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K Karlsruhe Institute of Technology (KIT) 2018 2018 8 7 3 cm Discovery of Kaon V particle K 0 S 3 cm + Discovery of Pion

  1. K 中間子の精密測定で探る物理 北原 鉄平 Karlsruhe Institute of Technology (KIT) 基研研究会 素粒子物理学の進展 2018 2018 年 8 月 7 日

  2. 3 cm

  3. Discovery of Kaon “V particle” K 0 S 3 cm π + Discovery of Pion Surprisingly for me, pion & kaon have been discovered in the same year π −

  4. KAON A GOLDEN CHANNEL ✦ Discovery of CP violation [’64] ✦ GIM mechanism and prediction of charm [’64-70] → November Revolution( J / ψ )[’74] ✦ CKM matrix and prediction of beauty/truth [’73] Probing new physics by precision measurements of kaon decays /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  5. Kaon! Kaon physics is still an exciting field! Discovery channel → Precision physics : FCNC and CP violation can be probed precisely using rare decay channels Br~ O (10 -11 ) There are many promising on-going experiments for kaon precisions; LHCb / NA62 / KOTO / KLOE-2 / TREK One can test our understanding of the SM, unitarity of CKM and ChPT, and also probe physics beyond the SM Probing new physics by precision measurements of kaon decays 2 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  6. Lattice [RBC-UKQCD] perturbative calculations collider meson effective theory (ChPT/dual QCD) search ε ’ K and ε K discrepancies? B < K L → ππ correlations could give stronger constraints LFUV CP -violating - FCNC (+) (+) K S → μ + μ - K L → π 0 νν reduce Th reduce Th uncertainty K S → π 0 μ + μ - uncertainty K L → π 0 l + l - K S → μ + μ - γ CPV decay Understanding K S → 4 l less sensitive because of LD contributions of ChPT K S → π + π - e + e -

  7. Kaon in LHCb LHCb experiment has been designed for efficient reconstructions of b and c Huge production of strangeness [ O ( 10 13 ) /fb -1 K 0S ] is suppressed by its trigger efficiency [ ε ~1-2% @LHC Run- I , ε ~18% @LHC Run- II ] LHCb Upgrade (LS2=Phase I upgrade, LS4=Phase II upgrade) could realize high efficiency for K 0S [ ε ~90% @LHC Run- III ] [M. R. Pernas, HL/HE LHC meeting, FNAL, 2018] In LHC Run- III and HL-LHC, we could probe the ultra rare decay Br~ O ( 10 -11 ) Probing new physics by precision measurements of kaon decays 4 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  8. Kaon & CP violation - Kaon = bound state of sd and CP transformation 0 i , 0 i = | K 0 i , CP | K 0 i = | K CP | K 1 ⇣ ⌘ 0 i CP | K 0 ± i = ±| K 0 where | K 0 | K 0 i ± | K p ± i , ± i ⌘ 1,2 1,2 1,2 2 are CP -eigenstates but are not mass-eigenstates, because nature does | K 0 ± i 1,2 not respect the CP symmetry 1 Short-lived mass eigenstate | K 0 + i + ✏ K | K 0 � � | K S i ' − i 1 2 p 1 + | ✏ K | 2 1 Long-lived mass eigenstate � | K 0 − i + ✏ K | K 0 � | K L i ' + i 2 1 p 1 + | ✏ K | 2 Lifetime difference is so large and mass difference is small (opposite from B 0 ) τ S = 0 . 89 × 10 − 10 sec. c τ S = 2 . 6 cm ∆ M K = 3 . 4 × 10 − 12 MeV τ L = 511 × 10 − 10 sec. c τ L = 15 m Probing new physics by precision measurements of kaon decays 5 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  9. Kaon & CP violation K 0 → π π J ( K 0 ) = J (2 π ) = S (2 π ) + L (2 π ) → L = 0 =0 =0 2 π state can not carry angular momentum → CP (2 π ) = +1 = CP even The CP violation was measured by A ( K L (almost CP odd) ! π + π − ( CP even)) / ε K = O (10 − 3 ) 6 = 0 [Christenson, Cronin, Fitch, Turlay, '64 with Nobel prize] No missing energy = K L K L beam π + e - ν , π + μ - ν π + π - π 0 invariant mass Probing new physics by precision measurements of kaon decays 6 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  10. K 0 → π + π -, π 0 π 0

  11. K 0 → ππ : two types of CP violation two types of CP violation : indirect CPV ε K & direct CPV ε ’ K : [Christenson, Cronin, Fitch, Turlay ’64 � K L → π + π � � with ε K = O (10 � 3 ) ∝ ε K + ε 0 A K with Nobel prize] K = O (10 � 6 ) � K L → π 0 π 0 � ε 0 ∝ ε K − 2 ε 0 A [NA48/CERN and KTeV/FNAL ’99] K 1 − B ( K L → π 0 π 0 ) B ( K S → π + π � ) ✓ ε 0 ◆  � = 1 K = O (10 � 3 ) Re 6 B ( K S → π 0 π 0 ) B ( K L → π + π � ) ε K x V td V td u,c,t x Δ S=1 d Δ S=2 S d S Direct CP violation Indirect CP violation g/ γ /Z u,c,t u,c,t x [Kaon mixing] penguin and W-box q q d S W box 0 K 0 ← → K q S ε 0 K ∝ Im [ V ⇤ ts V td ] ⇥ ts V td ) 2 ⇤ ε K ∝ Im ( V ∗ q u,c,t x q d Probing new physics by precision measurements of kaon decays 7 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  12. ε K discrepancy SM prediction of the indirect CP violation ε K is sensitive to | V cb | ε K (LD) = -3.6(2.0)% × ε K (SD) SM [Buras,Guadagnoli, Isidori ’10] ε K = ε K (SD) + ε K (LD) ε K (SD) ∝ Im λ t [ − Re λ t η tt S 0 ( x t ) + (Re λ t − Re λ c ) η ct S 0 ( x c , x t ) + Re λ c η cc S 0 ( x c )] ηλ 2 | V cb | 2 ⇥ | V cb | 2 (1 � ¯ ⇤ ' ¯ ρ ) η tt S 0 ( x t ) + η ct S 0 ( x c , x t ) � η cc S 0 ( x c ) Wolfenstein parametrization Leading contribution is proportional to | V cb | 4 | ε K | predictions inclusive | V cb | (±1 σ error bar) Theoretical prediction of ε K with errors are inclusive | V cb | is consistent with the exclusive | V cb | dominated by measured value, while there is 4.0 σ - | V cb |, η , η ct , η cc tension in exclusive | V cb | case measured value [LANL-SWME, 1710.06614] Wolfenstein parameters are determined by 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 the angle-only fit | ε K | × 10 3 | ϵ K |× 10 3 Probing new physics by precision measurements of kaon decays 8 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  13. ε K discrepancy ~ | V cb | discrepancy [HFLAV average, 1612.07233] [Bigi, Gambino, Schacht ‘17] Inclusive 3 σ 十 data: Belle, 1702.01521 exclusive assuming a simplified FF parametrization ( CLN ) Recent progress on exclusive | V cb | in B → D * transition Model independent form factors parametrization [Boyd-Grinstein-Lebed ( BGL ) ’97] Error will be reduced B → D ∗ ` ¯ ⌫ | V cb | excl . 40 . 6 +1 . 2 × 10 − 3 � � [Bigi, Gambino, Schacht ‘17] BGL = − 1 . 3 by future lattice result [Belle, + Similar recent progress [Grinstein, Kobach ‘17, Bernlochner, Ligeti, Papucci, Robinson ’17] 1702.01521] Probing new physics by precision measurements of kaon decays 9 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  14. Formulae of CP violating decay Precise definitions of K → ππ system time-dependence of K L -K S interference ✏ K ≡ 2 ⌘ + − + ⌘ 00 η 00 ≡ A ( K L → π 0 π 0 ) ∈ C exp. · e 43 . 52 � i 2 . 220 · 10 − 3 � � = 3 A ( K S → π 0 π 0 ) η + − ≡ A ( K L → π + π − ) K ≡ ⌘ + � − ⌘ 00 exp. · e 43 . 51 � i � 2 . 232 · 10 − 3 � ✏ 0 = ∈ C A ( K S → π + π − ) 3 Pion isospin decomposition of the physical states r r 1 2 | π 0 π 0 i = 3 | ππ i I =0 � 3 | ππ i I =2 Two pions ( I =1) can decompose into I =0,2 states with CG coefficients r r 2 1 | π + π − i = 3 | ππ i I =0 + 3 | ππ i I =2 ✏ 0 ≡ A ( K L → ( ⇡⇡ ) 0 ) 1 A ( K L ! ( ⇡⇡ ) 2 ) ! ⌘ A ( K S ! ( ⇡⇡ ) 2 ) p ✏ 2 ⌘ A ( K S ! ( ⇡⇡ ) 0 ) ⌧ ✏ 0 A ( K S ! ( ⇡⇡ ) 0 ) ⌧ ✏ 0 A ( K S → ( ⇡⇡ ) 0 ) 2 K = ✏ 2 + ! √ 2 ( ✏ 2 − ✏ 0 ) + O ( ✏ 0 ! 2 ) ✏ 0 2 ✏ 2 ! + O ( ✏ 0 ! 2 ) then ✏ K = ✏ 0 − √ Probing new physics by precision measurements of kaon decays 10 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

  15. Formulae of CP violating decay cont. Then, ✏ 0 ✓ ◆ ⇣ √ ⌘ � 1 ✏ 2 + ! K + O ( ! 2 ) = 2 ( ✏ 2 − ✏ 0 ) 2 ✏ 2 ! √ ✏ 0 − ✏ K 1  A ( K L → ( ⇡⇡ ) 2 ) A ( K L → ( ⇡⇡ ) 0 ) − A ( K S → ( ⇡⇡ ) 2 ) � + O ( ! 2 ) = √ A ( K S → ( ⇡⇡ ) 0 ) 2 K L and K S also can be decomposed into isospin eigenstates ( ) 0 K 0 , K 1 1 ⇣ ⌘ 0 i (1 + δ ✏ ) | K 0 i + (1 � δ ✏ ) | K | K S i ⌘ p p 2 1 + | δ ✏ | 2 1 1 ⇣ ⌘ 0 i (1 + δ ✏ ) | K 0 i � (1 � δ ✏ ) | K | K L i ⌘ p p 2 1 + | δ ✏ | 2 Let us define isospin amplitudes A ( K 0 → ( ππ ) I ) ≡ A I e i δ I δ I is a strong phase, which comes from the final pion state re-scattering 0 → ( ππ ) I ) ≡ ¯ A I e i δ I = A ∗ I e i δ I A ( K A ( K L → ( ππ ) 2 ) A ( K L → ( ππ ) 0 ) = e i ( � 2 − � 0 ) i Im( A 2 ) + δ ✏ Re( A 2 ) then i Im( A 0 ) + δ ✏ Re( A 0 ) A ( K S → ( ππ ) 2 ) A ( K S → ( ππ ) 0 ) = e i ( � 2 − � 0 ) Re( A 2 ) + i δ ✏ Im( A 2 ) Re( A 0 ) + i δ ✏ Im( A 0 ) Probing new physics by precision measurements of kaon decays 11 /38 Teppei Kitahara : Karlsruhe Institute of Technology, PPP2018, YITP, August 7, 2018

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