Bs → PV decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach Da-cheng Yan Ping Yang, Xin Liu, Zhen-Jun Xiao Nanjing Normal Univercity 2017.10.29 HFCPV @CCNU

Outline Motivation Framework and contents Numerical results Summary

Motivation（theory） (LO)

Motivation（theory） (NLO)

Motivation (experiment) First observation of the decay at LHCb JHEP 01, 012 (2016) Observation of and evidence for decays New J. Phys. 16, 123001(2014)

Framework and contents Transition matrix elements: the weak effective Hamiltonian can be written as: In PQCD factorization approach,

Framework and contents Wave functions • B_s meson the light-cone distribution amplitude:

Framework and contents Wave fuctions • Pseudo-scalar meson the light-cone distribution amplitude: Twist-2: Twist-3: Gegenbauer moments：

Framework and contents • decay constant: are:

Framework and contents • Vector meson the light-cone distribution amplitude: Twist-2: Twist-3: Gegenbauer moments：

Framework and contents Leading order contributins factorizable emission diagrams( ) hard-spectator diagrams( ) annihilation diagrams( ) annihilation diagrams( )

Framework and contents Total decay amplitudes at LO (general expression):

Framework and contents Next-to-leading order contributins (1) The NLO vertex corrections (VC). (2) The NLO contributions from the quark-loops(QL). (3) The NLO contributions from the chromo-magnetic penguin (MP) operator . (4) The NLO twist-2 and twist-3 contributions to the form factors of .

Framework and contents Next-to-leading order contributions (1) Vertex corrections redefinition of the Wilson coefficients : where M is the meson emitted from the weak vertex.

Framework and contents Vertex functions (NDR scheme) Phys. Rev. D 72, 114005 When M is a vector meson

Framework and contents (2) Quark loops : A kind of penguin correction ( transition): up quark loop : ~ charm quark loop : ~ QCD penguin loop : ~

Framework and contents The effective Hamiltonian ： Phys. Rev. D 72, 114005

Framework and contents (3)Chromo magnetic penguins (MP): A another kind of penguin correction ( transition): The effective Hamiltonian ：

Framework and contents (4) The form factors at NLO level (Phys.Rev. D 85, 074004) (Phys.Rev. D 89, 094004) NLO twist-2 and twist-3 contributions to form factors

Framework and contents Total decay amplitudes at NLO : Branching ratios (Br) and CP asymmetries:

Numerical results NLO contributions to the form factor Branching ratios

Numerical results The agreements between the PQCD predictions and the three measured values are indeed improved significantly due to the inclusion of the NLO contributions.

Numerical results CP-violating asymmetries

Summary • The effects of the NLO contributions on the PQCD predictions for the branching ratios and CP asymmetries of the considered decay modes are channel dependent. • From the variations of the ratios R1,2,3, one can see that the agreements between the PQCD predictions and the measured values are improved significantly due to the inclusion of the NLO contributions. • The effects from the inclusion of the NLO contributions to the form factor are always small: less than 10% in magnitude.

Thank you!