rare kaon decays - 2

July 2005 L. Littenberg – Varenna 1

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++• KL0• K• KLl+l-

• KL0l+l-


Cabibbo-Kobayashi-Maskawa (CKM) MatrixUnitary matrix connecting weak with mass eigenstates

Parameterization of Wolfenstein and Maiani:

= sin(Cabibbo) = 0.227 from Ke3, K2, decay

A 0.81 from semi-leptonic B decay, etc

0.18 From Vub/Vcb, B – B mixing,

0.33 CP-asymm in BJ/KS, K, etc.

_


Unitarity Relation

(1-2/2)

(1-2/2)

(1-2/2)


Wolfenstein parameterization to higher orderW-M parameterization only approximate, at (4) & beyond, not uniqueBuras 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

_

_ _

_

_

_


One-loop K DecaysShort distance contributions to K decays. These decays include KL0, K++, KL+-, KL0e+e-, KL0+-, 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 sinC, 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.


Rare K Decays & the Unitarity Triangle

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.




K++_

contains QCD corr. has been calc’d to NNLLA

Vts*Vtd

X 1.57(mt/170)1.15

= 4.210-11A4X2(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 ⅔0

e+⅓0 and radius = [1010 B(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


Uses of CKM Unitarity

-1/2

Hard-to-calculate parts subtract away


K Hadronic Matrix Element


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%

K+

+

l+



QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.


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


Precision of SM prediction

B(K++) = (8.00.9CKM0.6mt0.15µC

0.4mC) 10-11

Vcb

Reduced by factor2-3 by 3-loop NNLOcalculation


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+nK0p; KL + ℓ-, lepton missed

_


E787/949 Detector


• 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)

• + stops & decays in RS – detect ++e+ chain

• Photons vetoed hermetically in BV-BVL, RS, EC, CO, USPV, DSPV

E787/949 Technique


• 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 background functions• Likelihood Analysis

E787/949 Analysis StrategySignal region “the BOX”

Background sources

Analysis Strategy

Identify a priori. at least 2 independent cuts to target each background: K+

PNN1: p > p(K++0) = 205MeV/c

• K++0

• muon background (K++(),…)• Beam background• etc.


Calculation of backgrounds

Tag with

Tag kinematicsoutside box – in K2 peak

kinematics

Pho

ton

veto


Background CharacterizationBackground can be characterized using specially constructed functions

For muon backgrounds

R

measrm

RR

χ exp−

=

Neural net function for &

• K2(tail): K2 but range is small due to interactions in RS.• K2(band): multibody K++ decay (K+ +, etc.)

Changing cut position

Acceptance & background level at each point of parameter

Functions

⇓

⇓

Momentum (P) for and

+ + e+ in the + stopping counter


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) Westinghouse) Lower proton energy (by 10%, cost 10% in flux)) Problematic separators, worse K/π ratio (4 3)3), fewer K/proton (factor ~1.5) Total cost, factor 2

E787 E787 E949 E949


E787/949 Events

B(K++) = (1.47+1.30

-0.89)10-10

_


Combined E787/949 ResultCombined E787/949 Result

1.30 10

0.89( ) (1.47 ) 10BR K + + + −

−→ = ×

BR K( ) ( . )..+ +

−+ −→ = × 157 1 821 75 1

(68% CL interval)

E787 result:


K++ contour on the unitarity plane

Green arcs indicate this K++ result(including theoretical uncertainties)

• Contour in - plane courtesy of G. Isidori

Central value

90% interval

68% intervalCentral value off the “SM” Need more data!!


E787

• 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 K2 w/nasty correlation

• Improved photon vetoing in

E949 very encouraging.• Answer expected in a few

months.

pnn2 E949


Status & prospects for E949Status & prospects for E949

• E949 detector worked well

• Obtained ~2/3 sensitivity of E787 in 12 weeks (1/3 pnn1+1/3 pnn2)

• Found one new pnn1 candidate

• pnn2 analysis 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


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


Pros & cons of stopped-K technique

• 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 10s)– Need low veto thresholds– Limited K flux

• Most K’s interact (typ 4/5)

– Correlation of detector geometry w/CM system


P326 (NA48/3) K++ Proposal submitted to CERN for ~100 events


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


Kinematics

+ momentum cut requires a huge momentum mismeasurement to mistake a beam + for a final state particle (7535 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++ peak0.3% resolution on pK and1% resolution on p allows ~10% acceptance


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


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


Why is KL0 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 have l = 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 & sd

• Note ~ 1, = e2i

• Ratio between decay rates is• Then

_

_


KL0 & CP-violation – 2

• Use– to replace unmeasurable – yields

• where ris 0.954 is isospin breaking (mass diff., etc.)

• In SM, = (e.g. from BJ/KS)

– this comparison one of many clean tests of CP

– In this case parameters like CKM A and mt divide out

_


KL0 in the Standard Model_

Suppressed to the 1-loop level by GIM.

No competing long-distance contributions

KL0 is t-quark dominated in the loops

Direct CP-violating to ~1%

No significant QCD correction

Hadronic m.e. from Ke3

BR = (1.5580.025)10-3 (11.3m/mt) (Im t)2

< 2% intrinsic uncertainty due to

theoretical uncertainty that on mt

_


A Model-independent limit on B(KL0)• B(KL0) < 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(KL0) < 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

_

_ _

_

_


BSM

Beyond the SM, K’s don’t have to agree with B’s!


KL0 Beyond the SM• Unique because

– retains its clean connection to short distance parameters BSM

• NOT the case for e.g. BJ/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

_


are needed to see this picture.(pB/B)


Comparison of reach in MFV models


K in the MSSM

SMSoft breaking trilinear couplings

squark & chargino masses fixed

Sign ambiguity of

overall MSSM

coupling

From E949

_

rare kaon decays - 2

Documents