1 Federico Mescia INFN-Frascati CKM December 12-16, Nagoya The impact of rare K decays in New Physics searches The impact of rare K decays in New Physics searches ExperimentStandard ModelGolden Modes KTeV E787 E949 E391a KTeV

K L  ÷ K +  uncertainties at 15% due to present CKM accuracy

3 K L    K +    high-precision discovery lens! at 5% uncertainties with CKM updates from Babar/Belle/LHCb large room for New Physics essential exp. info

4 large unexplored room in principle, but is it still possible to expect deviations, despite constraints from the large amount of processes compatible with the Standard Model? reminder Mind at special cases, Paride’s talk tree-level processes  disfavoured for NP searches, normally (M W /) 2 ≤1% (Mind at special cases, Paride’s talk) FCNC loop processes  suitable for NP, only measured B=2, S=2 and B=1 transitions K rare decays  sd coupling and highest CKM suppression like ’ very clean like sin2 in any case, LHC will saturate the room left, won’t it?  ATLAS-CMS  new particles at the TeV scale by flavour conserving channels complementarity  LHCb at work  B s and B d information on bs/bd couplings Let’s not forget “The definitive answer is from experiments” G. Galileo 2 K  & K  can give some surprise, with small effects in B and EWPT Moreover, clean probe to higher scale  flav ~100 TeV 1

5 Two classes of “Beyond SM” scenarios: 1.Minimal Flavour Violation: flavour breaking induced only by SM Yukawa couplings, Y U & Y D. (Y: Wilson coefficient at  flav » 1 TeV ) Pattern: effects on B( K L   B( K +   B( K L    Peculiarity: K L    K L   ee correlation 2.New sources of Flavour Symmetry breaking arising at the TeV scale  Cecilia & Buras s  d new couplings no longer O ( 5 ) suppressed (s  d) BMFV = O ( 5 )  SM + O (  )  (new d.o.f) Many proposed models already killed from present data (B, K, EWPT & DM) One order of magnitude enhancement still possible in MSSM and LHT B(K L     in reach of E391a upgrade SM hierarchy of FV couplings: (s  d) MFV = O ( 5 )  [ SM + new d.o.f ] Specific realisations in SUSY, UED, LH, EFT Small deviations in specific models: B(K L    O(20%-30%) In specific models, stringent correlations can rise with either B physics ( B  BX, BX or EWPT (  )

6 Two classes of “Beyond SM” scenarios: 1.Minimal Flavour Violation: flavour breaking induced only by SM Yukawa couplings, Y U & Y D. (Y: Wilson coefficient at  flav » 1 TeV ) Pattern: effects on B( K L   B( K +   B( K +    Peculiarity: K L    K L   ee correlation 2.New sources of Flavour Symmetry breaking arising at the TeV scale  Cecilia & Buras s  d new couplings no longer O ( 5 ) suppressed (s  d) BMFV = O ( 5 )  SM + O (  )  (new d.o.f) Many proposed models already killed from present data (B, K, EWPT & DM) One order of magnitude enhancement still possible in MSSM and LHT B(K L     in reach of E391a upgrade SM hierarchy of FV couplings: (s  d) MFV = O ( 5 )  [ SM + new d.o.f ] Specific realisations in SUSY, UED, LH, EFT Small deviations in specific models: B(K L    O(20%-30%) In specific models, stringent correlations can rise with either B physics ( B  BX, BX or EWPT (  )

7 Two classes of “Beyond SM” scenarios: 1.Minimal Flavour Violation: flavour breaking induced only by SM Yukawa couplings, Y U & Y D. (Y: Wilson coefficient at  flav » 1 TeV ) Pattern: effects on B( K L   B( K +   B( K +    Peculiarity: K L    K L   ee correlation 2.New sources of Flavour Symmetry breaking arising at the TeV scale  Cecilia & Buras s  d new couplings no longer O ( 5 ) suppressed (s  d) BMFV = O ( 5 )  SM + O (  )  (new d.o.f) Many proposed models already killed from present data (B, K, EWPT & DM) One order of magnitude enhancement still possible in MSSM and LHT B(K L     in reach of E391a upgrade SM hierarchy of FV couplings: (s  d) MFV = O ( 5 )  [ SM + new d.o.f ] Specific realisations in SUSY, UED, LH, EFT Small deviations in specific models: B(K L    O(20%-30%) In specific models, stringent correlations can rise with either B physics ( B  BX, BX or EWPT (  )

8 D’Ambrosio,Giudice,Isidori,Strumia (02) Y D & Y U regulate flavour violation: U(3) 5 U(3) 5 flavour group new TeV O 6  functions of SM fields and Y D -Y U spurions, made invariant of U(3) 5 SU(3) 5 BLCP. - c 6 universal and real coef. Minimal Flavour Violation U(3) 5 EFT at TeV see Grinstein’s talk

9 D’Ambrosio,Giudice,Isidori,Strumia (02) Minimal Flavour Violation U(3) 5 EFT at TeV 1. CKM suppression (O( 5 )) still on; 2. the X coefficient unbounded from B processes or  K 13 operators K-raredecays K-rare decays D’Ambrosio,Giudice,Isidori,Strumia (02)

10 MFV enhancement: B( K L   B SM B( K +   B( K L    SM MFV model independent ap.

11 1.MFV- Phenomenological Model (CMFV) MFV- Specific Scenarios Buras,Gambino,Gorbahn,Jäger,Silvestrni (00) only Standard Model operators In a given model implementation, X bounded trough EWPT & B data. Deviations from SM can get smaller Bobeth,Bona,Buras,Ewerth,Pierini,Silvetrini,Weiler (05) box and g-peng. d.o.f frozen to their SM value X -> constrained by B processes s.d. couplings gauge invariant

12 SM Excl. at 68% CL E787-E949 lower bound Bobeth,Bona,Buras,Ewerth,Pierini,Silvetrini,Weiler (05) at 95% CL O (20-50%) enhancement B( K L   B SM B( K +   B( K L    ~SM MFV-EFT: X free D’Ambrosio,Giudice,Isidori,Strumia (02) Outcome: MFV + Exp. Evidence of K + excludes small vanishing K L BR Analysis on MFV-Phenomenological Model XY and E0

13 1.MFV-Phenomenological Model (CMFV) MFV- Specific Scenarios Buras,Gambino,Gorbahn,Jäger,Silvestrni (00) only Standard Model operators In a given model implementation, X bounded trough EWPT, B & K data. Deviations from SM can get smaller Bobeth,Bona,Buras,Ewerth,Pierini,Silvetrini,Weiler (05) box and g-peng. d.o.f frozen to their SM value 2.MFV+SUSY- Msugra-like D’Ambrosio,Giudice,Isidori,Strumia (02) a)SUSY spectrum:SM+4Higgs+SUSY partners H &  interactions ruled by CKM (super CKM basis) dark matter candidate stabilization of Higgs sector b)MFV scalar soft breaking terms proportional to SM Yukawa couplings

14 Largest effects by and, since enhanced by the large top mass down top H + down stop R  + mtmt mtmt Nir,Worah(98)/Buras,Romanino,Silvestrini(98)/Colangelo,Isidori(98) Analysis on MFV-MSSM (R-parity) +perm.+boxes no FV via gluino/neutralino common CKM factor enhancements due to flavour conserving parameters: 1.small tan 2 2.light spectrum; stop 150 GeV chargino 150 GeV charged Higgs 300 GeV 3.large a 4 ;maximal effects for sign(sign(a 4 ) Upper limits B( K L   B SM Isidori,F.M,Paradisi,Trine,Smith (06)  LHC the largest correlation from  Buras,Gambino,Gorbahn,Jager,Silvestrini (00) Isidori,F.M,Paradisi,Trine,Smith (06)

15 2.New sources of Flavour Symmetry breaking arising at the TeV scale Two classes of “Beyond SM” scenarios: MSSM: generic insertions 120 parameters free! MAMMA MIA! and … 27 new Flavour Changing couplings along the squark lines. What can we ever learn from K-rare? x

16 What can we ever learn from K-rare? Nir,Worah(98)/Buras,Romanino,Silvestrini(98)/Colangelo,Isidori(98) gluino, neutralino and chargino New FCNC transitions by The interplay between SU(2) L U(1) and Flavour symmetry prevents strong headaches:  appreciable sensitivity only to -up-squark diagrams by 1 effective coupling gluino diagrams negligible; 2.LR mass insertions  propto to quark masses  1.SU(2) L -conserving insertions, M LL/RR  q 2 /m 2 Z suppressed

17 What can we ever learn from K-rare? a lot K are the best probe of the flavour structure of the structure of the A U terms (M t ) Isidori,F.M,Paradisi,Trine,Smith (06) A-terms still unconstrained from B physics. small effects on LHcb/SuperB searches! “Houston, we have a problem” LHC - spectrum

18 CPV observables at comparison: large room left due to the large room left due to the A U terms Isidori,F.M,Paradisi,Trine,Smith (06) small impact on  K & sincomplementarity to LHCb/SuperB

19 appreciable sensitivity only to one effective coupling Buras,Ewerth,Jäger,Rosiek (04) Grossman-Nir bound is saturated B( K L   B SM How sizable are these effects? big Excl. at 68% CL E787-E949

20 K L    K L   ee correlation special opportunity to New Physics Searches

21 K L    K L   ee correlation  ; visible 1.alike to K s by  peng. ; visible effects oncurrent-current operators / F.M, Trine, Smith (06); F.M,Trine,Smith (06);

22 K L    K L   ee correlation  ; visible 1.alike to K s by  peng. ; visible effects oncurrent-current operators  2.contrary to K sensitive to helicity-suppressed operators F.M, Trine, Smith (06) Retico, Isidori (02)/Buras,Chankowaki,Rosiek,Slawianowska(02 )/ Foster,Okumura,Roszkowski (05) H 0 penguins at large tan but different mass insertions) copiare papers (as Bbut different mass insertions) copiare papers

23 Conclusions Combining all present th. and exp. information, large deviations on K & K  are still possible MFV: D’Ambrosio et al. ph MSSM: Buras et al. ph Isidori et al. ph Mescia et al. ph LHT: Blanke et al. ph E787-E949 ex ex E787-E949 ex ex GN Bound ph GN Bound ph Buras et al. ph K-rare decays large not covered parameter space! complementarity to Atlas/CMS searches new particles supplementarity to LHcb/SuperB activities gluinos

24 BACKUP

25 MSSM: SUSY model at low-energy 27 FC mass insertions free. MSSM: SUSY model at low-energy particle content: SM+4Higgs+SUSY partners SUSY softly broken trilinear scalar couplings, squark/slepton and chargino, masses R-parity conservation dark matter candidate new source of flavour violation x  LHC task

26 MFV-Phenomenological Model Buras,Gambino,Gorbahn,Jäger,Silvestrni (00) “stronger’’ correlations between K & B decays, module to neglect box contr. & poorly constrained  couplings  XY and E=0 Bobeth,Bona,Buras,Ewerth,Pierini,Silvetrini,Weiler (05) measured fixed free parametersfrozen to SM weakly constrained within present exp. accuracy XY and E=0

27 K L    K L   ee correlation  ; visible 1.like K s by  peng. ; visible effects oncurrent-current operators  2.contrary to K sensitive to helicity-suppressed operators F.M, Trine, Smith (06) Retico, Isidori (02)/Buras,Chankowaki,Rosiek,Slawianowska(02 )/ Foster,Okumura,Roszkowski (05) H 0 penguins at large tan but different mass insertions) (as Bbut different mass insertions)

28 QCD M. E.  F=2 b.  F=1 b. g-pen.  pen. Z-penH-pen. b  s    small MsMs B i B d  X s  OPE B d  X s OPE B s  fBfB A CP (B s  - A CP (B d  - bdbd MdMd B i B d  X d  OPE B d  fBfB A CP (B d  s  - s  d    tiny  B K K L   known  K +  + Known K L    + B T FCNC asymmetries and branching ratios within a th. err  15% K  peculiarities: highest CKM suppression and  S=1 coupling  like  ’  very clean  like sin2  measured  5% Th err.

29 What can we ever learn from K-rare? Nir,Worah(98)/Buras,Romanino,Silvestrini(98)/Colangelo,Isidori(98) 1. gluino diagrams negligible reduced sensitivity to LL/RR SU(2) L -conserving insertion and LR suppressed by down quark masses gluino, neutralino and chargino New FCNC transitions by The interplay between SU(2) L U(1) and Flavour symmetry prevents strong headaches. 2.appreciable sensitivity only, to -up-squark diagrams by 1 effective coupling

30

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32 What can we ever learn from K-rare? Nir,Worah(98)/Buras,Romanino,Silvestrini(98)/Colangelo,Isidori(98) 1. gluino diagrams negligible reduced sensitivity to LL/RR SU(2) L -conserving insertion and LR suppressed by down quark masses gluino, neutralino and chargino New FCNC transitions by The interplay between SU(2) L U(1) and Flavour symmetry prevents strong headaches. 2.appreciable sensitivity only, to -up-squark diagrams by 1 effective coupling