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Rare Kaon Decays - 2

Rare Kaon Decays - 2. Laurence Littenberg BNL E. Fermi School, Varenna - 25 July 2005. Organization. Introduction & general motivation Lepton Flavor Violation, etc. Brief review of Unitarity K +  +  K L  0  K  K L  l + l - K L  0 l + l -.

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Rare Kaon Decays - 2

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  1. Rare Kaon Decays - 2 Laurence Littenberg BNL E. Fermi School, Varenna - 25 July 2005 L. Littenberg – Varenna

  2. Organization • Introduction & general motivation • Lepton Flavor Violation, etc. • Brief review of Unitarity • K++ • KL0 • K • KLl+l- • KL0l+l- L. Littenberg – Varenna

  3. Cabibbo-Kobayashi-Maskawa (CKM) Matrix Unitary matrix connecting weak with mass eigenstates Parameterization of Wolfenstein and Maiani: _ L. Littenberg – Varenna

  4. Unitarity Relation (1-2/2) (1-2/2) (1-2/2) L. Littenberg – Varenna

  5. Wolfenstein parameterization to higher order W-M parameterization only approximate, at (4) & beyond, not unique Buras et al. (PR D50 (1994) 3433) introduced a version unitary to all orders At the moment, don’t need to go above (5): _ _ Where   (1- 2/2) &   (1-2/2) Main effect is to move vertex of unitary triangle to (, ) In terms of i  VidVis*: Im t= - Im c= A2 5 Re c= - (1- 2/2) Re t= - (1- 2/2)A25(1- ) Note that the area of any unitarity triangle = ½Jcp Where Jcp = -Im(Vts*VtdVus*Vud) = (1-2)½Im t Thus, a measurement of Im t would determine the area of all 6 U.T.’s _ _ _ _ L. Littenberg – Varenna

  6. One-loop K Decays Short distance contributions to K decays. These decays include KL0, K++, KL+-, KL0e+e-, KL0+-, etc. The hadronic matrix elements involved are known from common K decays such as K+0e+. These one-loop contributions can be cleanly calculated in terms of sinC, mt, mc, and the product of CKM elements Vts*Vtd  t. But there’s a Murphy’s Law to these processes. The same interactions that allow final state leptons to be detected mediate long-distance contributions. E.g.: To avoid this one must exploit decays containing a final state  pair. L. Littenberg – Varenna

  7. Rare K Decays & the Unitarity Triangle L. Littenberg – Varenna

  8. _ Vts*Vtd K++ contains QCD corr. has been calc’d to NNLLA X  1.57(mt/170)1.15 = 4.210-11A4X2(xt)[2+⅔(0e-)2+⅓(0-)2] calc. uncertainty only a few % In leading order in Wolfenstein parameters, B(K++) determines a circle in the ,  plane with center (0,0); 0 ⅔0e+⅓0and radius = [1010B(K++)]½/A2 Going beyond leading order, circle gets slightly squashed, BR formula becomes: The ellipse departs from a circle by only a factor : it’s 5% wider than it is tall L. Littenberg – Varenna

  9. -1/2 Uses of CKM Unitarity Hard-to-calculate parts subtract away L. Littenberg – Varenna

  10. K Hadronic Matrix Element L. Littenberg – Varenna

  11. K+ l+ +  Long-distance effects • Most long-distance contributions calculated years ago, e.g.: • Come out to be a few % of the short-distance charm contribution • New calculation of dimension-8 contribution to the charm piece by Isidori, Mescia & Smith (hep-ph/0503107) raises this contribution by 10% &  the SM branching ratio by 6% L. Littenberg – Varenna

  12. _ K++ & the U.T. • The usual U.T. is convenient for the B system, but is no more fundamental than the 5 other possible triangles. • One triangle can be completely determined by K measurements: • t + c + u = 0 (where i  Vis*Vid) • This triangle is rather elongated (base to height ~1000:1) • Usually see this information displayed in terms of real & imaginary part of t L. Littenberg – Varenna

  13. B(K++) = (8.00.9CKM0.6mt0.15µC 0.4mC)  10-11 Vcb Reduced by factor 2-3 by 3-loop NNLO calculation Precision of SM prediction L. Littenberg – Varenna

  14. _ Experimental considerations for K++ • 3-body decay,only 1 visible • + common K decay product • BR ~ few  10-11 • Backgrounds: • K++() • K+ + 0 • Beam • Beam + mis-ID as K+, then fakes K decay at rest • K+ decay in flight • 2 beam particles • K+nK0p; KL  + ℓ-, lepton missed pnn1 pnn2 L. Littenberg – Varenna

  15. E787/949 Detector L. Littenberg – Varenna

  16. Incoming 700MeV/c beam K+: identified by Č, WC, scintillator hodoscope (B4). Slowed down by BeO • K+ stops & decays at rest in scintillating fiber target – measure delay (2ns) • Outgoing +: verified by IC, VC, T counter. Momentum measured in UTC, energy & range in RS and target (1T magnetic field parallel to beam) E787/949 Technique • +stops & decays in RS – detect ++e+ chain • Photons vetoed hermetically in BV-BVL, RS, EC, CO, USPV, DSPV L. Littenberg – Varenna

  17. E787/949 Analysis Strategy Signal region“the BOX” PNN1: p > p(K++0) = 205MeV/c Background sources Identify a priori. at least 2 independent cuts to target each background: K+ • K++0 • muon background (K++(),…) • Beam background • etc. Analysis Strategy • Blind Analysis • Measure background level with real data • To avoid bias, • 1/3 of data  cut development • 2/3 of data  background measurement • Characterize backgrounds using back- • ground functions • Likelihood Analysis L. Littenberg – Varenna

  18. Calculation of backgrounds Tag with  kinematics Photon veto Tag kinematics outside  box – in K2 peak L. Littenberg – Varenna

  19. Changing cut position Acceptance & background levelat each point of parameter Functions Background Characterization Background can be characterized using specially constructed functions For muon backgrounds • K2(tail): K2 but range is small due to interactions in RS. • K2(band): multibody K++ decay (K+ +, etc.) Momentum (P) for  and  +  +  e+ in the + stopping counter Neural net function for  &  L. Littenberg – Varenna

  20. E787  E949 • Enhanced  veto, beam instrumentation • Much higher proton flux (65 TP) • Improved tracking and energy resolution • Higher rate capability due to DAQ, electronics and trigger improvements • Lower beam duty factor (Siemens  Westinghouse) • Lower proton energy (by 10%, cost 10% in flux) • Problematic separators, worse K/π ratio (4 3), fewer K/proton (factor ~1.5) • Total cost, factor 2 L. Littenberg – Varenna

  21. E787/949 Events _ B(K++) = (1.47+1.30-0.89)10-10 L. Littenberg – Varenna

  22. (68% CL interval) E787 result: Combined E787/949 Result L. Littenberg – Varenna

  23. K++ contour on the unitarity plane Green arcs indicate this K+p+nn result (including theoretical uncertainties) • Contour in r-h planecourtesy of G. Isidori Central value Central value off the “SM” Need more data!! 68% interval 90% interval L. Littenberg – Varenna

  24. Acceptance larger than for pnn1 (in principle) E787 bkgnd-limited at ~10-9, another factor 10 needed to get to S:B ~ 1 Main background from K2 w/nasty correlation Improved photon vetoing in E949 very encouraging. Answer expected in a few months. E949 pnn2 E787 L. Littenberg – Varenna

  25. E949 detector worked well • Obtained ~2/3 sensitivity of E787 in 12 weeks (1/3 pnn1+1/3 pnn2) • Found one new pnn1 candidate • pnn2analysis currently in progress – looks promising • AGS & beamline problems cost a factor ~2 in sensitivity/hour • DOE cut off experiment after 12 of 60 promised weeks • Currently seeking NSF support Status & prospects for E949 L. Littenberg – Varenna

  26. J-PARC K++ LOI • Stopped K+ experiment • Builds on E787/949 experience • Lower energy separated beam • Higher B spectrometer • More compact apparatus • Better resolution • Finer segmentation • Improved  veto (crystal barrel) • Aims for 50 events • Not an early experiment for J-PARC • Needs beamline • place on the floor • $ for detector L. Littenberg – Varenna

  27. PROs Long history The enemies are known Well-honed methods S/B good enough! Effective particle ID Easy to be hermetic Very pure beam In CM right away Clean separation of kinematics/part-ID CONs Decay in matter Nuclear effects Require ’s to stop ID sensitive to rates 3 timescales (up to 10s) Need low veto thresholds Limited K flux Most K’s interact (typ 4/5) Correlation of detector geometry w/CM system Pros & cons of stopped-K technique L. Littenberg – Varenna

  28. P326 (NA48/3) K++ Proposal submitted to CERN for ~100 events L. Littenberg – Varenna

  29. P326 Technique • Detection in-flight • High energy (75 GeV/c) unseparated beam (800 MHz!) • Careful design to keep halo to ~7MHz • Measure all beam tracks (“Gigatracker”) • Differential Cerenkov (“CEDAR”) for K ID • Redundant measurement of pion momentum • Two-stage magnetic spectrometer (straws in vacuum) • Require large missing momentum • Redundant pion I.D. • Magnetized hadron calorimeter (“MAMUD” + RICH) • (Almost) hermetic photon veto system • NA48 liquid Krypton calorimeter • Small angle charged & neutral vetoes (beam bent out of the way) • Wide-angle frame anti’s L. Littenberg – Varenna

  30. Kinematics + momentum cut requires a huge momentum mismeasurement to mistake a beam + for a final state particle (7535 GeV/c). Also guarantees large missing momentum, e.g. so that there’s plenty of  energy from K+ +0 Assumption of pion mass spreads out K++ peak 0.3% resolution on pK and 1% resolution on p allows ~10% acceptance L. Littenberg – Varenna

  31. Plan for P326 • 2005 • Gigatracker R&D • Vacuum tests • Technical design & cost estimate • 2006 • Detector tests in present beam • Construction & installation 2007-8 • Construct new beamline • Construct & install detectors • 2009-10 • Running • Expect ~80 events with S:B ~ 10:1 L. Littenberg – Varenna

  32. How to pursue K++? • In-flight has the “appeal of the new” • The only way to get >100 events • But requires 11 O.M. leap! • Watch out for tails, acceptance losses, the unexpected • Stopping experiment very well understood • Technique shown to have sufficient S/B • Any further improvements can increase acceptance • Note acceptance of 787/949 is ~0.002 • Plenty of room for improvement! • Could really know if 50-100 events possible • But so far very little support for such an experiment L. Littenberg – Varenna

  33. _ Why is KL0 CP-violating? • To lowest electroweak order in the SM • 0 is CP-even (can be thought of as 0Z*) • Spin of K is 0, so must havel = 1 • KL is CP-odd (to corrections of order K) • since • & |q/p| = 1-2Re K (from CP asymmetry in Kl3) • Define •   &  the phase between K mixing & sd • Note ~ 1,  = e2i • Ratio between decay rates is • Then _ L. Littenberg – Varenna

  34. _ KL0 & CP-violation – 2 • Use • to replace unmeasurable • yields • where ris  0.954 is isospin breaking (mass diff., etc.) • In SM,  =  (e.g. from BJ/KS) • this comparison one of many clean tests of CP • In this case parameters like CKM A and mtdivide out L. Littenberg – Varenna

  35. _ KL0 in the Standard Model Suppressed to the 1-loop level by GIM. No competing long-distance contributions KL0 is t-quark dominated in the loops Direct CP-violating to ~1% No significant QCD correction Hadronic m.e. from Ke3 BR = (1.5580.025)10-3 (11.3m/mt)  (Im t)2 < 2% intrinsicuncertainty due to theoretical uncertaintythat on mt _ L. Littenberg – Varenna

  36. _ A Model-independent limit on B(KL0) _ _ • B(KL0) < 4.4 B(K++) • Proposed by Y. Grossman & Y. Nir • Phys. Lett. B398 (1997) 163 • A consequence of the I = ½ Rule • trivial in the SM (imaginary part of amplitude < modulus) • True for almost any short-distance interaction, even if that interaction conserves CP • Expressed as a limit, E787/949 result is • B(K++)<3.22  10-10 @ 90% C.L. • Yields B(KL0) < 1.4  10-9 • Far better than any other limit • c.f. 2.86  10-7 from E391a • But still 50 times larger than SM expectation _ _ L. Littenberg – Varenna

  37. BSM Beyond the SM, K’s don’t have to agree with B’s! L. Littenberg – Varenna

  38. _ (pB/B) KL0 Beyond the SM • Unique because • retains its clean connection to short distance parameters BSM • NOT the case for e.g. BJ/KS where new physics can be observed but not interpreted. • probes the flavor structure of any new physics • A 10% deviation in B-physics can translate into an O(1) deviation in this decay. • See e.g. Buras et al., PRL 92 (2004) 101804 • Even if result agrees with B-physics prediction, gives unique constraint on new physics operators • A 10% measurement can probe new physics scales > 1000 TeV! • See Buras et al., hep-ph/0505171 L. Littenberg – Varenna

  39. Comparison of reach in MFV models L. Littenberg – Varenna

  40. _ K in the MSSM From E949 Sign ambiguity of overall MSSM coupling SM Soft breaking trilinear couplings squark & chargino masses fixed L. Littenberg – Varenna

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