Upper Limit Branching Ratios for Decays Involving K main ring and the Tevatron are both synchotrons...

Upper Limit Branching Ratios for Decays Involving KsUniversity of Colorado REU report

R.S. Tucker

August 9, 2006

1 Introduction

1.1 Research Experience for Undergraduates Overview

This summer I worked with Profs. John Cumalat and Kevin Stenson in high energy physics. My project wasto look at data from FOCUS (a.k.a. E831 at Fermilab) to determine if the rare decays D0 → Ksπ

+π−π+π−π+,D+ → Ksπ

+π−π+π−π+π−, D+ → KsKsKsπ+, and D+

s→ Ksπ

+ could be observed. I then compared thesedecays to other, previously seen decays to set upper limit branching ratios.

1.2 FOCUS

The FOCUS experiment (aka E831) is a charm photoproduction experiment. It is located in the Wideband Areaof Fermilab and collected data during the 1996-1997 fixed target run. Reconstruction of data began in 1998 andwas finished by the end of 1999. The analysis of this data continues to the present.

1.2.1 FOCUS Beamline

The FOCUS beamline begins as a proton beam, accelerated from rest to 800 GeV using a series of five accelerators.It begins as hydrogen gas, ionized by the addition of electrons. The H− ions are accelerated electrostatically to.750 MeV through a system of voltage dividing nodes (Cockcroft-Walton). They are then accelerated to 400 MeVusing a linear accelerator (LINAC). LINAC is a series of alternating high field and free field regions. As the ionsexit LINAC, they pass through a thick carbon foil which strips the ions of their electrons, leaving only protons.The booster, a synchotron about 500 ft. in diameter, accelerates a group of protons to 8 GeV. It takes 12 groupsof protons to fill the main ring at Fermilab. The main ring accelerates the protons to 150 GeV and injects theminto the Tevatron. The Tevatron uses liquid helium cooled superconduction dipole magnets to contain the protonbeam and accelerate it to 800 GeV. The main ring and the Tevatron are both synchotrons with diameter 1 km.

Proton extraction is a process of slowly removing the beam and sending it down fixed target beamlines. Electro-static devices and magnets in the switchyard split and direct the beam into three major areas: proton, neutrino,and meson. The beams in each of these areas are again split. The radio frequency acceleration cavities of theTevatron operate at 53 MHz, which means that the protons arrive at the experiment in regularly spaced 18 nsintervals.

To create the photon beamline, incident 800 GeV protons strike a cryogenically cooled liquid deterium target.The interactions produce many particles, but specifically they produce π0s that decay into 2 photons. A seriesof magnets and converters remove the other particles produced in the interactions. Powerful diple magnets sweepaway charged particles. The neutral particles in the beam strike a photon converter, which is a piece of lead50% of a radiation thick. In this process, the photons convert to e+e− pairs and other particles pass through.Quadropole magnets focus the electrons and positrons. These magnets bend the charged portion of the beamaround a dump that collects non-interacting neutral particles. Momentum recombining dipoles recombine the elec-trons and positrons (which have been split into two beams). The recombined beam is then focused and strikes the

1

Figure 1: FOCUS Beamline

radiator, a sheet of lead 20% of a radiation thick, where the bremsstralung process produces photons. Sweepingdipoles redirect the charged portion of the beam to a recoil positron detector and a recoil electron detector. Theneutral part of the beam continues towards the experiment target. The mean energy of the photons is around 190GeV. A lead wall and lead collimator remove background synchotron radiation.

An advantage to this process is that the interactions in the primary target caused by hadrons in the beam aregreatly reduced, as the hadron contamination of the beam is very low. A disadvantage to this process is that veryfew photons are generated relative to the number of protons in the beam.

1.2.2 FOCUS detector

The FOCUS detector is actually a system of smaller devices and detectors. These detectors provide particle track-ing and identification.

The following devices track and vertex particles in the FOCUS detector. Silicon microstrips are essentially reversebias semiconductors. Charge produced by ionizing particles is gathered at the end of each strip. A multiwire pro-portional chamber (PWC) is a mesh of wires in several planes. Each plane is alternately high voltage or grounded.The PWC is placed in a gas chamber, so that charged particles passing through ionize gas molecules. The electricfield accelerates the electrons removed from these particles toward the grounded wires. Along the way, the electronsionize more of the gas, and the cascade of charge that develops is deposited on the grounded wires. Straw tubechambers use the same concepts as PWCs. The difference between the two is that the voltage in a straw tube cham-ber is across a metal tube with a ground wire running through the center. In between these tracking devices aretwo magnets. The change in the slopes of the tracks through the magnets is used to find the momentum of a particle.

The following devices help with particle identification. Cerenkov detectors rely on the Cerenkov effect to tell thedifference between pions, kaons, and protons. The Cerenkov effect is a “shockwave” of light produced when aparticle travels faster than light travels through a specific medium. The presence or absence of this light is anindication of the particle identification. Calorimeters destructively measure the energy of particles. In electromag-

2

Outer Muon

R.P.C.'s

Beam

Direction

P.W.C.'s

Outer

Electromagnetic

Calorimeter

Cerenkov

Counters

Trigger

Hodoscope

P.W.C.

P.W.C.

Cerenkov

Counter

Magnet

Target Region

Magnet

Silicon Microstrips

Trigger CountersTargets

Inner

Electromagnetic

Calorimeter

Hadron

Calorimeter

Trigger

Hodoscope

Muon

Hodoscope

Muon FilterBeam

Calorimeter

Straw

Tubes

Target

Silicon

SpectrometerBeam

Direction

F0cusF0cusE831E831E831

Figure 2: FOCUS Detector

netic calorimeters, electrons and photons interact with the material in the calorimeter, producing other particlesthrough the bremsstralung and pair conversion processes. The electromagnetic calorimeters detect γ and π0 par-ticles. In hadron calorimeters, hadrons interact strongly with each to produce other hadrons, usually pions. Thehadron calorimeters detect K0

Lparticles and neutrons.The calorimeters are important because they detect neutral

particles which are, therefore, not detected in any of the tracking systems (which require ionization) In both typesof calorimeters, the final number of charged particles is proportional to the energy incident on the calorimeter.Muon detectors rely on the fact that muons are the only charged particles that can go through large amounts ofmaterial. Muon detectors are essentially charged particle detectors shielded with thick layers of steel. The triggersand hodoscopes use scintillation counters and logic circuits to separate interesting events from background events.

The signals recorded by all the devices in the FOCUS detector are analog. The data acquisition system (DAQ)had to transform these various analog inputs to a single digital stream, and record it on 8mm magnetic tape. TheFOCUS experiment is more thoroughly explained in [1] and [2].

1.3 Creation of Charm Particles

The charm particles are created through photon-gluon fusion. A high energy photon splits into a charm anti-charmpair. A hard gluon from a proton in the beryllium oxide target interacts with one of the quarks. Because quarksare colored, and all particles must be color neutral, they cannot exist as free quarks. They hadronize and formcolorless charm mesons or charm baryons.

The charm mesons analyzed in this report are the D0, D+, and D+s

particles. We looked for instances wheneach of these particles decayed to some combination of Ks, π, and K. These decays occur via the weak force,which is mediated by the massive bosons W± and Zo. A charm particle can only decay (change flavors) into adown or strange quark. In the decays analyzed in this report, the charm particle created (a D meson) travelsa few millimeters in the detector before it decays to some combination of kaons (strange particles) and pions(combinations of up and down quarks).

3

��

��

Target Material

Many particles created

from interaction

Decay vertex

Some

number

PhotonPhoton−gluon fusion

Interaction

(production vertex)

D particle

(charm & up, down, or strange)

charm

anti−charm

u

u

d

photon

proton

something

other than

a proton

K (kaon)s

of sπ

gluon

Figure 3: Creation of D particles and subsequent decay

*charm quarks only change flavors to down or strange quarks

anti−up

charm strange

anti−up

(carrier of weak force)

K particle

D particle0

−

W boson+

up

anti−down

π+particle

Figure 4: An example of a D0 particle decaying to a kaon and a pion

4

Ks6pi - exponential fit, no cuts

0

50

100

150

200

250

300

350

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 10748

1.989 0.9067E-01

179.1 / 95P1 37.30 22.46P2 1.865 0.000P3 0.8100E-02 0.000P4 56.58 0.9622P5 7.706 0.1070

Yield = 37±22

M=1865±0 MeV

σ=8.1±0 MeV

Significance = 1.68182

Ks6pi - exponential fit, with cuts

0

0.5

1

1.5

2

2.5

3

3.5

4

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 49

2.001 0.8872E-01

15.03 / 28P1 0.8804 1.556P2 1.865 0.000P3 0.8100E-02 0.000P4 0.2034 0.5855E-01P5 9.402 1.745

Yield = 1±2

M=1865±0 MeV

σ=8.1±0 MeV

Significance = 0.5

Figure 5: Ks6π data- single Gaussian with exponential background, before and after cuts are applied

Ks6pi Monte Carlo - Double Gaussian fit, no cuts

0

1000

2000

3000

4000

5000

6000

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 105612

1.892 0.9272E-01

831.9 / 92P1 0.4671E+05 1562.P2 1.865 0.7505E-04P3 0.7565E-02 0.8154E-04P4 592.0 23.80P5 780.9 27.69P6 -2032. 640.9P7 0.6040E-01 0.2120E-02P8 0.4612 0.1449E-01

Yield = 46708 ± 1562

M=1864.83±0.075 MeV

σ=7.565±0.082 MeV


Width of Gaussian 1 = 0.00756494


Ks6pi Monte Carlo - Double Gaussian fit, with cuts

0

500

1000

1500

2000

2500

3000

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 13137

1.873 0.5417E-01

257.6 / 92P1 0.1062E+05 165.4P2 1.865 0.9190E-04P3 0.3738E-01 0.2413E-02P4 27.00 2.417P5 28.50 5.853P6 -195.2 86.00P7 0.7091E-02 0.1024E-03P8 0.2355 0.9279E-02

Yield = 10622 ± 165

M=1865.26±0.092 MeV

σ=37.384±2.413 MeV




Figure 6: Ks6π Monte Carlo - double Gaussian with quadratic background, before and after cuts are applied

2 Applied Cuts

Each of the four channels I worked with this summer required similar techniques. In each ntuple of data, thesignal (if it exists) is obscured by tremendous amounts of background. We try to isolate the signal by reducingbackground. We do this by cutting events based on certain kinematic variables. Additionally, Monte Carlo methodsare used to simulate the data. The Monte Carlo is used as a measure of efficiency in the branching ratio. Thissection includes plots of both data and Monte Carlo for every signal and normalization channel. In each figure,the plot on the left is a mass plot with no cuts applied and the plot on the right is a mass plot with the final cutsapplied. Mass (measured in GeV) is on the x-axis and the number of events is on the y-axis.

2.1 Ksπ+π−π+π−π+π−/Ksπ

+π−π+π−

There was no easily observable signal in the Ks6π data, so the cuts were chosen by maximizing the Monte Carlosignal divided by the square root of the data background. The normalization mode for Ks6π is Ks4π. For thischannel, we required that the distance between the primary vertex and the secondary vertex, divided by the errorin that distance be greater than 8. For the pion daughters, we required that non-pion hypotheses be favored overthe pion hypothesis by no more than 5 units of log-liklihood. We required that there be more than two tracks in

5

Ks4pi data - Quadratic fit, no cuts

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 670089

1.921 0.1122

62.79 / 94P1 3468. 315.9P2 1.869 0.6893E-03P3 0.7788E-02 0.8106E-03P4 6482. 15.66P5 0.1119E+05 78.16P6 -0.1158E+05 728.9

Yield= 3468 ± 315.915

M=1868.73±0.689 MeV

σ=7.788±0.811 MeV


Ks4pi data - Quadratic fit, with cuts

0

50

100

150

200

250

300

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 10516

1.924 0.1082

96.85 / 94P1 1157. 51.36P2 1.867 0.4037E-03P3 0.8686E-02 0.4137E-03P4 83.43 1.623P5 201.5 8.932P6 242.1 87.18

Yield= 1157 ± 51.3567

M=1866.9±0.404 MeV

σ=8.686±0.414 MeV


Figure 7: Ks4π data - single Gaussian with quadratic background, before and after cuts are applied


0

2000

4000

6000

8000

10000

12000

14000

16000

18000

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 250098

1.872 0.8993E-01

1025. / 92P1 0.9067E+05 1279.P2 1.865 0.4189E-04P3 0.2823E-01 0.2997E-02P4 1721. 22.63P5 -2597. 48.21P6 -2392. 763.5P7 0.8147E-02 0.1375E-03P8 0.2478 0.1104E-01

Yield = 90675 ± 1279

M=1864.8±0.042 MeV

σ=28.233±2.997 MeV





0

1000

2000

3000

4000

5000

1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 34940

1.866 0.5015E-01

367.7 / 92P1 0.2760E+05 198.5P2 1.865 0.6079E-04P3 0.2086E-01 0.1420E-02P4 84.27 2.275P5 -118.8 10.34P6 -456.9 92.26P7 0.7828E-02 0.1403E-03P8 0.2046 0.1954E-01

Yield = 27597 ± 198

M=1864.79±0.061 MeV

σ=20.855±1.42 MeV




Figure 8: Ks4π Monte Carlo- double Gaussian with quadratic background, before and after cuts are applied

6

Ks5pi - exponential fit, no cuts

0

500

1000

1500

2000

2500

3000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 213025

1.872 0.7569E-01

173.7 / 65P1 430.1 115.8P2 1.871 0.000P3 0.7700E-02 0.000P4 1675. 5.372P5 5.085 0.3940E-01

Yield = 430±116

M=1871±0 MeV

σ=7.7±0 MeV


Ks5pi - exponential fit, with cuts

0

1

2

3

4

5

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 116

1.854 0.7738E-01

24.70 / 57P1 4.181 4.340P2 1.871 0.000P3 0.7700E-02 0.000P4 1.681 0.1732P5 2.110 1.183

Yield = 4±4

M=1871±0 MeV

σ=7.7±0 MeV

Significance = 1

Figure 9: Ks5π data- single Gaussian with exponential background, before and after cuts are applied


0

2000

4000

6000

8000

10000

12000

14000

16000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 195069

1.858 0.5689E-01

176.4 / 62P1 0.7504E+05 459.7P2 1.870 0.3999E-04P3 0.6798E-02 0.8800E-04P4 1484. 11.24P5 -85.47 70.56P6 -0.2916E+05 921.1P7 0.1771E-01 0.6285E-03P8 0.6774 0.1400E-01

Yield = 75038 ± 460

M=1869.62±0.04 MeV

σ=6.798±0.088 MeV





0

1000

2000

3000

4000

5000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 27437

1.868 0.2519E-01

223.4 / 62P1 0.2444E+05 173.0P2 1.870 0.5549E-04P3 0.6631E-02 0.9080E-04P4 55.87 2.052P5 -33.62 12.90P6 -1897. 150.3P7 0.1851E-01 0.7538E-03P8 0.7766 0.1294E-01

Yield = 24444 ± 173

M=1869.63±0.055 MeV

σ=6.631±0.091 MeV




Figure 10: Ks5π Monte Carlo - double Gaussian with quadratic background, before and after cuts are applied

the primary vertex. We required that there be only one candidate per event. The justification for this cut is thatwe choose only one candidate per event because it is highly unlikely that more than two charm particles are createdin each event. Even so, we usually only see one or two charm particles. We choose only the best candidate, basedon whether it comes from a D∗, has more than two tracks in the primary vertex, and has the highest l/sig (lengthbetween primary and secondary vertices divided by the error in that length). We eliminate any tracks consistentwith being e+e− pairs. We require that the error in the proper lifetime of the D0 particle be less than 0.08. Lastly,we require that adding tracks from the secondary vertex into the primary vertex does not significantly increase theconfidence level of the primary vertex.

2.2 Ksπ+π−π+π−π+/Ksπ

+π−π+

There was no easily observable signal in the Ks5π data, so the cuts were chosen by maximizing the Monte Carlosignal divided by the square root of the data background. The normalization mode for Ks5π is Ks3π. For thischannel, we required that the distance between the primary vertex and the secondary vertex, divided by the errorin that distance be greater than 15. For the pion daughters, we required that non-pion hypotheses be favored overthe pion hypothesis by no more than 5 units of log-liklihood, that is, the pi consistency had to be larger than-5.0. We required that there be more than two tracks in the primary vertex. We required that there be only one

7

Ks3pi data - quadratic fit, no cuts

0

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5000

7500

10000

12500

15000

17500

20000

22500

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 1546648

1.834 0.7919E-01

80.46 / 64P1 0.2643E+05 594.4P2 1.871 0.1956E-03P3 0.9298E-02 0.2174E-03P4 0.1605E+05 27.69P5 -0.1994E+05 245.1P6 -0.5003E+05 2920.

Yield= 26433 ± 594.443

M=1871.2±0.196 MeV

σ=9.298±0.217 MeV

Significance = 44.5

Ks3pi data - quadratic fit, with cuts

0

250

500

750

1000

1250

1500

1750

2000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 21625

1.852 0.6097E-01

218.3 / 64P1 0.1077E+05 120.9P2 1.871 0.1097E-03P3 0.9400E-02 0.1060E-03P4 147.9 2.730P5 -173.7 24.13P6 238.4 283.9

Yield= 10768 ± 120.927

M=1871.39±0.11 MeV

σ=9.4±0.106 MeV



Ks3pi Monte Carlo (resonant)- Double Gaussian fit, no cuts

0

5000

10000

15000

20000

25000

30000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 250860

1.855 0.5096E-01

203.3 / 62P1 0.1578E+06 516.0P2 1.869 0.2894E-04P3 0.1539E-01 0.3397E-03P4 1398. 11.12P5 -3155. 65.75P6 -0.2188E+05 983.0P7 0.7714E-02 0.9673E-04P8 0.3725 0.1871E-01

Yield = 157841 ± 516

M=1869.12±0.029 MeV

σ=15.39±0.34 MeV




Ks3pi Monte Carlo (resonant)- Double Gaussian fit, with cuts

0

2000

4000

6000

8000

10000

12000

14000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 80010

1.866 0.2543E-01


Yield = 71943 ± 291

M=1869.09±0.038 MeV

σ=16.718±0.395 MeV





8

3Kspi data - quadratic fit, no cuts

0

1000

2000

3000

4000

5000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 440812

1.869 0.7378E-01

72.38 / 64P1 -367.5 137.2P2 1.871 0.000P3 0.5000E-02 0.000P4 3880. 10.32P5 0.1286E+05 124.3P6 -0.2611E+05 1095.

Yield= -366 ± 137.172

M=1871±0 MeV

σ=5±0 MeV

Significance = -2.67153

3Kspi data - quadratic fit

0

2

4

6

8

10

12

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16

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1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 1214

1.893 0.6397E-01

40.90 / 55P1 2.183 5.864P2 1.871 0.000P3 0.5000E-02 0.000P4 6.142 0.3751P5 47.78 5.331P6 77.39 37.89

Yield= 2 ± 5.8639

M=1871±0 MeV

σ=5±0 MeV


Figure 13: 3Ksπ data- single Gaussian with quadratic background, before and after cuts are applied

3Kspi Monte Carlo - Double Gaussian fit, no cuts

0

5000

10000

15000

20000

25000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 445108

1.865 0.5921E-01

528.0 / 62P1 0.1223E+06 2419.P2 1.869 0.3190E-04P3 0.4106E-01 0.1044E-02P4 3722. 49.47P5 5080. 116.7P6 -0.8516E+05 2188.P7 0.4801E-02 0.3569E-04P8 0.5410 0.8188E-02

Yield = 122253 ± 2419

M=1869.33±0.032 MeV

σ=41.065±1.044 MeV




3Kspi Monte Carlo - Double Gaussian fit

0

2000

4000

6000

8000

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1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 39262

1.875 0.3028E-01

340.0 / 62P1 0.3106E+05 203.3P2 1.869 0.3614E-04P3 0.1519E-01 0.8245E-03P4 136.6 5.025P5 1084. 49.80P6 1657. 158.8P7 0.4466E-02 0.5417E-04P8 0.1851 0.9530E-02

Yield = 31057 ± 203

M=1869.29±0.036 MeV

σ=15.186±0.824 MeV




Figure 14: 3Ksπ Monte Carlo - double Gaussian with quadratic background, before and after cuts are applied

candidate per event. The justification for this cut is the same as above. We eliminate any tracks consistent withbeing e+e− pairs. We require that the momentum of the D0 particle be greater than 40 GeV . We require that theD0 particle decays outside the the material. Lastly, we require that adding tracks from the secondary vertex intothe primary vertex does not significantly increase the confidence level of the primary vertex.

2.3 KsKsKsπ+/Ksπ

+π−π+

There was no easily observable signal in the 3Ksπ data, so the cuts were chosen by maximizing the Monte Carlosignal divided by the square root of the data background. The normalization mode for 3Ksπ is Ks3π. For thischannel, we required that the distance between the primary vertex and the secondary vertex, divided by the errorin that distance be greater than 3. For the pion daughters, we required that non-pion hypotheses be favored overthe pion hypothesis by no more than 5 units of log-liklihood. We eliminate any tracks consistent with being e+e−

pairs. We require that the momentum of the D0 particle be greater than 40 GeV . We do not allow differentvees to share the same tracks. We require that the maximum absolute value of the normalized mass of any of thekaon daughters be less than three standard deviations of the nominal Ks mass. Lastly, we require that differencebetween the D0 mass and the combined 3Ks mass be greater than 0.15.

9

Ks3pi data - quadratic fit, no cuts

0

2500

5000

7500

10000

12500

15000

17500

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22500

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 1546648

1.834 0.7919E-01

80.46 / 64P1 0.2643E+05 594.4P2 1.871 0.1956E-03P3 0.9298E-02 0.2174E-03P4 0.1605E+05 27.69P5 -0.1994E+05 245.1P6 -0.5003E+05 2920.

Yield= 26433 ± 594.443

M=1871.2±0.196 MeV

σ=9.298±0.217 MeV

Significance = 44.5

Ks3pi data - quadratic fit, with cuts

0

2000

4000

6000

8000

10000

12000

14000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 629524

1.836 0.7861E-01

82.16 / 64P1 0.2435E+05 446.9P2 1.871 0.1613E-03P3 0.9275E-02 0.1777E-03P4 8607. 20.11P5 -9150. 179.5P6 -0.3300E+05 2120.

Yield= 24345 ± 446.863

M=1871.38±0.161 MeV

σ=9.275±0.178 MeV



Ks3pi Monte Carlo (resonant)- Double Gaussian fit, no cuts

0

5000

10000

15000

20000

25000

30000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 250860

1.855 0.5096E-01


Yield = 157841 ± 516

M=1869.12±0.029 MeV

σ=15.39±0.34 MeV




Ks3pi Monte Carlo (resonant)- Double Gaussian fit, with cuts

0

5000

10000

15000

20000

25000

30000

1.7 1.75 1.8 1.85 1.9 1.95

IDEntriesMeanRMS

100 250860

1.855 0.5096E-01


Yield = 157841 ± 516

M=1869.12±0.029 MeV

σ=15.39±0.34 MeV





10

Kspi data - quadratic fit, no cuts

0

2500

5000

7500

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15000

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1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 1445811

1.894 0.1107

97.21 / 91P1 0.2658E+05 632.0P2 1.872 0.2952E-03P3 0.1316E-01 0.3155E-03P4 0.1340E+05 24.11P5 -0.3675E+05 171.4P6 0.3978E+05 1061.P7 0.1381E-01 0.000P8 -438.7 433.3P9 1.972 0.000

Yield = -438 ± 433

M1=1872.23±0.295 MeV

M2=1972.06±0 MeV

σ=13.808±0 MeV

Significance = -1.01155



Kspi data - quadratic fit, with cuts

0

100

200

300

400

500

600

700

800

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 9276

1.875 0.6880E-01

191.6 / 91P1 4658. 78.32P2 1.872 0.2126E-03P3 0.1195E-01 0.2019E-03P4 24.99 1.082P5 -16.19 9.342P6 -131.5 51.16P7 0.1381E-01 0.000P8 129.4 24.45P9 1.972 0.000

Yield = 129 ± 24

M1=1872.32±0.213 MeV

M2=1972.06±0 MeV

σ=13.808±0 MeV




Figure 17: Ksπ data- single Gaussians with quadratic background, before and after cuts are applied

Kspi Monte Carlo - double Gaussian fit, no cuts

0

5000

10000

15000

20000

25000

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 278807

1.960 0.5007E-01


Yield = 231721 ± 582

M=1968.57±0.036 MeV

σ=12.641±0.077 MeV




Kspi Monte Carlo - double Gaussian fit

0

500

1000

1500

2000

2500

3000

3500

4000

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 30831

1.967 0.2435E-01


Yield = 29619 ± 178

M=1968.41±0.081 MeV

σ=23.86±0.994 MeV




Figure 18: Ksπ Monte Carlo- double Gaussian with quadratic background, before and after cuts are applied

2.4 Ksπ+/KsK

The Ksπ data was the only channel I worked with this summer that had an observable signal. The D+ peakis the larger peak; we were looking for the small Cabibbo supressed D+

speak. These cuts were also chosen by

maximizing the Monte Carlo signal over the square root of the data background. They were also optimized byvee type. The four types of vees we used are types 1,4,5, and 9. Types 1,4, and 5 are “magnet vees,” those thatdecay in downstream of the silicon strip detector. Type 1 vees are those in which both branches only go throughthree PWCs (stub-stub). Type 4 vees are those in which one branch goes through the first three PWCs and theother branch goes through all five (track-stub). Type 5 vees are those in which both branches go through all fivechambers (track-track). Type 9 vees are associated with the silicon strip tracks.

For all of the vee types the pi consistency of the pion and the vee daughters had to be larger than -5.0. We requiredthat the momentum asymmetry be less than .75 GeV. We required that the D0 lifetime be less than 3.5 lifetimesand the normalized mass of the Ks be less than two standard deviations from the nominal mass. We eliminateddaughters consistent with being muons.

For the magnet vees (types 1,4, and 5) we required that the error on the D0 lifetime be less than 0.08 ps. The

11

KsK data - quadratic fit, no cuts

0

2000

4000

6000

8000

10000

12000

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 811652

1.896 0.1120

149.5 / 91P1 3467. 258.3P2 1.872 0.000P3 0.8000E-02 0.000P4 7568. 13.36P5 -0.2042E+05 125.2P6 0.2358E+05 735.3P7 0.1000E-01 0.000P8 4748. 267.4P9 1.971 0.000

Yield = 4748 ± 267

M1=1872±0 MeV

M2=1971±0 MeV

σ=10±0 MeV




KsK data - quadratic fit, with cuts

0

20

40

60

80

100

120

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 2858

1.907 0.9566E-01

110.9 / 91P1 435.3 26.66P2 1.872 0.5322E-03P3 0.8143E-02 0.4874E-03P4 17.51 0.7548P5 -51.48 6.286P6 75.49 39.55P7 0.1068E-01 0.5796E-03P8 546.4 29.80P9 1.971 0.6007E-03

Yield = 546 ± 30

M1=1872.29±0.532 MeV

M2=1971.35±0.601 MeV

σ=10.684±0.58 MeV

Significance = 18.2



Figure 19: KsK data- single Gaussians with quadratic background, before and after cuts are applied

KsK Monte Carlo - double Gaussian fit, no cuts

0

5000

10000

15000

20000

25000

30000

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 234948

1.963 0.4490E-01


Yield = 201440 ± 500

M=1969.09±0.03 MeV

σ=9.909±0.059 MeV




KsK Monte Carlo - double Gaussian fit

0

500

1000

1500

2000

2500

3000

3500

1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

IDEntriesMeanRMS

100 22304

1.968 0.1984E-01


Yield = 21715 ± 151

M=1968.84±0.077 MeV

σ=22.883±1.06 MeV




Figure 20: KsK Monte Carlo- double Gaussian with quadratic background, before and after cuts are applied

12

momentum of the D0 had to be larger than 40 GeV and the momentum of the pion had to be larger than 15 GeV .We eliminated daughters consistent with being electrons. We also required that different vees cannot share tracks.We used an isolation cut on the secondary vertex of less 0.02. We required that the reduced chi-squared (χ2/DOF )for fit to the track of the daughters be less than 0.2. We also cut on the intersection of the pion and the Ksπmomentum vector. For vee type 1, we used an l/sig cut greater than 11 and an isolation cut on the secondary ver-tex less than 0.2. For vee type 4, we used an l/sig greater than 9. For vee type 5, we used an l/sig cut greater than 10.

Vee type 9 is the only non-magnet vee type, and it had a seperate set of cuts. We used an l/sig cut greater than 7.We required that other tracks put into the secondary vertex could not increase the confidence level of the secondaryvertex. We required the same for the primary vertex. We required the error on the lifetime of the D0 be less than.12 ps. Lastly, we required that the error in the z-coordinate of the vertex of the vee be less than 1.5.

3 Fitting the plots

In order to determine the number of events in each signal, we fit the data or Monte Carlo with some type of Gaus-sian function. For the high multiplicity channels (Ks6π and Ks5π) we use a Gaussian function with an exponentialbackground to fit the data. Because there is no signal, the Gaussian has a fixed mass and width. For the otherchannel in which we do not see a signal (3Ksπ), we use a Gaussian function with a quadratic background. Again,its mass and width are fixed. For all four channels described in this report, the Monte Carlo plots were fitted witha double Gaussian function with a quadratic background. The Ksπ data was fitted with a Gaussian function witha quadratic background, as well. The mass and width of the large Gaussian (the D+ peak) were not fixed, whilethe mass and width of the smaller Gaussian (the D+

speak) were held fixed. In the instances when we had to fix

either the mass or the width, the values for these variables were chosen by using the comparable Monte Carlo values.

Both the Ksπ and KsK plots look different from the others because there are two peaks in each plot. The firstpeak (that is, the peak at lower mass/the right peak) is where a D+ particle has decayed to either Ksπ or KsK.The second/higher mass peak is where a D+

sparticle has decayed to either Ksπ or KsK. The D+

sdecays are

Cabibbo supressed. One of the more interesting problems of the summer was reflection in the Ksπ data. We addedtwo functions to the fit for Ksπ to account for reflections from KsK. These reflections occur when the secondkaon in KsK data is misidentified as a pion. To create these functions we used KsK Monte Carlo that had beenmisidentified as Ksπ. The reflection from D+ → KsK is the blue function in fig. 17 and the reflection fromDs → KsK is the red function.

4 Uncertainties

The uncertainties in our branching ratios can be broken down into two main types: statistical and systematic.There are many types of systematic uncertainties. Each uncertainty described below was added in quadrature toget a total relative systematic uncertainty. This value is factored into the upper-limit calculation for channels inwhich no signal was observed or it is quoted with the branching ratio in the case the a signal is observed.

4.1 Statistical

The stastical uncertainty was a fairly simple calculation in which the uncertainty in the yield was divided by theyield for both normalization data and Monte Carlo and the signal Monte Carlo. All three statistical uncertaintieswere added in quadrature to get an overall statistical uncertainty. These stastical uncertainties were then factoredinto the total relative systematic uncertainty. The stastical uncertainty on the signal data is reported with thebranching ratio.

4.2 Systematic

We had many measures of systematic uncertainty. These include how the data was fit, whether the Monte Carloincluded resonance, how the branching ratios changed as the cuts were varied, and the inherent tracking uncertain-

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ties of the experiment.

To determine the uncertainty due to the fitting function for the Monte Carlo, both the normalization and signalMonte Carlo were fit two ways. The first was a single Gaussian function with a quadratic background; the secondwas a double Gaussian function with a quadratic background. We took the percent difference between the ratioof the yields from the signal and normalization Monte Carlo fit with a single Gaussian function and the ratio ofthe yields from the signal and normalization Mont Carlo fit with a double Gaussian function. To determine theuncertainty due to the fitting function for the normalization data, we fit it with a single Gaussian function and adouble Gaussian function (both with quadratic backgrounds). We took the percent difference in yield between thetwo as our measure of uncertainty. The fit uncertainty from the Monte Carlo was added in quadrature with the fituncertainty from the normalization data to determine an overall fit uncertainty.

Resonance occurs when a D particle (in our case) decays to intermediate particles and then those particles de-cay to the final products. Ks5π, for example, can decay as follows: D+ → Ksa

+

1 and a+

1 → ρ(1450)π+ andρ(1450) → π+π−π+π−. The uncertainty due to resonance was calculated through the use of resonant and non-resonant Monte Carlo. We fit the resonant and non-resonant Monte Carlo identically (using the same function andsame cuts) and took the percent difference in the yields as our measure of uncertainty.

Another measure of systematic uncertainty was the stability of the branching ratios as the cuts were varied. Branch-ing ratios depend on both data and Monte Carlo, which is simulation of the data. If the Monte Carlo accuratelysimulates the data, the branching ratio should remain constant, even if the cuts are changed. We use this uncer-tainty because it is impossible to perfectly model the data. For the three channels in which no signal was seen(Ks6π, Ks5π, and 3Ksπ), we recorded the corrected yield (data yield divided by Monte Carlo yield) of the nor-malization mode while varying each cut individually. We then took the standard deviation of the corrected yieldsas our uncertainty. For the channel in which we saw signal (Ksπ), we used a similar process, except that we usedthe branching ratio instead of the corrected yield.

The last systematic uncertainty was due to the tracking efficiencies inherent in the experiment. The uncertaintyon charged tracks is .2% and the uncertainty on Ks tracks is 7.1 %.

Statistical Systematic (fit) Systematic (resonance) Cut Stability Tracking Uncertainty

Ks6π/Ks4π 0.048 0.131 0.231 0.001 0.004Ks5π/Ks3π 0.014 0.082 0.074 0.001 0.0043Ksπ/Ks3π 0.020 0.051 0.040 0.001 0.137Ksπ/KsK 0.063 0.445 0.000 0.013 0.000

Total Relative Systematic Uncertainty

Ks6π/Ks4π 0.270Ks5π/Ks3π 0.1123Ksπ/Ks3π 0.153Ksπ/KsK 0.450

5 Conclusion

5.1 Branching Ratios and Upper Limits

For the channels in which no signal was seen, we cannot calculate a definitive branching ratio. Instead, we calculatean 95% confidence level upper limit on the branching ratio. To do so, we integrated the branching ratio likelihoodfunction

p(B) ∝1

√

B2

σ2

B

+ 1

σ2ε

exp

[

−(B − B)2

2(B2σ2ε

+ σ2B

)

]{

erf

[

BBσ2ε

+ σ2B√

2σεσB

√

B2σ2ε

+ σ2B

]

− erf

[

(S − 1)σ2B− Bσ2

ε(B − BS)

√2SσεσB

√

B2σ2ε

+ σ2B

]}

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from 0 to our upper limit L. That is, 0.95 =L∫

0

p(B)dB. The results are given in the table below.

Upper Limit Branching Ratio

Ks6π/Ks4π 0.0135Ks5π/Ks3π 0.00343Ksπ/Ks3π 0.0035

Because we observed a signal in Ds → Kspi, we quote a conventional branching ratio.

Branching Ratio

Ksπ/KsK 0.223±.100±.04

5.2 Final Thoughts

The results I found this summer will eventually be published, so I intend to continue working with Profs. Cumalatand Stenson after the REU program is finished. We still have some work to do on the all the channels. I wouldlike to say tank you to Profs. Cumalat and Stenson for making this summer such a positive experience, for givingme the opportunity to tour Fermilab and give a talk to the FOCUS collaboration, and for being extremely patientwith a clueless undergraduate physics student.

I would also like thank everyone involved with the REU program for offering research opportunities to undergradu-ates. I consider my time at the University of Colorado an extremely valuable. Thank you for letting me be involvedin “real” physics.

References

[1] Eric W. Vaadering, Ph.D. thesis, University of Colorado at Boulder, 2000.

[2] FOCUS Collaboration, http://www-focus.fnal.gov, August 9, 2006.

[3] J.M. Link et.al. [FOCUS Collaboration], “A Study of D0 → K0sK0

sX decay channels,” Phys. Lett. B607, 59

(2005)

[4] Kevin Stenson, “A more exact solution for incorporating multiplicative systematic uncertainties in branchingratio limits,” University of Colorado at Boulder.

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Upper Limit Branching Ratios for Decays Involving K main ring and the Tevatron are both synchotrons...

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