The Discovery Potential of rare K and B decays. Andreas Weiler TU Munich

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1 The Discovery Potential of rare K and B decays Andreas Weiler TU Munich

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

3 Flavour in the SM Yukawas are responsible for flavour transitions _ Yukawa = Q L Y D D R H + Q L Y U U R (H) c _ Y D = (m d, m s, m b )/v Y U = V CKM (m u, m c, m t )/v mt >> mi and VCKM has a hierarchical structure There are no FCNCs on tree level.

4 Flavour change is small Y D = (m d, m s, m b )/v Y U = V CKM (m u, m c, m t )/v i Y U i i We have no idea why YU and YD are the way they are. Generally, NP models are struggling since we have no theory of flavour. We want NP to show up at around a TeV (Higgs stabilization). K-K mixing e.g. shows no generic flavour violation up to 10 3 TeV.

5 Flavour precision tests General structure of a decay rate Energy scale Γ = (non-pert. QCD) x QCD RG x (Vckm SM short dist.+ NP) theoretical uncertainty Three strategies for precision tests: 1) hadronic uncertainties cancel in asymmetries A mix partial cancelation: Br(B q µ + µ CP (B s ψφ) )/ M q 2) hadronic matrix element from Experiment ( K π νν ) 3) inclusive, non-perturbative ~ (ΛQCD/mb) 2 ( B X s γ )

6 FCNCs in the SM interesting Flavour channels s d ~ λ 5 ΔMK, εk, ε /ε, K L π 0 ll, K π νν b d ~ λ 3 ΔMd, B d µ + µ, B X d γ b s ~ λ 2 ΔMs, B s µ + µ, B X s l + l, B X s γ A F B (B X s l + l ) B K γ theoretical error increasing SM contribution < 15 % < 10% < 5%

7 FCNCs in the SM interesting Flavour channels s d ~ λ 5 ΔMK, εk, ε /ε, K L π 0 ll, K π νν b d ~ λ 3 ΔMd, B d µ + µ, B X d γ b s ~ λ 2 ΔMs, B s µ + µ, B X s l + l, B X s γ A F B (B X s l + l ) B K γ theoretical error increasing SM contribution < 15 % < 10% < 5%

8 FCNCs in the SM interesting Flavour channels s d ~ λ 5 ΔMK, εk, ε /ε, K L π 0 ll, K π νν b d ~ λ 3 ΔMd, B d µ + µ, B X d γ b s ~ λ 2 ΔMs, B s µ + µ, B X s l + l, B X s γ A F B (B X s l + l ) B K γ theoretical error increasing SM contribution < 15 % < 10% < 5%

9 FCNCs in the SM interesting Flavour channels s d ~ λ 5 ΔMK, εk, ε /ε, K L π 0 ll, K π νν b d ~ λ 3 ΔMd, B d µ + µ, B X d γ b s ~ λ 2 ΔMs, B s µ + µ, B X s l + l, B X s γ A F B (B X s l + l ) B K γ theoretical error increasing SM contribution < 15 % < 10% < 5%

10 Comparison of sensitivities D Ambrosio, Giudice, Isidori, Strumia 02; Buras,Bryman, Isidori, Littenberg 05

11 plan of the talk Interesting NP flavour observables of the future rare Kaon decays: the four golden modes, status of the SM calculation, NP searches B Xsγ (new result) rare B decays and large tanß Conclusions

12 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)

13 4 golden modes Br(K L π 0 µ + µ ) Br(K L π 0 e + e ) 60-ε! Br(K + π + ν ν) 24 carat Br(K L π 0 ν ν)

14 Potential of K->pivvK πν ν ν ν Z K + s u t W V td d π + u + box Dominated by short distance contributions o sigma(k + )theory ~ 4% o sigma(kl)theory ~ 2%

15 Potential of K->pivvK πν ν ν ν Z ) A(K + π + ν ν) = B + (λ c Pc + λ t X(v) K + s u t W V td d π + u A(K L π 0 ν ν) = B L Im [λ t X(v)] λ t = V tsv td λ c = V csv cd + box B+ and BL from K + π 0 e + ν Dominated by short distance contributions o sigma(k + )theory ~ 4% o sigma(kl)theory ~ 2%

16 Potential of K->pivvK πν ν ν ν Z ) A(K + π + ν ν) = B + (λ c Pc + λ t X(v) K + s u t W V td d π + u A(K L π 0 ν ν) = B L Im [λ t X(v)] λ t = V tsv td λ c = V csv cd + box B+ and BL from K + π 0 e + ν pure short-distance Dominated by short distance contributions o sigma(k + )theory ~ 4% o sigma(kl)theory ~ 2%

17 SM Calculation OPE # run # match mb MZ, mt,... MX HQET eff. weak Hamiltonian Fermi Theory SM SUSY, xd,?...

18 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 is SU(2)L breaking: powerlike GIM * large CPV phase in dominant top contribution * charm effects: 1) negligible in KL: O(mc 2 /mt 2 )<<1 for dominant direct CPV-Amplitude 2) small in K + ~30% ( next to next slide)

19 SM prediction of KdL->pv K L π 0 ν ν [ ] Im (V B(K L π 0 2 ν ν) = κ ts V td ) L λ 5 X κ L = r KL 3α 2 B(K + π 0 e + ν e ) 2π 2 s 4 W τ(k L ) τ(k + ) * 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 B(K L π 0 ν ν) = (2.8 ± 0.6) Buras, Gorbahn, Haisch, Nierste 06 Brexp / BrSM < (90% C.L.) E391 KTEV, E391a (soon to be improved!)

20 SM prediction of KdL->pv K L π 0 ν ν [ ] Im (V B(K L π 0 2 ν ν) = κ ts V td ) L λ 5 X κ L = r KL 3α 2 B(K + π 0 e + ν e ) 2π 2 s 4 W τ(k L ) τ(k + ) X = 1.46 ± 0.04 (NLO) Buchalla & Buras 93, 99; Misiak & Urban 99 t * 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 B(K L π 0 ν ν) = (2.8 ± 0.6) Buras, Gorbahn, Haisch, Nierste 06 Brexp / BrSM < (90% C.L.) E391 KTEV, E391a (soon to be improved!)

21 SM prediction of KdL->pv K L π 0 ν ν [ ] Im (V B(K L π 0 2 ν ν) = κ ts V td ) L λ 5 X κ L = r KL 3α 2 B(K + π 0 e + ν e ) 2π 2 s 4 W τ(k L ) τ(k + ) X = 1.46 ± 0.04 (NLO) Buchalla & Buras 93, 99; Misiak & Urban 99 r KL = ± isospin t * 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 Marciano & Parsa 96 B(K L π 0 ν ν) = (2.8 ± 0.6) Buras, Gorbahn, Haisch, Nierste 06 Brexp / BrSM < (90% C.L.) E391 KTEV, E391a (soon to be improved!)

22 SM prediction for K K->piv + π + ν ν [ (Im(V (K + π + ν ν) = κ ts V td ) + λ 5 X ) 2 + ( Re(V ts V td ) λ 5 X + Re(V csv ) ] 2 cd ) (P c + δp c ) λ

23 SM prediction for K K->piv + π + ν ν [ (Im(V (K + π + ν ν) = κ ts V td ) + λ 5 X ) 2 + ( Re(V ts V td ) λ 5 X + Re(V csv ) ] 2 cd ) (P c + δp c ) λ

24 SM prediction for K K->piv + π + ν ν [ (Im(V (K + π + ν ν) = κ ts V td ) + λ 5 X ) 2 + ( Re(V ts V td ) λ 5 X + Re(V csv ) ] 2 cd ) (P c + δp c ) λ * theoretical error of QCD corrections to the charm contribution Pc factor ~4 smaller thanks to NNLO calculation * Pc error now dominated by Δmc Buras, Gorbahn, Haisch, Nierste 05!"#!!"#

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

26 SM prediction for K K->piv + π + ν ν [ (Im(V B(K + π + ν ν) = κ ts V td ) + λ 5 X ) 2 + ( Re(V ts V td ) λ 5 X + Re(V csv ) ] 2 cd ) (P c + δp c ) λ * theoretical error of QCD corrections to the charm contribution Pc factor ~4 smaller thanks to NNLO calculation * Pc error now dominated by Δmc Buras, Gorbahn, Haisch, Nierste 05

27 SM prediction for K K->piv + π + ν ν [ (Im(V B(K + π + ν ν) = κ ts V td ) + λ 5 X ) 2 + ( Re(V ts V td ) λ 5 X + Re(V csv ) ] 2 cd ) (P c + δp c ) λ * theoretical error of QCD corrections to the charm contribution Pc factor ~4 smaller thanks to NNLO calculation * Pc error now dominated by Δmc Buras, Gorbahn, Haisch, Nierste 05

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

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

30 MFV SM Yukawa couplings are the only source of flavour violation. All flavour violation is proportional to VCKM. Strong correlations between K and B physics.

31 K + and KL in specific MFV models Littlest Higgs: slight suppression Universal ED: <9-10% enhancement CMFV MSSM: % suppression General pattern: Buras, Uhlig, Poschenrieder 05 Buras, AW, Spranger 03 Buras, Gambino, Gorbahn, Jäger, Silvestrini 00 NP contribution to ΔMd interferes constructively with SM ΔF =2 Amplitude S in the above models and Buras, Blanke 06 ( V NP td V SM td ) 2 = S SM S SM + S NP < 1 Br(K)exp > Br(K)SM immediately falsifies most MFV models!

32 MFV upper bound SM model independent 95%C.L. upper bound Bona, Buras, Bobeth, Ewerth, Pierini, Silvestrini, AW 05 Universal CKM fit from UTfit: Bona et. al 05 using universal UTfit + B Xsγ + B Xsl + l -

33 MFV upper bounds Bona, Buras, Bobeth, Ewerth, Pierini, Silvestrini, AW (05) 7<=8 92):; ):; 678 9(/:; 345!/! >! " $! %%"# <: <<! +**,2 +*',2 /,-=*,0 <A D D : & BDC BNL AGS E787, E949! "!/ > E " $ %% # <: : << +.,( +.,0 -,*=',( +),2!*'. KTEV (90% C.L.) < (90% C.L.) E391 # $ <: ;!/! " F 2 %% # +),0 +.,* -,1=',0 +(.! " <: C! &!/! 5 " ' ' # +1,. +),2 -,1=*,' +),'!*' <80 0 (90% C.L.) CDF! " <: <:! &!/! G " ' ' # +0,0 +*,/ *,*=',. +*,(!*' - low/moderate tanß!

34 Beyond MFV rare K decays are a very sensitive probe for non-mfv flavour violation since (s d) ~ λ 5 suppression is not built in the model anymore.

35 Generic MSSM Nir & Worah 97 Buras, Romanino, Silvestrini 97 Colangelo & Isidori 98 Buras, Ewerth, Jäger, Rosiek 04 Isidori, Mescia, Paradisi, Smith, Trine 06 Flavor structure probes Susy breaking mechanism Room for sizable deviations even if ΔF=2 sector agrees well with SM very sensitive to new sources of flavor symmetry breaking due to λ 5 suppression of SM amplitude s ũ L χ t R ũ L d Amplitude SU(2)L 1 M 2 Z V Z sd Z weakly constrained X (peng) SUSY (M 2 LR ) d t (M 2 LR ) s t M 4 SUSY small tanß

36 Generic MSSM Buras, Ewerth, Jäger, Rosiek 04 includes all present constraints ΔMK, εk, b sγ,... saturation of Grossman-Nir bound SM KL could be 20-30x enhanced in reach of E391a

37 Generic MSSM II Isidori, Mescia, Paradisi, Smith, Trine 06 "(K +! # + $$) "(B d! µµ)!m B d * SUSY / * SM & 13 real & positive & 23 =0 '& 13 ', 'A 23 ' ( ) A 0 '& 13 ' (GeV) K + best probe of up-type trilinear soft Susy breaking terms L soft (A U Y U ) ij Q i LU j R φ

38 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, SuperB,... * SM prediction for K +, KL together with a 10% measurement allows precision test of the flavor structure of NP

39 Status of KL π 0 l + l - Buchalla, D Ambrosio, Isidori; Isidori, Smith, Unterdorfer 04, Smith, Mescia, Trine 06 Br(K L π 0 l + l ) = [ C l mix + C l int ( Imλt 10 4 ) + C l dir ( Imλt 10 4 ) 2 + C l CPC ] indirect CPV interference of direct and indirect direct CPV CP conserving substantial progress in theory precision associated with light quark loops experimental input from NA48 Cdir e = (4.62 ± 0.24)(ω2 7V + ω2 7A ) Cint e = (11.3 ± 0.3)ω 7V, C e mix = 14.5 ± 0.05, C e CPC 0, C µ dir = (1.09 ± 0.05)(ω2 7V ω2 7A ) C µ int = (2.63 ± 0.06)ω 7V, C µ mix C µ CPC = 3.36 ± 0.20, = 5.2 ± 1.6, Br(K L π 0 µ + µ ) = (1.5 ± 0.3) Br(K L π 0 e + e ) = ( ) % C.L. < < KTEV 00 KTEV 03

40 Br(K L π 0 l + l ) = Status of KL π 0 l + l - Buchalla, D Ambrosio, Isidori; Isidori, Smith, Unterdorfer 04, Smith, Mescia, Trine 06 [ C l mix + C l int ( Imλt 10 4 ) + C l dir ( Imλt 10 4 ) 2 + C l CPC ] indirect CPV interference of direct and indirect direct CPV CP conserving Direct CPV amplitude: * clean probe of independent NP structures and CPV beyond SM * important if beyond-mfv NP is found

41 Br(K L π 0 l + l ) = Status of KL π 0 l + l - Buchalla, D Ambrosio, Isidori; Isidori, Smith, Unterdorfer 04, Smith, Mescia, Trine 06 [ C l mix + C l int ( Imλt 10 4 ) + C l dir ( Imλt 10 4 ) 2 + C l CPC ] indirect CPV interference of direct and indirect direct CPV CP conserving Direct CPV amplitude: * clean probe of independent NP structures and CPV beyond SM * important if beyond-mfv NP is found NP *++! # T3"):*80+, +?)^$5)! (",140,- "$ ^5!R Q ν, Q 9V, Q 10A " N " O

42 B X s γ new NNLO results? 1 4"6 )! 4"6#$

43 B X s γ Charm mass dependence enters first at NLO: Strong scheme ambiguity in mc/mb only be resolved at NNLO 7 m c /m b = 0.29 ± 0.02 (pole mass) Br(Eγ > 1.6GeV) B m c /m b = 0.22 ± 0.04 (MS) ALEPH 98 Belle 04 CLEO 01 WA BaBar 02 BaBar 05 Belle 01 CLEO 95 (old NLO) 0

44 very involved calculation M. Misiak, 1, 2 H. M. Asatrian, 3 K. Bieri, 4 M. Czakon, 5 A. Czarnecki, 6 T. Ewerth, 4 A. Ferroglia, 7 P. Gambino, 8 M. Gorbahn, 9 C. Greub, 4 U. Haisch, 10 A. Hovhannisyan, 3 T. Hurth, 2, 11 A. Mitov, 12 V. Poghosyan, 3 M. Ślusarczyk,6 and M. Steinhauser 9 b t γ LO s NNLO b u, c, t s W W γ 1) 3-loop matching (complete) 2) 3 and 4-loop mixing (almost) 3) most difficult: 3-loop matrix element (interpolation between mc/mb>>1 and αs 2 nf approximation)

45 Cut in photon energy Events/100 MeV Belle 04 Eγ > 1.8 GeV to suppress background E*! [GeV] BaBar Eγ > 1.9 GeV, CLEO Eγ > 2.0 GeV

46 Cut in photon energy with cut E0>Eγ three relevant scales: Neubert 04; Becher, Neubert 06 (hard) mb (jet) (Δ mb) 1/2 (soft) Δ=mb -2E0 1GeV OPE in terms of (ΛQCD/Δ) n and αs(δ) Γ H 2 J S hard jet soft calculate NNLO corrections to multiscale OPE to resum large logarithms

47 7 Br(Eγ > 1.6GeV) B ALEPH 98 Belle 04 CLEO 01 BaBar 02 BaBar 05 Belle 01 CLEO 95 Brexp WA Brth 0 Br( B X s γ) exp Br( B X s γ) th = 1.19 ± 0.09 exp ± 0.10 th NNLO estimate of Becher/Neubert 06 including effect of photon energy cut using the recent NNLO result of Misiak et. al 06

48 MFV MSSM at large tanß Hall, Ratazzi, Sarid Babu,Kolda Chankowski, Slawianowska Bobeth, Ewerth, Krüger, Urban Huang, Liao, Yan, Zhu Isidori, Retico Dedes, Dreiner, Nierste Dedes, Pilaftis Chankowski, Rosiek Foster, Okumura, Roszkowski

49 Specific pattern: Br(Bs μ + μ - ) ~ (tanß) 6 Key players Babu, Kolda 02 F / ΔMs ~ (ΔMs) SM - c (tanß) 4 I J & K J & 9 "'&"!# X "'&"!# 2 $ &'( & / 0 1 0!&'( &" > 2 $! " > b u H ± Buras, Chankowski, Rosiek, Slawianowska 02 l! Br(Bu τ ν) ~ Br(Bu τ ν) SM - d (tanß) 2 Isidori, Paradisi 06 Br( B X s γ for AU<0. ) chargino and H ± contributions tend to cancel using UTfit 05 and CDF/D0 result; UTfit 06 -> 0.96 (ΔMs) exp /(ΔMs) SM = 0.8 ± 0.12 RBτν=(Br(Bu τ ν) ) exp /(Br(Bu τ ν) ) SM = 0.7 ± 0.3 pre-ichep 06, post-ichep -> R=0.85

50 + Bs μ μ vs. ΔMs Buras, Chankowski, Rosiek, Slawianowska 02 (ΔMs)exp/(ΔMs)SM Figure 23: Correlation between Ms /( Ms )SM and Bs,d µ+ µ in the MSSM

51 MFV-MSSM and large tanß Isidori, Paradisi excluded by B s! µµ Bs μ + μ - '(&M Bs ) < 10% 0.6<RBτν<0.9 allowed B(B s! µµ) < 10 (8 tanß tan # < R B$% < < 10 9 &a µ < B X s γ excluded by B! X s " MH± M H

52 MFV-MSSM and large tanß Isidori, Paradisi excluded by B s! µµ Bs μ + μ - '(&M Bs ) < 10% 0.6<RBτν<0.9 B(B s! µµ) < 10 (8 tanß tan # < R B$% < <RBτν<0.8 1 < 10 9 &a µ < B X s γ excluded by B! X s " MH± M H

53 Outlook and conclusions We are puzzled by the flavour problem Rare K decays are very sensitive probe into TeV scale flavour violation. Best test of MFV and generically expect large deviations in non-mfv scenarios. Beginning of the era of precision flavour tests of NP Very interesting NP scenario Little Higgs with T parity: see C. Tarantino s talk for a discussion of the signatures. Theorist s nirvana: measure K π νν and B s µ + µ

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