CKMfitter A Mathematica based Version

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1 CKMfitter A Mathematica based Version Andreas Jantsch IKTP Institutsseminar, TU Dresden November 9, 2006

2 Content 1) CKM matrix & Unitarity Triangle 2) The CKMfitter package Original Fortran based version New Mathematica based version 3) Standard Model Fits Results of BEAUTY ) New Physics B-meson mixing Charged Higgs contributions (Two-Higgs-Doublet model) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 2

3 1. The CKM matrix & Unitarity Triangle Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 3

4 The CKM matrix quark masses generation described by Higgs mechanism electroweak eigenstates (d, s, b ) mass eigenstates (d, s, b) mixing matrix VCKM : d ' ' s ' = b V CKM d s b = V ud V us V ub V cd V cs V cb V td V ts V tb d s b untitary, complex 3 3 matrix: 4 independent parameter: 3 mixing angles & 1 global phase non-vanishing phase CP violation (CPV) in the Standard Model several parametriziations: PDG, Wolfenstein,... Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 4

5 The Unitarity Triangle V CKM = V ud V us V ub V V V cd V cs V cb V td V ts V tb + =1 e.g. 1 V ud V ub V cd V cb V td V tb = 0 V cd V cb depends on 4 real parameters: A, λ, É, i = V ud V ub V cd V cb Constraining: A, λ, É, Observables with theoretical predictions f(a, λ, É, ) in Standard Model including external theoretical parameters usually taken from Lattice QCD Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 5

6 Constraints K Kaon mixing B,, V ub / V cb B X (u,c) l Ru R t m d, m s B meson mixing B D () K (),... sin2 B J/ Ks,... Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 6

7 2. CKMfitter Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 7

8 CKMfitter Group Goals Consistency between data & the Standard Model Constraints on CKM & QCD parameters Predictions of observables Consistency between data & New Physics models Publications Eur. Phys. J. C21, , 2001 Eur. Phys. J. C41, 1-131, Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 8

9 The Method Statistical approach Frequentist based approach: specific scheme to treat theoretical errors: Rfit Method Search for : 2 min,global Scan: determination of 2 min in each scan point 2 2 min - 2 min,global Plot: 1-CL = Prob( 2, n dof ) (approximation) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 9

10 The Original CKMfitter Package Code Publicly available More than lines Fortran code Minimization: MINUIT (CERNLIB) Output: hbook file Plots using PAW Difficult fit problem Non-linear systems Mirror solutions from trigonometric functions Problem CPU time consumption dictionary Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 10

11 The Mathematica based Version Mathematica interface Usage of symbolic calculations during fit preparation Load dynamically only necessary inputs & theories no static dictionary Usage of full simplified expressions and derivatives transformed into simplest form Fortran based minimization Very compact Fortran code from fit preparation just 2, nothing else Routine: dmng coded by David M. Gay (from NetLib.org) unconstraint minimization using exact analytical gradients Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 11

12 Structure CKMfitter.nb 1. Fit Preparation 2. Minimization & Scan 3. Output Preparation load write run read save analysis flags theory packages experimental inputs Chi2 file (CHi2.F) minimir minimir output data table & plot Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 12

13 The Mathematica based Version Look-Up Table (LUT) input Some inputs are not just x ± x (e.g.,,...) 2 (observable) from a LUT Only in binned form Cubic spline interpolation Mathematica routine by J. M. Herrmann Called by separate Fortran based subroutine Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 13

14 Performance Tests Conditions CPU: Intel PIII 1266 MHz Memory: 2048 MB OS: Scientific Linux Compiler: gnu f77 -O Original package: Fortran & CERNLIB New version: Mathematica 5.2 & Fortran Granularity: 200 x 200 in (É, ) Fits / Point: 2 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 14

fit results and 2 minimum small discrepancies from different cubic

15 Comparison The original CKMfitter: Combined global fit: 23 h The Mathematica based version: Combined global fit: 10 min consistent fit results and 2 minimum small discrepancies from different cubic spline interpolations Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 15

16 3. Standard Model Fit Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 16

17 V ud & V us V ud : superallowed nuclear beta decays ( ) theoretically very clean Vud = ± CKM 2005 V us : semileptonic Kaon decays e.g. K + 0 e + e Vus = ± PDG 2006 V ud and V us are the main inputs to constrain the CKM parameter Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 17

18 V cb & V ub V cb : V ub : semileptonic B decays semileptonic B decays main constraint on A 2 large background: B X c l incl. meas.: B X c l incl. meas.: B X u l Vcb = (41.70 ± 0.70) 10-3 HFAG Summer 2006 Vub = (4.48 ± 0.24 ± 0.39) 10-3 PDG 2006 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 18

19 UT angle charmless B decays Isospin analysis: B and B Dalitz plot analysis: B performed by CKMfitter group using results from BABAR and Belle multiple solutions combined 2 -function used as LUT input file Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 19

20 UT angle direct CP violation in B D () K () decays combined methods of: Gronau-London-Wyler (GLW) Atwood-Dunietz-Soni (ADS) Giri-Grossman-Soffer-Zupan (GGSZ) performed by CKMfitter group combined 2 -function used as LUT input file Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 20

21 sin2 Time dependent CP asymmetry in the B d system: A CP t = B 0 f CP B 0 f CP B 0 f CP B 0 f CP sin2 sin m d t e.g. fcp + - theoretically very clean currently best constraint on (É, ) B (cc) K S,L, J/ K* 0 (BABAR) B J/ K S,L (Belle) sin2 = ± Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 21

22 K CPV in mixing & CPV in the interference between mixing and decay 00 = A K L 0 0 A K S = A K L + - A K S + - K = K = (2.221 ± 0.008) 10-3 (KTeV & KLEO) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 22

23 K K = G 2 F m 2 W m K f 2 K B K { cc S x c I[V cs V cd 2 ] tt S x t I[V ts V td 2 ] m K 2 ct S x c, x t I[V ts V td V cs V cd 2 ] } Perturbative QCD: S(x q )... Inami-Lim-function Lattice QCD: B K... bag factor (Lattice QCD) xq = m q ²/m W ² f K... decay constant q1q2... perturbative corrections lep. Kaon decay Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 23

24 m q m q = G 2 2 F m W m 6 2 B q B f 2 B q B B q S m 2 t 2 m W V tq V 2 tb Lattice QCD: f Bq 2... decay constant B q... bag factor Measurements: md = (0.507 ± 0.004) ps -1 (HFAG) ms = (17.77 ± 0.12) ps -1 (CDF) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 24

25 BR(B ) helicity suppressed annihilation decay sensitive to (fbd V ub ) 2 helps to reduce fbd dependence in m d BR B = G 2 2 F m B d m 8 Bd f 2 B d V ub 2 combined 2 -function used as LUT input file sensitive to possible charged Higgs contributions Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 25

26 The (É, ) Plane Inputs: V ud, V us V cb Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 26

27 The (É, ) Plane Inputs: V ud, V us V cb Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 27

28 The (É, ) Plane Inputs: V ud, V us V cb m d Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 28

29 The (É, ) Plane Inputs: V ud, V us V cb m d m d & m s Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 29

30 The (É, ) Plane Inputs: V ud, V us V cb m d m d & m s ε K Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 30

31 The (É, ) Plane Inputs: V ud, V us V cb m d m d & m s ε K V ub, BR(B ) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 31

32 The (É, ) Plane Inputs: V ud, V us V cb m d m d & m s ε K V ub, BR(B ) sin2 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 32

33 The (É, ) Plane Inputs: V ud, V us V cb m d m d & m s ε K V ub, BR(B ) sin2 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 33

34 Inputs: V ud, V us V cb Global Fit m d m d & m s ε K V ub, BR(B ) sin2 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 34

35 Global Fit Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 35

36 Global Fit Results = = A = = J = at 95.5%CL Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 36

37 Standard Model Tests Only angles (no theory) No angles (theory dominated) CP violating CP conserving imply CPV Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 37

38 4. New Physics Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 38

39 New Physics in B mixing Assumption: A unitary 3 3 CKM matrix No NP in tree-mediated decay amplitudes Vub /V cb and UT angle remain unchanged New Physics contributions to ΔB = 2 transitions: B 0 H SM NP B 0 B 0 H SM B 0 =r d 2 e i2 d SM values rd 2 = 1 and 2 d = 0 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 39

40 New Physics in B mixing Inputs: V ud, V us V ub V cb m d r 2 d sin(2+2 d ) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 40

41 New Physics in B mixing Inputs: V ud, V us V ub V cb m d r 2 d sin(2+2 d ) cos(2+2 d ) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 41

42 New Physics in B mixing Inputs: V ud, V us V ub V cb m d r 2 d sin(2+2 d ) cos(2+2 d ) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 42

43 New Physics in B mixing Inputs: V ud, V us V ub V cb m d r 2 d sin(2+2 d ) cos(2+2 d ) d Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 43

44 New Physics in B mixing Inputs: V ud, V us V ub V cb m d r 2 d sin(2+2 d ) cos(2+2 d ) d A SL = ± Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 44

45 New Physics in B mixing Inputs: V ud, V us V ub V cb m d r 2 d sin(2+2 d ) cos(2+2 d ) d A SL = ± Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 45

46 Excursus: A SL A SL CP violation in B-mixing A SL = [ B 0 t l X ] [ B 0 t l X ] [ B 0 t l X ] [ B 0 t l X ] The only observable depending on both parameters, r d 2 & 2 d A SL = R SM 12 sin 2 d 2 M 12 r d I SM 12 cos 2 d 2 M 12 r d 12 / M 12 ) SM LO: Laplace et al. (2002) only contributions of O(z) & O(1/mb ), z = m c 2/m 2 b NLO: Beneke et al. (2003) higher corrections in z and 1/mb, penguin contributions ( B = 1) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 46

47 Two-Higgs-Doublet Models 2HDM: indroduce a second Higgs doublet scalar field preferred by MSSM tan = v1 /v 2, with v i = < i > 3 neutral & 2 charged Higgs additional charged Higgs contribution to BR(B ) BR B= G 2 2 F m B m 8 B f B2 V ub 2 1 m l 2 m H tan 2 m 2 B 2 m H 2 Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 47

48 Two-Higgs-Doublet Models inputs: V ub & BR(B ) constraint on (m H+,tan) small mh+ are excluded for large tan LEP (direct search): mh+ > 78.6 GeV/c 2 (95% CL) B X s (Gambino et al.) mh+ > 350 GeV/c 2 (99% CL) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 48

49 Conclusion Summary New version more than 100 times faster than original package Theory packages implemented: CKM matrix, Meson Mixing (m d, m s, K, A SL,... ), B [ SU(2)] for the Standard Model New Physics implemented in B d mixing & K-mixing (model independent) l and model dependend: New Physics in B l (2HDM) Outlook Implement missing theory packages (, K,...) New Physics in B s mixing (model independent) Dresden, Nov 9, 2006 A. Jantsch - Institutsseminar 49

CP Violation in the B system

CP Violation in the B system Outline: Mixing induced CPV and B s mixing phase s Search for CPV in B s mixing Direct CPV in B DK and CKM phase Direct CPV in charmless B decays new Ulrich Uwer Heidelberg