Experimental Results on Flavour Oscillations and CP-Violation

0.3 MB·English

by  P. K. Behera

Experimental Results on Flavour Oscillations and CP-Violation
Prafulla Kumar Behera (on behalf of the BABAR Collaboration).
TheUniversity ofIowa,IowaCity, USA.E-mail:[email protected]
30yearsagoM.KobayashiandT.Masakawa(wontheNobelPrizeinphysics2008fortheirfamous
theory), gave a theory to explaining CP violation. This theory predicted that large CP violation
would be observed in B mesons . In the last 10 years, Both the B-factories (BABAR at Stanford
Linear Accelerator Center, USA and Belle at KEK, Japan) have observed large CP violation as
predicted by the KM mechanism. The ground breaking experimental results of Flavor Oscillation
and CP violation in B and D mesons are summarized and compared with the Standard Model
expectations.
9 I. INTRODUCTION
0
0
TheoriginofCP violationintheStandardModel(SM)
2
is contained in a complex phase within the Cabibbo-

n Kobayashi-Maskawa(CKM) matrix [1]. With one single
a
phase, the SM predicts clear patterns for quark mixing
J
and CP violations, to be satisfied by all processes. The
1 unitarity relation V V∗ +V V∗ +V V∗ = 0 among
1 ud ub cd cb td tb
the elements of the first and third columns of the CKM

] matrix is represented in the complex plane by a Unitar-
ex βity=Triaanrgg[leV(UTV)∗w/VithVa∗n]g,leγs α==aarrgg[[−VVtdVVt∗∗b//VVudVVu∗∗b]]., FIG. 1: Asymmetric energy e+e− collision at Υ(4S).
- − cd cb td tb − ud ub cd cb
p The angle β, which is the phase of V and appears in
td
e B0 B0 mixing, induces mixing assisted CP violation
h first−observed by BABAR and Belle in the B0 J/ψK0 of the Υ(4S) resonance in the e+e− rest system. Since
[ → S
decays in 2001. the B flight length in x-y is only 30µm as compared

1 The B-Factorieshavedemonstratedthat CP violation to 200µminz-direction,theapp∼roximationδr=δz=
v intheB mesonsystemisconsistentwiththeSMdescrip- z ∼-z canbemade,wherez andz arethezdecay
6 tion given in Eq.[1]. vceprtexteasgof the taggedB with mtageasuredcpflavorand z is
6 cp
4 the CP-eigenstate vertex measured. Since flavor has to
A (δt)=S sin(δm δt) C cos(δm δt). (1)
1 CP f d − f d be conserved in the BB system, at any given moment
. whenthe taggedB is identified,the otherB hasto be of
1 whereδtisthedifferencebetweentheproperdecaytimes
theoppositeflavor,asshowninFig.1,clockedasδt=0.
0 ofthetwomesonsandδm isthemassdifferenceoftheB
9 d Furthermore,becauseoftheasymmetricnature,thesep-
mesonmasseigenstates[52]. ThesineterminEq.1comes
0 arationdistancebetweenthe twodecayvertexesmakesa
fromthe interferencebetween directdecayanddecay af-
: good measurement of the decay distance possible; since
v ter a B0 B0 oscillation. A non-zero cosine term arises
Xi fromthe−interferencebetweendecayamplitudeswithdif- the20B0flµimghitnlze-ndgitrhecitnioxn-,ythiseoanplypr∼ox3im0µamtioansδcro=mpδazr=edzto
r ferent weak and strong phases (direct CP violation) or ∼- z can be made (Fig. 1). BABAR and Belle collectecdp
a from CP violation in B0 B0 mixing, where the latter tag
− a total of 531 fb−1, and 850 fb−1, respectively with
is predicted to be small in the SM and has not been ob- BABAR concluding its data∼taking in April 2008.
served to date. The presence of new physics beyond SM
could in general change this picture; for this reason it is
very important to over-constrain the UT, making many
III. MEASUREMENTS OF β
independent measurements looking for inconsistencies in
the SM.
A. sin2β from b→¸cs
II. ASYMMETRIC ENERGY e+ e− COLLISION InterferencebetweenB0 f andB0 B0 f leads
AT Υ(4S) to time-dependent asymme→try Eq[1]. T→he J/→ψK0 and
S
b ¸csdecays(J/ψK0,ψ(2S)K0,χ K0,η K0,andJ/ψ
Study of time-dependent CP violation requires large K→∗) provide theoreticLally cleanSmeca1surSemecntSs of sin2β.
datasamplesofBmesondecayswithprecisedecaylength They are dominatedby a single decay amplitude and S
f
measurements. The asymmetric energy e+e− colliders, = sin2β for J/ψK0. Extending to other b ¸cs decays,
S →
PEP-II and KEKB, operating at Υ(4S) facilitates this we obtain sin2β = -η S . The SM corrections to this
f f
measurementbyprovidingpairofBBfromstrongdecays relation are believed to×be very small and (10−4) [5].
O
2
Events / ( 0.4 ps )Events / ( 0.4 ps )Raw asymmetryRaw asymmetry--242400000000....0000005555 BB 00 ttaaggss ab)) athnesdindB2eβc0a→ycaBnDC0(b.∗e)+pJDs/oiψn(t∗e2π)n−β0tifdairsleolcfymraoymmsb.e→aaMscucacordilenoddrc-eisoncunaptyBrpsir0beus→tsieodnJi/nfψrtoeπmr0-
Events / ( 0.8 ps )Events / ( 0.8 ps )442255220055 BB 00 ttaaggss c) insaldospmeicntaatteodr b→tryeecodlioargraallmowwedhilteretehediBag0ra→m.DT(∗h)+eDw(e∗a)−k
Raw asymmetryRaw asymmetry--0000....005555 d) Spash=ainsesitnoh2feβtbhien→CabcKcsMsendcmeecaoatfyrspix;eonengleeumiwne-onmuteldidniveaoxtlepvdeecdctoiCnsttr=hibeu0staiaomnndes
--55 00 55 DD t t [[ppss]]
in SM. The time dependent measurements of the decay
0.5 ps340000 (d) B0 → J/y K0 qq==+- 11 aJ/nψdπC0=by B0e.0ll8e ex0p.1e6rim0e.n0t5a[1re2]S. T=he−b0r.6a5nc±hi0n.g21fr±ac0ti.o0n5
es / 200 ofB0 J−/ψπ0±canbe±usedtoconstrainpossiblepenguin
ntri100 contrib→utions to the SU(3)-related decay J/ψ K0 [13],
E 0 S
y andis measuredto be (J/ψπ0)=(1.69 0.14 0.07)
metr0.5 10−5. RecentlyBABARBmeasuredS = 1.±23 0.±21 0.0×4
Asym-0.05 awnhdicChc=or−re0sp.2o0n±ds0t.o19a±4σ0.e0v3idfeonrcCePfo-re−vCePn vB±io0la→tioJn±/ψ[1π40],.
-7.5 -5 -2.-5x D 0t(ps2).5 5 7.5 BABAR’s measurement is consistent with Belle’s result.
f
The decay B0 D(∗)+D(∗)− is a Vector-Vector (VV)
→
FIG.2: Topfigureshowsthebackgroundsubtracted∆tdis- final state. It can have contributions from L = 0, 1, 2
tribution and the symmetries for events with good tags for angularmomentumstatesandthereforetobothCP-even
BABAR and thebottom figure for Belle (B0 →J/ψK0). and CP-odd components. It is necessary to measure the
S
CP-odd fraction R , and then to take into account the
⊥
dilution due to the admixture. Belle’s preliminary re-
sult [16] of R =0.116 0.042 0.004 and CP parame-
The latest measurement from BABAR [6] are sin2β= ⊥ ± ±
ters: S = 0.93 0.24 0.15andC = 0.16 0.13 0.02.
0.670 ± 0.031 ± 0.013, C = 0.026 ± 0.020 ± 0.016[53]; The publi−shed B±ABAR±measurement [1−5] fou±nd a c±onsis-
the δtdistributionandthe measuredrawasymmetryare
tentvalueofR =0.143 0.034 0.008andCP parame-
shown in Fig. 2. Belle recently updated their results as ⊥ ± ±
ters: S = 0.66 0.19 0.04andC = 0.02 0.11 0.02.
shown in Fig. 2 and obtained sin2β = 0.642 0.031 − ± ± − ± ±
0.017, C = 0.018 0.021 0.014 [7]. The n±ew BABA±R Belle claims a 3.2σ evidence of direct CP violation in
and Belle averagei±s sin2β =±0.657 0.025using J/ψK0 B0 → D+D−; S = −1.13 ± 0.37 ± 0.09 and C =
decay. Belle has updated their resu±lts for the ψ(2S)KS0 n−o0t.9s1u±pp0o.r2t3ed±b0y.06BA[1B7A]R. ’Tshmiseaissuurneemxepnetct[e1d8]i.n SBMothanodf
decaymode [8], using 657× 106 BB pairs,with sin2β = the measurements from BABAR are consistent with the
0.718 0.090 0.033andC = 0.019 0.020 0.015;
± ± ± ± SM prediction of tree dominance [19] and therefore with
both are in goodagreementwith the B0 J/ψK0 mea-
→ S theresultinb ccs. Proposednewphysicsmodelscould
surement. →
causesizablecorrections[20];itisthereforeimportantto
reduce experimental uncertainties further.
B. Four-fold ambiguity of β
IV. MEASUREMENT OF α
There remains a four-fold ambiguity for the value of The angle α is measured with a time-dependant anal-
β, 21.70, (21.7 + 180)0, 68.30, and (68.3 + 180). One ysis of decays of neutral B mesons, B0 h+h−, with h
approach for resolving this ambiguity is to measure = π,ρ, a . These are sensitive to an effe→ctive parameter
1
cos2β, using a time-dependent angular analysis of B0 α due to the interplay of the Tree and the Penguin
J/ψK∗0(K0π0) and B0 D0π0. BABAR [9] perform→ed dieafgframs. Hence, Onecandetermine α α [21] using
this analysSisusingusing→88 106 BB pairsandobtained isospin relations in the decays B0 h+−h−e,fBf0 h0h0,
cos2β = 2.72+−00..0759 ± 0.27×(sin2β = 0.731). A similar and B± → h0h±. The procedu→re of measur→ing the
analysiswasperformedbyBelle[10]using275 106BB so-called “isospin-triangles” requires large dataset and
×
pairsobtainingcos2β =0.87 0.74 0.12(sin2β =0.726), leaveswith up to eight-fold ambiguities. A less stringent
theerroronmeasurementis±toola±rgetoresolvethefour- relation sin2(α α ) < (B h0h0)/ (B h0h±)
eff
− B → B →
fold ambiguity. Belle’s recent measurement of a time- holds [22],whichismoreaccessiblewithcurrentdatasets
dependent Dalitz analysis of B0 D0π0 [11] disfavors thantheisospinanalysisasitdoesnotrequiretotagthe
the 68.30 solution. → flavor of the decaying B.
3
1 - C.L. 10..281 (b) 0.18 Belle pewnliittchaatmperdpelsiietnunvdtoelsvst.iantIgitstpciaecnns.tnaIogttownbaaesls,rohelvloawetdieovfnoesrrh,tiphpoeia1nm2teoudnngokundtoiffw[2en9rs-]
00..46 1 - C.L.00..46 that the variation of the strong phase of the interfering
ρ resonance in the dalitz plot provides the necessary de-
0.2 0.2
greesof freedomto constrainα with only the irreducible
0
0 50 100 a (d1e5g0rees) 00 30 6f02 (de9g0ree1s2)0 150 180 (pαerf→ormαed+tπh)isaamnabliygsuiistya.ndTmheeaBsuArBeAdRαe=xp(e8r7im+4e5n)t0 t[3h0u]s.
−13
FIG. 3: Left Fig:α expressed as one minus the confidence Belle [31] performed this analysis resulting in a tighter
level as afunction of angle. Anupperboundon δαof 390 at constraint of 680 <α<950 at 95% C.L for the solution
the90% CL. The curveshows thebounds on α using isospin compatible with SM.
method alone, while theshaded region shows the result with
SU(3) requirement. Right Fig: same values from Belle using
iBsoBsp→inπaπnadlyesciasya.ndSodliirdecltinCePanadsymdamshetrliyneininBd0ic→ateπs0πC0.Lan=d D. α from B→a1π
68.3% and 95%, respectively.
The analysis of the decay B0 a±π∓ where a±
π∓π±π± has been used to extrac→t α1with a quasi-1tw→o-
A. α from B→ππ bodyapproximation. BABAR[32]performedthis analysis
using349 fb−1ofdataandmeasuredα =(78.6 7.3)0,
eff
±
with no evidence for the direct or mixing induced CP
The decay B ππ can be used to extract sin2α.
BABAR [23] and →Belle [24] performed an isospin anal- vtiioonlastifoonr. SUO(n3c)e-retlhaetemdedaescuaryems e(nBt+s of braa+n(c1h2in7g0)πfraocr-
ysis to extract α, using the available information B+ a−(1260)K+ andthe decaysB →K1(1270)π and
(S+−,C+−,C00,B+−,B+0,B00), shown in Fig. 3. The B →K1(1400)π) become available, qu→antit1ative bounds
preferred value of α=(96+10)0 for BABAR, which is con- → 1
−6 on δα obtained with method [33] will provide significant
sistent with Belle measurement of α=(97 11)0.
constraints on the angle α through the measurement of
±
α in B0 a±(1260)π∓ decays. Recently BABAR [34]
eff → 1
performed an analysis to measure these decay modes to
B. α from B →ρρ constrain α α . Theyobservedthechargedandneu-
eff
| − |
traldecaymodesforthefirsttimeandfoundnoevidence
InB0 ρ+ρ− decays,aspinzeroparticle(theB0 me- for direct CP asymmetry.
son) deca→ys into two spin 1 particles (ρ± mesons). Each
ρ± mesondecaysinto a π±π0 pair,where the quarkcon-
tent of the final decay product is similar to ππ. The V. MEASUREMENT OF γ
presence of a π0 in the final state adds to experimen-
tal challenge of the measurement. The CP analysis of At the beginning of the B-Factory (e+e− Υ(4S)
B0 ρ+ρ− is further complicated by the presence of BB) era, it was thought to be not possible→to measu→re
→
one amplitude with longitudinal polarization and two γ and it could only be measured at hadron collider like
amplitudeswithtransversepolarization. Thedecayisob- CDFandD0. Latterseveralmethodshavebeenpursued
servedto be dominated by the longitudinal polarization. using different common decay modes such as CP eigen-
There is good agreement between the measurements in states(Gronau,London,andWyler(GLWmethod)[35]),
ρ+ρ− from BABAR [25] and Belle [26] for CP violation. suppressed Kπ charge combinations (Atwood, Dunietz,
The HFAG average for the longitudinal components are andSoni(ADSmethod)[36]),andK0π+π−decays(Giri,
Cρ+ρ− = 0.06 0.13,Sρ+ρ− = 0.05 0.17. Forthefirst Grossman, Soffer, and Zuppan (GGSSZ method) [37]).
time, BAB−AR [2±7] showed a prel−imina±ry time-dependant
measurement of B0 ρ0ρ0 decay. Using 427 106 BB
pairs, BABAR measur→es (B0 ρ0ρ0) = (0.84× 0.29
A. The GLW method
0.17) 10−6,f =0.70 B0.14 →0.05,S =0.5 ±0.9 0.±2,
L L
× ± ± ± ±
C =0.4 0.9 0.2. Consistently,Belle[28]setanupper
limLit of ±(B0 ± ρ0ρ0)<1.0 10−6 at a 90% confidence In the GLW method, CP eigenstates with even or
level (C.BL). → × odd parity Dc±p are obtained final states common to
D0 and D0. The branching fractions ± , − , and
BCP± BD0
+ have been measured[54], where the observables
BD0
C. α from B →ρπ are constructed from their ratios, such as RCP±
( − + + )/( − + + )/2 and A± ( − ≡
BCP± BCP± BD0K BD0K CP ≡ BCP± −
The decay B0 π+π−π0 can be used to measure the + )/( − + + ). BABAR [38] published a mea-
angle α, in princi→ple however this is not a CP eigenstate sBuCrPe±mentBCoPf±B± BCPD±∗K±, with decay modes D∗0
decay. Performing an isospin analysis is extremely com- D0γ,D0π0, and →D0(D0) reconstructed in CP-even→(
4
the K0π− and K0π+ for λ= 1 for D∗ D0γ and +1
S S − →
forotherdecays,respectivelyand ( )aretheam-
D+ D−
plitudes of the D0(D0) K0π+πA− decAay. These decays
→ S
are describedin a detailedmodel involving severalinter-
mediate resonancesextracted fromlargecontrolsamples
of flavor-tagged D∗+ D0π+ decays produced in cc
events. The Cartesian→variables x∗ = r∗ cos(δ∗ γ),
y∗ = r∗ sin(δ∗ γ) are used by∓the eBxperimBen∓ts to
av∓oid thBe bias Br∗∓being positive definite. Belle recon-
B
structed the decays B∓ D∗0K∓, with D∗0 D0π0
FIG. 4: Left Fig: For BABAR, 1− CL as a function of γ and D0 K0π+π−, an→d measured r = 0.16→ 0.04,
including statistical and systematic uncertainties and their r∗ = 0.2→1 0.S08 and γ = (76+12)0 [40B] using 657± 106
correlations. Thedashed(upper)anddotted(lower)horizon- B ± −13 ×
BB pairs. BABAR recently published a result based on
tal lines correspond to the one- and two-standard deviation
383 106BB pairs[41]. Inadditiontothemodeusedby
intervals, respectively. Right Fig: For Belle, Projections of
confidence regions for B+ → D∗K+ mode onto the (r, γ) Bell×e, BABAR also reconstructed the decays D∗0 D0γ,
planes. Contours indicate projections of one, two and three B± D0K∗±[K0π±], and D0 K0K+K−.→BABAR
standard deviation regions. deter→mines the (x,Sy)∗ parameter→s witSh the same accu-
∓
racyasBelle. BABARdatafavorssmallerr values(r =
B B
0.086 0.035,r∗ =0.135 0.51,kr =0.163+0.088)[55] ,
± B ± S −0.105
K+K−,π+π−), CP-odd (K0π0,K0ω,K0φ), and flavor- and thus a larger error on γ ( γ = (76+23)0. The result
S S S −24
s0p.0e9cific0m.0o1d,esA(CKP+−π+=).+T0h.e0y6obt0a.i1n0edA0C.P0+2,=R−CP0.+11=± faonrd(xB,eyll)e∓airnetshheowBn∓in→FDig0.K4.∓ decay mode from BABAR
± ± ±
1.31 0.13 0.04, R = 1.10 0.12 0.04. The
CP−
± ± ± ±
accuracy of this measurement does not allow a determi-
nation of γ with GLW method alone but it contributes
to improving the overall precision when combined with
other methods. VI. SIN2β FROM b→qqs PENGUIN DECAYS
The decay B0 φK0 is dominated by a penguin dia-
B. The ADS method gram. The SM am→plituSde is expressed by
Decays with similar overall amplitudes are selected to P V∗V Pu+V∗V Pc+V∗V Pt (2)
maximizetheinterferenceandthereforesensitivitytoCP ∼ ub us cb cs tb ts
V∗V (Pc Pt)+V∗V (Pu Pt) (3)
asymmetries. Favored B D decays followed by sup- ∼ cb cs − ub us −
→
pressedD decays,or vice-versaprovide anidealdata set
forthesestudies. Itispossibletodefinearatioofbranch- Where V∗V can be eliminated using one of the CKM
tb ts
iBaB2nnrBBgd→+fr→rDaCDscsPuitsnpiuoKγpanKs/ssiB+ynom)δBf/→sm(/uBDeRpBtfpra−rive→eKssDs.esa=duspaBKrnADe2−dlAle+fDa+Sv[r3oB29r=e]Bd+Brde+(2ce→BrecDnBaDty−rslsuBy→pacKDsop+ssRuuγ)bpAcKlDois−sShδeB=−=d, Ouifidnr(esiAnttatλtirc4eiat(ryρmlt−,roeObliaη→(t)Ai)oλincsc2sss),u,aVpcncp∗obdrVneltcessaasie+dndssVctCouo∗bmKsViMpnuas2rβ+ee.ldeVTmttoh∗beVentthtssseec=fiwornhs0ditc.thteeTrrammhree,.
D B B ADS For other b s penguin modes, there are additional
mDe→asuKre+mπe−n,tsbasoefdtohne65d7ec×a1y06cBhaBinpaBir−s. T→hey dDoKn−ot, tsimonallfrcoomntrbibut→iuontsr.eeFdoriaBgr0am→, η′K(AS0λ,4f(0ρKS0,iηa))c,onctarnibbue-
observeastatisticallysignificantsignalinthesuppressed → O −
mode, obtaining RADS = (8.0+−65..37+−22..08) × 10−3, and ptrriebsuetnito.nTfrhoemBt0he→bπ0KuS0traeneddiωaKgrS0amca.nInalasdodhitaivoen,athcoense-
A = ( 0.13+0.97 0.26). These results are used to →
ADS − −0.88± modes contain b sdd instead of b sss. Considering
set a 90% C.L upper limit of rB <0.19. these effects, the→SM corrections up→to (λ2) 5% can
O ≡
bepossibleintheextractionofsin2β andthemagnitudes
of corrections can vary in different modes [42]. A larger
C. GGSZ method deviationexceedingthesecorectionswillbeanindication
of new physics in penguin loops.
ThethreebodydecaysofD0 andD0 suchasK0π+π− Individual results from BABAR and Belle, as well as
S
or K0K+K− depend on the interference of Cabibbo al- theiraveragesforeachdecaymode ofb spenguinand
S
lowed, doubly-Cabibbo suppressed, and CP eigenstate, most recent sin2β from b ccs [43], sho→wn in Fig. 5 are
decayamplitudes. TheB± D0(D0)K± amplitudecan mutually consistent. All s→in2β measurements, except
→ eff
wbehewrreitmte2n aasndA∓(m∗)2(ma2−re,mth2+e)s∝quAarDe∓d+invλarrB∗iaeni(tδB∗m±aγs)sAeDs±of, φvaKluS0e, πof0πsi0nK2βS0,=an0d.6K7+K0−.0K20fraorme wbithicncs∼. 1σ from the
− + ± →
5
CDF Run II L = 1.0 fb-1
sin(2b eff) ≡ sin(2f eff) HHFFAAGG
1 CKM2008 1
b→+-000000ppwph¢K K K K K K KSScc000fprfs Kf K KK K K KS0SSSSS WBBABBABBABBABBABBABBABBABABBAaevaevaevaevaevaevaevaevavaevoeeeeeeeeeeBlBlBlBlBlBlBlBlBBllllllllllreeeeeeeeerrrrrrrrrrlaaaaaaaaaadaaaaaaaaaarrrrrrrrrr ggggggggggAeeeeeeeeeeveragHFAGe CKM2008 HFAGHFAGHFAGHFAGCKM2008HFAGHFAGCKM2008CKM2008HFAGHFAGCKM2008CKM2008CKM2008HFAGCKM2008HFAGCKM2008CKM2008CKM2008000...666148-- 0000000000++±--..........0000 2563561874....002212P67405716232495..51R 0±±±±±±±±±±±±55.E- 9 0000000000000000000+±L-0...................00 I2013234074657548500 ..000000000M22+-680201681979475229969.........00I646666990 ..N12±±±±±±±±±±±±±±±±±±±±74340277380 A 00000000000000000000++++++++++----------R....................0000000000000000000000000000000001124001....................Y231112111111050500212324838738927774178022787158691332323413 foFaosnIrcGdila.ullaln6t:cidoeLenrAmplitudeUct.123a-a-2p010000yinp0temires 1 oddde.saa6afindtt4tsaaavg5ie t––– ies5uvs i111rtry.. ss66:ec 44u255o5s s.ssm8h (tps1obshta0-1wtie.n osBnelydt)s0h.-1Be5L0smoowesaec2sri0ullrapetlddsoiiaogttnana2:iDfi5mcmfaTrnspc e(ehlpq=ies1tu%-u31e)l0donegcayvra∆itlhummess
-2 -1 0 1 2
FIG. 5: Summary of effective sin2β measurement in b → s rived V /V =0.2060 0.0007(exp)+0.0081(theor),and
decay modes, compared to the world average sin2β value in | td ts| ± −0.0060
found no evidence of CP violation. The D0 [48] experi-
b→c¸s.
ment also measured a stringent limit of 17 < δm < 21
s
ps−1 at 90% C.L with 1 fb−1.
∼
VII. CP VIOLATION IN BB MIXING
IX. MIXING AND CP VIOLATION IN THE D0
SYSTEM
The SM allows CP violation in BB mixing itself in
analogytoǫ inK0 system[44]. Thisleadsto q/p = 1,
k | |6 The D0 system is unique among the neutral mesons
where p and q are the coefficients relating the mass and
becauseitistheonlyoneinwhichmixingproceedsviain-
flavor eigenstates of the neutral B mesons, because M
12 termediatestateswithdown-typequarks(up-typequarks
and Γ have different phases. In SM we expect the ob-
12 insupersymetricmodels). TheD0-D0rateisexpectedto
servable effect to be 1 − |pq|2 ≃ Im(MΓ1122) ∼ O(10−3). besmall(10−4 orless)inSM.BABAR[49]foundevidence
Observation of a significantly large effect would be an of D0-D0 mixing in the variationin decay time distribu-
exciting result. BABAR [45] has measured |pq| − 1 = tionfor D0 K+ π− comparedto thatofthe Cabibbo-
( 0.8 2.7 1.9) 10−3 using 232 106 BB pairs. favored deca→y D0 K− π+. Belle [50] also found evi-
B−elle [4±6] me±asured×q =1.0005 0.00×40 0.0043. The dence of D0-D0 m→ixing with 3.2σ using 540 fb−1 data.
|p| ± ±
results from BABAR and Belle are consistent with unity. More recently the CDF [51] has found evidence for mix-
This implies that CP violation in B0-B0 mixing is be- ing in D0 decays. No evidence for CP violation is found
low the (10−2) level. These measurements are already by BABAR, Belle, and CDF experiments.
O
limited by their systematic uncertainties.
X. SUMMARY
VIII. MIXING AND CP VIOLATION IN THE B0
s
SYSTEM The B-Factories have observed CP violation in sev-
eral B decays. All categories of CP violation in B de-
The determination of B0- B0 oscillation frequency re- cays are consistent with SM expectations. The preci-
s s
lated to ∆m can be used to extract the magnitude of sion of sin2β measurements is now measured to better
s
V , one of the nine elements of the CKM matrix. The than 4% and significantly constrains the UT. The decay
ts
CDF experiment [47] reported an observation of B0- B0 B ππ,ρρ,ρπ,anda π areusedtostudy α. The decay
mixing, measuring δm = 17.77 0.10 0.07 ps−1swiths ρ+→ρ− gave stringent c1onstraint on α. There are other
s
a data sample of 1 fb−1 from pp¯±collisio±ns at √s = 1.96 decays which are being investigated and hopefully will
TeV. The amplitude values and B0 B0 oscillation fre- contribute to the measurement of α. At the begining
quency∆m areshowninFig.6,ansd−itissconsistentwith of the B-Factory (e+e− Υ(4S) BB) era, it was
s
→ →
the SM expectation. Using this value of ∆m they de- thought to be not possible to measure the angle γ. The
s
6
dalitz analysis of B± D0K± has the best sensitivity served in B0-B0, B0-B0, and D0-D0. Constraints on
forγ. Thedecayb s→penguinisofprimefocusbecause both ∆Γ and ∆m fosr Ds0-D0 mixing will allow further
→
of sensitivity to physics beyond SM. studiesofCP violationwhichremainsapotentialground
Mixing but no evidence of CP violation has been ob- for observing New Physics.
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D 76, 052007 (2007). symbolsφ1,φ2,φ3 fortheanglesα,β,γ,andAf =−Cf
[26] K. Abe et al., Belle Collaboration, Phys. Rev. D 76, for the parameter describing direct CP violation. In the
011104 (2007). present article we will follow the α, β, γ, C nomencla-
f
[27] B. Aubert et al., the BABARCollaboration, ture.
arXiv:0708.1630[hep-ex] [53] Here and in the following, unless otherwise noted, the
[28] TheBelleCollaboration,LaThuile2008preliminary,un- first error is statistical and the second one systematic,
published. they are combined if only one error is given
7
[54] The superscripts refer to the charge of the B, the sub- [55] The amplitude ratio B± → D0K± events is described
scripttotheCP parityoftheDeigenstateDC±P ortothe by krS, with k taking in to account non-resonant KS0π±
flavorof te D for flavor-specificdecays respectively. contributions.