1 / 30

Power Corrections and the Meson Distribution Amplitudes in LaMET

Power Corrections and the Meson Distribution Amplitudes in LaMET. Jiunn-Wei Chen National Taiwan U. Collaborators (LP3): Saul D. Cohen, Tomomi Ishikawa, Xiangdong Ji, Luchang Jin, Huey-Wen Lin, Yu-Sheng Liu, Yi-Bo Yang, Jianhui Zhang, Rui Zhang, Yong Zhao.

danaholt
Download Presentation

Power Corrections and the Meson Distribution Amplitudes in LaMET

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Power Corrections and the Meson Distribution Amplitudes in LaMET Jiunn-Wei Chen National Taiwan U. Collaborators (LP3): Saul D. Cohen, Tomomi Ishikawa, Xiangdong Ji, Luchang Jin, Huey-Wen Lin, Yu-Sheng Liu, Yi-Bo Yang, Jianhui Zhang, Rui Zhang, Yong Zhao

  2. Ji’s Quasi-PDF (LaMET)(Phys. Rev. Lett. 110 (2013) 262002) • Quark PDF in a proton: • Boost invariant in the proton momentum direction, rest frame OK • Quark bilinear op. always on the light cone • What if the quark bilinear is slightly away from the light cone (space-like) in the proton rest frame?

  3. Then one can find a frame where the quark bilinear is of equal time but the proton is moving.

  4. Then one can find a frame where the quark bilinear is of equal time but the proton is moving.

  5. Then one can find a frame where the quark bilinear is of equal time but the proton is moving. • Analogous to HQET: need power corrections & matching---LaMET (Large Momentum Effective Theory)

  6. Quasi-PDF • OPE yields op. symmetric but not traceless .

  7. Quasi-PDF • RHS: trace • LHS: trace, twist-4, • One loop matching , OPE

  8. We need:

  9. We need:

  10. We need:

  11. We need: Now we have 6.8 > 3 >> 0.15 ~ 0.2,0.14 > 0.1 (GeV) Hadron momentum big enough s.t. higher loop matching might be more important than power corrections.

  12. Mass Corrections (Lin, JWC, Cohen, Ji, 1402.1462; JWC, Cohen, Ji, Lin, Zhang, 1603.06664) • Computed to all orders in

  13. Twist-4 Corrections • Rossi & Testa: rather than !

  14. Power Divergence in Quasi-PDF(Ishikawa, Ma, Qiu, Yoshida; JWC, Ji, Zhang) . All orders (Ji, Zhang, Zhao; Ishikawa, Ma, Qiu, Yoshida)

  15. Twist-4 Corrections • Rossi & Testa: rather than ! • This does not happen after the power divergence in the quark bilinear is subtracted/renormalized. (Only one counterterm is needed for this task.)

  16. Twist-4 Corrections (JWC, Cohen, Ji, Lin, Zhang, 1603.06664)

  17. Lots of Work on the RG of Wilson Coefficient Xiong, Ji, Zhang, Zhao (GPD: Ji, Schafer, Xiong, Zhang; Xiong, Zhang) Factorization (Ma, Qiu; Li; OPE: Izubuchi, Ji, Jin, Stewart, Zhao), Linear divergence & LPT (Ishikawa, Ma, Qiu, Yoshida; JWC, Ji, Zhang;Xiong, Luu, Meissner; Rossi, Testa; Constantinou et al.; Wang, Zhao, Zhu), RI (Monahan & Orginos; Yong & Stewart; Constantinou et al.), NPR(Constantinou et al.; LP3; Ji, Zhang, Zhao; Ishikawa, Ma, Qiu, Yoshida; Green, Jansen, Steffens), E vs. M spaces (Carlson et al.; Briceno et al.), …

  18. Meson Distribution Amplitudes (DAs) Common inputs in the factorization theorems of ( ) (tagging) (CPV) Simplest thing to test LaMET!

  19. Why SU(3)? • Two folds: • Exp: large difference in direct CPV of (HFAG) (CDF)

  20. Why SU(3)? • Th: At , ChPT predicts (JWC, Stewart, PRL 2004): • Chiral logs all absorbed by the decay constants • Scales: >> >> meson mass • Matching the twist-2 operators in ChPT • (JWC,Ji; Arndt, Savage, 2001)

  21. Are we crazy? eta from connected diagrams • disconnect diagrams: • Dominated by u,d states when time longer than the energy difference between the s and u,d states • The energy difference is suppressed by inversed momentum. Plateau reached at for , so we are safe. • mixing to negligible: Under this approximation,

  22. Lattice Computation • Lattice: • Fermions: MILC highly improved staggered quarks (HISQ) Clover (valence) • Gauge fields/links: hypercubic (HYP) smearing, 967 config., 4 source locations • n = 2,3,4 (w/ momentum smearing: Bali, Lang, Musch, Schafer, ‘16)

  23. We need: However, in this exploratory study, we have 5.2 >> 1.65 > 0.11 <(!) 0.2,0.31 > 0.2 (GeV)

  24. SU(3)

  25. Summary • We are moving to the large momentum region where power corrections are less important than the matching. However, it is important to confirm that twist-4 is indeed small. • Meson DA should provide a good test for LaMET. But we need to reach like the proton PDF.

  26. Outlook • Further tests (non-singlet)---Know whether it works within 3 years (~20%)? • Singlet PDF’s: s, c, b and gluons Additional 3-5 yrs? • If it works, complimentary to exp.: PDF (isov. sea, small and large x’s, non-valence partons), DA, GPD, TMD …

  27. Backup slides

  28. Mass Corrections (Lin, JWC, Cohen, Ji, 1402.1462; JWC, Cohen, Ji, Lin, Zhang, 1603.06664)

More Related