# Presentation: 793432

## The Physics of KL0

- Laurence Littenberg
- BNL
- 20 June 2005

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## Cabibbo-Kobayashi-Maskawa (CKM) Matrix

- Unitary matrix connecting weak with mass eigenstates

- Parameterization of Wolfenstein and Maiani:

|  = sin(Cabibbo) = 0.227 | from Ke3 decay |
| --- | --- |
| A  0.83 | from semi-leptonic B decay, etc |
|   0.19 | From Vub/Vcb, B – B mixing, |
|   0.35 | K, etc. |

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## Unitarity Relation

## 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 = 1⁄2*J**cp*
- Where  *J**cp *= -Im(Vts*****VtdVus*****Vud) = ****(1-****2)1⁄2Im ****t** **
- Thus, a measurement of Im ****t would determine the area of all 6 U.T.’s

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## One-loop K Decays

## K++

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## Uses of CKM Unitarity

## K Hadronic Matrix Element

## K++ & the U.T.

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## E949

## E787/949 Events

- B(K+******+******) =
-  (1.47+1.30-0.89)10-10

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## Why is KL0 CP-violating?

- To lowest electroweak order in the SM
- 0 is CP-even (can be thought of as 0Z*)
-  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
- Ratio between decay rates is
- Then

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## 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 mt drop out

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## K in the Standard Model

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- Suppressed to the 1-loop level by GIM.
- No competing long-distance contributions
**K****L********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% intrinsic            uncertainty due to
- theoretical uncertainty        that on mt

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## 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 = 1⁄2  Rule
- trivial in the SM (imaginary part < 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

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## KL0 & the U.T.

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## BSM

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

## 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 seen but not interpreted.
-  probes the flavor structure of any new physics
- A 10% deviation in B-physics translates into an (1) deviation in this decay.
- 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!

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- See hep-ph/0505171

## The Flavor Problem (G. Isidori)

- Precise data from loop-induced F=2 processes (K & B mixing) impose stringent bounds on possible new degrees of freedom BSM
- Two possible solutions –
-  pessimistic (unnatural) new physics > 100 TeV (the nightmare of LHC), KL0 still probes scales >1000 TeV
- new physics~ 1TeV, much more to learn from rare K decays!  Can access underlying flavor symmetry in a model independent way.

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## Comparison of reach in MFV models

## K in the MSSM

- SM

- Soft breaking trilinear couplings
- squark & chargino masses fixed

- Sign ambiguity of
- overall MSSM
- coupling

- From E949

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## Optimized S/B vs. Signal for KOPIO(assuming SM B(KL0 ))

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## Discovering New Physics - Early

## Constraining New Physics - Early

## Discovering/Constraining New Physics

## Summary & Outlook

- Excellent discovery potential for non-SM physics
- Unique connection with underlying parameters
- Extremely rapid progress in first part of KOPIO run
- 5 discovery if  BR 0.6< BRSM or >1.7 BRSM
- If find Br ~ BrSM
- Likelihood analysis using ~150 evts
- Precision on BR: 14%;   Im t: 7%
- Rule out non-SM effects outside (1  0.24)  BRSM
- Unique constraint on some BSM operators

## Extras

## KL0 in the Standard Model 

- KL0 in the Standard Model

- Pure direct CP-violating (state-mixing very small)
- Calculation in in terms of fundamental parameters good to 2%
- In terms of usual unitarity triangle parameters B(KL0) = 410-10 A4 ****2
- Gives height of U.T. without triangulation
- With **K****+********+****** can determine ****** **as well
- Also note that B(K**L********0******) = 1.56 10-4[Im(Vts*Vtd)]2  1.56 10-4[ Im****t]2
- Im****t present triangulated to ~10%
- a dedicated experiment could directly measure it to this precision
- There are only a few solid measurements on the Unitarity Plane
**None is better!**

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