Standard Model. Overview

Transcription

1 Standard Model Quark mixing and CP violation Overview Quark weak and trong eigentate generation review K 0 mixing 3 generation review K 0 mixing, B 0 mixing CP violation Alternative parametriation of CKM matrix 1

2 Weak and trong eigentate Quark interact through the trong force Gluon couple to trong (phyical) quark eigentate q hadron Quark alo interact through the weak force W couple to weak quark eigentate q q related to q through mixing matrix q admixture of q and v.v. q 1 q 1 q 1 q g q u, c W q Weak, trong eigentate u d c t Strong quark eigentate Gluon couple to trong quark eigentate oervale hadron u d W c W t W Weak quark eigentate W oon couple to weak quark eigentate (convention to change ottom memer of family) Weak quark eigentate are admixture of trong quark eigentate

3 Weak, trong eigentate d W W W = d Strong, weak eigentate related y mixing matrix Mixing matrix i unitary (invere = complex conjugate) Two quark familie d W W = co θ c in θ c -in θ c co θ c d Mixing matrix i x Condition of unitarity 1 unknown parameter Uually taken a Caio angle θ c quantifie mixing etween two generation alue not predicted y SM! 3

4 Two generation (K 0 mixing) Explain K 0 -K 0 mixing: u,cu, c, t dd, W - W+ d, u, c, t d u,c W couple to d W, W Amplitude for tranition proportional to Caio angle and quark ma CKM matrix 3x3 matrix = CKM matrix (1973 efore charm!) Element decrie every weak quark tranition SM doe not predict exitence of or value for matrix element (coupling of W to quark). Input y experimental data CKM = ud cd td u c t u c t 4

5 Effect on K 0 mixing Mixing: Extra contriution from top due to mall W admixture d, u, c, t d u,cu, c, t dd, W - W+ u,c t Coupling proportional to quark ma and CKM matrix element Here charm CKM element dominate Box amplitude α Σ Σ i id * j * jd a ij i=u,c,t j=u,c,t Amplitude f(m q ) B 0 mixing u, c, t d, W - W+ d, u, c, t Mixing: expect B 0 d and B 0 ytem to mix like K 0 Now top CKM matrix element dominate B 0 mixing fater than B 0 d a t > td Amplitude α Σ Σ i id * j * jd a ij i=u,c,t j=u,c,t 5

6 t Ma eigentate not the ame a weak eigentate Different meaurement enitive to thee K 0 mixing enitive B 0 mixing enitive B 0 meon mixing B 0 d: m d = 0.489±0.08 p -1 B 0 : m > 16.6 p -1 td < t e -t/τ m / m d = t / td Input to SM P mix (t) = 0.5*(1-co( m t)) 6

7 Bd mixing very well meaured B mixing Statu now: Unoerved: x = m/γ(>16.6 p SM (UTfit) prediction of ~0p -1 Tevatron may oerve mixing y 007 Fit to experimental data 7

8 CP violation CP violation: CP violation oerved in K 0 -K 0 ytem C + C - C + /C - = (1+ε)/(1-ε), ε ~.10-3 Mut e included in SM CKM matrix allow CP violation (ut doe not predict magnitude) N. Big Bang equal matter:antimatter. Univere now matter. Need quite a lot of CP violation for thi to happen. d d CP violation CKM element containing quark mot enitive to phae Quark Antiquark CP violation if, anti- decay rate different Unitary CKM matrix 4 free parameter (3 angle; 1 phae = CP) = ud u u cd c c td t t d * ud * u * u d = * cd * c * c * td * t * t * u / W -+ u 8

9 4 parameter If CKM parameteriation i correct All mixing and weak decay mut give conitent reult The phae you extract from CP violation in the K ytem will predict the amount of CP violation in the B ytem Make many meaurement and tet whether CKM formalim work Note: Doen t exactly explain origin of CP CP violation Need 3 generation of quark to introduce CP violation into theory d W W W = d Mixing matrix i 3x3. Unitarity contraint 4 independent parameter 3 angle quantify mixing etween (1,3) (,3) (1,) generation, 1 complex phae (mechanim for introducing CP) 9

10 CP Angle Unitarity relation often repreented graphically.. ud u * + cd c * + td t * = 0 Im Side meet if no NP contriution (η,ρ) ud u * α td t * CP violation if height non-zero γ β cd c * Re CP Angle Angle α,β,γ jut comination of CKM matrix element.. Im ud u * α td t * γ cd c * (η,ρ) β * = ttd α arg * uud * t td β = π arg * ccd * = uud γ arg * ccd Re 10

11 CKM matrix Alo Wolfentein parameteriation O(λ 3 ): 1 λ 3 Aλ ( 1 ρ iη) λ Aλ 3 Aλ ( ρ iη) CKM = λ 1 Aλ + λ 1 O ( λ 4 ) To enure unitarity coδ 3 13 λ = 1 A = ρ = η = inδ 1 3 in θ c λ = inθ 1 0. Relating parametriation 1 λ 3 Aλ ( 1 ρ iη) λ Aλ 3 Aλ ( ρ iη) CKM = λ 1 Aλ + td e iβ β = B 0 d mixing phae δγ = B 0 mixing phae γ = weak decay phae λ e t iδγ 1 If η=0, no CP violation O u e ( λ 4 ) β = tan γ = tan 1 1 δγ = ηλ iγ η 1 ρ η ρ 11

12 CP violation in B 0 ector CP violation in B 0 ector expected to e large (complex CKM matrix element involving are large) Experimentally Chooe decay channel, meaure aymmetry A CP meaured A CP = Γ(B(t) f) Γ(B(t) f) Γ(B(t) f) + Γ(B(t) f) λ f = (q/p)(a f /A f ) A f dir = ( λ f -1)/( λ f +1) A f mix = Im(λ f ) /( λ f +1) A f = Re(λ f ) /( λ f +1) = Ratio of CKM matrix element m meaured in mixing A f dir co( mt) +A f mix in( mt) coh ( Γt/) A f inh( Γt/) Γ = 0 for B 0, Γ/Γ ~0.1 for B CP violation in B 0 ector Eg. B 0 π + π - aymmetry A CP = Γ(B(t) f) Γ(B(t) f) Γ(B(t) f) + Γ(B(t) f) meaured Meaured in mixing = in( mt) Im q Af p Af p, q original admixture of B 0, B 0 in ma eigentate (ratio of CKM matrix element) like C +,C - Ratio of CKM matrix element in α 1

13 CP violation in B 0 ector Other decay involve other CKM matrix coupling, hence other angle β, γ B 0 d J/Ψ K 0 ; A CP α in β B 0 d D 0 K* 0 ; A CP α in γ Huge program of work at Baar, Belle (B 0 d), CDF, D0 (B 0 ) to invetigate conitency of SM relationhip Future work planned at LHC 13

14 CP violation tudie Im (η,ρ) ud u * α td t * γ β cd c * Current tatu Re β,meaured well at Baar, Belle α can e meaured well at Baar, Belle γ can only e meaured well at LHC But Although CP violation meaurement in SM conitent Can only explain converion of ~1 galaxy worth of matter in univere! There mut e another CP violating mechanim (which we don t know aout in SM) 14

15 Review Weak, trong quark eigentate are different Admixture quantified in CKM matrix Matrix can e parametried a 3 angle, 1 phae Phae i mechanim in theory for CP violation No SM prediction for matrix parameter Meaurement underway to tet SM prediction of relationhip 15