1/4/2008 lhcb tuesday meeting 1 global fits to γ and the impact of cleo-c jim libby and guy...

1/4/20081/4/2008 LHCb Tuesday MeetingLHCb Tuesday Meeting 11

Global fits to Global fits to γγ and and the impact of CLEO-cthe impact of CLEO-c

Jim Libby and Guy WilkinsonJim Libby and Guy Wilkinson

(University of Oxford)(University of Oxford)


OutlineOutline

Motivation for the global fitMotivation for the global fit The LHCb inputs to the fitThe LHCb inputs to the fit Strategy and validation of the fitStrategy and validation of the fit Adding additional information beyond the original Adding additional information beyond the original

individual mode DC04 studiesindividual mode DC04 studies– New constraint on New constraint on δδDD

KKππ from CLEO-cfrom CLEO-c An aside on CP conventionsAn aside on CP conventions

– Non-resonantNon-resonant BB00→DK→DKππ – The CLEO-c measurements of the coherence factor and The CLEO-c measurements of the coherence factor and

average strong phase ofaverage strong phase of D→K3D→K3ππ Global fit results for several different scenariosGlobal fit results for several different scenarios

– Precision on Precision on γγ at tree level including time-dependent at tree level including time-dependent measurementsmeasurements

OutlookOutlook


MotivationMotivation

We are now using several different D final We are now using several different D final states to measure states to measure γγ withwith BB++→DK→DK+ + andand BB00→DK→DK*0*0::

– D→KD→Kππ and D→hh and D→hh – D→K3D→K3ππ– D→KD→K00ππππ

γγ is not the only common parameter:is not the only common parameter:– there is rthere is rB B (ratio of colour/CKM favoured amplitude (ratio of colour/CKM favoured amplitude

to the suppressed amplitude) and to the suppressed amplitude) and – δδB B (strong phase between these amplitudes)(strong phase between these amplitudes)


Motivation cont.Motivation cont.

It has been seen that the greater the number of constraints It has been seen that the greater the number of constraints on the ADS fit, in particular ron the ADS fit, in particular rBB, the more stable the results, the more stable the results– Will give us ultimate precision expected on Will give us ultimate precision expected on γγ

Therefore, combining all modes in a global fit to data will Therefore, combining all modes in a global fit to data will provide thisprovide this– Also include the coherence factor constraints from CLEO-cAlso include the coherence factor constraints from CLEO-c– The values and estimates of uncertainties on cThe values and estimates of uncertainties on ci i and sand si i not yet not yet

available so will use Bondar and Poluektov estimates available so will use Bondar and Poluektov estimates

Why not just combine the results via the correlation Why not just combine the results via the correlation matrices?matrices?– Some non-Gaussian behaviour has been observedSome non-Gaussian behaviour has been observed– Somewhat easier (for me) to implement a global fit in the first Somewhat easier (for me) to implement a global fit in the first

instanceinstance


Input from the Input from the selection studies – 2 selection studies – 2 fbfb−−1 1

ModeMode SignalSignal BkgBkg NoteNote AuthorsAuthors

BB++→D(K→D(K++ππ−−)K)K++ 28k28k 17.5k17.5k

2006-0662006-066 M. PatelM. PatelBB++→D(K→D(K−−ππ++)K)K++ 0-5000-500 780780

BB++→D(h→D(h++hh−−)K)K++ 4k4k 7.2k7.2k

BB00→D(K→D(K++ππ−−)K)K*0*0 1.7k1.7k 850850

2007-0502007-050 K. Akiba & K. Akiba & M.GandelmanM.Gandelman

BB00→D(K→D(K−−ππ++)K)K*0*0 300300 850850

BB00→D(h→D(h++hh−−)K)K*0*0 500500 500500

BB++→D(K→D(K++33ππ)K)K++ 30.5k30.5k 46k46k 2007-0042007-004 A. PowellA. Powell

BB++→D(K→D(K−−33ππ)K)K++ 0-6000-600 1.2k1.2k

BB++→D(K→D(K00ππ++ππ−−)K)K++ 5k5k 1.2k-1.2k-4.7k4.7k

2007-0412007-041 V. Gibson, C. V. Gibson, C. Lazzeroni & JL Lazzeroni & JL


Global fit strategyGlobal fit strategy

Toy experiments with combined Toy experiments with combined individual individual χχ2 2 from the different from the different ADS/GLW rates and Dalitz binsADS/GLW rates and Dalitz bins– Use relative efficiencies and branching Use relative efficiencies and branching

fractions to relate normalisation factorsfractions to relate normalisation factors Include constraints fromInclude constraints from CLEO-cCLEO-c Can include or remove Can include or remove

measurements to see their global measurements to see their global impactimpact


2-body charged fit 2-body charged fit validationvalidation Code an extension of the model-independent Dalitz fitCode an extension of the model-independent Dalitz fit

First reproduce Mitesh’s sensitivity studies as presented in First reproduce Mitesh’s sensitivity studies as presented in his recent LHCb note to validate ADS/GLW methodhis recent LHCb note to validate ADS/GLW method– rrBB=0.077, =0.077, γγ=60° and =60° and BB=130°=130°– Constraint ofConstraint of σσ(cos(cosDD) = 0.2) = 0.2– 1000 experiments with 2 fb1000 experiments with 2 fb−1−1

– Uncertainty on error ~0.3 to 0.4Uncertainty on error ~0.3 to 0.4°°

D D ( (°)°) -25-25 -16.6-16.6 -8.3-8.3 00 8.38.3 16.616.6 2525

((°) °)

globalglobal 9.69.6 9.69.6 9.49.4 8.78.7 8.48.4 9.39.3 9.29.2

((°)°)

MiteshMitesh 9.69.6 8.88.8 8.58.5 8.28.2 9.19.1 9.29.2 9.29.2


KKππ and hh and hh toy experimentstoy experiments

MiteshNote

δKπ=16.6

rB δB()

δKπ() γ()


2-body neutral fit 2-body neutral fit validationvalidation Also reproduced Kazu and Miriam’s sensitivity Also reproduced Kazu and Miriam’s sensitivity

studies as presented in LHCb-2007-050studies as presented in LHCb-2007-050– rrBB=0.4, =0.4, γγ=60° and =60° and DD=3°=3°– Constraint ofConstraint of σσ(cos(cosDD) = 0.1) = 0.1– 1000 experiments with 2 fb1000 experiments with 2 fb−1−1

– Uncertainty on error ~0.3 to 0.4Uncertainty on error ~0.3 to 0.4°°B B ( (°)°) 00 1010 2020 3030 6060 9090 120120 180180

((°) °)

globalglobal 8.28.2 8.28.2 9.09.0 10.210.2

11.3 11.3 (RMS(RMS

))

13.213.2(RMS(RMS

)) 9.49.4 5.85.8

((°)°)

2007-2007-050050 8.78.7 8.88.8 8.98.9 9.99.9 -- -- -- 6.46.4

Some points have non-Gaussian behaviour


New things to be New things to be addedadded CLEO-c measure CLEO-c measure DD

KKππ with double-with double-tagged events in a manner similar to tagged events in a manner similar to the coherence analysisthe coherence analysis– Also constrain D-mixingAlso constrain D-mixing

The recent measurement The recent measurement arXiv:0802.2264 [hep-ex]:arXiv:0802.2264 [hep-ex]:–

However, the analysis uses a different However, the analysis uses a different CP convention to the ADS framework:CP convention to the ADS framework:

)22( 1416

K

D

0000 n rather tha DDCPDDCP


CP formalismCP formalism Why does this matter?Why does this matter?

– The parameters rThe parameters rDDKKππ andand DD

KKππ

are defined asare defined as::

– However, we use the ratios of DHowever, we use the ratios of D0 0 and Dand D0 0 to the to the same final state in the CLEO-c coherence and LHCb same final state in the CLEO-c coherence and LHCb ADS analyses which are different in the two CP ADS analyses which are different in the two CP formalismsformalisms

KD

KD ir

DK

DK

exp0

0

)(exp exp

)K c-CLEO and ADS ( exp

0

0

ADS

0

0

0

0

KcCLEO

KD

KD

KD

KD

KD

KD

irDK

DKir

DK

DK

irDCPK

DK


Nature is cruelNature is cruel

Therefore we need to subtract 180Therefore we need to subtract 180° ° from the measured value of from the measured value of D D before before inputting it to the ADS analysisinputting it to the ADS analysis

D D ( (°)°) -25-25 -16.6-16.6 -8.3-8.3 00 8.38.3 16.616.6 2525

((°)°) 9.49.4 9.59.5 9.59.5 8.78.7 8.78.7 9.19.1 9.49.4

D D ( (°)°) -190-190 -174-174 -158-158 -144-144 -130-130

((°)°) 12.712.7 10.810.8 13.813.8 12.612.6 10.810.8

A few degrees worse

Smaller asymmetry between suppressed B+ and B− modes

Old

New


B→DKB→DK**

Coherence effects Coherence effects exist in modes with a exist in modes with a K* from contributions K* from contributions from non-resonant Kfrom non-resonant Kππ

Example from Pruvot Example from Pruvot et al.et al. (hep-ph/0703292) (hep-ph/0703292)

Considers B Dalitz plot Considers B Dalitz plot and model in K* and model in K* regionregion– For rFor rSS=0.4, k=1 in the =0.4, k=1 in the

absence of pollution absence of pollution find rfind rSS from 0.3 to 0.45 from 0.3 to 0.45 and k=0.95±0.03and k=0.95±0.03

Systematic effect Systematic effect

p refers to position in DKπ phase space


CLEO-c 4-body CLEO-c 4-body constraintsconstraints

(RK3)2 = -0.20 ± 0.23 ± 0.09

<RK3cos(K3)> = -0.60 ± 0.19 ± 0.24

RK3cos( K– )

= 0.00 ± 0.16 ± 0.07K

°4 points in RK3π-K3π space considered

• RK3π= 0.2 and K3π= 144°• RK3π= 0.4 and K3π= 130°• RK3π= 0.2 and K3π= 250°• RK3π= 0.0 and K3π= 180° (phase doesn’t matter)

1 2

3

4

Applied as four individual constraintsgiven non-Gaussian behaviour of combination


Charged ADS two and Charged ADS two and four bodyfour body Baseline assumptionsBaseline assumptions

– Input values of rInput values of rBB=0.1, =0.1, γγ=60=60°° and and BB=130°=130°

– rrDD=0.616 (PDG 2007)=0.616 (PDG 2007)

– Four-body coherence factor central valuesFour-body coherence factor central valuesD D ( (°)°) -190-190 -174-174 -158-158 -144-144 -130-130

((°) 2-body no °) 2-body no

CLEOCLEO 12.9*12.9* 12.0*12.0* 10.010.0 10.010.0 10.010.0

((°) + CLEO°) + CLEO 10.3*10.3* 9.4*9.4* 10.010.0 10.010.0 9.39.3

((°) + 4-body but °) + 4-body but

no CLEO K3no CLEO K3ππ 10.4*10.4* 10.4*10.4* 9.99.9 9.29.2 8.18.1

((°) + CLEO K3°) + CLEO K3ππ 8.68.6 9.39.3 8.08.0 7.37.3 6.76.7* Non-Gaussian so RMS quoted


Why incoherence is Why incoherence is still useful?still useful?

– No dependence on rNo dependence on rB B when Rwhen RK3K3ππ=0 =0

– The better determination of rThe better determination of rBB improves the 2-body improves the 2-body dominated determination of dominated determination of γγ

)cos(2)())(( 33

3232

KDBK

KDB

KDBD RrrrrKKB

Add 4-body + CLEO-c


Varying RVarying RK3K3ππ and and K3K3ππ

DD (°) (°) -190-190 -174-174 -158-158 -144-144 -130-130

RK3π= 0.2 and K3π= 144°

8.68.6°° 9.39.3°° 8.08.0°° 7.37.3°° 6.76.7°°

RK3π= 0.4 and K3π= 130°

6.66.6°° 6.46.4°° 6.36.3°° 6.06.0°° 5.65.6°°

RK3π= 0.2 and K3π= 250°

8.88.8°° 8.98.9°° 8.08.0°° 7.17.1°° 6.86.8°°

RK3π= 0.2 and K3π= 180°

8.38.3°° 9.19.1°° 9.19.1°° 7.37.3°° 6.76.7°°


Neutral ADS/GLW Neutral ADS/GLW estimated impact of 4 estimated impact of 4 bodybody No selection for No selection for BB00→D(K3→D(K3ππ))KK*0*0

Assume background and signal scale Assume background and signal scale in the same way asin the same way as BB++→D(K3→D(K3ππ))KK+ + to to begin withbegin with

B B ( (°)°) 00 4545 9090 135135 180180

((°) 2-body + °) 2-body +

CLEOCLEO 5.75.7 10.010.0 7.87.8 9.19.1 5.35.3

((°) + 4-body but °) + 4-body but

no CLEO K3no CLEO K3ππ 5.85.8 10.910.9 8.58.5 9.19.1 5.25.2

((°) + CLEO K3°) + CLEO K3ππ 5.55.5 10.310.3 8.08.0 9.09.0 5.15.1


Combine and include Combine and include DalitzDalitz Combine the ADS/GLWCombine the ADS/GLW

– No No BB00→D(K3→D(K3ππ))KK*0 *0 given the limited impactgiven the limited impact Add Dalitz with the largest background Add Dalitz with the largest background

considered in DC04 studiesconsidered in DC04 studies– Effective uncertainty is 9-10Effective uncertainty is 9-10° ° in global fitin global fit– Standalone uncertainty 13°Standalone uncertainty 13°

B B ( (°)°) 00 4545 9090 135135 180180

Combined B+/B0 Combined B+/B0 ADS/GLWADS/GLW

4.64.6°° 7.67.6°° 6.36.3°° 7.17.1°° 4.64.6°°

+ model + model independent independent DalitzDalitz

4.24.2°° 5.75.7°° 5.35.3°° 5.75.7°° 4.24.2°°


Systematic Systematic uncertaintiesuncertainties


Dalitz systematic Dalitz systematic uncertaintiesuncertainties Really need to take measured uncertainties on cReally need to take measured uncertainties on ci i and and

ssi i from CLEO-cfrom CLEO-c– will be available soonwill be available soon

In the meantime perform fit without Dalitz informationIn the meantime perform fit without Dalitz information– Benchmark point RBenchmark point RK3K3ππ=0.35=0.35– σσ((γγ)=7.6° )=7.6° without Dalitzwithout Dalitz ( (σσ((γγ)=5.5° )=5.5° with Dalitzwith Dalitz))– EffectiveEffective σσ((γγ) ) from Dalitzfrom Dalitz 8.0° ( 8.0° (cf Dalitz alonecf Dalitz alone 12.2°) 12.2°)

Global fit working as more than sum of partsGlobal fit working as more than sum of parts– Add 5° in quadrature to effective statistical uncertainty Add 5° in quadrature to effective statistical uncertainty

forfor ψψ(3770) (3770) data related uncertaintydata related uncertainty This is the latest Bondar and Poluektov number This is the latest Bondar and Poluektov number

arXiv:0801.0840arXiv:0801.0840 Need to check this myselfNeed to check this myself

– Recombine Recombine σσ((γγ)=5.9° including Dalitz error - 10% degradation)=5.9° including Dalitz error - 10% degradation


Addition of Addition of uncorrelated uncorrelated measurementsmeasurements


0.5 fb0.5 fb-1 -1 and 10 fband 10 fb-1-1

With 0.5 fbWith 0.5 fb-1-1::– σσ((γγ)=11.4° at my benchmark point and )=11.4° at my benchmark point and

reasonably well behavedreasonably well behaved– Very non-Gaussian without CLEO-c Very non-Gaussian without CLEO-c

constraintsconstraints– No Dalitz systematic (presumably small effect No Dalitz systematic (presumably small effect

with low LHCb statistics)with low LHCb statistics) With 10 fbWith 10 fb-1-1

– σσ((γγ)=2.1° No Dalitz systematic error)=2.1° No Dalitz systematic error– σσ((γγ)=2.8° with Dalitz systematic error)=2.8° with Dalitz systematic error


OutlookOutlook

1/4/2008 lhcb tuesday meeting 1 global fits to γ and the impact of cleo-c jim libby and guy...

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