Table Of ContentNeutral kaon interferometry at KLOE and KLOE-2
Izabela Balwierz∗
onbehalfoftheKLOEandKLOE-2collaborations†
2 JagiellonianUniversity,InstituteofPhysics
1
E-mail: [email protected]
0
2
n Neutral kaons produced in correlated pairs at a phi-factory offer unique possibilities to perform
a
fundamental tests of CPT invariance, as well as of the basic principles of quantum mechanics.
J
9 TheanalysisofthedatacollectedbytheKLOEexperimentatDAFNEisstillongoingwiththe
1
aimofimprovingpreviousresultsandlimitsonseveralparametersdescribingCPTviolationand
] decoherence. Ancillarymeasurementsliketheregenerationcrosssectiononthebeampipemate-
x
rialsarealsoinprogressandwillbeveryusefultoreducethesystematicuncertainties. Prospects
e
- onimprovementsattheKLOE-2experiment, aimingatanincreaseoftheintegratedluminosity
l
c
ofaboutafactoroftenwithanupgradeddetector,willbealsodiscussed.
u
n
[
1
v
3
1
1
4
.
1
8thInternationalConferenceonNuclearPhysicsatStorageRings-Stori11,
0
2 October9-14,2011
1 INFN,LaboratoriNazionalidiFrascati,Italy
:
v
i
X ∗Speaker.
r †The KLOE collaboration: F. Ambrosino, A. Antonelli, M. Antonelli, F. Archilli, I. Balwierz, G. Bencivenni,
a
C.Bini, C.Bloise, S.Bocchetta, F.Bossi, P.Branchini, G.Capon, T.Capussela, F.Ceradini, P.Ciambrone, E.Czer-
win´ski,E.DeLucia,A.DeSantis,P.DeSimone,G.DeZorzi,A.Denig,A.DiDomenico,C.DiDonato,B.DiMicco,
M. Dreucci, G. Felici, S. Fiore, P. Franzini, C. Gatti, P. Gauzzi, S. Giovannella, E. Graziani, M. Jacewicz, J. Lee-
Franzini, M. Martemianov, M. Martini, P. Massarotti, S. Meola, S. Miscetti, G. Morello, M. Moulson, S. Müller,
M.Napolitano,F.Nguyen,M.Palutan,A.Passeri,V.Patera,I.PradoLonghi,P.Santangelo,B.Sciascia,M.Silarski,
T.Spadaro,C.Taccini,L.Tortora,G.Venanzoni,R.Versaci,G.Xu,J.Zdebik,and,asmembersoftheKLOE-2collab-
oration: D.Babusci,D.Badoni,V.Bocci,A.Budano,S.A.Bulychjev,L.CaldeiraBalkeståhl,P.Campana,E.Dané,
G.DeRobertis,D.Domenici,O.Erriquez,G.Fanizzi,G.Giardina,F.Gonnella,F.Happacher,B.Höistad,L.Iafolla,
E.Iarocci, T.Johansson, A.Kowalewska, V.Kulikov, A.Kupsc, F.Loddo, G.Mandaglio, M.Mascolo, M.Matsyuk,
R.Messi,D.Moricciani,P.Moskal,A.Ranieri,C.F.Redmer,I.Sarra,M.Schioppa,A.Sciubba,W.Wis´licki,M.Wolke
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
1. TheFrascatiφ-factoryfacility
1.1 TheKLOEexperimentattheDAFNEcollider
The DAFNE φ-factory [1], located at the Frascati laboratory (LNF) of INFN, is an e+e−
√
accelerator, working at the φ resonance peak s=m ≈1019 GeV with the φ production cross
φ
section equal to σ(e+e− →φ)≈3.1 µb. DAFNE consists of 3 main parts: a linear accelerator,
an accumulator and two storage rings in which electrons and positrons collide (Fig. 1 left). The
KLOE detector is placed at the center of one of the two interaction points. Data were collected
from2001to2006correspondingto∼2.5fb−1ofintegratedluminosity,i.e. ∼2.5billionφ meson
decaysintoneutralkaonpairs. Theyear2006wasspentoncollectingabout250pb−1 ofoff-peak
data.
TheKLOEdetector(Fig. 1right)consistsofacylindricaldriftchamber(DC)[2],surrounded
byanaelectromagneticcalorimeter(EmC)[3],bothinsertedinasuperconductingcoilwhichpro-
duces an axial magnetic field of 0.52 T, parallel to the beam axis. The diameter and length of DC
are 4 m and 3.3 m, respectively. The chamber is filled with 90% of helium and 10% of isobutan.
Momentumreconstructionfromthecurvatureofthetrackhasafractionalaccuracyof σp (cid:39)0.5%.
p
Thespatialresolutionisbelow200µminthetransverseplane(”ϕ-coordinates”)andtheaccuracy
of vertex reconstruction is about (cid:39)1 mm. EmC is a sampling calorimeter consisting of an altem-
ating stack of 1 mm scintillating fiber layers glued between thin grooved lead foils. The whole
calorimeter consists of a ”barrel” and two ”end caps” and covers almost 4π solid angle. Energy
andtimeresolutionsofthiscalorimeter,foraphoton’senergyinarangefrom20to500MeV,are
equal to σ(E)= √5.7% and σ(t)= √54ps ⊕50 ps, respectively. The beam pipe of KLOE at
E(GeV) E(GeV)
the interaction point has a spherical shape, 500 µm thick, with 10 cm radius and is built from an
alloyofberylliumandaluminum. Insidethesphere,a50micronthickberylliumcylinder,coaxial
withthebeam,provideselectricalcontinuity.
Figure1: Left: TheDAFNEfacilityscheme,right: schemeoftheKLOEdetector. Thefiguresareadapted
from[4].
2
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
1.2 Neutralkaonsataφ-factory
AtKLOEneutralkaonsareproducedinanentangledstates,inadecayoftheφ meson,which
is a vector meson with JPC =1−−. The branching ratio for the φ decay into K0K¯0 is about 34%
and at DAFNE it corresponds to about 106 neutral kaons produced per pb−1 in an antisymmetric
quantumstatewithquantumnumbers1−− [5]:
|i(cid:105) = √1 (cid:2)(cid:12)(cid:12)K0(+(cid:126)p)(cid:11)(cid:12)(cid:12)K¯0(−(cid:126)p)(cid:11)−(cid:12)(cid:12)K¯0(+(cid:126)p)(cid:11)(cid:12)(cid:12)K0(−(cid:126)p)(cid:11)(cid:3)=
2
N
= √ [|K (+(cid:126)p)(cid:105)|K (−(cid:126)p)(cid:105)−|K (+(cid:126)p)(cid:105)|K (−(cid:126)p)(cid:105)], (1.1)
S L L S
2
where N [5] is a normalization factor. In the second row the strangeness basis {(cid:12)(cid:12)K0(cid:11), (cid:12)(cid:12)K¯0(cid:11)},
suitable to describe kaons production, is changed to {|K (cid:105), |K (cid:105)} basis, appropriate to describe
S L
decaysofkaons.
AtKLOEkaonshavemomentaofabout110MeV.Duetothelargelifetimedifferenceofboth
kaons (τ ≈51 ns, τ ≈90 ps) there is also large difference in their mean decay lengths, namely
L S
for K it is about 6 mm whereas for K about 3.5 m. This fact enables to identify the K mesons
S L L
decays by the presence of K decays into two pions close to the interaction region. This type of
S
selectionatKLOEiscalledtheK tagging. Whatisuniqueataφ-factoryandnotpossibleatfixed
L
target experiments is tagging of the K mesons, which in the KLOE detector is realized by direct
S
hitsofK intothecalorimeter.
L
1.3 Neutralkaoninterferometry
If we now consider that both kaons decay into some final states f and f at the proper times
1 2
t andt ,wecanwritethedecayintensitydistributionasafunctionofthedecaytimedifference∆t
1 2
betweenbothkaondecays[5]:
I(f1,f2;∆t) = C12 (cid:104)|η1|2e−ΓL∆t+|η2|2e−ΓS∆t−2|η1||η2|e−(ΓS+2ΓL)∆tcos(∆m∆t+∆ϕ)(cid:105)(1.2)
Γ +Γ
S L
withaphasedifference∆ϕ =ϕ −ϕ and:
2 1
|N|2 (cid:104)f|T|K (cid:105)
C = |(cid:104)f |T|K (cid:105)(cid:104)f |T|K (cid:105)|2, η =|η|eiϕi ≡ i L . (1.3)
12 1 S 2 S i i
2 (cid:104)f|T|K (cid:105)
i S
Eq. (1.2) holds for ∆t ≥ 0, while for ∆t < 0 the substitutions ∆t → |∆t| and 1 ↔ 2 have to be
applied. Here,apartfromtheexponentialdecaytermsofK andK wehavealsointerferenceterm
L S
thatischaracteristicatφ-factories. Fromthisdistributionforvariousfinalstates f (Fig. 2)onecan
i
determine directly: Γ , Γ , ∆m, η, ∆ϕ and perform tests of CP and CPT symmetries comparing
S L i
experimentaldistributionswiththetheoreticalpredictions.
2. SearchfordecoherenceandCPTviolationinentangledneutralkaons
2.1 Testofquantumcoherenceinφ →K K →π+π−π+π− decays
L S
If one now considers the case in which both K and K decay into any identical final states
L S
f = f ,forexampleK →π+π−andK →π+π−,fromequation(1.3)canbeseenthatη =η =
1 2 L S 1 2
3
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
Figure2: Left: theI(π+π−,π0π0;∆t)distributionforCP-conservingevents(solidline)andwithsmallCP
violation(dashedline). Right: theI(π−(cid:96)+ν,π+(cid:96)−ν¯;∆t)distributionforCPT-conservingevents(solidline)
andwithsmallCPTviolation(dashedline). ∆t isgiveninunitsofK lifetimeτ . Thefiguresareadapted
S S
from[5].
η andϕ =ϕ . Substitutingthisto(1.2)oneobtains:
1 2
I(f1= f2;|∆t|)= C12|η|2(cid:104)e−ΓL|∆t|+e−ΓS|∆t|−2e−(ΓS+2ΓL)|∆t|cos(∆m|∆t|)(cid:105). (2.1)
Γ +Γ
S L
Theaboveequationimpliesthattwokaonscannotdecayintothesamefinalstatesatthesametime.
It is visible in Fig. 3, where I(π+π−,π+π−;|∆t|) is equal to 0 for |∆t|=0. What it really means
isthat,eventhoughthetwokaonsarespatiallyseparated,behaviorofoneofthemisdependenton
what the other does. This counterintuitive correlation is of the type first pointed out by Einstein,
PodolskyandRosenintheirfamouspaper[6].
It has been suggested that the initial state soon after the φ-meson decay, spontaneously fac-
torizes to an equal weight mixture of states |K (cid:105)|K (cid:105) or |K (cid:105)|K (cid:105) causing decoherence. This is
S L L S
calledtheFurry’shypothesisofspontaneousfactorization[7]. Ingeneraldecoherencedenotesthe
transition of a pure state into an incoherent mixture of states [5], meaning that entanglement of
particles is lost. The decoherence parameter ζ can be introduced by multiplying the interference
term by a factor (1−ζ). In general ζ depends on the basis in which the initial state is expressed:
{(cid:12)(cid:12)K0(cid:11),(cid:12)(cid:12)K¯0(cid:11)}or{|KS(cid:105),|KL(cid:105)},andinKSKL basisitreads[5]:
I(π+π−,π+π−;∆t)∝e−ΓL∆t+e−ΓS∆t−2(1−ζSL)e−(ΓS+2ΓL)∆tcos(∆m∆t). (2.2)
Avalueofζ =0correspondstotheusualquantummechanicscase,ζ =1tothetotaldecoherence
anddifferentvaluestointermediatesituationsbetweenthesetwo. Hence,thedecoherenceparam-
eter measures the amount of deviation from the predictions of quantum mechanics. Fig. 3 shows
sensitivityofthedoubledecayratedistributiontothevalueofζ. Thebiggestdiscrepancyisfor∆t
closeto0.
At KLOE tests of the coherence were performed by analyzing data corresponding to the
∼1.5fb−1 ofintegratedluminosity. Thedeterminedexperimentaldistributionoftheφ →K K →
L S
4
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
Figure3: TheI(π+π−,π+π−;|∆t|)distributionsforquantummechanicscase, ζ =0, andfortwogreater
thanzerovaluesofthedecoherenceparameter. Thefigureisadaptedfrom[8].
π+π−π+π−intensityasafunctionoftheabsolutevalueof∆t isshowninFig.4. Currentmeasure-
mentsshowthattherearenodeviationsfromquantummechanics[9]:
ζ = (0.3±1.8 ±0.6 )·10−2,
SL stat syst
ζ = (1.4±9.5 ±3.8 )·10−7. (2.3)
00¯ stat syst
ThisresultcanbecomparedtotheoneobtainedbytheCPLEARdata[10]: ζ =0.4±0.7andthe
00¯
BELLEcollaborationresultmeasuredintheBmesonsystem[11]: ζB =0.029±0.057.
00¯
Figure4: Fitto∆t distributionoftheeventsφ →K K →π+π−π+π−. Pointsdenoteexperimentalresults
L S
and histogram shows results of the MonteCarlo simulations. This binning was chosen due to the time
resolutionσ(∆t)∼τ . Thefigureisadaptedfrom[12].
S
5
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
2.2 CPTviolationinentangledKstates
There are several hypothesis of possible CPT violation sources, one of them related to quan-
tum gravity effects that could induce loss of information about the initial state, that is in striking
conflictwithquantummechanicsanditsunitarityprinciple. Thisdecoherencenecessarilyimplies
CPT violation in the sense that the quantum mechanical operator generating CPT transformation
cannot be consistently defined. The resulting loss of particle-antiparticle identity could induce a
breakdownofthecorrelationofinitialstateimposedbyBosestatistics. Asaresulttheinitialstate
gainssmallsymmetricterm[13]:
|i(cid:105) ∝ (K0K¯0−K¯0K0)+ω(K0K¯0+K¯0K0)
∝ (K K −K K )+ω(K K −K K ) (2.4)
S L L S S S L L
The parameter ω is a new complex CPT violation parameter that could be measured only in
(cid:16) (cid:17)
entangledsystems. Oneexpectsthatitisatmost[5]: |ω|2=O E2/MPlanck ≈10−5⇒|ω|∼10−3.
∆Γ
In some specific microscopic models of space-time foam arising from non-critical string theory it
ispredictedtobeupto[14]: |ω|≈10−4−10−5. Fortheomegaparameterthemaximumsensitivity
isexpected,asforthedecoherenceparameter,forK K →π+π−π+π− decays(Fig. 5left).
S L
Figure5:Left:thetheoreticalI(π+π−,π+π−;∆t,ω)distributionwithoutCPTviolation(solidline),ω=0,
andforthreedifferentthanzerovaluesofω (dashedlines)isshown(thefigureisadaptedfrom[8]). Right:
acontourplotofℑω versusℜω atthe68%and95%ofconfidencelevel(thefigureisadaptedfrom[9]).
This analysis was performed by the KLOE collaboration on the same I(π+π−π+π−;∆t) dis-
tribution as before, using ∼1.5 fb−1 of data, by fitting the decay intensity distribution modified
including ω parameter. The obtained result (Fig. 5 right) is consistent with no CPT violation
effects[9]:
ℜω = (cid:0)−1.6+3.0 ±0.4 (cid:1)·10−4,
−2.1STAT SYST
ℑω = (cid:0)−1.7+3.3 ±1.2 (cid:1)·10−4. (2.5)
−3.0STAT SYST
The upper limit at 95% confidence level for the module is |ω|≤1.0·10−3. The accuracy already
reaches the interesting Planck scale region. In comparision, in the B meson system only the real
partofitwasestimatedandwithminorprecision[15]: −0.0084≤ℜω ≤0.0100.
6
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
3. K regenerationatKLOE
S
KLOE results on decoherence and CPTV parameters are dominated by statistical errors. At
KLOE-2thiserrorisexpectedtobereducedbyaboutfactor10andsystematicaluncertaintieswill
play the dominant role. One of the main sources of systematic uncertainty is the K regeneration.
S
It affects measurement of the CPV channel, K →π+π−, in the sense that when K reaches the
L L
reg
regenerating material, it can regenerate into K and then almost immediately decay into K →
S S
π+π−. These decays of regenerated K can be confused as CPV decays of K . This background
S L
havetobecarefullyrejectedandsubtractedfromthemeasureddistribution(Fig.4).
TherearethreemainregeneratorsatKLOE:thecylindricalandthesphericalbeampipes,de-
scribedbefore,andtheinnerwallofthedriftchamber. Onthetransverseradiusdistribution(Fig.6),
(cid:112)
ρ = x2+y2, obtained with loose selection cuts, the regenerated events appear as peaks on the
exponentialbackground. Fromtheanalysisofthesedistributionsonecanevaluatetheregeneration
crosssectionandtheimpactofregenerationonthedecoherenceandCPTVparameters.
Figure6: Thetransverseradiusdistributionforregisteredφ →K K →π+π−π+π−decaysfromtheMon-
L S
teCarlo simulations (left) and data (right). For the cylindrical elements, so beryllium beam pipe and inner
wallofthedriftchamber,theregeneratedeventsappearassymmetricalpeaksandaresituatedat4.4cmand
25cm,respectively. Sphericalbeampipecorrespondstothepeakat10cm. Thefigureisadaptedfrom[16].
4. KLOE-2plans
The upgraded KLOE detector, KLOE-2, at the DAFNE machine upgraded in luminosity, is
abouttostarttakingdata. Thephysicsprogram[17]isextendedincomparisontotheKLOEone.
TheDAFNEacceleratorisassumedtodeliveranintegratedluminosityuptoabout20fb−1 during
the next 3 years. Thanks to a new inner tracker detector [18] there will be possible to improve
resolutionofthedecayvertexreconstructionbyabout3times. This,inturn,willallowtoimprove
theresolutionon∆t andconsequentlythesensitivitytoparametersoftheinterference.
7
NeutralkaoninterferometryatKLOEandKLOE-2 IzabelaBalwierz
5. Conclusions
The entangled neutral kaon system is an excellent laboratory for the study of CPT symmetry
andthebasicprinciplesofquantummechanics. Severalparametersrelatedtopossibledecoherence
and CPT violation (due to quantum gravity effects) have been measured at KLOE, in same cases
withaprecisionreachingtheinterestingPlanckscaleregion. AllresultsareconsistentwithnoCPT
violationandnodecoherence.
KLOE-2 at DAFNE upgraded in luminosity is going to start taking data. Neutral kaon inter-
ferometry,CPTsymmetryandquantummechanicstestsareoneofthemainissuesoftheKLOE-2
physicsprogram.
Acknowledgments
We acknowledge support by Polish Ministry of Science and Higher Education through the Grant
No. 0469/B/H03/2009/37, by MPD program of Polish Science Foundation and by the Euro-
peanCommunity-ResearchInfrastructureIntegratingActivity”StudyofStronglyInteractingMat-
ter” (acronym HadronPhysics2, Grant Agreement n. 227431) under the Seventh Framework Pro-
grammeofEU.
References
[1] J.Lee-Franzini,P.Franzini,[arXiv:hep-ex/0702016v2](2007)
[2] M.Adinolfietal.(KLOEcollaboration),NuclearInstrumentsandMethodsA488(2002)51
[3] M.Adinolfietal.(KLOEcollaboration),NuclearInstrumentsandMethodsA482(2002)364
[4] P.Franzini,M.Moulson,[arXiv:hep-ex/0606033v2](2006)
[5] A.DiDomenico,FrascatiPhysicsSeries43(2007)1
[6] A.Einstein,B.Podolsky,N.Rosen,PhysicalReview47(1935)777
[7] W.H.Furry,PhysicalReview49(1936)393
[8] A.DiDomenico,TalkattheFPP6conference,Va¨xjo¨,June2011
[9] A.DiDomenico(KLOECollaboration),JournalofPhysics: ConferenceSeries171(2009)012008
[10] R.A.Bertlmannetal.,PhysicalReviewD60(1999)114032[arXiv:hep-ph/9902427v1]
[11] A.Goetal.(BelleCollaboration),PhysicalReviewLetters99(2007)131802
[12] F.Ambrosinoetal.(KLOECollaboration),PhysicsLettersB642(2006)315
[13] J.Bernabeuetal.,PhysicalReviewLetters92(2004)131601[arXiv:hep-ph/0310180v1]
[14] J.Bernabeuetal.,PhysicalReviewD74(2006)045014[arXiv:hep-th/0606137v1]
[15] E.Alvarezetal.,JHEP0611(2006)087[arXiv:hep-ph/0605211v2]
[16] I.Balwierz,DiplomaThesis,JagiellonianUniversity(2011)
[17] G.Amelino-Cameliaetal.(KLOE-2Collaboration),EPJC68(2010)619[arXiv:1003.3868v3]
[18] G.Amelino-Cameliaetal.(KLOE-2Collaboration),[arXiv:1002.2572v1](2010)
8
