CKM Matrix and CP Violation in Standard Model

Transcription

1 CKM Matrix ad CP Violatio i Stadard Model Origi of CKM Matrix. B meso produc,o at B factories Lecture 13 Shahram Rahatlou Fisica delle Par,celle Elemetari, Ao Accademico

2 Outlie Origi of Cabibbo-Kobayashi-Maskawa (CKM) Matrix What is it? Where does it come from? Why do we care about it? How is it related to the quark masses? Why ad how is it related to CP violatio? Overview of experimetal measuremets of CKM elemets CP violatio i the Stadard Model Little bit of History Types of CP violatio B mesos ad their importace Formalism of CP Violatio at B factories Overview of experimetal measuremets B physics at LHC 2

3 Stadard Model 3

4 Mass of Quarks i the Stadard Model For each geeratio we have oe left-haded SU(2) doublet, ad two righthaded siglets SU(3) triplet SU(2) doublet hypercharge Q-T 3 Quarks iteract with Higgs field via Yukawa couplig Eigestates of weak iteractios Geeric complex matrix of yukawa couplig costats Quarks acquire mass through because of spotaeous symmetry breakig Mass matrices for up ad dow quarks. Elemets are complex! 4

5 Weak Iteractios ad Mass Eigestates Diagoalize mass matrices to obtai mass eigestates Rotate quark fields by with uitary complex matrices V ul, V ur, V dl, V dr Choose arbitrary phases so that M is diagoal Lagragia for weak iteractios of quarks Uiversality of weak iteractios: same costat g for all coupligs Lagragia after goig from iteractio to mass eigestates No more uiversal couplig costat! 5

6 No More Uiversality of Weak Iteractios I absece of CKM matrix all weak iteractios have same couplig This is referred to as uiversality of weak iteractios g Because of CKM matrix couplig depeds o quarks ivolved i the trasitio Uiversality is broke! V ij 6

7 Cabibbo-Kobayashi-Maskawa Matrix V = V V CKM ul dl V Vud Vus Vub = V V V Vtd Vts V tb CKM cd cs cb Origi of CKM matrix is the differece betwee mass eigestates ad weak iteractio eigestates Lagragia of Stadard Model is diagoal i weak eigestates with uiversal couplig costat Uiversality is broke whe movig from iteractio basis to mass basis ecessary to obtai Lagragia for mass terms after spotaeous symmetry breakig V CKM is a uitary complex matrix 7

8 Properties of CKM Matrix Necessary for CP Violatio i SM Today we kow there are three flavors, or geeratios of quarks But this was ot the case whe CKM matrix was first proposed i 1973! 8

9 How do we kow there oly 3 geeratios of matter? 9

10 Number of eutrio families from CERN 10

11 Families of Matter kow i 1972 Three Quarks for Muster Mark! Joyce u? d s Oly 2 families were kow e µ ν ν e µ Charm quark ot eve observed yet! 11

12 Kobayashi-Maskawa Mechaism of CP Violatio 1972 Two Youg Postdocs at that time! Proposed a darig explaatio for CP violatio i K decays CP violatio appears oly i the charged curret weak iteractio of quarks There is a sigle source of CP Violatio Complex Quatum Mechaical Phase δ ΚΜ i iter-quark couplig matrix Need at least 3 Geeratio of Quarks (the ot kow) to facilitate this CP is NOT a approximate symmetry, δ ΚΜ 1, it is MAXIMALLY violated! 12

13 1974: Discovery of charm i J/psi 13

14 1977: Discovery of bottom i FNAL µ + PRL (1977) µ - ϒ(1S) ϒ(1S) ϒ(2S) ϒ(3S) 14

15 Features of CKM Matrix Relative magitudes d s b u c t 15

16 Wolfestei Parameterizatio of CKM Matrix Wolfestei first saw a patter with 4 parameters Cabibbo agle with 2 geeratios V CKM = 1 λ 2 /2 λ Aλ 3 ( ρ iη ) λ 1 λ 2 /2 Aλ 2 Aλ 3 (1 ρ iη) Aλ O ( λ4) λ A = V 2 = Vcb λ 2 2 ρ η Vub λ ( V ) cb + = ( V ) η ρ = ta arg ub? us e 1 1 -iβ e -i γ 16

17 Measuremets of CKM Elemet Magitudes e - e - e - p υ e K π b u l υ d c! # # # # # # # # # # # # " V ud = ( ±0.02% ) V cd =.230 ( ±5% ) V td ( ±7% ) V us = ( ±0.4% ) V cs =1.006 ( ±2% ) = = V ts ( ±6% ) V ub =0.004 ( ±12% ) V cb =0.041 ( ±3% ) V tb =0.89 ( ±8% ) $ & & & & & & & & & & & & % b D l + e- c l + K t b PDG review of CKM b quark plays a special role i determiatio of CKM elemets! 17

18 Measurig CKM Elemets Measuremets related to first 2 geeratios briefly discussed here Most measuremets established sice a while Mostly focus o decays of B mesos ad related measuremets because B factories at SLAC ad KEK sice 1999 have allowed a detailed study of may B decays that were ot available previously B mesos are a excellet laboratory to study CP Violatio observatios of 2 differet types of CP violatio i B mesos sice 2001! First observatio i 1964 with eutral Kaos Redudat measuremets of same observables i differet processes allow to verify CKM paradigm Discrepacies could be a sig of New Physics beyod Stadard Model For example: use measuremets to verify uitarity of CKM matrix 18

19 From Hadros to Quarks CKM matrix elemets describe processes at quark level but processes observed experimetally ivolve hadros Theory is used to relate measuremets with hadros to quatities defied for quarks HQET, OPE, Lattice QCD Ultimately must verify theories with measuremets Whe models are used to iterpret data this should be described clearly ad some kid of error assiged to the model-depedecy 19

20 Typology of Tree Decay Amplitudes 20

21 CKM Elemets i First Two Geeratios 21

22 Measurig V ux ad V cx 22

23 V ud : β Decays 23

24 Super-allowed pio β decay 24

25 V us : Semileptoic K Decays 25

26 di-muo Productio i Deep Ielastic Scatterig 26

27 Semileptoic D decays 27

28 Semileptoic D decays 28

29 Hadroic or Semileptoic? 29