Measurements of the CKM angle gamma with BABAR

0.13 MB·English

by  Fernando Martinez-Vidal

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Measurements of the CKM angle at BABAR
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x FernandoMartínez-Vidal∗†
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InstitutodeFísicaCorpuscular(IFIC),UniversitatdeValència-CSIC,
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ApartadodeCorreos22085,E-46071Valencia,Spain
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h E-mail: [email protected]
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1 TherecentmeasurementsoftheCKMangleg bytheBABARexperimentarereported.Theanalyses
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9 havebeenperformedusingthecompletesampleof468millionBBpairscollectedbytheBABAR
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detectorattheSLACPEP-IIasymmetric-energyBfactoryduringtheyears1999-2007.
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35thInternationalConferenceofHighEnergyPhysics-ICHEP2010,
July22-28,2010
ParisFrance
∗Speaker.
†OnbehalfoftheBABARCollaboration.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
MeasurementsoftheCKMangleg atBABAR FernandoMartínez-Vidal
In the standard model (SM) of particle physics, CP violation in the quark sector of weak
interactions arises from a single irreducible phase in the Cabibbo-Kobayashi-Maskawa (CKM)
that describes the mixing of quarks [1]. The unitarity of the CKM matrixV defines a unitarity
triangle (UT)inthecomplexplane. CPviolation measurements andsemileptonic decay rates(and
othermethods)canbeconveniently displayedandcomparedasconstraintsontheanglesandsides,
respectively, of this triangle. Inconsistencies between all these (in general) precise and redundant
constraints can be used to search for new physics (NP). As today, there is an impressive overall
agreement between all measurements [2]. Among these the angle g , defined as the phase ofV
ub
in the Wolfenstein parametrization [1], is particularly relevant since it is the only CP-violating
measurement that, together withthedetermination oftheCP-conserving magnitude ofV , selects
ub
aregion oftheUTapexindependently ofmosttypesofNP,andthusconstitutes aSMcandle type
of measurement. Current constraints, provided by theBABARand Belle experiments, make use of
B± →D(∗)K± and B± →DK∗± decays, and are still weak (∼15◦). Neutral B decays have also
beenproposed, althoughdonotyetprovidesignificantconstraints.
Theangleg fromB±→D(∗)K±andB±→DK∗±decaysisdeterminedmeasuringtheinterfer-
encebetweentheamplitudesb→uandb→c,whentheneutralDmesonisreconstructedinafinal
stateaccessible frombothD0 andD0 decays. Sincebothamplitudes aretreelevel,theinterference
isunaffected byNPappearing intheloops, making thetheoretical interpretation ofobservables in
terms of g very clean. Thedisadvantage is that the branching fractions of the involved decays are
small due to CKM suppression (10−5−10−7), and the size of the interference, given by the ratio
r between the magnitudes of the b→u and b→c amplitudes, is small due to further CKM and
B
colorsuppressions (∼10%). Asaconsequence, themeasurementsarestatistically limitedandone
has tocombine complementary methods applied onthesameBdecay modessharing thehadronic
parameters (r and d , i.e. the relative magnitude and phase of the b→u and b→u transitions)
B B
andg ,anduseasmanyaspossible differentBdecaymodestoimprovetheoverallsensitivity tog .
In this talk we present the most recent determinations of g obtained by BABAR, based on the
full data sampleofcharged Bmeson decays produced ine+e− →¡ (4S)→B+B− andrecorded in
theyears1999-2007,about468×106 B+B−pairs. WehavestudiedB±→D(∗)K±andB±→DK∗±
decays,withtheneutralDmesonsreconstructedinanumberofdifferentfinalstates: D→K0h+h−,
S
with h = p ,K (Dalitz plot method); D → K±p ∓ (ADS method); and D → f , with f a CP-
CP CP
eigenstate (GLWmethod)[3].
One of the charged B mesons produced in the¡ (4S) decay is fully reconstructed, with effi-
ciencies ranging between 40% (for low-multiplicity decays with no neutrals) and 10% (for high-
multiplicity decays with neutrals). The selection is optimized to maximize the statistical sensi-
tivity. The reconstruction efficiencies have substantially improved (20% to 60% relative) with
respect toour previous measurements based on384×106 B+B− pairs, reflecting improvements in
tracking and particle identification, and optimization of analysis procedures. Signal B decays are
characterized by means of two nearly independent kinematic variables exploiting the constraint
fromtheknownbeamenergies: thebeam-energym ≡ E∗2 −|p∗|2 andtheenergy-difference
ES q beam B
D E ≡E∗−E∗ . Sincethemainsourceofbackground comesfromqqcontinuum production, ad-
B beam
ditional discrimination is achieved using multivariate analysis tools, from the combination (either
alinearFisherdiscriminant F,oranon-linear neural networkNN)ofseveralevent-shape quanti-
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MeasurementsoftheCKMangleg atBABAR FernandoMartínez-Vidal
ties. Thesevariablesdistinguish betweenspherical BBeventsfrommorejet-likecontinuum events
andexploit thedifferent angular correlations inthetwoeventcategories. Thesignalisfinallysep-
arated from background through unbinned maximum likelihood (UML) fits to the B± →D(∗)K±
and B± →DK∗± data using m , D E, and F or NN. B± →D(∗)p ± decays, which are about 12
ES
timesmoreabundantthanB±→D(∗)K±,haveasimilartopologybutarediscriminatedbymeansof
excellent pion andkaon identification provided bydE/dxandCerenkov measurements, and show
negligible CP-violating effects (r ∼1%). Therefere, these decays provide powerful calibration
B
andcontrol samplesfornegativetestsofCPviolation.
In the Dalitz plot (DP) method the amplitude for a B− decay has for the b→c transition the
DP of the D0 decay, while for the b→u transition the DP is the corresponding to the D0 decay.
If we assume no D mixing nor CP violation in the D decay, and use as independent kinematic
variables s =m2(K0p ±), then the two DPs are one rotated 90◦ to each other. This is of critical
± S
importance since allows to determine directly from data the strong charm phase variation for D0
and D0, as well as well as the hadronic parameters r and d , and the weak phase g , provided
B B
that aDdecay amplitude model isassumed. ForB+ decays one hasto interchange the D0 and D0
DPs,andchangethesignofg . Thisresults inaninterference termproportional toourobservables
x ≡r cos(d ±g )andy ≡r sin(d ±g ),i.e. therealandimaginarypartsoftheratioofb→u
± B B ± B B
and b → c amplitudes for B± decays. We reconstruct B± → DK±, D∗K± with D∗ → Dp 0,Dg ,
and B± →DK∗± with K∗± →K0p ± decays, followed by neutral D meson decays to the 3-body
S
self-conjugate finalstates K0h+h−,withh=p ,K. FromtheUMLfitwedetermine thesignal and
S
background yields in each of the eight different final states for each B charge, along with theCP-
violatingparametersx andy [4]. Wefind1507B±signalcandidateswithK0p +p −,and268with
± ± S
K0K+K−. Prior totheCP fit, wemodel the D0 and D0 decay amplitudes as acoherent sum of S-,
S
P-,andD-waves,anddeterminetheiramplitudesandphases(alongwithotherrelevantparameters)
relative to the dominant two-body CP-eigenstates K0r (770) (for K0p +p −) and K0a (980) (for
S S S 0
K0K+K−), using a large (≈ 6.2×105) and very pure (≈ 99%) signal sample of flavor tagged
S
neutralDmesonsfromD∗+→D0p + decaysproducedine+e−→ccevents[5]. Fromthe(x ,y )
± ±
+ L
y- a) y*-+ b) C 1 c) B-+ fi DK-+
0.2 0.2 1 - B-+ fi D*K-+
0.8 B-+ fi DK*-+
Combined
0.6
0 0
0.4
1s
-0.2 -0.2
0.2
2s
0
-0.2 0 0.2 -0.2 0 0.2 -150-100 -50 0 50 100 150
x+- x*+- g (deg)
Figure1: 1s and2s contoursinthe(x ,y )planesfor(a)B±→DK±and(b)B±→D∗K±,forB−(solid
± ±
lines)andB+(dottedlines)decays.(c)1−CLasafunctionofg forB±→DK±,D∗K±,DK∗±decays.The
dashed(upper)anddotted(lower)horizontallinescorrespondtothe1s and2s intervals,respectively.
confidence regions for each of the 3 different B decay modes –Fig. 1.(a)(b)– we determine, using
a frequentist procedure, 1s [2s ] intervals for g –Fig. 1.(c)–. We obtain g (mod 180◦) =(68±
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MeasurementsoftheCKMangleg atBABAR FernandoMartínez-Vidal
14±4±3)◦ [39◦,98◦], where the three uncertainties are statistical, experimental systematic, and
amplitude model systematic. We also determine the hadronic parameters rDK± = (9.6±2.9)%
B
[3.7,15.5]%, rD∗K± =(13.3+4.2)% [4.9,21.5]%, k rDK∗± =(14.9+6.6)% [0,28.0]% (k =0.9±0.1
B −3.9 B −6.2
takes into account the K∗ intrinsic width), and the strong phases d DK±, d D∗K±, and d DK∗± [4]. A
B B B
3.5s evidence of direct CP violation (g 6= 0) is found from the combination of the 3 channels,
whichcorrespondstothesignificanceoftheseparationbetweenthe(x ,y )and(x ,y )solutions
+ + − −
inFig.1.(a)(b).
In the ADS method, we reconstruct B± → DK±, D∗K± with D∗ → Dp 0,Dg , followed by
D decays to both the doubly-Cabibbo-suppressed (DCS) D0 final state K+p − and the Cabibbo-
favored(CF)K−p +,whichisusedasnormalizationandcontrolsample. Finalstateswithopposite-
sign kaons arise either from the CKM favored B decay followed by the DCS D decay or from
the CKM- and color-suppressed B decay followed by the CF D decay, producing an interfer-
ence which can be potentially large since the magnitudes of the interfering amplitudes are simi-
lar. However, their overall branching ratios are very small (∼10−7) and background suppression
becomes crucial. The UML fit directly determines the three branching fraction ratios R be-
ADS
tween B decays with opposite-sign and same-sign kaons, and the three yields of B decays with
same-sign kaons, using m and NN. The threeCP asymmetries A are inferred from all these.
ES ADS
We obtain first indications of signals for the B± → DK± and B± → D∗K± (with D∗ → Dp 0)
opposite-signmodes–Fig.2–,withsignificancesof2.1s and2.2s ,respectively[6]. Themeasured
branching fraction ratios areRDK =(1.1±0.5±0.2)×10−2,R[Dp 0]K =(1.8±0.9±0.4)×10−2,
ADS ADS
and R[Dg]K = (1.3±1.4±0.8)×10−2, and the CP asymmetries are ADK = −0.86±0.47+0.12,
ADS ADS −0.16
A[Dp 0]K = 0.77±0.35±0.12, and A[Dg]K = 0.36±0.94+0.25. From these results and external
ADS ADS −0.41
measurements of the relative amplitude and phase of D0 to D0 mesons decaying into the K−p +
final state [7] we infer, using a frequentist procedure similar to that used in the DP method,
rDK± =(9.5+5.1)%[0,16.7]%,rD∗K± =(9.6+3.5)%[0,15.0]%,andthestrongphasesd DK±,d D∗K±,
B −4.1 B −5.1 B B
ingoodagreement withthoseobtained withtheDPtechnique.
22)) 1188 22)) 66
V/cV/c 1166 (a) V/cV/c (b)
ee ee 55
MM 1144 MM
5 5 1122 5 5 44
2.2. 2.2.
s/(s/( 1100 s/(s/( 33
ntnt 88 ntnt
ee ee
vv 66 vv 22
EE EE
44
11
22
00 00
55..22 55..2222 55..2244 55..2266 55..2288 55..33 55..22 55..2222 55..2244 55..2266 55..2288 55..33
mm ((GGeeVV//cc22)) mm ((GGeeVV//cc22))
EESS EESS
Figure 2: Projections on m for (a) B± →DK± and (b) B± →D∗[Dp 0]K±, D→K∓p ± opposite-sign
ES
decays, for ADS samples enriched in signal (NN >0.94). The points with error bars are data while the
curvesrepresentthefitprojectionsforsignalplusbackground(solid),thesumofallbackgroundcomponents
(dashed),andqq¯backgroundonly(dotted).
In the GLW method, we reconstruct B± → DK± decays, followed by D decays to non-CP
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MeasurementsoftheCKMangleg atBABAR FernandoMartínez-Vidal
(D0 → K−p +), CP-even (K+K−, p +p −), and CP-odd (K0p 0, K0f , K0w ) eigenstates. The par-
S S S
tial decay rate charge asymmetries A for CP-even and CP-odd D final states and the ratios
CP±
RCP± of the charged-averaged B meson partial decay rates in CP (R±K/p ) and non-CP (RK/p ) de-
cays (normalized to the corresponding B± → Dp ± decays, to reduce systematic uncertainties)
provide four observables from which the three unknowns g , r and d can be extracted (up to
B B
an 8-fold ambiguity for the phases). The signal yields, expressed in terms of A , R± and
CP± K/p
RK/p are extracted from UML fits to mES, D E, and F. We identify about 500 B± → DK±
decays with CP-even D final states and a similar amount for CP-odd D final states, and mea-
sure[8]A =0.25±0.06±0.02, A =−0.09±0.07±0.02, R =1.18±0.09±0.05, and
CP+ CP− CP+
R =1.07±0.08±0.04. TheparameterA isdifferentfromzerowithasignificanceof3.6s ,
CP− CP+
andconstitutesevidencefordirectCPviolationinB±→DK±decays. Theseresultscanbewritten
intermsoftheobservables x usingtherelationship x =[R (1∓A )−R (1∓A )]/4.
± ± CP+ CP+ CP− CP−
Excluding the D→K0f , f →K+K− channel to facilitate the combination with the DP method,
S
wefindx =−0.057±0.039±0.015 andx =0.132±0.042±0.018, which areconsistent (and
+ −
of similar precision) with the DP method. From these results and using a frequentist procedure
similar to that used previously weinfer 24%<r <45% [6,51]%, and mod 180◦, 11◦ <g <23◦
B
or81◦<g <99◦ or157◦ <g <169◦ [7◦,173◦].
WehavereportedtherecentprogressinthedeterminationoftheCKMangleg ,usingthecom-
pleteBABARdatasampleandthreedifferentandcomplementary methods(DP,ADS,andGLW).A
coherentandconsistent setofresultsong andthehadronicparameterscharacterizing theBdecays
has been obtained. The central value for g , around 70◦ with a precision around 15◦, is consistent
withindirectdeterminationsfromCKMfits[2]. Aproperaverageofallthethreemethodsusingthe
fullBABARsampleofB±→D(∗)K±,DK∗±decaysisforeseen. Weobtainx−−x+=0.175±0.040
bycombiningthex measurementsfromtheDPandGLWmethodsforB±→DK±decays,which
±
is different from zero with a significance of 4.4s , thus constitutes strong evidence for direct CP
violationinthesechargedBdecays. Finally,wehavethefirstsignofanADSsignalinB±→DK±
andB±→D(∗)K± decays.
References
[1] N.Cabibbo,Phys.Rev.Lett.10,531(1963);M.KobayashiandT.Maskawa,Prog.Theor.Phys.49,
652(1973);L.Wolfenstein,Phys.Rev.Lett.51,1945(1983).
[2] J.Charlesetal.,http://ckmfitter.in2p3.fr/;M.Bonaetal.,http://www.utfit.org/.
[3] A.Giri,Y.Grossman,A.SofferandJ.Zupan,Phys.Rev.D68,054018(2003);D.Atwood,I.Dunietz
andA.Soni,Phys.Rev.Lett.78,3257(1997);Phys.Rev.D63,036005(2001);M.Gronauand
D.London,Phys.Lett.B253,483(1991);M.GronauandD.Wyler,Phys.Lett.B265,172(1991).
[4] P.delAmoSanchezetal.(BABARCollaboration),Phys.Rev.Lett.105,121801(2010);B.Aubertet
al.(BABARCollaboration),Phys.Rev.D78,034023(2008).
[5] P.delAmoSanchezetal.(BABARCollaboration),Phys.Rev.Lett.105,081803(2010).
[6] P.delAmoSanchezetal.(BABARCollaboration),Phys.Rev.D82,072006(2010).
[7] E.Barberioetal.(HFAGGroup),arXiv:0808.1297v3.
[8] P.delAmoSanchezetal.(BABARCollaboration),Phys.Rev.D82,072004(2010).
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