kaon physics

Kaon PhysicsR. RayFermilabJuly 6 - 9, 2005New determination of |Vus|

Using very rare K decays to search for new physics

Future efforts

Summary

Physics in Collision 2005 R. Ray - Fermilab

Resolution of the CKM Unitarity ProblemUnitarity Problem1 -(|Vud|2 + |Vus|2 + |Vub|2) = 0.0043 0.0019 (PDG 2002)

2s difference from unitarityFirst Row


2002 PDG |Vux| Evaluations|Vud| = 0.9734 0.0008 from 0+ 0+ nuclear b decays, neutron decay.

|Vus| = 0.2196 0.0023 from K+, K0 decays to pen (pmn not used by PDG because of large form factor uncertainties)

|Vub| = (3.6 0.7) 10-3 from semileptonic B decays2003 K+ measurement from BNL E865 consistent with unitarity

Interesting to revisit KL measurements (PDG fit values based on averagesof many old experiments with large errors)


Determination of Vus by Measurement of Kl3 DecaysMeasurement of ratesB(K pen), B(K pmn)Measurement of form factors neededto calculate phase space integralsRadiative corrections(theory)Form factors at t=0 (theory)WANT THISGKl3 = B(Kl3)/tL(tL from PDG)Only external measurement(New measurement from KLOE now available!)


2003: BNL E865 Measurement of B(K+ p0e+n) Using 70,000 K+e3 decays normalized to K+ p+p-, K+ p0m+n, K+ p+p0p0, they found B(K+e3) to be 5% higher than PDG.

Result is consistent with CKM unitarity at 1% level.

Assumes other K+ branching ratios are correct.Data/MC comparison fore+ momentum from p0 e+e-g decay for signal and normalization modes.


New Measurements in 2004

the kaon revolution - MarcianoKTeV measured 6 largest branching fractions and KL semileptonic form factors (Ke3 and Km3) + Ke3g and Km3g

NA48 measured KL pen/charged fraction, Ke3 FF and B(KL p0p0p0), Ke3g and Km3g

KLOE measured 4 main KL branching fractions, KL lifetime, B(KS pen). Also a new measurement of B(K+ m+n) and first observation of B(KS pmn).

New K+e3 measurement from NA48

New K+e3 branching fraction and FF results from ISTRA+.


KTeV measures the following 5 ratios of partial decay rates:

These six decay modes account for 99.93% of KL decays, so ratios may be combined to determine branching fractions.

NA48 measures:

G(KL p e n) / G(2 track) and B(KL p0p0p0), Ke3 FF, B(Ke3)

KL measurements consistent with KTeV, K result consistent with E865

KLOE (e+e- K+K-, KLKS) can tag one kaon and measure branching fractions using accompanying kaon. They measure branching fractions for the 4 main KL decay modes.

KL Branching Ratio MeasurementsE.g.


Simple event reconstruction and selection may be used to distinguish different decay modes with very little background


KTeV Measured Partial Width RatiosData - MC Comparison for Radiative Photon Candidates

It is critical to model radiation properly in MCRadiation changes Ke3 acceptance by 3%. Effect on other modes is < 0.5%

Both KTeV and NA48 have published new measurementsof B(Ke3g) and B(Km3g)

ModePartial Width RatioGKm3 / GKe30.6640 0.0014 0.0022G000 / GKe30.4782 0.0014 0.0053G+-0 / GKe30.3078 0.0005 0.0017G+- / GKe3(4.856 0.017 0.023)10-3G00 / G000(4.446 0.016 0.019) 10-3


Comparison of KTeV, NA48, KLOE and PDG KL Branching FractionsValue based on PDG-style fit to all new measurements (KTeV, KLOE, NA48)


KLOE KL Lifetime MeasurementsIndirect method - From BR measurements

Detector acceptance depends on tL. SB(KL major decays)[tL] + 0.0036 1 tL

tL = (50.72 0.14 0.33) ns

Direct Method using KL p0p0p0 - Fit proper time distribution.

tL = (50.87 0.16 0.26) nsCombining both KLOE results:

tL = (50.81 0.23) ns Old PDG Average: tL = (50.98 0.4) ns

New measurement of t soon! Sum of rare decays


Semileptonic Form Factor Measurements

(to determine IK integrals).

Phase space, no form factorPhase space with form factorIK depends on the two independent semileptonic FFs.t/mp2t/mp2Ke3 Km3

y y

- y


KL Form Factor ResultsLinear ModelKm3 Form Factor


Charged Kaon DecaysNew measurement of semileptonic form factors from ISTRA+

New measurements of B(K p0en):

BUT, decay modes used as normalization for K p0en have not been re-measured. (KLOE, NA48)

Also, new measurement of K+ lifetime is needed (KLOE)


Input to Recent |Vus| Calculation

B(KLe3): KTeV, KLOE, NA48B(KLm3): KTeV, KLOEB(KSe3): KLOEB(K+e3): E865, NA48, ISTRA+tL: KLOE + PDG averagetS: KTeV, NA48 averaget+: PDGShort-distance radiative correction = 1.023 (Sirlin)

Long-distance radiative corrections: (Andre, Cirigliano et al.) de = 0.0104 0.002 dm = 0.019 0.003 de+ = 0.0006 0.002

f+(0) = 0.961 0.008 (Leutwyler - Roos)


Comparison with Unitarity|Vus| = 0.2261 0.00211 -(|Vud|2 + |Vus|2 + |Vub|2) = 0.0004 0.0011 Unitarity restored!Average of all recent resultsaccounting for correlations|Vus|f+(0) = 0.2173 0.0008 Uses updated |Vud| = 0.9739 0.0003(Hardy, Towner; Marciano, Sirlin - KAON 2005)Using f+(0) = 0.961 0.008 (Leutwyler - Roos):


Consistency of BR and FF results withLepton Universality Compare for Ke3 and Km3 1.0058(10)from T. Andre0.6622(18)from KTeVSame test with PDG values gives 1.0270 0.0182


Very Rare Kaon Decays


The theoretically cleanest processes in meson decays

Suppressed to the 1-loop level by GIM, no tree level pollution.

No competing long-distance contributions.

No significant QCD corrections

Hadronic m.e. from K pen


B(K+ p+nn)[SM] = C+ |Vcb|4 [(r - rc)2 + (sh)2] = (8.0 1.0) x 10-11

__~ 5% error due to charmError on measured parametersTheoretical error ~ 1%!Controls amountof CPV in SM__

_

K+ p+nnKL p0nnCP ConservingCP ViolatingCKMVtdIm(VtsVtd) ~ hContributionstop and charmonly topBR scale dep. 20% (LO) 5% (NLO)10% (LO)1% (NLO)BR (SM)(8.0 1.0)x10-11(3.0 0.6)x10-11BR (Exp.)(1.47 )x10-10 (BNL 787)< 5.9x10-7 (KTeV)


Testing the Standard ModelIn K pnn the phase b arises from Z0 diagrams (DS=1) while in A(J/y KS) it originates in the Bd - Bd box diagram (DB=2)

Any non-minimal contribution to Z0 diagrams could lead to a violation of:

Any deviation from this relation is a definitive sign of new physics

This is one of the cleanest tests of the SM

Complementary to searches at the energy frontier

When new physics appears at the TeVatron/LHC, rare decays will help to understand the details

__


Some Predictions from Beyond the Standard ModelComplied by S. Kettell__

B(K+ pnn) x 10-11B(KL p0nn) x 10-11SM8.0 1.03.0 0.6Minimal Flavor Violationhep-ph/031020819.19.9Enhanced EW PenguinsNP B697 1337.5 2.131 10Extra down type singlet quark modelhep-ph/04081421510MSSMhep-ph/04081424050


E391a at KEKExperimental method

(1) Measure g hit position and energy(2) Reconstruct Z decay vertex assuming M(2g) = M(p0)(3) Require missing Pt and decay vertex in fiducial volume


Pencil Beam

~ 4 cm x 4 cm at CsI

improves transverse momentum resolution

Hermetic photon veto

reject background from KL 2p0 where two photons are missing

Vacuum

10-5 pa in decay region

minimize background from neutron interactions

detectors in low vacuum region (~0.1 Pa) separated from high vacuum region by thin membrane

In Run I, part of vacuum membrane drooped into beam resulting in neutron backgrounds. Fixed for Run II.

E391a (cont.)


KEK E391a (cont.)


Kaon Decay Background

KL 2p0 background estimated using Monte Carlo simulation

4g invariant mass for both KL 2p0 and 3p0 accurately reproduced

The expected number of events is 0.02 in the signal region and 0.05 in the side band regionKL 2p0 E391a (cont)


Summary of E391a Background Estimation


Preliminary E391a Result from 10% of Run I Data SampleMulti p0 backgroundfrom neutron interactionsp0 Pt vs. Reconstructed Z VertexSingle p0 backgroundfrom neutron interactionsZ(cm)Signal BoxNo events in the signal box

S.E.S. = 1.17 x 10-7

BR < 2.86 x 10-7 (90% C.L.)

Based on 1.14 x 109 KL decays

~ 2X better than previous KTeV limit

Run II data in hand

With anticipated Run III data the Grossman-Nir limit may be within reachSevere cuts required to reduce background from membrane. Resulting acceptance 10x lower than design.

Runs II and III will have higher acceptance and lower background.


E787 (1995-98) observed two candidates with a background of 0.15 0.05 events

B(K+ p+nn) = (1.57 ) x 10-10+1.75- 0.82_E787/949 (cont.)Results from region 1E949 is a modest upgrade to E787 to accommodate higher rates

SES goal of < 10-11 5-10 SM events

Only 20% of running time realized

E949 observed one additional event

SignalBackgroundE78720.14 0.05E94910.30 0.03


KL p0e+e- and KL p0m+m-


KTeV: KL p0e+e-BR(KL p0e+e-) 3.50 x 10-10 (90% C.L.) (1999) [PRL 93, 021805 (2004)]BR(KL p0e+e-) 2.8 x 10-10 (90% C.L.) (1997+1999)Blind analysis Box

130 < mgg < 140 MeV/c2485 < meegg < 510 MeV/c2Signal ellipse 2s1 event in signal ellipse

0.99 0.35 expected background events 1999 DataM(eegg)M(gg)


KTeV: KL p0m+m-2 events in signal region

0.87 0.15 expected background events1997 DataNew result on 1999 data expected soon


Sensitivity of KL p0ee(mm) to New Physics


Importance of KS p0e+e- aS is one of two form factorsIndirect CP violating contributionB(KL p0e+e-)IND = B(KS p0e+e-)/ 330Interference termsensitive to Im(lt) = Im(VtdVts*)

Direct CP violating termExtraction of aS from B(KS) along with a measurement of B(KL)allows for extraction of Im(lt) ~ h


NA48: First Observation of KS p0e+e- 0 events found in control region

7 events found in signal region

Probability of background only ~ 10-10


NA48: First Observation of KS p0m+m-0 events found in control region

6 events found in signal regionResults for aS are consistent for p0e+e- and p0m+m-


Future Efforts


Summary


Extra Slides


Summary of KL Lifetime Measurements


Determination of |h+-| Using B(KL p+p-)KTeV: |h+-| = (2.239 0.005 KTeV 0.008EXT) x 10-3

(using new average tL)


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