Search For Dark Matter: Dark Photon And Z' Boson

Search for Dark Matter: Dark Photon and Z’ Boson Shihao Wu Advisors: Dr. Aleksandrs Aleksejevs and Dr. Svetlana Barkanova Grenfell Campus of Memorial University of Newfoundland June 15, 2016 Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 1 / 19

Introduction Outline Dark Photon and Z’ Boson Channel NLO Calculation Results X Model Conclusion Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 2 / 19

Dark Photon and Z’ Boson Extension of U(1) Symmetry Including additional section of U(1) symmetry enable SM to interact with more particles. 1 µν LQED where Aµν µ Aν ν Aµ kin Aµν A , 4 The A’ couples to SM particles through kinetic mixing of U(1)Y & U(1)’ [Holdom (1986)]: 1 1 1 Lkin Bµν B µν Bµν A0µν A0µν A0µν , 4 2 cos θW 4 where Bµ cos θW Aµ sin θW Zµ . Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 3 / 19

Dark Photon and Z’ Boson Dark Photon and Z’ Boson Both dark photon and Z’ have different masses and couplings to the original SM particles defined by the set of mixing parameters. H. Davoudiasl, et. al., arXiv:1203.2947v2, Phys. Rev. D 85, 115019 (2012) Dark photon is parity conserving, consisting of kinetic mixing between dark vector and photon. Lint eQf f γµ f · (Aµ A0µ ) e f (cVf γµ cAf γµ γ5 )f · Z µ (1) sin θW cos θW Z’ Boson is parity violating, consisting of a combination of kinetic and mass mixing between dark vector, photon and Z boson. Lint eQf f γµ f ·(Aµ A0µ ) m0 0Z δ mZZ , where δ 2 3 · 10 5 e f (cVf γµ cAf γµ γ5 )f ·(Z µ 0Z A0µ ), sin θW cos θW (2) is an arbitrary model-dependent parameter. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 4 / 19

Channel Channel The scattering channel used is e e µ µ . The collaborating experiment is the Belle II in Japan, where the energy level is at 10.57 GeV. Born level: One loop level: Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 5 / 19

Asymetry Asymetry New physics focuses on parity violating interaction. However, the magnitude of PV interactions is small comparing to parity conserving interactions. Asymetry (ALR )is introduced as the physical observable for the calculations. ALR σL σR σL σR (3) ALR cancels the parity conserving portions and emphasizes the party violating new physics contribution. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 6 / 19

NLO Calculation NLO Calculation All calculations were done in the Next to the Leading Order to meet the precision requirement. High precision focused search, Dark photon is parity conserving. Z’ boson is parity violating. (most sensitive in ALR ) Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 7 / 19

NLO Calculation Comparison between Born and NLO ALR vs θ for both Born (Red) and NLO (Blue) SM calculations. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 8 / 19

NLO Calculation Mathematica Packages Different ALR were calculated with different masses (MDV/MDVZ) and coupling mixings ( 2 ). All calculations were executed on Mathematica with FeynArts, FormCalc, Form and LoopTools packages. FeynArts: Generating Feynman diagrams and amplitude; FormCalc and Form: Generating analytical expressions for ALR ; LoopTools: Integration tool. T. T. J. V. R. Hahn, Comput. Phys. Commun., 140 418 (2001); Hahn, M. Perez-Victoria, Comput. Phys. Commun., 118, 153 (1999); Vermaseren, arXiv:math-ph/0010025, (2000); Shtabovenko, R. Mertig and F. Orellana, arXiv:1601.01167 (2016); Mertig, M. Bhm, and A. Denner, Comput. Phys. Commun., 64, 345-359 (1991). Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 9 / 19

Results Results Dark Photon 1.5 -0.35 ALR H90 L @10-3D ALR H90 L @10-3D 1.0 -0.40 -0.45 0.5 0.0 -0.50 -0.5 0.00 0.02 0.04 0.06 0.08 0.10 Ε2 ALR vs 2 for dark photon, at MDV 8 GeV. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) 0 5 10 mDP HGeVL 15 20 ALR vs mass for dark photon, at 2 10 2 . June 15, 2016 10 / 19

Results Results Z’ Boson 1.0 ALR H90 L @10-3D ALR H90 L @10-3D -0.55 -0.60 -0.65 0.5 0.0 -0.5 -0.70 0.00 0.02 0.04 0.06 0.08 0.10 Ε2 ALR vs 2 for Z’ boson, at MDVZ 8 GeV. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) 0 5 10 mZ ' HGeVL 15 20 ALR vs Mass (MDVZ) for Z’ boson, at 2 10 4 . June 15, 2016 11 / 19

Results Exclusion Plots Exclusion Plots are generated to demonstrate the sensitive sections of masses (MDV and MDVZ) and coupling mixing ( 2 ) for dark photon and Z’ boson. Exclusion plot for dark photon. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) Exclusion plot for Z’ Boson June 15, 2016 12 / 19

Results Energy Dependence Since Belle II experiment has a fixed energy level, which could potentially influence the ALR value. However, the energy dependence ( S) of asymmetry(ALR ) is equitable. ALR vs S for both dark photon and Z’ boson, where MDV MDVZ 20 GeV, 2 0.01 Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 13 / 19

Future Development X Model Figure : A interacts with SM through new physics particles (NP) loop. In this model, A oscillates through a pair of other new physics particles which then interact with SM particles through a coupling as X : µ1 a12 e iδ1 iφ1 a22 e iδ2 iφ2 , X : µ2 a12 e iδ1 iφ1 Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) (4) a22 e iδ2 iφ2 , (5) June 15, 2016 14 / 19

Future Development X Model f fX Lagrangian g Lfintfx gX f γ µ (1 γ5 )f 0 Xµ gX f 0 γ µ (1 γ5 )fXµ 2 2 g e , sin θW (6) gX a12 e iδ1 iφ1 a22 e iδ2 iφ2 X X V Lagrangian LXint X V { ie cot θW µ X ν ν X µ Xµ Zν µ X ν ν X µ Xµ Zν Xµ Xν ( µ Zν ν Z µ ) ie µ X ν ν X µ Xµ Aν µ X ν ν X µ Xµ Aν Xµ Xν ( µ Aν ν Aµ ) }gX gX (7) Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 15 / 19

Future Development X Model Charge asymmetry: A σ σ σ σ 3D plot for Asymmetry in portions per trillion (ppt) vs δ1 and φ1 with a1 0.1, a2 0.2, mX 50 GeV, δ2 δ1 and φ2 φ1 . Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 16 / 19

Future Development X Model 100 Amax /- [ppt] 10 1 0.100 0.010 0.001 0 20 40 60 MX (GeV) 80 100 Amax in portions per trillion (ppt) vs Mass with a1 0.1, a2 0.2. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 17 / 19

Conclusion Conclusion Z’ boson has a better response to 2 , up to 102 more than dark photon; Provides the possible range for Belle II experiment to look for new physics particles; If Z’ boson is not found in Belle II experiment, exclusion plot will expand and benefit future search; X model provides a promising explanation for dark matter, yet more research are needed; Computer algebra packages can improve the precision calculation effectively. Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 18 / 19

Acknowledgment Acknowledgment Many thanks to Grenfell Campus of Memorial University of Newfoundland NSERC Shihao Wu (Grenfell Campus of Memorial University of Newfoundland) June 15, 2016 19 / 19

Dark Photon and Z' Boson Dark Photon and Z' Boson Both dark photon and Z' have di erent masses and couplings to the original SM particles de ned by the set of mixing parameters. H. Davoudiasl, et. al., arXiv:1203.2947v2, Phys. Rev. D 85, 115019 (2012) Dark photon is parity conserving, consisting of kinetic mixing between dark vector and .