Minimal Flavor Violating Z boson. Xing-Bo Yuan. Yonsei University

Transcription

1 Minimal Flavor Violating Z boson Xing-Bo Yuan Yonsei University Yonsei University, Korea 21 Sep 2015

2 Outline 1. Standard Model and Beyond 2. Energy Scalar of New Physics Beyond the SM From Naturalness: Higgs boson Form Flavor Physics: meson mixing 3. Minimal Flavor Violation 4. Minimal Flavor Violating Z boson Collaboration with Prof.C.S.Kim and Dr.Y.Zheng 2 / 34

3 Standard Model 3 / 34

4 Flavor Physics and Standard Model β decay K L µ + µ K 0 K 0 K L π + π B 0 B 0 4 / 34

5 0 Higgs discovery Local p-value -2-4 CMS 1 s -1 = 7 TeV, L = 5.1 fb s -1 = 8 TeV, L = 5.3 fb 1σ 2σ 3σ 4σ -6 5σ Local p Combined obs. Exp. for SM H H γγ H ZZ H WW H ττ 7σ H bb m H (GeV) 1-1 ATLAS s = 7 TeV: "Ldt = fb -1 s = 8 TeV: "Ldt = fb Obs. Exp. ±1! m H [GeV] 6σ 0! 1! 2! 3! 4! 5! 6! mass: m h = 126 GeV spin party Yukawa coupling gauge coupling 5 / 34

6 New Physics Beyond the SM Experimental argument: Neutrino oscillation Dark Matter Origin of the Baryon Asymmetry Dark Energy Gravity Theoretical argument: 19 free parameters, particle masses and mixing patterns gauge group and particle representation origin of EW symmetry breaking, why Higgs mechanism / 34

7 What we know about New Physics Energy Scale 7 / 34

8 Outline 1. Standard Model and Beyond 2. Energy Scalar of New Physics Beyond the SM From Naturalness: Higgs boson From Flavor Physics: meson mixing 3. Minimal Flavor Violation 4. Minimal Flavor Violating Z boson 8 / 34

9 NP Scale: from Naturalness If SM is an effective theory below NP scale Λ Higgs mass receives quadratically divergent radiative corrections t δm 2 h = +... = c 16π 2 Λ2 Unnatural cancellation for large Λ e.g. Λ GUT = O( 16 ) GeV, Λ Planck = O( 18 ) GeV fine-tuning m 2 h = m2 h,0 + c 16π 2 Λ2 = 126 GeV 2 reg. independent Possible Answer: Λ NP = O(1) TeV. There must be new degree of freedom that manifest themselves in high energy collisions at the TeV energy scale. δm 2 h = t + NP / 34

10 NP Scale: from Flavor Physics Meson mixing: B d B d, B s B s, K 0 K 0 Feynman Diagram b W Mass eigenstate s u, c, t u, c, t s W + b Time evolution B H s = B s + ɛ B s 1 + ɛ 2 i dψ(t) dt B L s = ɛ B s + B s 1 + ɛ 2 ( ) = Ĥψ(t) ψ(t) = Bs B s Hamiltonian Ĥ = ˆM i ( 2 ˆΓ M11 i = 2 Γ 11 M 12 i 2 Γ ) 12 M 21 i 2 Γ 21 M 22 i 2 Γ 22 / 34

11 NP Scale: from Flavor Physics Mass difference Numerics M s M s H M s L = 2 M 12 Ms SM Ms exp = (17.3 ± 2.6) ps 1 = ( ± 0.021) ps 1 NP contribution within EFT: M 12 = M12 SM + M 12 NP M12 NP Ck Λ 2 B s ( bγ k s) 2 B s NP NP scale 2 5 TeV C12 4 1/2 K 0 K 0 Λ NP > 2 3 TeV C13 4 1/2 B d B d 3 2 TeV C23 4 1/2 B s B s 11 / 34

12 NP scale: problem From naturalness argument about Higgs mass Λ NP = O(1) TeV From flavor physics 2 5 TeV C12 4 1/2 K 0 K 0 Λ NP > 2 3 TeV C13 4 1/2 B d B d 3 2 TeV C23 4 1/2 B s B s Flavor Problem: if we insist on the theoretical prejudice that NP has to emerge in the TeV region, we have to conclude that the new theory possesses a highly nongeneric flavor structure. C ij should be not generic derived from EFT, but appears in SUSY, technicolor,... Solution? C ij = (λ t V tiv tj ) 2 C = Λ NP > few TeV 12 / 34

13 NP scale: problem and solution From naturalness argument about Higgs mass Λ NP = O(1) TeV From flavor physics 2 5 TeV C12 4 1/2 K 0 K 0 Λ NP > 2 3 TeV C13 4 1/2 B d B d 3 2 TeV C23 4 1/2 B s B s Flavor Problem: if we insist on the theoretical prejudice that NP has to emerge in the TeV region, we have to conclude that the new theory possesses a highly nongeneric flavor structure. C ij should be not generic derived from EFT, but appears in SUSY, technicolor,... Solution: Minimal Flavor Violation hypothesis C ij = (λ t V tiv tj ) 2 C = Λ NP > few TeV 13 / 34

14 Outline 1. Standard Model and Beyond 2. Energy Scalar of New Physics Beyond the SM 3. Minimal Flavor Violation Flavor Puzzle Natural Flavor Violation Minimal Flavor Violation 4. Minimal Flavor Violating Z boson 14 / 34

15 Flavor Puzzle In the SM, the flavor structure comes from the Yukawa couplings L SM = L gauge + L Higgs + L Yukawa It can not account for the matter-antimatter asymmetry of the universe. All the flavor data is consistent with the SM prediction. 15 / 34

16 Flavor Puzzle Diagonal Yukawa coupling: mass spectrum is strongly hierarchical, e.g. m u m c m t Non-diagonal flavor mixing matrix small for quarks large for leptons V CKM = 1 λ λ λ 1 λ 2 U PMNS = λ 3 λ λ 0.22 Suppression of the Flavor Changing Neutral Current (FCNC) for quarks consistent with all the flavor data small room for New Physics contribution FCNC in NP models should be naturally suppressed 16 / 34

17 Natural Flavor Conservation Natural Flavor Conservation hypothesis (NFC) S.Glashow and S.Weinberg, PRD, 1977 Basic idea No tree-level FCNC coupling in NP models Flavor conservation follows from the group structure and representation content of the theory, rather than from the particular values of the parameters. Example: NFC Two-Higgs doublet model Quarks receive their mass from one neutral Higgs. Realized by discrete Z 2 symmetry 17 / 34

18 Progress for how to naturally suppress FCNC : From NFC To MFV 1987: B. Chivukula and H. Georgi, PLB [SU(3) U(1)] 5 flavor symmetry Flavor symmetry breaking and spurion: QL Y D HD R SUSY with minimal flavor violation 1996: G. Branco, W. Grimus and L. Lavoura, PLB A class of 2HDM: FCNC couplings of the neutral Higgs are related in an exact way of the CKM. 2001: A.J.Buras, P.Gambino, M.Gorbahn, S.Jager, L.Silvestrini, PLB Here we will concentrate on models like the SM, the 2HDM I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM [14] and in which all flavourchanging transitions are governed by the CKM matrix with no new phases beyond the CKM phase. 18 / 34

19 Minimal Flavor Violation Minimal Flavor Violation hypothesis (MFV) G.D Ambrosio, G.Giudice, G.Isodori, A.Strumia, NPB, 2002 MFV: the dynamics of flavor violation is completely determined by the structure of the ordinary Yukawa couplings and all CP violation originates from the CKM phase. Effective theory with MFV 19 / 34

20 MFV: Realization in EFT Flavor symmetry SU(3) 3 q = SU(3) QL SU(3) UR SU(3) DR SU(3) 2 l = SU(3) L L SU(3) ER Flavor symmetry breaking Lagrangian: Yukawa interaction L Y = Q L Y D D R H + Q L Y U U R H c + L L Y E E R H + h.c. Flavor symmetry recovering formally, assigned transformation property, spurions Y U (3, 3, 1) SU(3) 3 q Y D (3, 1, 3) SU(3) 3 q Y E (3, 3) SU(3) 2 l Choose basis (field redefinition by flavor symmetry) Y U = V λ u Y D = λ d Y L = λ l 20 / 34

21 MFV: Realization in EFT Spurion representation Y U (3, 3, 1) SU(3) 3 q Y D (3, 1, 3) SU(3) 3 q Y E (3, 3) SU(3) 2 l Example: effective FCNC operators for down-type quarks Q L Y U Y U Q L D R Y D Y UY U Q L D R Y D Y UY U Y DD R Basic flavor changing couplings for down-type quarks { (Y U Y U (λ FC ) ij = ) ij λ 2 t V3i V 3j, i j 0, i = j 21 / 34

22 MFV: Lepton Sector V.Cirigliano, B.Grinstein, G.Isidori, M.B.Wise, NPB, 2005 Not straightforward: Quark MFV = Lepton MFV Mechanism for neutrino masses Minimal field content: SM field (L i L and ei R ) Extended field content: SM field + ν i R 22 / 34

23 MFV: Lepton Sector with minimal field content Flavor symmetry G LF = SU(3) L SU(3) E Flavor symmetry breaking Lagrangian L = ē R λ e H L L 1 2Λ LN ( L c Lτ 2 H)g ν (H T τ 2 L L ) + h.c. vē R λe L v2 2Λ LN ν c Lg ν ν L + h.c. U(1) LN breaking is independent from G LF breaking small ν mass is attributed to the smallness of v/λ LN Flavor symmetry recovering: spurion representation L L V L L L λ e V R λ e V L e R V R e R Basis LFV coupling g ν V L g ν V L = g νg ν = Λ2 LN v 4 Ûm2 νû 23 / 34

24 Outline 1. Standard Model and Beyond 2. Energy Scalar of New Physics Beyond the SM 3. Minimal Flavor Violation 4. Minimal Flavor Violating Z boson Why Z boson Minimal Flavor Violating Z Experimental constraints 24 / 34

25 Z boson Z boson/additional U(1) gauge symmetry Grand Unified Theoryies, e.g. E 6 SU(5) U(1) χ U(1) φ EWSB scenarios, e.g. little Higgs, extra dimension,... Models to explain Darker Matter Dr.Jeong s talk@last week Bottom-up approach L = Γ L ll lγ µ P L l Z µ + Γ L qq qγµ P L q Z µ + L R Γ ll and Γ qq are generally 3 3 coupling matrix used to explain exp data: e.g. recent b sl + l anomaly, A t FB too many parameters, no correlation 25 / 34

26 Z boson within MFV Lagrangian L = Γ L ll lγ µ P L l Z µ + Γ L qq qγµ P L q Z µ + L R Coupling matrix within MFV Γ L ll = λ L Λ 2 LN v 4 ν i m 2 ν i U lνi U l ν i Γ R ll = 0 Γ L qq = κλ2 t V tqv tq Γ R ll = 0 Numerics: Λ LN = 14 GeV, m ν1 = 0.2 ev i i Γ ll = λ L i i i i / 34

27 Z boson: constraints from exp data Model parameter: (λ L, κ, m Z ) Experimental Constraints τ µν ν (2σ), τ eν ν, µ eν ν (G F ) τ 3µ, µ 3e, τ ± e ± µ + µ, τ ± e µ ± µ ±, τ ± µ ± e + e, τ ± µ e ± e ± τ µγ, τ eγ, µ eγ a µ (3σ) NTP: ν µ N νnµ + µ LEP: e + e e + e /e + µ /τ + µ /... µ e conversion: µ N e N, µ e + µ + e B s B s, B d B d, K 0 K 0 mixing B K µ + µ (F L /2.9σ), B s φµ + µ (3.1σ), R(K) = B(B Kµ + µ )/B(B Ke + e ) (2.6σ) 27 / 34

28 Z boson: τ µν ν τ µν ν, τ eν ν, µ eν ν tree-level (SM)+loop-level (SM+NP) τ µν ν: 2σ discrepancy between SM and exp data µ eν ν: used to extract G F < Λ L m Z' TeV 28 / 34

29 Z boson: τ 3µ τ 3µ, µ 3e, τ ± e ± µ + µ, τ ± e µ ± µ ±, τ ± µ ± e + e, τ ± µ e ± e ± tree-level processes µ 3e provides most stringent bounds among all the lepton processes 8 6 Λ L m Z' TeV 29 / 34

30 Z boson: a µ Anomalous magnetic moment: a µ = (g 2) µ /2 Longstanding discrepancy with the SM: a µ = a exp µ a SM µ = (2.9 ± 0.9) 9 Due to no right-handed Z coupling, a NP µ is always negative within MFV Z. Therefore, MFV Z can not explain a µ problem. 30 / 34

31 Z boson: meson mixing B s B s, B d B d, K 0 K 0 mixing SM: loop-level vs NP: tree-level K 0 K 0 mixing: possible large long-distrance contributions B s B s provides most stringent bounds among all the quark processes Κ m Z' TeV 31 / 34

32 Z boson: recent b sl + l anomaly 0.5 C 9 e C e (C µ 9 = Cµ, Ce 9 = Ce ): model-independent NP contributions to b sl+ l Blue region: allowed regions of (C µ 9, Ce 9 ) from all the b sl+ l data. Red line: allowed region of (C µ 9, Ce 9 ) in MFV Z. It is very near to the blue contour but does not intersect with it. MFV Z can not explain the current b sl + l data. 32 / 34

33 Z boson: combined constraints ΛL mz' TeV Blue: combined allowed region of κ/m Z. (B s B s mixing is the strongest). Orange: combined allowed region of λ L /m Z. (µ 3e is the strongest). All the lepton decay or conversion processes put constraints on λ L /m Z. The anomaly in τ µν ν and a µ can not be explained within MFV Z. 33 / 34

34 Thank You! 34 / 34