DSS17 at HERMES and COMPASS kinematics
Using DSS17
Apply DSS17 with MMHT and NNPDF at (x, Q2) of HERMES data points and
COMPASS, we find the theoretical results of both should be close.
The effect of Q2 evolution is not enough to explain the difference between
two data sets.

31. Kaon multiplicity
Using DSS17

32. Check HERMES data K+

33. Check HERMES data K-
Error!
It should be
𝛼=0.38
𝛼=0.07
𝛼=0.02
𝛼=0.00

34. Log to Log & Linear to Linear:
Fit well?

35. MK+(x, Q2) and MK-(x, Q2) Red point: usual integral method
Blue cross: integrate z by HERMES method
Black point: HERMES
For positive and negative kaon,
The PDFXFF values are higher than
The experimental values.

36. Charged Kaon Multiplicity
Similar check on COMPASS kinematics is needed.

37. Three regions Phys.Lett. B766 (2017) 245-253 by
M.Boglione, J.Collins, L.Gamberg, J.O.Gonzalez-Hernandez, T.C.Rogers, N.Sato,
LO cross section: PDF X FF

39. Is it the reason of the serious inconsistency between
pion and kaon multiplicities? How to prove or falsify it?

40. Summary and outlook Is DSS17 good as they claimed?
Can one extract the strange PDFs from the current SIDIS data?
Is there tension between COMPASS and HERMES data of SIDIS?
Is there tension between the pion and kaon multiplicities?
Is the contribution of the central region able to explain the difference between HERMES and COMPASS data?

41. Two data sets of SIDIS cause many confusions, but two cups of ice cream are just perfect!