S, T and U parameters

Transcription

1 S, T and U parameters Karamitros Dimitrios Physics Department, Division of Theoretical Physics, University of Ioannina, GR-45110, Greece 19/04/2013, Crete

2 Motivation For light external fermions we only need loop corrections to the gauge propagators (oblique corrections) 1. 1 D. C. Kennedy, ``Renormalization of electroweak gauge interactions,'' FERMILAB-CONF T

3 Motivation For light external fermions we only need loop corrections to the gauge propagators (oblique corrections) 1. The effect of the oblique corrections to the EW observables can be written in terms of some finite parameters. 1 D. C. Kennedy, ``Renormalization of electroweak gauge interactions,'' FERMILAB-CONF T

4 Motivation For light external fermions we only need loop corrections to the gauge propagators (oblique corrections) 1. The effect of the oblique corrections to the EW observables can be written in terms of some finite parameters. We can use these finite parameters for precision measurements at low energies. 1 D. C. Kennedy, ``Renormalization of electroweak gauge interactions,'' FERMILAB-CONF T

5 Oblique corrections Assumptions-Approximations 1. Electroweak gauge symmetry: SU(2) U Y (1). 2. Negligible external fermion masses. 3. The scale of new physics is much greater than the Electroweak scale.

6 1PI Diagrams We need to calculate only 1PI diagrams (2nd assumption) The general form of this diagram is Π µν IJ = ig µν Π IJ (q 2 ) + iq µ q ν F IJ (q 2 ).

7 1PI Diagrams We need to calculate only 1PI diagrams (2nd assumption) The general form of this diagram is Π µν IJ = ig µν Π IJ (q 2 ) + iq µ q ν F IJ (q 2 ). The term F IJ (q 2 ) does not contribute.

8 Definitions EW Noether currents in the Isospin and electric charge basis: J µ W = e J µ 1 s W J µ γ = ej µ Q J µ Z = e ) (J µ 3 s W c s2 J µ Q W

9 Definitions 1PI corrections in the Isospin and electric charge basis Π WW (q 2 ) = e2 s 2 Π 11 (q 2 ) W Π γγ (q 2 ) = e 2 Π QQ (q 2 ) Π Zγ (q 2 ) = Π ZZ (q 2 ) = e2 ( Π3Q (q 2 ) s 2 Π QQ (q 2 ) ) s W c W e2 s 2 W c2 W ( Π33 (q 2 ) 2s 2 Π 3Q (q 2 ) + s 4 Π QQ (q 2 ) )

10 Definitions 1PI corrections in the Isospin and electric charge basis Π WW (q 2 ) = e2 s 2 Π 11 (q 2 ) W Π γγ (q 2 ) = e 2 Π QQ (q 2 ) Π Zγ (q 2 ) = Π ZZ (q 2 ) = Because of U Q (1) e2 ( Π3Q (q 2 ) s 2 Π QQ (q 2 ) ) s W c W e2 s 2 W c2 W ( Π33 (q 2 ) 2s 2 Π 3Q (q 2 ) + s 4 Π QQ (q 2 ) ) Π γγ (0) = Π γz (0) = 0.

11 S, T and U parameters Taylor expansion of Π's at q 2 = 0 Π 11 (q 2 ) Π 11 (0) + q 2 d dq 2 Π 11(q 2 ) q 2 =0, Π 33 (q 2 ) Π 33 (0) + q 2 d dq 2 Π 33(q 2 ) q 2 =0, Π QQ (q 2 ) q 2 d dq 2 Π QQ(q 2 ) q 2 =0, Π 3Q (q 2 ) q 2 d dq 2 Π 3Q(q 2 ) q 2 =0.

12 S, T and U parameters Observations: Six Taylor coefficients.

13 S, T and U parameters Observations: Six Taylor coefficients. Three basic EW parameters (α, G F and M Z ).

14 S, T and U parameters Observations: Six Taylor coefficients. Three basic EW parameters (α, G F and M Z ).. Three finite linear combinations!

15 S, T and U parameters These three finite combination are known as S, T and U parameters 2 2 M. E. Peskin and T. Takeuchi, `Estimation of oblique electroweak corrections,'' Phys. Rev. D 46 (1992) 381

16 S, T and U parameters These three finite combination are known as S, T and U parameters 2 S = 16π ( Π 33 (0) Π 3Q (0)) T = 4π s 2 c 2 m 2 (Π 11 (0) Π 33 (0)) Z U = 16π (Π 11 (0) Π 33 (0)) where Π IJ (0) d dq 2 Π IJ(q 2 ) q 2 =0 2 M. E. Peskin and T. Takeuchi, `Estimation of oblique electroweak corrections,'' Phys. Rev. D 46 (1992) 381

17 S, T and U parameters Are these parameters finite? The infinite parts of the Pi's are of the form Π ( ) 11 (q2 )=Π ( ) 33 (q2 ) ( A + q 2 B ) log(λ)

18 S, T and U parameters Are these parameters finite? The infinite parts of the Pi's are of the form Π ( ) 11 (q2 )=Π ( ) 33 (q2 ) ( A + q 2 B ) log(λ) Π ( ) 3Q (q2 ) q 2 B log(λ)

19 S, T and U parameters Are these parameters finite? The infinite parts of the Pi's are of the form Π ( ) 11 (q2 )=Π ( ) 33 (q2 ) ( A + q 2 B ) log(λ) Π ( ) 3Q (q2 ) q 2 B log(λ). S, T and U are finite!

20 S, T and U parameters Estimation of S, T and U for almost degenerate masses of fermions S new fermions (T 3L T 3R ) 2 T m2 M 2 Z U Dm2 M 2 N. Limited space for chiral fermions! non-decoupling effect

21 Examples Example I: ψ L,R ( ) Y ψu ψ d ( ) Y Example II: Q Y qu L q d L, χ Y 1 L,R, L,R, q Y+1 R 1, q Y 1 R 2.

22 Example I

23 Example I

24 Example I

25 Example II

26 Example II

27 Example II

28 Outlook Parametrization of corrections to the EW observables in terms of three parameters!

29 Outlook Parametrization of corrections to the EW observables in terms of three parameters! Easy to calculate diagrams (only oblique corrections and no counterterms)!

30 Outlook Parametrization of corrections to the EW observables in terms of three parameters! Easy to calculate diagrams (only oblique corrections and no counterterms)! High energy physics contributions that affect low energy experiments!