On-shell Renormalization of Chargino and Neutralino Masses in the MSSM

1. On-shell Renormalization of Chargino and Neutralino Masses in the MSSM 徐庆君 杭州师范大学理学院 全国第九届重味物理和CP破坏研讨会 2011.10.15 杭州 • References:  • Chatterjee, M. Drees, S. Kulkarni and Q. Xu, arXiv:1107.5208 [hep-ph] • Q.Xu, Ph.D. thesis, arXiv:0912.5160 [hep-ph] • M. Drees, W. Hollik and Q.Xu, hep-ph/0610267, JHEP 0702:032,2007

2. Outline • Supersymmetry and the MSSM • Renormalization of Chargino and • Neutralino Sector • Application of our work All possible choices Radiative corrections to Chargino and Neutralino masses Carefully study possible singularities and instabilities

3. Supersymmetry and the MSSM Supersymmetry (SUSY) is a solution to the SM • Make the Higgs mass at higher orders stable • SUSY connects Fermions to Bosons • It is not yet been observed, SUSY is broken • MSSM: minimal Supersymmetric Standard Model cancel quadratic and logarithm div. No extra quadratic div. Logarithm div. exist • Two Higgs doublets five Higgs bosons

4. Supersymmetry and the MSSM Particle Content of the MSSM

5. Supersymmetry and the MSSM Advantages • Stabilize the Higgs mass • Better unification of • the coupling constants • R-parity conserved Lightest Supersymmetric Particle (LSP) is stable Dark Matter Candidate: New phenomenology: Supersymmetric Particles decay to LSP, missing energy Complaint • Lots of free parameters; • Unknownsoft-breaking terms and mechanism; • Not observed yet, neither the Higgs boson.

6. Supersymmetry and the MSSM ATLAS and CMS does not see SUSY, neither other new physics • Three SUSY Breaking Mechanism: 1. mSUGRA (minimal Supergravity), CMSSM (mSUGRA) is ruled out! 2. AMSB (Anomaly Mediated Supersymmetry Breaking), 3. GMSB (Gauged Mediated Supersymmetry Breaking) • Other SUSY models: FVMSSM, R-parity Violated MSSM, NMSSM • Luminosity will be increased Possibility will be enhanced • ILCcan do a better work. SUSY is still one of the interesting new physics models

7. Charginos and Neutralinos at tree level Digitalization 6 eigenstates: 4 neutralinos and 2 Charginos is bino-like, , or largest coupling is wino-like, , or largest is higgsino-like, with largest 7

8. Determine Chargino and Neutralino Masses 3 measured masses 3 MSSM Parameters 1-loop 1-loop Other Chargino and Neutralino masses Three Main tasks: Renormalization of the Chargino and Neutralino Sector （all possible choices) Radiative corrections to Chargino and Neutralino masses Carefully study possible singularities and instabilities 8

9. Renormalization of Chargino and Neutralino Sector Renormalization Scheme • On shell renormalization scheme See: A. Denner, Fortschr.Phys.41(1993)307; Counterterms are fixed in a way that finite renormalized parameters are equal to physical quantities renormalization scheme UV divergent part proportional to is Euler’s constant Counterterms are defined that they only contain UV divergent part of bare parameters or fields

10. Renormalization of Chargino and Neutralino Sector fixed in Chargino and Neutralino sector Same as in SM see: A. Denner, Fortschr.Phys.41(1993)307 fixed in Higgs sector, DRbar scheme

11. Renormalization of Chargino and Neutralino Sector 3 counterterms 3 masses are chosen to be inputs • Principles: • Choose masses of lighter states, since they are easy detected at colliders; • Choices should not give large corrections to other masses.

12. Renormalization of Chargino and Neutralino Sector Tools: FeynArts, FormCalc and LoopTools 12

13. Renormalization of Chargino and Neutralino Sector

14. Renormalization of Chargino and Neutralino Sector Parameters: Correction to higgsino-like neutralino mass in scheme 1b: Inputs at Correction to wino-like chargino mass in scheme 3b: inputs at

15. Experiment (1.) determine the characteristic of measured Charginos and Neutralions (Higgsino-like, wino-like, or bino-like?) (2.) choose three inputs and the proper renormalization scheme to determine the MSSM parameters Theory calculation Interesting parameters choose three proper input states further calculation Application of our work 谢谢！ 15

16. Backup Slide Define: Parameters:

17. Backup Slide Parameters: Scheme 1a: inputs Scheme 1b: inputs singularity at absolute value of negative eigenvalue of Neutralino mass matrix ( ) at , eigenvalue is positive give mass to discontinuity is excluded at LEPII!

18. Backup Slide Parameters: Scheme 1a: inputs Scheme 1b: inputs Behavior badly at Discontinuities due to change of bino-like Neutralino

19. Backup Slide Parameters: singularity at Scheme 2b: inputs Discontinuity due to change of bino-like Neutralino

20. Backup Slide Parameters: No singularity at Scheme 2c: inputs Discontinuities due to change of bino-like Neutralino and wino-like Chargino, respectively

21. Backup Slide Parameters: Scheme 2c: inputs Discontinuities due to change of bino-like Neutralino and higgsino-like neutralino

22. Backup Slide Parameters: Scheme 3a: inputs Large instability at Behavior poorly for

23. Backup Slide Parameters: Scheme 3b: inputs No singularity at

24. Backup Slide Parameters: Scheme 3b: inputs When , denominator of counterterms vanish instability Better than that at