The Discovery Potential of Kaon Physics

Transcription

1 The Discovery Potential of Kaon Physics Andreas Weiler TU Munich DIF06, Frascati

2 next 28 minutes Why are rare Kaon decays so promising? Four golden modes, status of the SM calculation New physics models and their predictions MFV and Susy, UEDs, warped ED, littlest Higgs... Conclusions

3 Perspective Lessons from the past: 60!MK rare low energy processes like!mk 87 ARGUS at Desy!MBd (charm), Bd - Bd osc. and EWPT (top), can tell us a lot about heavy particles 9x LEP prior to their discovery Present 99-now Belle/Babar SM works remarkably well (surprisingly also in the least understood sector, the flavor sector) Future In order to test NP indirectly we need theoretically very clean observables, preferably with small SM contribution.

4 The flavor problem L EF T = Λ 2 φ 2 + L(5) Λ + L(6) Λ 2 ": NP scale natural stabilization of the Higgs mass e.g. O (6) ( sd)2 Λ 2 " < 1 TeV K K mixing: " >10 3 TeV Two solutions: 1) " beyond LHC reach 2) " ~ 1 TeV but flavor-mixing somewhat protected

5 4 golden modes Br(K L π 0 µ + µ ) Br(K L π 0 e + e ) Br(K + π + ν ν) 24 carat Br(K L π 0 ν ν)

6 Potential of K->pivvK πν ν * Suppression of SM amplitude due to hierarchical CKM (s#d~$ 5, b#d~$ 3, b#s ~ $ 2 ) and power-like GIM * Long distance effects small and well under control K + s u ν t W Z ν V td d π + u + box ) A(K + π + ν ν) = B + (λ c Pc + λ t X(v) A(K L π 0 ν ν) = B L Im [λ t X(v)] * Dominated by short distance contributions o sigma(k + )theory ~ 4% o sigma(kl)theory ~ 2% λ t = V tsv td λ c = V csv cd K + π 0 e + ν B+ and BL from pure short-distance

7 General properties L (6) eff = 4G F 2 Q (6) ν = l=e,µ,τ α 2πs 2 W i=u,c,t C i (µ)q (6) ν ( s L γ µ d L )( ν ll γ µ ν ll ) C i (M W ) m 2 i V isv id Λ 2 QCD λ m 2 c(λ + iλ 5 ) m 2 t (λ 5 + iλ 5 ) u c t * Z penguin Amplitude ~ SU(2)L breaking => powerlike GIM mechanism * large CPV phase in dominant top contribution * charm effects: 1) negligible in KL: ~ mc 2 /mt 2 for dominant direct CPV- Amplitude 2) small in K + ~30% (# next to next slide)

8 SM prediction of KdL->pv K L π 0 ν ν [ Im (V B(K L π 0 ν ν) = κ ts V td ) L * short distance dominated (>99%) * very small theoretical error ~ 2% * 85% of total error CKM input * precise and direct measurement of amount of CPV in SM λ 5 κ L = r KL 3α 2 B(K + π 0 e + ν e ) 2π 2 s 4 W ] 2 X τ(k L ) τ(k + ) X = 1.46 ± 0.04 (NLO) Buchalla & Buras 93, 99; Misiak & Urban 99 r KL = ± isospin Marciano & Parsa 96 t B(K L π 0 ν ν) = (2.8 ± 0.6) Brexp / BrSM < (90% C.L.) E391 KTEV, E391a (soon to be improved!)

9 SM prediction for K K->piv + π + ν ν [ (Im(V B(K + π + ν ν) = κ ts V td ) + λ 5 ) 2 ( Re(V X + ts V td ) λ 5 X + Re(V csv cd ) λ ) ] 2 (P c + δp c ) * theoretical error of QCD corrections to the charm contribution Pc factor ~4 smaller thanks to NNLO calculation * Pc error now dominated by!mc Buras, Gorbahn, Haisch, Nierste 05!"#!!"# g s d g c c % %!mc theory Pc NLO = 0.369±0.033±0.037±0.009! 0.37±0.07 Pc NNLO = 0.375±0.031±0.009±0.009! 0.38±0.04 &S Buchalla, Buras 94 Buras, Gorbahn, Haisch, Nierste 05

10 SM prediction for K K->piv + π + ν ν [ (Im(V B(K + π + ν ν) = κ ts V td ) + λ 5 ) 2 ( Re(V X + ts V td ) λ 5 X + Re(V csv cd ) λ ) ] 2 (P c + δp c ) * theoretical error of QCD corrections to the charm contribution Pc factor ~4 smaller thanks to NNLO calculation * Pc error now dominated by!mc Buras, Gorbahn, Haisch, Nierste 05 * LD and dim8 effects in 'Pc are ~ " 2 F" 2 /mc 2 ~10% of charm contribution, 6% enhancement of BrK + * LQCD could improve accuracy to 1-2% Isidori, Mescia & Smith 05 m c q 2 s d % % OP K " Λ QCD " " % % χpt Isidori, Martinelli & Turchetti 05 δp c = 0.04 ± 0.02

11 SM prediction for K K->piv + π + ν ν B(K + π + ν ν) = (8.0 ± 1.1) * theoretical error of QCD corrections to the charm contribution Pc factor ~4 smaller thanks to NNLO calculation * Pc error now dominated by!mc Buras, Gorbahn, Haisch, Nierste 05 * LD and dim8 effects in 'Pc are ~ " 2 F" 2 /mc 2 ~10% of charm contribution, 6% enhancement of BrK + * LQCD could improve accuracy to 1-2% Isidori, Mescia & Smith 05 Isidori, Martinelli & Turchetti 05 Buras, Gorbahn, Haisch, Nierste 05 B exp + = ( ) E787 (2), E949 (1)

12 Status of KL#" 0 l + l - Br(K L π 0 l + l ) = Buchalla, D Ambrosio, Isidori; Isidori, Smith, Unterdorfer 04 [ ( ) ( Cmix l + Cint l Imλt + Cdir l Imλt ) 2 + C l CPC ] indirect CPV interference of direct and indirect direct CPV CP conserving * substantial progress in theory error associated with light quark loops experimental input from NA48???? # 79@ # 9%&' # ;9" #?!? ) BBIF * G I. ) GIA * CH I ' ) BIA *. IB ).???? % 79@ % 9%&' % ;9" %?!? ) HIJ * CF I ) CK I *. IA ' ) C. I *.C I ) HIB * CF I Br(K L π 0 µ + µ ) = (1.5 ± 0.3) Br(K L π 0 e + e ) = ( ) % C.L. < < KTEV 00 KTEV 03

13 Status of KL#" 0 l + l - Br(K L π 0 l + l ) = Buchalla, D Ambrosio, Isidori; Isidori, Smith, Unterdorfer 04 [ ( ) ( Cmix l + Cint l Imλt + Cdir l Imλt ) 2 + C l CPC ] indirect CPV interference of direct and indirect Direct CPV amplitude: * clean probe of independent NP structures and CPV beyond SM * e.g. for enhanced EW penguins Br(KL#" 0 ( + ( - ): 4-5x bigger Buras, Fleischer, Recksiegel, Schwab 04 direct CPV NP *++! # T3"):*80+, +?)^$5)! (",140,- CP conserving "$ ^5!R Q ν, Q 9V, Q 10A " N " O

14 CKM and rare K decays f the so-called golden relation (sin 2β) ψks = (sin 2β) πν ν. test of the golden relation Could help improve the knowledge of CKM parameters However, more interesting is the 201x scenario: * CKM known to great precision independent of NP from Belle, BaBar, LHCb,... * SM prediction for K +, KL together with a 10% measurement allows precision test of the flavor structure of NP

15 New physics MFV MFV models general Flavor violation (Susy, warped ED)

16 Minimal Flavor Violation Buras, Gambino, Gorbahn, Jäger, Silvestrini (00) EFT approach: D Ambrosio, Giudice, Isidori, Strumia (02) In the limit of vanishing Yukawas SM acquires G=U(3) 5 SU(3)Q#SU(3)u#SU(3)d global symmetry. EFT approach Yukawa = Q L Y D D R H + Q L Y U U R (H) c Yukawas formally transform as YD ~ (3,1,3*) YU ~ (3,3*,1) MFV= effective field theory constructed with SM fields and Y s is invariant under G and CP 7 new parameters, aka independent Wilson coefficients, to describe all NP in B and K decays (more for large tan)) & all flavor changing processes governed by universal CKM

17 MFV parameters K 0 K 0 -mixing (ε K ) Bd,s 0 B d,s 0 -mixing ( M s,d) K πν ν, B X d,s ν ν K L µ µ, B d,s l l K L π 0 l + l ε, S = 1 Nonleptonic B = 1 B X s γ B X s gluon B X s l + l S(v) S(v) X(v) Y (v) Y (v), Z(v), E(v) X(v), Y (v), Z(v), E(v) X(v), Y (v), Z(v), E(v), E (v) D (v), E (v) E (v) Y (v), Z(v), E(v), D (v), E (v) dominant part Z-penguin trade for C7eff((b)

18 Bona, Buras, Bobeth, Ewerth, Pierini, Silvestrini, AW 05 Universal CKM fit from UTfit: Bona et. al 05

19 MFV upper bounds 7<= ):; 92):; 9(/:;!/! >! " $! %%"# <: <<! +**,2 +*',2 /,-=*,0 <A D D : & BDC! "!/ > E " $ %% # <: : << +.,( +.,0 -,*=',( +),2!*'. BNL AGS E787, E949 < KTEV 4 (90% (90% C.L.) C.L.) E391 # $ <: ;!/! " F 2 %% # +),0 +.,* -,1=',0 +(.! &!/!! 5 " ' ' "# <: C +1,. +),2 -,1=*,' +),'!*' 0! &!/!! G " ' ' "# <: <: +0,0 +*,/ *,*=',. +*,(!*' - Any violation implies new sources of flavor and CP violation! Bona, Buras, Bobeth, Ewerth, Pierini, Silvestrini, AW (05)

20 Comparison of sensitivities D Ambrosio, Giudice, Isidori, Strumia 02; Buras,Bryman, Isidori, Littenberg 05 MFV : 1 Λ 2 ( Q L Y U Y Uγ µ Q L )( L L γ µ L L )

21 K + and KL in specific MFV models Littlest Higgs: slight suppression Universal ED: <9-10% enhancement MFV Supersymmetry: % suppression General pattern: NP contribution to!md interferes constructively with SM!F =2 Amplitude S in the above models and ( ) V NP 2 td Vtd SM = Buras, Uhlig, Poschenrieder 05 Buras, AW, Spranger 03 Buras, Gambino, Gorbahn, Jäger, Silvestrini 00 S SM S SM + S NP < 1 => talk by S. Fajfer on rare D decays Br(K)exp > Br(K)SM immediately falsifies most MFV models!

22 Beyond MFV MSSM with general flavor violation EW symmetry breaking in warped Extra Dimensions

23 Generic MSSM Nir & Worah 97 Buras, Romanino, Silvestrini 97 Colangelo & Isidori 98 Flavor structure probes Susy breaking mechanism Room for sizable deviations even if!f=2 sector agrees well with SM Sensitive to new sources of flavor symmetry breaking due to $ 5 suppression of SM amplitude s ũ L χ t R Z ũ L d weakly constrained Amplitude SU(2)L X (peng) SUSY small tanß 1 MZ 2 V Z sd (M 2 LR ) d t (M 2 LR ) s t M 4 SUSY For large tanß, RR Higgs-mediated Z-penguin A ~ mb 2 tanß 4 enhancement possible Paradisi & Isidori 05

24 Generic MSSM Buras, Ewerth, Jäger, Rosiek 04 includes all present constraints!mk, *K, b#s+,... saturation of Grossman-Nir bound KL could be 20-30x enhanced in reach of E391a! Figure 7: Distributions of X and Br(K L π 0 ν ν), Br(K + π + ν ν) for tan β = 2.

25 EWSB in the Randall- Sundrum model light fermions tr Planck brane Z Q L = ( tl b L ) SM brane Higgs Fermion geography + deformed Z wavefunction: O(1) effects in rare K decays due to tree-level FCNCs Burdman 02; Agashe, Perez, Soni {including custodial SU(2)R and Zbb constraint} 04

26 Conclusions One of the most promising precision measurements to probe beyond SM particles with TeV mass and quark-flavor quantum numbers Rare Kaon decays are ideal test/killer of MFV Models with general flavor violation still allow for large deviations from SM See talk by talk by P. Paradisi for more NP opportunities in Kaon physics Discussions with A. J. Buras, U. Haisch, S. Jäger, and L. Silvestrini are gratefully acknowledged

27 Whatever nature has been hiding from us, Kaon physics has the potential to reveal it. Please measure!