RooFit toy MC sensitivity studies for + s and m s from B s →D s /K channels at LHCb Shirit...

RooFit toy MC sensitivity studies for +s and ms from Bs→Ds/K channels at LHCb

Shirit Cohen NIKHEF MSc Colloquium

May 11th 2007

11th May 2007 Shirit Cohen Master Colloquium 2

Outline Introduction The LHCb detector & physics goals CP violation & interest in Bs→D-

sπ+, Bs→DŦ

sK± decay channels RooFit sensitivity studies: concept, experimental

and physics input parameters, decay models and likelihood function description

Results from sensitivity studies Summary & conclusions


Introduction Matter dominated universe Matter-anti matter difference in weak force, CP

violating processes In the Standard Model via the quark-mixing (CKM)

matrix, via its phases LHCb experiment designed to study CP violation,

performing measurements in the b-quark sector Motivation for measuring the CKM phase


The LHCb detector

p p

~ 10-250 mrad yz~ 10-300 mrad xz

Non bending plane view


Detector detailed

Single arm forward spectrometer Limited angular acceptance but very

good time and mass resolutions Optimal luminosity 2∙1032cm-2s-1

1012 bb pairs produced per year Bending magnet 4.2Tm bending power VeLo very close to interaction point Good separation of -K

b b


Main LHCb physics goals

CKM matrix angles, ,,for example via time dependent CP

asymmetry observable

s mixing phase

Precision measurement of ms mass difference CDF measurement

Δms = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps-1

s decay rate difference Rare decays measurements Signs of New Physics

iud us ub

CKM cd cs cbi

td ts tb

V V V e

V V V V

V e V V

b→s transitions through loop diagrams, sensitive to NP

0sB

b

s b

st

t

W W

Vtb Vts

VtbVts

0sB

*

*

SM

NP


Bs meson system

0sB

b

s b

s

t tW

WVtb Vts

VtbVts

0sB

*

*

Bs0 b s

B s0 bs

flavour eigenstates

mass eigenstates

BH ,L p Bs0 q B s

0

Bs oscillations box diagram

BH ,L t e im H ,L H ,L / 2 t BH ,L 0 mass eigenstates time dependence

decay amplitude into a final state f

A f f T Bs0

,

A f f T B s0

,

if there is more than one contribution, the decay amplitudes can be written as a sum

A f Akei k e ik

k

A f Akei k e ik

k

,

strong phase keeps value, weak phase changes sign under CP transformation f

f

f A

A

q

p

f

ff A

A

p

q ,

Example: Bd →


Bs time dependent decay probability

For charge conjugate final states:

f → f, λf → λf, Af→Af, p/q → q/p

B s

0 f

t A f

2 p

q

2

1 f

2 e s t

2 cosh

st

2Df sinh

st

2 C f cosmst S f sinmst

Bs

0 ft A f

21 f

2 e s t

2 cosh

st

2Df sinh

st

2C f cosmst S f sinmst

21

Re2

f

ffD

2

1

Im2

f

ffS

2

2

1

1

f

f

fC

* In this project we assume |p/q|=1

decay oscillations

Feynman calculus is in f !

Bs →Ds-K+

Bs →Ds-K+

Bs →Ds+K-

Bs →Ds+K-


CP violation in Bs meson system In mixing, if |p/q|1, giving

In decay, if |Af||Af|, giving

can occur only if two decay amplitudes with different strong and weak phases contribute to the same final state

In interference, when

and possible, and there is a relative phase between mixing (e.g arg(q/p)=s) and decay (e.g. arg(Af/Af))

f

f

f A

A

q

p

prob Bs0 B s

0 prob B s0 Bs

0

Bs0 f B s

0 f

Bs0 f

Bs0 B s

0 f

expected to be small ~10-2 in Bs section

can occur also in charged mesons and baryons

Bs0 Ds

K

f

ff A

A

p

q ,

f A f A f


Bs→Ds decay channel

Single decay diagram→ no CP violation

Flavour specific decay Branching fraction:

(3.4±0.7)·10-3

One diagram means

f=λ f =0 (|Af|=|A f |), leading to

Df=Sf=0, Cf=1.

(two unique Bs→Ds equations)

→ Parameters to measure: Δms, ΔΓs

Bs

0Ds

t e s t coshst

2 cos mst

B s

0Ds

t e s t coshst

2 cos mst

b

s

c

s

d

u

Bs Ds

+

0-


Bss

b

b

s

Bs→DsK decay channel

Non flavour specific decay, four decay diagrams exist (four Eq.)

2 diagrams and a relative phase → Time dependent CP violation |λf|=|λ f | → Df, Cf, Sf coefficients non 0

→ Parameters: |λf|, arg(λf), arg(λ f )

to extract +s, ΔT1/T2

Bs→ D-sK+

Bs→ D+sK-

(2.0±0.6)·10-4

(2.2±0.7)·10-5

Branching fractions

+s = [arg( f ) - arg( f )] /2

ΔT1/T2 = [arg( f ) + arg( f )] /2

Ds-

b

s

u

s

s

c

Bs K++ 00b

s

c

s

s

u

BsDs

-

K+

0

b

s

u

s

s

c

Bs K-

Ds+

0

T1

T2


Bs→Dsh decay channels

The topology of the decay channels Bs→Ds-π+ and

Bs→DsŦK± is very similar

Bs→Ds-π+ can be used for Δms measurement

Bs→DsŦK± can be used to extract the CP angle +s

Standard Model prediction ≈ 60° s ≈ 0.02° can be determined by Bs→J/ channel

btag

Bs K

K

/K

Ds

Primary Vertex ~1cm ~6mm

Event topology

0

SV


Toy MC sensitivity studies Goal -

Obtain expected sensitivity for measuring ms and +s at LHCb from Bs→Ds and Bs→DsK decay channels

Approach – Define decay models Probability Distribution Functions (PDF’s) according to

decay equations & including experimental effects Generate events for all decay flavours, simulating 5 years of data taking Fit decay models back to the events. Simultaneous fit of both decay channels

in order to achieve best sensitivities and have correlations taken care of Repeat experiment many times, estimate sensitivities from collected output

Input data - Experiment-related parameters from full LHCb GEANT4 simulation Physics parameter values agreed with WG

Tools - RooFit toolkit for data modeling & ROOT data analysis framework Ganga, LHC(b) interface for running jobs on the GRID/ CERN


Experimental parameters (1/2)

Common Bs→Dsh selection, topological cuts

For Dsπ: require bachelor particle reconstructed as π

For DsK: require bachelor particle reconstructed as K and a cut on ΔLKπ in order to get rid of misidentified π’s

Signal event yields Bs reconstructed mass from Ds

-π+ and DsŦ K± channels

(after the trigger) Reconstructed Bs mass resolution 14MeV

B/S limits and central values Specific central values used for toy MC

Results for B/S ratios

Channel B/S at 90% CL

(bb combinatorial)

B/S at 90% CL

(bb specific)

Bs→Ds-π+ [0.014,0.05]

C.V 0.027±0.008

[0.08,0.4]

C.V 0.21±0.06

Bs→DsŦ K± [0,0.18]

C.V 0.0

[0.08,3]

C.V 0.7±0.3

Bs reconstructed mass from Bs→Dsπ, signal and major background

Bs reconstructed mass from Bs→DsK, signal and major background

Bs→Ds- π+ 140k ± 0.67k (stat.) ± 40k (syst.)

Bs→DsŦ K± 6.2k ± 0.03k (stat.) ± 2.4k (syst.)

Event yields for 2fb-1 (define as 1y)


Experimental parameters (2/2) Proper time per-event error

distribution Due to detector resolutions on

vertices, tracking, momenta etc. PT per-event error distribution

parameterization used in toy MC Acceptance function after triggers

and offline selection Low PT Bs’s rejected due to

misplaced vertex requirements and low significance impact parameter

Fraction of high PT Bs’s rejected due to high impact parameter

Acceptance parameterization used in toy MC

Tagging efficiency tag=0.5812, mistag fraction =0.328

Proper time per-event error distribution

Acceptance function

mean value 33fs

most probable value 30fs


RooFit sensitivity studies (1/2) Following previous work done with FORTRAN (LHCb-2003-103) Building PDF components using the RooFit package From the components we construct a decay PDF described by

PDFB→f(rec,mrec|Δrec) for the Bs→Ds and Bs→DsK decay channels (and for the different flavours)

Events are generated according to decay PDF, meaning an event is a set of “rec,mrec,Δrec”


RooFit sensitivity studies (2/2) The components that are used in PDFB→f(rec,mrec|Δrec):

Signal rec distribution – Bs decay equation, include ω smearing Signal mrec distribution – Gaussian distribution Background rec distribution – decaying particle with Bs/2 Background mrec distribution – flat distribution Resolution function: per-event proper time error (with scale factor) Acceptance function on rec

Construction Implementing the acceptance function on signal proper time distribution (and

same for background) Constructing PDFsig = PDFsig(rec,mrec| Δrec) and same for background Adding signal and background with fsig, fbg (calculated from B/S ratios)

Generate events from each decay flavour separately, fit the desired parameters from all decay flavours simultaneously

L, L

Bs0 f

, LB s

0 f

, LBs

0 f

, LB s

0 f

,


Likelihood description

0 0

0 , Pr , , , , , Pr , , , , ,s s s s

s

B D B D K

rec rec rec sig bg rec rec rec sig bgB fi i

L ob m S S ob m S S

Likelihood function

s,ms,s

f ,f ,s,ms,s with ,

0

Pr , , , , ,

1 , , ,

rec rec rec sig bg

bg sig rec sig sig rec rec sig

ob m S S

f m m t A t G t S

, ,bg bg rec bg bg rec rec bgf m m t A t G t S dt

signal proper time including mistagged events

signal reconstructed Bs mass

bg proper time

bg reconstructed Bs mass

acceptance function

resolution function: proper time per-event error, with signal scale factor

resolution function: proper time per-event error, with bg scale factor


Physics and experimental input parameters for toy MC

central values of specific background used for B/S estimation

acceptance function per-event proper time

error distribution

Parameter Input value

ΔΓs/Γs 0.1

Δms 17.5 (ps)-1

|λf| 0.37

Arg(λf) = ΔT1/T2 - (+s) -60° = -1.047 rad

Arg(λ f ) = ΔT1/T2 + (+s) 60° = 1.047 rad

ω 0.328

Event yield (1y) Dsπ

Event yield (1y) DsK

140K

6.2K

B/S ratio for Dsπ

B/S ratio for DsK

0.2

0.7

εtag 0.5812

σ(mrec) 14MeV

Physics

Experimental


Example for single decay flavor PDFBs→Ds

-π+ projections on (rec,mrec,Δrec)

Bs→Ds-K+ projections on (rec,mrec,Δrec)

Δrecmrecrec

Δrecmrecrec

(5y)


Sensitivity results from tagged events Two Dsπ equations, four DsK equations, simultaneous fit performed Collected data from many “experiments” of 5y tagged data,

scaled results to 1y Fit a Gaussian to the fitted values from all the “experiments”, make pull

distribution

Parameter Δms (ps)-1 ω Arg(λ f) rad Arg(λ f ) rad |λf| +s ° ΔT1/T2 °

input value 17.5 0.328 1.047 -1.047 0.37 60 0

fitted value 17.5 0.328 1.056 -1.042 0.37 60.29 0.5

resolution 5y 0.003 0.001 0.116 0.143 0.03 5.68 5.43

resolution 1y 0.007 0.003 0.26 0.32 0.07 12.7 12.14pull fitted mean 0.04 -0.07 0.06 0.1 0.1 -0.01 0.1

pull fitted sigma 1.02 1 1.05 1.04 1.01 1 1.03

Data from 400 “experiments”


Example for distributions for 400 exper.

+s°

values

Δms (ps)-1

values

Δms pull +s pull

# ev

ents

# ev

ents

# ev

ents

# ev

ents


Bs→DsK untagged events

Meaning events with no information if the decaying meson

was a Bs or a Bs

Decay equations for Bs→DsK untagged events:

One cannot observe the Bs oscillations using untagged events

Untagged events still hold information on the phases through Ref, Ref

Add untagged events to the analysis in order to increase the sensitivities to the phases

Bs

0 / B s0 f

t A f

2

1 f

2

e

s t

2 cosh

st

2D

f sinh

st

2

Bs

0 / B s0 f

t A f

21 f

2 e s t

2 cosh

st

2Df sinh

st

2

21

Re2

f

ffD

Df

2Ref

1 f

2


Adding untagged DsK events

Projections over proper time (ps)

ss DB ss DB

KDB ss KDB ss

KDB ss KDB ss

KDBB sss / KDBB sss /


Results from tagged+untagged events Two Dsπ equations, four DsK equations + two untagged DsK equations.

Collected data from 400 “experiments” of 5y tagged+untagged data, scaled results to 1y

Fit a Gaussian to the fitted values from all the experiments, check pulls

Parameter Δms ω Arg(λ f) rad Arg(λ f ) rad |λf| +s ° ΔT1/T2 °

input value 17.5 0.328 1.047 -1.047 0.37 60 0

fitted value 17.5 0.325 1.064 -1.044 0.37 60.37 0.48

resolution 5y 0.003 0.001 0.105 0.118 0.03 4.59 4.61

resolution 1y 0.007 0.003 0.23 0.26 0.06 10.26 10.31pull fitted mean 0.06 -0.09 0.1 0.03 0.05 0.06 0.1

pull fitted sigma 1.03 1 1.01 1.05 1.08 0.95 0.97

Δms (ps)-1

values

+s°

values# ev

ents

# ev

ents


Results with different input values Including tagged+untagged

events, similar as in last section

Running with different strong phase values (all other parameters unchanged; +s = 60° )

Running with different B/S ratios for Bs→ DsK channel (all other parameters unchanged; +s = 60°, Bs→Ds

-π+ B/S value = 0.2 )

ΔT1/T2 ° -20 0 20

σ(+s )° 11.2 10.3 10.4

Different strong phase input value

Bs→DsK

B/S value

0.0 0.7 2.0

σ(+s )° 9.6 10.3 11.1

Different B/S input value for Bs→ DsK


Extra check: fitting mistag fraction & signal scale factor simultaneously Signal scale factor used for checking PT error estimation Mistag fraction and PT errors damp the Bs oscillations Fitting both parameters simultaneously could be problematic,

correlated effects Fitting the five regular floating parameters + signal scale factor Running 400 “experiments”, fits converge Decreased resolution on ω, signal scale resolution of ~10%.

Weak, strong phase and Δms resolutions remain unchanged.

Parameter Δms (ps)-1 ω Arg(λ f) rad Arg(λ f ) rad |λf| +s ° ΔT1/T2 °

Signal scale factor

input value 17.5 0.328 1.047 -1.047 0.37 60 0 1.175

fitted value 17.5 0.328 1.05 -1.04 0.37 60.3 0.43 1.176

resolution 5y 0.003 0.003 0.1 0.11 0.03 4.7 4.65 0.04

resolution 1y 0.007 0.006 0.23 0.25 0.06 10.5 10.4 0.1pull fitted mean 0.03 -0.1 0.09 0.04 0.09 0.04 0.11

pull fitted sigma 1 1.19 0.98 1.07 1 1.01 1.28


Summary & conclusions Code for RooFit toy MC sensitivity studies developed Sensitivity results look good, pulls are fine Including untagged events improves the +s

resolution 12° → 10° Expect LHCb to measure (Δms) = 0.007(ps)-1 and (+s) = 10.3° for nominal input values

CDF measurement Δms = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps-1

Obtained resolutions with different input values for strong phase and Bs→DsK B/S ratio

LHCb-2007-041, results quoted in the “Flavour at the era of LHC” Yellow Report


Backup slides


Outlook A possible scenario before the LHCb measurement of


Outlook A possible scenario after the LHCb measurement of


Backup I likelihood description

extract from

LHCb-2007-041Total likelihood

PDF models, smearing: mistag fraction, background, detector’s acceptance & resolution

Likelihood function for B→f

Physics parameters that go in


Fitting signal scale factor and mistag fraction simultaneously - pull distributions

Backup II

+s pull

pull

Ssig pull


The LHCb detector

Non bending plane view


Interesting parameters Dsπ case: flavor specific decay, two decay diagrams exist. For this

channel: λf=λ f =0 (|Af|=|A f |), leads to Df=Sf=0, Cf=1.

→ Parameters to measure: Δms, ΔΓ

DsK case: non flavor specific decay, 4 decay diagrams exist,

time dependent CP violation. |λf|=|λ f |.

→ Parameters: |λf|, arg(λf), arg(λ f ) to extract +s, ΔT1/T2

arg(λf) = ΔT1/T2 - (+s)

arg(λ f ) = ΔT1/T2 + (+s) Assume |p/q|=1

Only 2 unique Dsπ equations

4 unique DsK equationsBs→ Ds

-π+ (3.4±0.7)·10-3

Bs→ D-sK+

Bs→ D+sK-

(2.0±0.6)·10-4

(2.2±0.7)·10-5

Estimated branching fraction % (used for DC04 selection study)


Bs meson system

0sB

b

s b

st

t

W W

Vtb Vts

VtbVts

0sB

*

*

0sB

b

s b

s

t tW

WVtb Vts

VtbVts

0sB

*

*

Bs0 b s

B s0 bs

flavour eigenstates

mass eigenstates

BH ,L p Bs0 q B s

0

Bs oscillations box diagrams

BH ,L t e im H ,L H ,L / 2 t BH ,L 0 mass eigenstates time dependence

decay amplitude into a final state f

A f f T Bs0

,

A f f T B s0

,

decay amplitudes can be written as a sum

A f Akei k e ik

k

A f Akei k e ik

k

,

strong phase keeps value, weak phase changes sign under CP transformation


Bs decay equations

f : final state, Ds-π+ or Ds

-K+

For charge conjugate final states:

B → B ,f → f, λf → λf, Af→Af ,p/q → q/p

B s

0 f

t A f

2 p

q

2

1 f

2 e s t

2 cosh

st

2D f sinh

st

2 C f cosmst S f sinmst

Bs

0 ft A f

21 f

2 e s t

2 cosh

st

2Df sinh

st

2C f cosmst S f sinmst

21

Re2

f

ffD

2

1

Im2

f

ffS

2

2

1

1

f

f

fC

Bs→Ds- π+

Bs→Ds- π+

Bs→Dsπ physics decay model

* In this project we assume |p/q|=1

38Shirit Cohen Master Colloquium11th May 2007

Matter dominated universe Matter-anti matter difference in weak force, CP

violating processes In the Standard Model via the quark-mixing (CKM)

matrix, via its phases LHCb experiment designed to study CP violation,

performing measurements in the b-quark sector Motivation for measuring the CKM phase

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RooFit toy MC sensitivity studies for + s and m s from B s →D s /K channels at LHCb Shirit...

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