# Presentation: 321612

## New measurement of the 

**New measurement of the **
******+****→********+******** branching ratio**** **

- _

**Zhe Wang (E949 collaboration)**
**Brookhaven National Laboratory**

**2008 at Cornell, U. Wisconsin and Fermi Lab**

## Slide 2

**Notes:**
predecessor

## _

**FCNC**** is permitted through ****loop**** diagrams,**
**however it is highly suppressed.**

|  | Quark contents | Mass
(MeV/c2) | Lifetime
(ns) |
| --- | --- | --- | --- |
| K+ | us | 493.7 | 12.4 |
| + | ud | 139.6 | 26.0 |
|  | - | ≈0 | ∞ |

- -

- -

**Notes:**
K+, S=+1
No flavor-changing neutral currents (FCNC) has been found by the early 70’s
FCNC is a test ground for each new model.
They must suppress FCNC.
Standard Model get its success in the late of last century.
These three diagrams are the SM prediction for this process.
They happened through W box and penguin diagrams.
As we know it is the weak interaction, this process is highly suppressed.

## Branching ratio prediction

- Short-distance interaction dominant

- Relevant hadronic operator matrix element can be extracted from +→0e+

- Effective Hamiltonian:

- X: Wilson coefficients

- M.K. Gailard and Benjamin W. Lee 1974

**Notes:**
This is the effective hamiltonian. It can discribed as a V-A interaction.
Gf is fermi weak coupling constant. alpha is electromagnetic fine structure constant. 
theta W is the weinberg angle. VcsVcd shows the interchange of charm quarks
and VtdVts shows the interchange of top quarks.
sbard is V-A charged quark current. nunu is for lepton part.
X is the wilson coefficient coming from the integration of box and penguin diagrams.
Short-distance interaction is dominant in the process.
trouble is from hadronic operator matrix element.
if you notice that pi0 consists of u ubar, due to isospin symmetry
the hadronic operator matrix element can be extracted from pi0 branching ratio.

## Rare process  BR~10-10 with small theory uncertainty (8%)

** ****(sensitive to new physics)**

**top quark contribution ~70%**
**  ****(sensitive to V****td****)**

**Precise theory prediction:**** ****(0.85±0.07)×10****-10**
**(50% of the error is from CKM parameters)**

**Rare process****  ****BR~10****-10**** ****with small theory uncertainty (8%)**

- arXiv: hep-ph/0405132 Andrzej J. Buras, et. al.

## Searching for the holy grail

**Searching for the holy grail**

- “Just look for a decay of a short-lived particle with 109 background, with a poor signature and no kinematic closure.”

- The theorist

- The experimentalist

- Marco S. Sozzi at CKM2008

## High intensity K+ beam is supplied by AGS

**Pt target**

**K****+**** beam**

**Detector**

**High intensity K****+**** beam is supplied by AGS**

**K****+**** : ********+**** ~ 3 : 1**

**Low energy separated beamline**

**6×10****12**** protons/2 sec-long spill/ 5 sec        21 GeV/c **

**3.5×10****6**** incident K****+****/spill**

**Alternating gradient synchrotron**

**Notes:**
The AGS (Alternating Gradient Synchrotron) can accelerate and extract a beam of
around 60*10to12 protons at a momentum of 24 GeV/c over a 2 second spill every 5 second. The protons are directed onto a platinum target and lots of particles are produced among them, pi+ and K+.

The particles produced near 0 degree are directed into the Low Energy Separated Beamline (LESBIII) which purifies the beam, separate the K+ from the pi+ and focusses them on the E949 target. Kaons with 710 MeV/c momentum were transported down this beamline.

The low energy separated beam line III collects and focuses kaons produced at the production target. Two electrostatic separators sweep pions and protons out of the beam. The resulting beam is further selected by a second dipole magnet.

The beam incident on the E949 target contains 3 K+ for every pi+ and was the purest kaon beam in the world. Approximately 3.5*10to6 K+ stop in the E949 target during each spill.

## _

** ********+******** trigger**
**   ****142×10****6 ****on tape**
** ****K************************ monitor**
** ****K******************** monitor**
** ****beam ************ scattering**
** ****Charge exchange (****K********n ********K****0****p,**** K****0****S ********************) **

## 

**1. K****+**** stop in detector target and decay at rest**
**2. Measure and identify ********+**** **
**3. Veto on any other activity in the detector**

- _

***K********* ****goes in**

********* ********* ****comes out**

- 

- 

- 

**No additional particles**

## K+ beam

**K****+**** beam**
**710 MeV/c**

**Notes:**
This is a CAD display of the whole detector.
It is developed based on it predecessor E787 experiment.
Very complicated.
It is composed of lots sub detector.
I will introduce the detail of them

## Beam detectors

**Beam detectors**

** ****Cerenkov counter**

** ****B4 counter**

**Top half of side view**

** ****Wire chamber**

** ****Active degrader**

**Notes:**
The first detector the Kaon sees is the Cerenkov counter. It allow us to separate kaon and pion. It operates on the principle when the particle is going faster than the speed of light in material, it will emit photons at a certain angle. Photons from kaon which is closed to the track will be reflected to Kaon tube. And photon from pion totally internal reflected to pion tube.
Then the kaon will see two wire chambers. It provides a very good spacial separation. It can also tell whether there is a pileup in this event.   
What follows is BeO and Active degrader. The basic idea is to let the Kaon slow down and stop in our target and decay at rest.
The last beam detector is B4 hodoscope which consists of two planes scintillator fibers.
It can provide position and time information, and it can help to do the particle ID.

Beryllium Oxide, with high density and low atomic number, minimizes multiple scattering.

## E949 Target

**    ****(ADC, TDC and CCD)**
** ****I counter **
** ****V counter **

**E949 Target**

**End view of target**

****

****

********

**Top half of side view**

**Notes:**
Here Kaon comes to the target. 
The plot at bottom left is the end view of the target. It is 12 cm across. It is composed by 413 5 by 5 cm scintillator fibers and a number of edge fibers. The other end of the fiber is connected to a PMT. Each PMT is read out by ADC, TDC and CCD. Each fiber is 3.1 meters long
What happened is the kaon slows down and slows down due to electromagnetic processes, and decay at rest in fiducial volumn. Then from the scintillation light read out from the other end, we know the energy and the time when a kaon come in. And from the pulse information got from ccd we can know the decay process precisely.
Two layers of plastic scintillating counters that around the target is I counter and V counter. They help to define the fiducial region and give precise time measurement. That will make sure Kaon decay at rest.
Like the plot at bottom right, it shows the time profile of beam pion and kaon decay in flight with kaon decay at rest.

## Drift chamber, range stack

- P

- E

- R

- momentum, energy and range of + of **K****+ ****→ ********+********o**

** ****Drift chamber**
** ****Range stack**
**   ****Momentum, energy and**
**   ****range measurement**

- MeV

- MeV

- cm

**Top half of end view**

**Drift chamber, range stack**

********

**Notes:**
The total mass in the active region of UTC, excluding inner and outer support tubes and innermost and outermost foils, amounts to 2E-3 radiation lengths.

Next the particle from kaon decay goes into the drift chamber, UTC. There is a magnetic field parallel to the beam direction. So you see a red pi+ curve in end view of the detector. We measure the curvature of the track with a bunch of points in drift chamber. Then we know the momentum of the pion.
Pion then enters the range stack. It consists of 19 layers of 1.9cm scintillators, azimuthally segmented into 24 sectors. It provides energy and range measurement for the pion+.
And it is also an important photon veto detector.
For the monochromatic pion peak from Kpi2 event, the momentum resolution is .......

## →→e chain

**Range stack**

** ****Range stack**
**   ****500 MHz waveform digitizer**
**    ****Pion, Muon ID**
** ****Range stack straw chamber**

- →→e chain

**Notes:**
Another important function of range stack is pion identification. Each scintillator is not only read out by ADC and TDC, but also multiplexed and read by 500MHz waveform digitizer.  Each A pion comes in, slow down. The we want to do is wait until pion decays there. Then tell the difference between pion and muons. 
Please see the plot on the right side. That’s the signal from four layer of range stack upstream end and downstream end. Read it from bottom to the top. 
A pion come in at layer 11, then muon the product of pion decay comes out, the pink histogram. We know the lifetime of muon is long. After a while the pulse of positron comes out. From this signature the pion is very well indetified.

## Photon veto detector

** ****Active Degrader**
** ****Target fibers**
** ****Endcap veto**
** ****Barrel veto**
** ****Barrel veto liner ......**

**Photon veto detector**

**E787**

**E949**

**4****π**** sr coverage**

**Notes:**
Almost every detector is photon veto detector.

## pnn2

**Signal box and background overview**

**pnn2**

**pnn1**

## pnn2

**After the trigger**

**P vs R of ********+**

**pnn2**

**pnn1**

**Notes:**
Now it is time to give you a general idea of background and signal box.
Every thing could be a background. Open PDG booklet, turn to Kaon
section, we have to carefully think about every thing there.
the plot shows range and momentum of the charged decay product.
mainly pi+ and mu+.

## Important background list

|         Cut 
Bkg | Kinematics cuts (P/R/E)  | Particle ID (K//) | Photon veto | Target pattern | Timing cuts |
| --- | --- | --- | --- | --- | --- |
| K scattering |  |  |  |  |  |
| K |  |  |  |  |  |
| Beam |  |  |  |  |  |
| muon |  |  |  |  |  |
| Ke+ |  |  |  |  |  |
| Charge exchange
Kn K0p |  |  |  |  |  |

**Important background list**

## Strategy 1: avoid bias in cut tuning

**Strategy 1: ****avoid bias in cut tuning**

**Full data set**

**1/3 data**

**2/3 data**

**...**

- 

**Beam bkg**

**Background **
**study**

**Background**
** ****estimate**

**Open the box**

**Freeze cuts**

## Strategy 2: blind analysis - bifurcation

**Step 1: Background isolation**
**Step 2: Suppress each background with two independent cuts**

## Strategy 2: blind analysis - bifurcation

**Strategy 2: ****blind analysis - bifurcation**

**Step 3: Check the correlation**

**Notes:**
There is no correlation between these cuts.
This is the critical requirement of this analysis method.
Cut1 and Cut2 can be loosened and the number of observed events
in the loosened box should still be consistent with prediction.

## Ktarget scattering background

**Typical pattern in target:**

## Transversal Scattering

**Transversal Scattering**

- PNN2

## Longitudinal scattering

**Longitudinal scattering**
**CCD pulse cut**

## Measure K++0 background

**Photon tagged**

**CCD pulse**

**Target cut**

**B**

******scat**** tagged**

**C+D**

**Photon cut**

**C**

## Beam background

** ****Single beam: particle ID, timing**

** ****Double beam: **
**    ****redundant particle ID along beam line**** **

** ****Cerenkov**
** ****Wire chamber**
** ****Target**
** ****B4**
** ****AD**

## Muon background

** ****Range momentum**
** ****dE/dx range stack **
** **→→e **chain**

**K****+********+******
**K****+********+**********

## -

**Ke4 MC event**

**K****+**

- +

- -

- e+

**A Ke4 candidate from data**

**Their energy could be very low**

- signal region

## Ke4 (K++-e+) background

** ****A Ke4-rich sample is tagged in data by selecting events with extra energy in target.**
** ****Use MC to evaluate the rejection of cuts**
** ****The ********-**** annihilation**
**energy spectrum**
**is from our **
**experimental**
**measurement**

**Notes:**
pi- energy deposit spectrum
empirical spectrum

## Charge exchange (Kn K0p) background

**Charge exchange (****K********n ********K****0****p****) background**

** ****A CEX rich sample is tagged in data by selecting events with a gap between K****+**** and ********+**
**  ****Model K****L**** momentum from K****S**** monitor sample **
** ****Use MC to evaluate the rejection**

**Character:**
** ****a gap between**** K****+**** and**** ********+**
** ****z info of ********+**** is not consistent with K****+ ****track**** **

**Notes:**
Jean Roy thesis
Klong with a kinetic energy of only 10 MeV has a velocity of 6cm/ns

## Single/double cut(s) failure study   -- look for a loophole

** ****Usually introduce a cut or a group of cuts aiming at a background**
** ****By inverting the cut(s) the background is selected**
** ****The number of events and their characteristic can be predicted**
** ****If observation is not consistent with prediction a new background is found or your cuts are not complete**

## Acceptance measurement

** ****Accidental hits and noise will bias acceptance measurement, so data (monitor sample) is used.**
**   ****example:**
**   ****Acc loss of**** ****photon veto cut on**** K****+******
******No photon in the final state of************+****→********+******
**   ****Acc of photon veto is measured with**** ****K****+******

** ****MC is only used to measure the acceptance of kinematics box cuts and detector solid angle**
** ****BR(****K****+********+********0****) is measured to validate acceptance measurement**

## Total background and sensitivity

**Total background and sensitivity**

**SES is the branching ratio for a single event observed w/o background**

**For E787+E949 pnn1 SES=0.63×10****-10**

## Outside box study

** ****Keep signal region blinded**
** ****Relax photon veto or ccd pulse cut**
** ****Check the predicted events and observed events in the extended region ****A’**

## Division of signal region – We know more about cuts

** ****Acceptance and background is not uniformly distributed in the signal region**
** ****A candidate in a cleaner region is less likely to be background**

**Momentum (MeV/c) of:**

**Signal**

**K****+********+********-****e****+******

**Lower box of p (MeV/c):**
**   ****p>140**
**Tight p box:**
**   ****p>165**

## Cell information – 9 cells

**Four cuts are tightened to define 9 cells**
** ****Kinematics box**
** ****Photon veto**
** **→→e
** ****timing (delay coincidence)**

## Surprise me!

## Three candidates are found

**Three**** candidates are found**

## _

** ****BR=****(7.89±      )×10****-10**
** ****The probability of all ****3**** events to be due to background alone is ****0.037**
** ****due to signal of SM prediction and background is ****0.056**
** ****SM prediction:**
**BR=(0.85±0.07)×10****-10**

**9.26**

**5.10**

**Notes:**
likelihood ratio method

## Combined with all E787/E949 result

** ****BR=****(1.73±      )×10****-10**
** ****The probability of all ****7**** events to be due to background alone is ****0.001**
** ****due to signal of SM prediction and background is ****0.06**
** ****SM prediction:**
**BR=(0.85±0.07)×10****-10**

**1.15**

**1.05**

## Conclusion

** ****BR(********+****→********+********) ****=****(1.73±      )×10****-10**
** ****Our measurement is twice of standard model prediction, however consistent with it within uncertainty**
** ****E787/E949 made tremendous progress on rare K decay study**
**    ****25 years ago only a limit <1.4×10****-7**
**      ****Found 3 candidates in this study **
**    ****(7 candidates totally)**

**1.15**

**1.05**

- _

**arXiv:hep-ex/0808.2459**** has been accepted by PRL for publication.**

## Your questions are welcome!

**Your questions are welcome!**

## BACKUP

## K++E787/E949

- K++****E787/E949**

- K00****E391a****

**An independent measurement for CKM unitary triangle in Kaon sector**

**BR and ******

## Cerenkov counter, B4

**Cerenkov counter, B4**

- 

**K**

## Expecting: 

** ****Next: rare K****+**** decay experiment NA62**
** ****Next: rare K****0****L**** decay experiment E391a**

## Before isospin breaking correction:

**Before isospin breaking correction:**

*X is a monotonically increasing function with*