Particle Physics Presentation

Introduction Background Invariant Mass Distributions Decay Angles References

Relativistically Boosted Psi and B MesonDecays

Drew Silcock

University of Bristol

Wednesday 23rd October, 2013


Outline

Introduction

BackgroundPurposeROOT

Invariant Mass DistributionsTwo body ψ(3770)→ D0D0

Three body B+ → D0D0K+

Four body D0→ K+K−K−π+

Decay Anglesψ(3770)→ D0D0

B → (ψ(3770)→ D0D0)K

References


Introduction

● Aim of project is to examine the product particles of variousmeson decays, in particular B , D and ψ(3770) meson decays.

● The invariant mass distributions of the product particles areexamined in three decays:

▶ Two body ψ(3770)→ D0D0

▶ Three body B+ → D0D0K+

▶ Four body D0→ K+K−K−π+

● The decay angles of the resultant particles are then examinedin the lab frame in the following decays:

▶ ψ(3770)→ D0D0

▶ B → (ψ(3770)→ D0D0)K


Purpose

● ψ(3770) decays are interesting because in a ψ(3770) decay,the D0 and D0 are produced in a quantum correlated state.

● This quantum correlation allows better access to D0 strongphase information (the phases introduced by the strong force).D0 phase information is critical information that allows us toaccurately measure CP violation in beauty decays (B → D K ,a big part of Bristol’s LHCb programme).

● The amount of CP violation that occurs in such processes isimportant because CP violation helps to explainmatter-antimatter asymmetry (i.e. why is the universe full ofmatter and not anti-matter?).


Purpose

● But at present the amount of CP violation measured to occurdoes not account for the asymmetry that we see; there simplyis not enough CP violation to justify the amount of asymmetrywe see.

● Interestingly, ψ(3770) decays can also be used to measuresymmetry violations in the charm system, thanks to thequantum correlations in the decay.

● Analysis of the amount of CP violation in both beauty andcharm could lead to a better explanation of matter-antimatterasymmetry, or to the discovery of New Physics™.


ROOT

● The ROOT C++ libraries were used to simulate and analyse thedecay events.

● In particular the TGenPhaseSpace class was used to generateMonte Carlo (MC) phase space for n-body decays of constantcross-section as per Frederick James’ 1968 paper, Monte CarloPhase Space.

● The GetDecay() method, inheriting from TGenPhaseSpace,generates Lorentz vectors for the decay products given.

http://root.cern.ch/root/html/TGenPhaseSpace.html

http://cds.cern.ch/record/275743



Code

1 TLorentzVector parent(0.0,0.0,0.0, PARENTMASS);2 Double_t masses[2] = {DAUGHTER1MASS, DAUGHTER2MASS};3

4 TGenPhaseSpace event;5 event.SetDecay(parent, 2, masses);6

7 TLorentzVector *daughter1 = event.GetDecay(0);8 TLorentzVector *daughter2 = event.GetDecay(1);


Code

This example code demonstrates the basic method; once you startlooking at longer decay chains and relativistically boosting andanalyzing them, it gets a lot more complicated! (And uglier...)


Invariant Mass Distributions

● The invariant mass distributions of the daughter particles wascalculated by summing the TLorentzVectors of the decayproducts and applying ROOT’s TLorentzVector::M() method:

TLorentzVector particleSum = *daughter1 + *daughter2;Double_t invariantMass = particleSum.M();

● This method sums the square of each component of the fourmomentum to find the Minkowski norm of the fourmomentum, or the proper mass.

● If the right products are used, this invariant mass is the massof the parent particle.

http://root.cern.ch/root/html/TLorentzVector.html#TLorentzVector:M


Invariant Mass Distributions

The equations determining this in natural units (c = 1) are:

P =

⎛

⎜⎜⎜

⎝

P0

P1

P2

P3

⎞

⎟⎟⎟

⎠

=

⎛

⎜⎜⎜

⎝

Epxpypz

⎞

⎟⎟⎟

⎠

(1)

∥P∥2 = PµPµ = PµηµνPν = E 2− ∣p∣2 = m2 (2)

where ηµν is the Minkowski metric, here defined as:

ηµν =

⎛

⎜⎜⎜

⎝

1 0 0 00 −1 0 00 0 −1 00 0 0 −1

⎞

⎟⎟⎟

⎠

(3)


Two body ψ(3770)→ D0D0

Invariant mass distribution of the D0 and D0 matches exactly withthe mass of the parent particle:

]2

) [GeV/c0

D0

m(D

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 40

20

40

60

80

100

310×

(3770) Meson Decayψ(3770) Meson Decayψ

Entries 100000

Mean 3.77

RMS 4.948e06

(3770) Meson Decayψ


Three body B+→ D0D0K+

Three bodies, so more complicated (and prettier):

]2)2

) [(GeV/c

+K0

(D2m5

67

89

1011

12

]2)

2

) [(GeV/c

+K0D(

2m

56

78

910

1112

0

5

10

15

20

25

30

35

]2)2

) [(GeV/c

0D0

(D2m

1214

1618

2022

24

]2)

2

) [(GeV/c

+K0(D

2m

56

78

910

1112

0

10

20

30

40

50

60


Three body B+→ D0D0K+

● A three body decay has a two-dimensional phase space, so thisis best visualised as a density plot of the invariant massdistributions of combinations of two of the particles.

● They are not unique and can be inferred from one another dueto momentum conservation laws.

● If there were no intermediate resonances in the decay, thisshould decay roughly uniformly throughout the phase space,meaning given if this MC were repeated an infinite number oftimes, the distribution would be approximately flat-topped.Considering the finite number of iterations made, this isn’tbad!

● An example of an intermediate resonance in this decay that weare very interested in is B → ψ(3770)K , which is notsimulated here but which we will look at later.



● Also looked at phase space for uniform four body decays.● These produce five dimensional phase space, which is hard tovisualise. I’ve just projected these onto axes to turn them into1D projections which can easily be plotted and understood.

● (If you want to know more about visualising multi-dimensionalphase spaces, talk to Dan Saunders.)



]2 m(K K) [GeV/c1 1.05 1.1 1.15 1.2 1.25

0

50

100

150

200

250

300

350

400

K KK K

]2) [GeV/cπ m(K 0.65 0.7 0.75 0.8 0.85 0.9

0

50

100

150

200

250

300

350

400

πK πK

]2 m(K K K) [GeV/c1.5 1.55 1.6 1.65 1.7

0

50

100

150

200

250

300

350

400

K K KK K K

]2) [GeV/cπ m(K K 1.15 1.2 1.25 1.3 1.35

0

50

100

150

200

250

300

350

400

πK K πK K



● If I had simulated intermediate resonances in the decay wewould see rich strong phase information arising from theinterference between these decays.

● If you’re interested in this, the structure of such decays using“Dalitz Plot Analysis” has been done by Bristol’s particlephysics team for D0

→ KKππ deacys, and Jack Benton is nowdoing a Dalitz plot analysis of D → ππππ decays.

● The D0→ K+K−K−π+ decay strong phase information has

never been observed! For interest, I tabulated the possibleintermediate resonances:


Light Unflavored Mesons (S = C = B = 0)Particle Name Mass [MeV] Full width, Γ [MeV] JP Decay Channelf0(980) 980 ± 10 40 → 100 0+ f0(980)→ KKa0(980) 980 ± 20 50 → 100 0+ a0(980)→ KKφ(1020) 1019.45 ±

0.024.26 ± 0.04 1− φ(1020)→ K+K−

b1(1235) 1229.5 ± 3.2 142 ± 9 1+ b1(1235)→ [φ→ K+K−]π and

b1(1235)→ [K∗(892)± → Kπ]K±

a1(1260) 1230 ± 40 250 → 600 1+ a1(1260)→ [f0(1370)→ KK]π anda1(1260)→ [f2(1270)→ KK]π anda1(1260)→ K[K∗

(892)→ Kπ] + c.c.f2(1270) 1275.1 ± 1.2 185.1+2.9

−2.4 2+ f2(1270)→ KKf1(1285) 1281.8 ± 0.6 24.3 ± 1.1 1+ f1(1285)→ KKπη(1295) 1294 ± 4 55 ± 5 0− η(1295)→ a0(980)πa2(1320) 1318.3 ± 0.6 107 ± 5 2+ a2(1320)→ KKf0(1370) 1200 → 1500 200 → 500 0+ f0(1370)→ KKη(1405) 1409.8 ± 2.5 51.1 ± 3.4 0− η(1405)→ [a0(980)→ KK]π and

η(1405)→ KKπ andη(1405)→ [K∗

(892)→ Kπ]Kf1(1420) 1426.4 ± 0.9 54.9 ± 2.6 1+ f1(1420)→ KKπ and

f1(1420)→ K[K∗(892)→ Kπ] + c.c.

a0(1450) 1474 ± 19 265 ± 13 0+ a0(1450)→ KKρ(1450) 1465 ± 13 265 ± 13 0+ ρ(1450)→ K[K∗

(892)→ Kπ] + c.c.η(1475) 1476 ± 4 85 ± 9 0− η(1475)→ KKπ and

η(1475)→ [a0(980)→ KK]π andη(1475)→ K[K∗

(892)→ Kπ] + c.c.f0(1500) 1505 ± 6 109 ± 7 0+ f0(1500)→ KKf ′2(1525) 1525 ± 5 73+6

−5 2+ f ′2(1525)→ KK


Light Unflavored Mesons (S = C = B = 0)Particle Name Mass [MeV] Full width, Γ [MeV] JP Decay Channelη2(1645) 1617 ± 5 181 ± 11 2− η2(1645)→ [a2(1320)→ KK]π and

η2(1645)→ KKπ andη2(1645)→ [K∗

(892)→ Kπ]K andη2(1645)→ [a0(980)→ KK]π

π2(1670) 1672.2 ± 3.0 260 ± 9 2− π2(1670)→ [f2(1270)→ KK]π andπ2(1670)→ K[K∗

(892)→ Kπ] + c.c.φ(1680) 1680 ± 20 150 ± 50 1− φ(1680)→ KK and

φ(1680)→ K[K∗(892)→ Kπ] + c.c.

ρ3(1690) 1688.8 ± 2.1 161 ± 10 3− ρ3(1690)→ KKπ andρ3(1690)→ KK andρ3(1690)→ [a2(1320)→ KK]π

ρ(1700) 1720 ± 20(ηρ0 &π+π−)

250 ± 100(ηρ0 & π+π−)

1− ρ(1700)→ KK andρ(1700)→ K[K∗

(892)→ Kπ] + c.c.

f0(1710) 1720 ± 6 135 ± 8 0+ f0(1710)→ KKπ(1800) 1812 ± 12 208 ± 12 0− π(1800)→ [K∗

(892)→ Kπ]K−

φ3(1850) 1854 ± 7 87+28−23 3− φ3(1850)→ KK and

φ3(1850)→ K[K∗(892)→ Kπ] + c.c.

f2(1950) 1944 ± 12 472 ± 18 2+ f2(1950)→ KKf2(2010) 2011+60

−80 202 ± 60 2+ f2(2010)→ KKa4(2040) 1996+10

−9 255+28−24 4+ a4(2040)→ KK and

a4(2040)→ [f2(1270)→ KK]π

f4(2050) 2018 ± 11 237 ± 18 4+ f4(2050)→ KK andf4(2050)→ [a2(1320)→ KK]π

f2(2300) 2297 ± 28 149 ± 40 2+ f2(2300)→ KK


Strange Mesons (S = ±1,C = B = 0)Particle Name Mass [MeV] Full width, Γ [MeV] JP Decay ChannelK∗

(892) 895.5 ± 0.8 46.2 ± 1.3 1−

K∗(892)→ KπK∗

(892)± 891.66 ± 0.26 50.8 ± 0.9 1−

K∗(892)0 895.94 ± 0.22 48.7 ± 0.8 1−

K1(1270) 1272 ± 7 90 ± 20 1+ K1(1270)→ K[f0(1370)→ KK]

K1(1400) 1403 ± 7 174 ± 13 1+ K1(1400)→ K[f0(1370)→ KK]

K∗(1410) 1414 ± 15 232 ± 21 1− K∗

(1410)→ KπK∗

0 (1430) 1425 ± 50 270 ± 80 0+ K∗

0 (1430)→ KπK∗

2 (1430)± 1425.6 ± 1.5 98.5 ± 2.7 2+ K∗

2 (1430)→ KπK∗

2 (1430)0 1432.4 ± 1.3 109 ± 5 2+

K∗(1680) 1717 ± 27 322 ± 110 1− K∗

(1680)→ KπK2(1770) 1773 ± 8 186 ± 14 2− K2(1770)→ K[f2(1270→ KK] and

K2(1770)→ K[φ→ K+K−]

K∗

3 (1780) 1776 ± 7 159 ± 21 3− K∗

3 (1780)→ KπK2(1820) 1816 ± 13 276 ± 35 2− K2(1820)→ K[f2(1270)→ KK]

K∗

4 (2045) 1045 ± 9 198 ± 30 4+ K∗

4 (2045)→ Kπ


Decay Angles

● TGenPhaseSpace simulates decays in the rest frame of thedecay parent. In this frame, all decay pairs decay in oppositedirections, so the decay angle is 180°.

● I’m interested in what this angle looks like in the lab frame. Inother words, in the frame relativistically boosted by theLorentz vector of the decay parent. These are typically movingwith v ∼ c , so where in the rest frame two particles decayed180° apart, in the lab frame the angle is very small.

● The distribution of this angle allows us to distinguish theimportant decays that we are looking for from the background.


Decay Angles

Daughter 1

Daughter 2

α = 180° Daughter 1

Daughter 2

v ∼ c α ≃ 0 − 5°v = 0

Parent

Parent

Rest Frame Lab Frame


ψ(3770)→ D0D0

● Before the decay angle in the lab frame can be calculated, firstyou need the Lorentz vector of the parent ψ(3770).

● To this end, momentum component distributions wereobtained from a LHCb Monte Carlo simulation.

● These momentum component distributions were fitted tomathematical functions.

● The MC simulation of the ψ(3770)→ D0D0 decay was thenrepeated a large number of times and each time the products’4-momenta were boosted by a random vector fitting themomentum distributions from the mathematical fit to the MCsimulation.


ψ(3770)→ D0D0

[MeV/c]x

p30 20 10 0 10 20 30

310×0

1000

2000

3000

4000

5000

6000

in Lab Framex

p in Lab Framex

p

[MeV/c]y

p30 20 10 0 10 20 30

310×0

1000

2000

3000

4000

5000

6000

in Lab Framey

p in Lab Framey

p

[MeV/c]z

p0 100 200 300 400 500 600

310×0

2

4

6

8

10

310×

in Lab Framez

p in Lab Framez

p

Note that these are not perfect fits, but they are sufficientlyaccurate for our purposes.


ψ(3770)→ D0D0

● Need to confirm independence of px , py and pz in order to usethem independently for TGenPhaseSpace simulation.

● Correlation factors between components calculated andtabulated:

px py pzpx 1 0.00640212 0.0150375py 0.00640212 1 0.0167604pz 0.0150375 0.0167604 1

● Following plots visualise this independence:


ψ(3770)→ D0D0

[MeV/c]x

p

50 40 30 20 10 0 10 20 30 40

310×

[MeV

/c]

y p

30

20

10

0

10

20

30

40

50

310×

(3770) (Scatter)ψ for y

Versus px

p (3770) (Scatter)ψ for y

Versus px

p

[MeV/c]

x p105

05

10

310×

[MeV/c]

y

p

10

5

0

5

10

0

500

1000

1500

2000

2500

3000

3500

4000

(3770) [Lego]ψ for y

Versus px

p (3770) [Lego]ψ for y

Versus px

p

[MeV/c]x

p

10 5 0 5 10

310×

[M

eV

/c]

y p

10

5

0

5

10

310×

(3770) (Contour)ψ for y

Versus px

p (3770) (Contour)ψ for y

Versus px

p

[MeV/c]x

p

0 200 400 600 800 1000

310×

[M

eV

/c]

z p

30

20

10

0

10

20

30

40

50

310×

(3770) (Scatter)ψ for z

Versus px

p (3770) (Scatter)ψ for z

Versus px

p

[MeV/c]

x p0 20 40 60 80100120140160180200

310×

[MeV/c]

z

p

10

5

0

5

10

0

1000

2000

3000

4000

5000

6000

7000

(3770) (Lego)ψ for z

Versus px

p (3770) (Lego)ψ for z

Versus px

p

[MeV/c]x

p

0 20 40 60 80 100 120 140 160 180 200

310×

[M

eV

/c]

z p

10

5

0

5

10

310×

(3770) (Contour)ψ for z

Versus px

p (3770) (Contour)ψ for z

Versus px

p

[MeV/c]y

p

0 200 400 600 800 1000

310×

[M

eV

/c]

z p

50

40

30

20

10

0

10

20

30

40

310×

(3770) (Scatter)ψ for z

Versus py

p (3770) (Scatter)ψ for z

Versus py

p

[MeV/c]

y p0 20 40 60 80100120140160180200

310×

[MeV/c]

z

p

10

5

0

5

10

0

1000

2000

3000

4000

5000

6000

7000

(3770) (Lego)ψ for z

Versus py

p (3770) (Lego)ψ for z

Versus py

p

[MeV/c]y

p

0 20 40 60 80 100 120 140 160 180 200

310×

[M

eV

/c]

z p

10

5

0

5

10

310×

(3770) (Contour)ψ for z

Versus py

p (3770) (Contour)ψ for z

Versus py

p


ψ(3770)→ D0D0

Final plot of decay angle between D0 and D0 in lab frame:

]° Angle [ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

20

40

60

80

100

120

140

160

180

310×

0D and 0Boosted Angle Between D

0D and 0Boosted Angle Between D

Note that all decays are below ≃ 5°.


ψ(3770)→ D0D0

● Importance of this graph is that the decay angle is highlypeaked around ∼ 0.5°

● This makes it very useful for distinguishing this interestingdecay channel from the uninteresting background, whichshould not be peaked but more evenly angularly distributed(although it may have some angular dependence).


B → (ψ(3770)→ D0D0)K

● The same was done of the B meson, using LHCb MCmomentum data for B → D Bach decay. (The Bach is either akaon or a pion.)

● However, no B momentum data present, so used conservationof momentum to deduce B momentum components from thesum of the product D and Bach mesons, usingPB,i = PD,i + PBach,i for i ∈ {x , y , z}.

● Correlation factor matrix:

px py pzpx 1 0.0165178 -0.00486466py 0.0165178 1 0.017408pz -0.00486466 0.017408 1


B → (ψ(3770)→ D0D0)K

(MeV/c)y

p30 20 10 0 10 20 30 40

310×

x p

50

40

30

20

10

0

10

20

30

40

310×

for B (Scatter)y

Versus px

p for B (Scatter)y

Versus px

p

(MeV/c)

y p

30 2010 0

10 20 3040

310×x

p

5040

3020

100

1020

3040

0

20

40

60

80

100

for B (Lego)y

Versus px

p for B (Lego)y

Versus px

p

(MeV/c)y

p30 20 10 0 10 20 30 40

310×

x p

50

40

30

20

10

0

10

20

30

40

310×

for B (Contour)y

Versus px

p for B (Contour)y

Versus px

p

(MeV/c)z

p0 0.2 0.4 0.6 0.8 1

610×

x p

50

40

30

20

10

0

10

20

30

40

310×

for B (Scatter)z

Versus px

p for B (Scatter)z

Versus px

p

(MeV/c)

z p

00.2

0.40.6

0.81

610×x

p

5040

3020

100

1020

3040

0

20

40

60

80

100

120

140

160

180

200

for B (Lego)z

Versus px

p for B (Lego)z

Versus px

p

(MeV/c)z

p0 0.2 0.4 0.6 0.8 1

610×

x p

50

40

30

20

10

0

10

20

30

40

310×

for B (Contour)z

Versus px

p for B (Contour)z

Versus px

p

(MeV/c)z

p0 0.2 0.4 0.6 0.8 1

610×

y p

30

20

10

0

10

20

30

40

310×

for B (Scatter)z

Versus py

p for B (Scatter)z

Versus py

p

(MeV/c)

z p

00.2

0.40.6

0.81

610×y

p

3020

100

1020

3040

0

20

40

60

80

100

120

140

160

for B (Lego)z

Versus py

p for B (Lego)z

Versus py

p

(MeV/c)z

p0 0.2 0.4 0.6 0.8 1

610×

y p

30

20

10

0

10

20

30

40

310×

for B (Contour)z

Versus py

p for B (Contour)z

Versus py

p


B → (ψ(3770)→ D0D0)K

(MeV/c)x

p50 40 30 20 10 0 10 20 30 40

310×0

50

100

150

200

250

300

350

400

450

500x

B Meson px

B Meson p

(MeV/c)y

p30 20 10 0 10 20 30 40

310×0

50

100

150

200

250

300

350

400y

B Meson py

B Meson p

(MeV/c)z

p0 0.2 0.4 0.6 0.8 1

610×0

100

200

300

400

500

600

700

zB Meson p

zB Meson p


B → (ψ(3770)→ D0D0)K

Final decay angle graphs:

In rest frame of parent B :

]° Angle [ 179 179.2179.4179.6179.8 180 180.2180.4180.6180.8 1810

2

4

6

8

10

610×

(3770) and KψNonBoosted Angle Between (3770) and KψNonBoosted Angle Between

]° Angle [ 0 10 20 30 40 50

0

0.5

1

1.5

2

2.5

610×

0D and

0NonBoosted Angle Between D

0D and

0NonBoosted Angle Between D


B → (ψ(3770)→ D0D0)K

In lab frame:

]° Angle [ 0 1 2 3 4 5 6

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

610×

(3770) and KψBoosted Angle Between (3770) and KψBoosted Angle Between

]° Angle [ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.456

10×

0D and

0Boosted Angle Between D

0D and

0Boosted Angle Between D


B → (ψ(3770)→ D0D0)K

● Once again, we find that the decay angle is sharply peakedaround ≃ 1.5° for the ψ(3770) −K angle and ≃ 0.4° for theD0

−D0 angle.● This is good, because it means that the decay angle canaccurately be used to distinguish this interesting decay from allthe uninteresting background decays going on.

● This allows us to isolate more ψ(3770) decays for symmetryviolation studies.


References

● http://root.cern.ch/root/html/TGenPhaseSpace.html

● http://cds.cern.ch/record/275743

http://root.cern.ch/root/html/TGenPhaseSpace.html


Date post:	09-Aug-2015
Category:	Documents
Upload:	drew-silcock
View:	17 times
Download:	0 times

Particle Physics Presentation

Documents