Distribution Amplitudes of K and from Lattice QCD

Distribution Amplitudes of K* and φ from Lattice QCD Jun Hua Shanghai Jiao Tong University PRL. 127. 062002(2021) (Lattice Parton Collaboration) 第十三届粒子物理学术会议（2021） 1

OUTLINE • Motivation • LCDA by Large-Momentum effective theory • Numerical results • Summary 2

Motivation OUTLINE Consider a B meson decay process QCD factorization: separating the processes with different energy scales Perturbative! Wilson coefficients Non-perturbative, but UNIVERSAL DA 3

Motivation OUTLINE • 4

Research OUTLINE of LCDA • Hadron light-cone distribution amplitudes (LCDAs) have been introduced four decades ago in the context of the QCD description of hard exclusive reactions. —— : Asymptotic 6 x(1 -x) —— : CZ model —— : Light-cone sum rule • Asymptotic LCDA —Theor. Math. Phys. 42 (1980) 97 • QCD sum rules (CZ model)—Nucl. Phys. B 201 (1982) 492 • Light-cone sum rule —Z. Phys. C 44 (1989) 157 • Lattice calculations —Phys. Lett. B 190 (1987) 151 • QCD sum rules— JHEP. 08 (2007), 090 • Light-front quark model —Phys. Rev. D 75 (2007) 034019 • Dyson-Schwinger equations —Phys. Rev. D 90 (2014) 014011 • …… —JHEP 08. 065(2019) 5

Lattice QCD OUTLINE gluons Target LCDA — defined via a meson-to-vacuum matrix element gluons Credit: M. Savage@NNPSS 2015 • Mellin moments by OPE PRD. 92. 014504(2015), JHEP 04. 082 (2017), JHEP 08. 065(2019)…… • Large-momentum effective theory(La. MET__PRL. 110. 262002 (2013)) PRD. 102. 094519(2020), ar. Xiv: 2011. 09788(2020)…… 6

Large-Momentum effective theory OUTLINE Define a new matrix element with an equal-time correlator, named quasi-PDF/DA: Can be calculated on lattice directly! X. Ji. Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110, 262002 (2013). X. Ji. et al. —ar. Xiv: 2004. 03543(2020) 7

LCDA in La. MET OUTLINE time 8

LCDA in La. MET OUTLINE • This work is based on 2+1+1 flavor ensembles generated with tree level tadpole improved clover fermion action and tadpole improved Symanzik gauge action; • Basic informations of three ensembles used in this calculation: 9

LCDA in La. MET OUTLINE Light speed term Discretization effects 10

Hybrid renormalization OUTLINE Work range ? RI/MOM renormalization scheme Y. K. Huo et al. a. Xriv: 2103. 02965 • • • (0 ≤ |z| ≤ Z_s ), RI/MOM renormalization (Z_s ≤ |z| ≤ Z_l ), modified mass renormalization (|z|≥ Z_s ), physics-based extrapolation X. ~Ji, et al. Nucl. Phys. B 964, 115311 (2021) 11

LCDA in La. MET OUTLINE • (Z_s ≤ |z| ≤ Z_l ) Fitted Chi 2: 0. 15 m-1: The coefficient of the power divergence m 0: a. Renormalon effect b. Pole mass c. Finite Pz effects d. Fitting effect. c 1, c 2: ln(z) scale infrared divergence c 0: overall factor 12

Hybrid renormalized Quasi DA OUTLINE • The real part and the imaginary part of quasi DA in coordinate space after Hybrid renormalization: 13

Why extrapolation? OUTLINE The Fourier transformation and inverse problem Cutoff Possible Solutions: R. Zhang et al —ar. Xiv: 2005. 13955(2020) 14

Why extrapolation? OUTLINE The cutoff problem of quasi DA without large z extrapolation: ❖ Asymptotic behavior at x~0, 1: ❖Coordinate space: 15

Inverse matching from quasi to LCDA OUTLINE Matching kernel —Y. S. Liu, W. Wang, J. Xu, Q. A. Zhang…PRD 99(2019). 094034 Delta function Plus function Discretization Quasi DA LCDA 500*500 16

LCDA in La. MET OUTLINE Our final result after matching from DA Quasi DA to LCDA: One can extract Gegenbauer moments from LCDAs by: 17 17

Summary OUTLINE • We present the first lattice QCD calculation of LCDAs of vector mesons K* and φ using Large-Momentum effective theory. • The hybrid renormalization scheme including modified mass renormalization and physical based extrapolation is firstly adopted to avoid extra nonperturbative effects in renormalizing non-local operator. • The entire LCDAs of K* and φ are given and the Thank you very much ! Gegenbauer moments are also extracted from our results. 18