May. 3 (17 at KAIST Byeong Rok Ko (IBS/CAPP
Charge-conjugation and Parity combined symmetry Charge-conjugation : not only electrical charge but also all the internal quantum numbers Parity : left-right symmetry mt > mb > mc > ms > md > mu
3 Charge-conjugation and Parity combined symmetry Charge-conjugation : not only electrical charge but also all the internal quantum numbers Parity : left-right symmetry mt > mb > mc > ms > md > mu FCNC
4 Charge-conjugation and Parity combined symmetry Charge-conjugation : not only electrical charge but also all the internal quantum numbers Parity : left-right symmetry mt > mb > mc > ms > md > mu Charm Decays FCNC
5 Andrei Sakharov CPV is necessary to explain current matter and anti-matter asymmetry in our Universe CPV is very crucial to understand our Universe Nobel prize in physics Cronin and Fitch in 198 (CPV in K system, Kobayashi and Maskawa in 8 (CPV in the SM
6 CPV in strong interaction With axion, this would be gone Prof. Yoo : CAPP axion group leader, please ask him detail about it CPV in weak interaction CPV in lepton sector With PMNS matrix, it can happen Prof. Yoo : an expert, please ask him detail about it CPV in quark sector With CKM matrix, Observed! This is for today SM CPV! CPV = SM CPV, from now on
7 Higgs gives mass You might be told this Higgs and CPV are inseparable in the SM No Higgs, No CPV in the SM CPV in the SM originates from a single complex number in the CKM matrix Correct statement CPV in the SM originates from the Yukawa interaction More fundamental statement ; Yukawa interaction : between a Dirac field and a Higgs field V shows up in weakly charged current interaction V CKM CKM V * CKM violates CP operation in weakly charged current interaction Again, No Higgs, No CPV in the SM CPV in 1964 (Cronin and Fitch Higgs in 1
8 Two-state quantum system (two-level system quantum superposition of two independent quantum states D ( t = α( t D β( t D SM weak interaction allows this transition for neutral states mixing (oscillation for charged states : D ( t = γ ( t D to conserve electric charge Γ( Dt ( f Γ( Dt ( f ACP ( t Γ ( Dt ( f Γ ( Dt ( f CP Γ( D( t f = f H D( t q, D( t = g ( t D g ( t D, A p f H D, B f H D p Γ( Dt ( f = f H Dt (, Dt ( = g ( t D g ( t D, A f H D, B f H D q t independent pa qa f : final state λ, λ, H : weak hamiltonian, qb pb g ( t : time evolution, p and q : complex parameters ± Γ : partial decay width non-zero A ( t CPV details in pdg.lbl.gov
9 After tedious calculation Γ( Dt ( f Γ( Dt ( f t term t 1 term t term A λ q p A λ pq λ λ pa qb qa pb, t A CP t term : decay rate without mixing, term : decay rate with mixing, A if q p 1, even if AA= 1 CP if AA 1 1 t term : decay rate from interference of the two, A if λ λ, even if AA= 1 and q p= 1 CP direct CPV, both neutral and charged particles indirect CPV, only neutral particles
1 Charm Decays FCNC
11 FCNC processes? will visit it later Charm Decays FCNC
1 Wolfenstein parameterization; Expanding in λ (λ~.1 diagonal off-diagonal CPV a single complex number, non-zero η in the CKM Matrix CPV should involve V ub and V td
13 charmed particles : D ( cu, D ( cu, D ( cd, D ( cd charmed particle decays Vcs V and cs Vud Vcd and Vus Cabibbo favored : Cabibbo suppressed Vcs V ud Vus V cd V us
14 charmed particles : D ( cu, D ( cu, D ( cd, D ( cd charmed particle decays Vcs V and cs Vud Vcd and Vu s Cabibbo favored : Cabibbo suppressed Vcs V ud Vus V cd V us
15 charmed particles : D ( cu, D ( cu, D ( cd, D ( cd charmed particle decays Vcs V and cs Vud Vcd and Vu s Cabibbo favored : Cabibbo suppressed CPV in the charmed particle decays ~ without V ub and V td Vcs V cd V ud Vus V us
16 Charm Decays FCNC FCNC processes? do you still remember this?
17 Charm Decays FCNC FCNC processes? can be interpreted into V VVV ~ VVV V CPV ~ VVVV ~. cb ub cs ij us ci ui cj uj cs us cd ud CPV in the charmed particle decays with in quantum loop process, but very very suppressed V ub
18 Looking at SM CPV only CPV in weak interaction among quarks No Higgs, No CPV in the SM Direct CPV and indirect CPV CKM element related to CPV : V ub and V td CPV in charm decays : very very suppressed since V ub can enter the decays through quantum loops, and V ub contribution in loops ~negligible
19 LHCb at LHC, Fixed target experiment, protons hit protons, Belle II at SuperKEKB, e e - collisions
KEKB Tsukuba Japan ~3 km Precursor of superkekb 8 GeV e - E CM ~1.6 GeV 3.5 GeV e
1 Precursor of Belle II KEKB Belle Detector E CM ~1.6 GeV 3.5 GeV e
B mesons Other than B mesons, charm, tau, etc..
3 Mixing first D D mixing should be measured first! B B mixing observation in 1987, but CPV in B decays in 1
D D mixing in D K π decays 4 always measure D and D together can't distinguish DCS from CF * have to use D D πs K ππs decay to identify DCS and CF same charged π right sign (RS, opposite charged π wrong sing (WS similar to Young's double-slit
D D mixing in D K π RS decay decays 5 mixing DCS VcsVusVcdVud VcdVus CF VV cs ud O 6 (1 effectively just CF d ecays time-dependent decay rate Γ RS t ( t τ A e τ CF t D A CF : decay time, τ: lifetime, : amplitude of CF decay
D D mixing in D K π WS decay decays 6 mixing CF VVVV cs us cd ud VV cs ud DCS V V cd us O(1 coherent sum of DCS and mixing time-dependent decay rate DCS ΓWS( t τ A e R R y' τ R : ratio of DCS to x' = xcosδ ysin δ, D CF decay ra tes interference 4 τ t t τ x' y' t CF D D y' = ycosδ xsin δ, mixing δ : relative strong phase between DCS and CF decay amplitudes
D D mixing in D K π decays 7 Γ RS ( t τ A e CF t τ t τ ΓWS( t τ ACF e RD RD y' τ ' ' 4 τ t x y t taking a ratio of the two decay rates Rt ( τ Γ WS = Γ RS ( t τ ( t τ R D t x' y' t RDy' τ 4 τ Mixing parameters : R D, y, and x
D D mixing in D K π Results decays 8 R ( t τ = R D doesn t fit to the data well R D (1-3 3.53±.13 x (1-3.9±. y (1-3 4.6±3.4 χ = χ Mixing χ No Mixing = 9.3 No mixing probability : 4.34 1 5.1standard deviations from No mixing hypothesis First observation of D D mixing in ee consistent with the SM 7 collisions
D D mixing in D K π Results decays 9 x -y contour plot the best fit point 5σ away from no mixing - 1 (line, 3 (dashed-line, and 5 (dots standard deviations from the best fit (point - : no mixing
CPV in D D mixing through the decay D K π 3 Belle just made an observation, Worthwhile to study furthermore, But quite limited statistics direct CPV in the decay indirect CPV in the mixing indirect CPV in interference between the two
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3 indirect CPV : decay rate with mixing and decay rate from interference of two interference phenomenon, Young s double-slit direct CPV : decay rate without mixing D f Γ( D f Γ( D f Weak Weak Strong Strong ACP sin( ϕ1 ϕ sin( δ1 δ Γ( D f Γ( D f Subscripts 1 and : decay paths requires two different decay paths, should interference each other too easy to be homework CPV Interference phenomena
33 Charged particles do not have CPV due to mixing, Difference between D ( cd and D ( cd decays
CPV in D K π S D KSπ SM CPV in decays decays 1 ( ( KS = 1 ε K (1 ε K, ε : CPV in K system (1 ε 34 -coherent sum of the two states K π D = K π D K π D S -No CPV expected in the SM because with CF and DCS decays other than known SM CPV from K system; (-.33±.6%
CPV in S D K ACP A π S D K π exp. D = K π S = = Γ( D Γ( D N( D N( D A ( D K π K K S D K π CP S S K K decays π Γ( D π Γ( D S S π π A ( K KS KL ππ ( KS ππ ( K exp., N( D N( D K K S S π π K K N(number of decays experimentally measured = σ ( e e cc Γ Γ ε ε επ ( S S, π π production asymmetry CPV in D CPV in K K No asymmtry expected asymmetry in σ π system due to No worry! ( NK btw ( NK asymmetry in σ( Nπ btw σ( Nπ Removing A exp. Γ : partial decay width, K K σ S K ππ mixing 35 D K A S π CP PRD 84, 11151(R (11 is everything in this measurement, which is very non-trivial business
CPV in D Results K π S decays ~1.7 M signals (white region : statistical error <.1% Red shaded : peaking from Ds KsK if K is misidentified to π Blue hatched : random combinations D A CP K S π = (.363 ±.94 ±.67% 3.σ away from zero unique evidence for CPV in charm decays 36 D K π = (.4 ±.94 ±.67% A CP consistent with zero (the SM mother daughters mother daughters particle D (cd Ks (sd π (ud Ds (cs Ks (sd K (su M (GeV/c 1.87.498.14 1.968.498.494
CPV in D Results K π S decays 37 D K S π = (.363 ±.94 ±.67% A CP 3. σ away from zero with the Belle result unique evidence for CPV in charm decays~4.6 sigma away from zero Confirmation of CPV in K system in1964
CPV in D KK S and D KK decays b, s, d 38 V ub Singly Cabibbo suppressed charm decays V ub contribution CPV expected CPV ~ VV ~. cb ub
Summary 39 Origin of CPV in the SM : Higgs CPV Interference phenomena Indirect CPV in D wrong sign decays Direct CPV in D Ks π decays Expect very small CPV in singly Cabibbo suppressed decays Need at least two decays -D mixing in 1, but CPV in charm is not established yet B B mixing observation in 1987, but CPV in B decays in 1
Origin of CPV in the SM * *,,,,,, * * * * only if ( 1, (, ( ( quarks interaction of Charged Current (CC ( ( particles, resulting in physical is absorbed in, 1, (where ( ( VEV ( (where After spontaneous symmetry breaking (quark sector only Heading to the CKM is conseved then, if ( CKM CKM CC CC CKM CKM ij d L u L CKM mass Li ij u L d L mass Li mass Li ij d L u L mass Li weak Li weak Li weak Li weak Li CC weak Lj ij d L mass Li mass weak d u R d u d u L d u diag mass Ri diag u ij mass Li mass Ri diag d ij mass Li d u ij d u ij weak Rj weak Li u ij weak Rj weak Li d ij quark Yukawa ij ij Ri Li ij Li Rj ij Li Rj ij Ri Li ij Li Rj ij Ri Li ij Yukawa V V L L CP V V V V V u W V V d d W V V u u W d d W u L d V d q q V VV V M V M u M u d M d v Y v M u u M d d M L CP Y Y Y Y Y Y CP Y Y L = = = = = = = = = = = = µ µ µ µ µ µ µ µ γ γ γ γ φψ ψ ψ φ ψ ψ φ ψ φψ ψ ψ φ ψ φψ ψ 4
D D mixing in D K π Method decays the mixing parameters can be extracted by fitting time-dependent ratios of WS to RS decay rates using RS decay time at Belle t x' y' t Rt ( τ RD RDy' τ 4 τ Note the ratio with convolution Rt ( τ = Γ Γ WS RS ( t τ R ( tτ t τ dt ( τ ( t τ R ( tτ t τ dt ( τ R : 4 Gaussians from RS decay time e t τ cancel out 41 t resolution : ~.3 t/τ ~1 fs most of events :~1. t/τ ~4 fs take into account the t resolution using convolution Note e t τ does not cancel out very complicate functional form extracting RD, y', and x' from Rt ( τ, not from Rt ( τ for Belle t : true decay time, t : experimental decay time
D D mixing in D K π decays 4 time-integrated decay rate: R WS =(3.851±.59x1-3 in bins of the decay time get the time-dependent decay rates
Input :, output : dot with oval 43
44 CP asymmetry in D K π exp. S decays Removing A : everything in this CPV measurement Use two VERY large and CPV free resonance samples (CF decays D K ππ and D K ππ decays : > 1 times of D K π S to measure statistics K π two decays have the same particles, A and A cancel out isolation of the other A π ε : Beam pipe Silicon : Beam pipe as a ε ( σ ( K σ ( K ε calculated A D - Nucl. σ ( K function of p K S - Nucl. and σ ( K - Nucl. based on well - Nucl. A π ε non-trivial business known PRD 84, 11151(R (11 4 4
Different decays identified through Dalitz plot analysis CF: D K *- π,dcs: D K * π -,CP: D ρ Ks Time dependent matrix element is: M has mixing parameters as well as CPV parameter q/p Both q/p and φ can be extracted with time-dependent Dalitz analysis (mixing parameters, x and y can be as well 45 decay ( Amplitude for ( and, ( where ( (, ( ( (, (,, ( / ( 1 1 D D A A e e Ks m m t e t e m m A p q t e t e m m A t m m M j im j t j = = = Γ ± ± π ] 1 [(, sin(, cos(, t y t t i e t x e t x e e p q p q Γ ± Γ Γ Γ Γ = φ
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