ChPT tests at the NA48 and NA62 experiments at CERN

0.27 MB·

by  NA48/2

ChPT tests at the NA48 and NA62 experiments at
CERN
6
1
0
2 Dmitry MADIGOZHIN∗†

n (JINR,Dubna)
a E-mail: [email protected]
J

9
TheNA48/2CollaborationatCERNhasaccumulatedunprecedentedstatisticsofrarekaondecays
2
in theK modes: K (+ )(K p +p e n ) andK (00)(K p 0p 0e n ) withnearlyone
] e4 e4 − ±→ − ± e4 ±→ ±
x percentbackgroundcontamination.Thedetailedstudyofformfactorsandbranchingrates,based
e
onthese data, hasbeencompletedrecently. Theresultsbringsnew inputsto lowenergystrong
-
p interactionsdescriptionandtestsofChiralPerturbationTheory(ChPT)andlatticeQCDcalcula-
e
h tions. Inparticular,newdatasupporttheChPTpredictionforacuspinthep 0p 0 invariantmass
[
spectrumatthetwochargedpionsthresholdforKe4(00)decay.Newfinalresultsfromananalysis

1 ofabout400K p gg raredecaycandidatescollectedbytheNA48/2andNA62experiments
± ±
v →
atCERNduringlowintensityrunswithminimumbiastriggerconfigurationsarepresented. The
4
1 resultsincludeamodel-independentdecayratemeasurementandfitstoChPTdescription.
0
8
0
XIIthInternationalConferenceonHeavyQuarks&Leptons2014
.
1 25-29August2014
0
SchlossWaldthausen,Mainz,Germany
6
1
:
v
Speaker.
i ∗
X †fortheNA48/2andNA62Collaborations: F.Ambrosino,A.Antonelli,G.Anzivino,R.Arcidiacono,W.Baldini,
r S.Balev, J.R.Batley,M.Behler,S.Bifani,C.Biino, A.Bizzeti,B.Bloch-Devaux, G.Bocquet, V.Bolotov, F.Bucci,
a
N.Cabibbo,M.Calvetti,N.Cartiglia,A.Ceccucci,P.Cenci,C.Cerri,C.Cheshkov,J.B.Chèze,M.Clemencic,G.Col-
lazuol,F.Costantini,A.CottaRamusino,D.Coward,D.Cundy,A.Dabrowski,G.D’Agostini,P.Dalpiaz,C.Damiani,
H. Danielsson, M. De Beer, G. Dellacasa, J. Derré, H. Dibon, D. Di Filippo, L. DiLella, N. Doble, V. Duk, J. En-
gelfried, K. Eppard, V. Falaleev, R. Fantechi, M. Fidecaro, L. Fiorini, M. Fiorini, T. Fonseca Martin, P.L. Frabetti,
A.Fucci,S.Gallorini,L.Gatignon,E.Gersabeck,A.Gianoli,S.Giudici,A.Gonidec,E.Goudzovski, S.GoyLopez,
E.Gushchin,B.Hallgren,M.Hita-Hochgesand,M.Holder,P.Hristov,E.Iacopini,E.Imbergamo,M.Jeitler,G.Kalmus,
V. Kekelidze, K. Kleinknecht, V. Kozhuharov, W. Kubischta, V. Kurshetsov, G. Lamanna, C. Lazzeroni, M. Lenti,
E. Leonardi, L. Litov, D. Madigozhin, A. Maier, I. Mannelli, F. Marchetto, G. Marel, M. Markytan, P. Marouelli,
M.Martini,L.Masetti,P.Massarotti,E.Mazzucato,A.Michetti,I.Mikulec,M.Misheva,N.Molokanova,E.Monnier,
U.Moosbrugger,C.MoralesMorales,M.Moulson,S.Movchan,D.J.Munday,M.Napolitano,A.Nappi,G.Neuhofer,
A.Norton,T.Numao,V.Obraztsov,V.Palladino,M.Patel,M.Pepe,A.Peters,F.Petrucci,M.C.Petrucci,B.Peyaud,
R. Piandani, M. Piccini, G. Pierazzini, I. Polenkevich, I. Popov, Yu. Potrebenikov, M. Raggi, B. Renk, F. Retière,
P.Riedler,A.Romano,P.Rubin,G.Ruggiero,A.Salamon,G.Saracino,M.Savrié,M.Scarpa,V.Semenov,A.Sergi,
M.Serra,M.Shieh,S.Shkarovskiy,M.W.Slater,M.Sozzi,T.Spadaro,S.Stoynev,E.Swallow,M.Szleper,M.Valdata-
Nappi,P.Valente,B.Vallage,M.Velasco,M.Veltri,S.Venditti,M.Wache,H.Wahl,A.Walker,R.Wanke,L.Widhalm,
A.Winhart,R.Winston,M.D.Wood,S.A.Wotton,O.Yushchenko,A.Zinchenko,M.Ziolkowski.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
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avocluuummeKevlar window DCH H1Mea gtanentDk C+H 4HodoLKrHACZMUV 10 cm
1 cm Quadruplet tank Spectrometer
0 50 100 200 250 m
Figure1: NA48/2beamline
1. Introduction
Investigation of rare kaon decays allows for the determination of Chiral Perturbation Theory
(ChPT) constants and provides the basis for its validity checks. Analysis of high statistics data
samplescollectedbyNA48/2andNA62(R phase)experimentsinseveraldecaymodesallowsthe
K
stringent testsofChPTpredictions.
The main goal of NA48/2 experiment was the search for CP-violating asymmetry in K
±
→
3p decays [1]. Additionally, it has provided in 2003-2004 a large data sample for charged kaon
±
raredecaystudies. In2007-2008, theNA62experiment[2](R phase) hascollected another large
K
datasamplewiththesamedetector(described in[3])butmodifiedbeamline.
Two simultaneous K+ and K beams were produced by 400 GeV/c protons on a beryllium
−
target(Fig. 1). Particlesofoppositechargewithacentralmomentumof60GeV/candamomentum
band of 3.8% (rms) (74 GeV/c 1.9% for NA62 R phase) were selected by the system of
K
± ±
magnetsandcollimators. Bothbeamsofabout1cmwidthwerefollowingalmostthesamepathin
thedecay volumecontained ina114mlongvacuum tank. Thebeamsweredominated byp ,the
±
kaoncomponent wasabout6%.
Charged products of K decays were measured by the magnetic spectrometer consisting of
±
four drift chambers (DCH1–DCH4)and adipole magnet located between DCH2and DCH3. The
spatial resolution ofeachDCHwasnearly90m mandthemomentumresolution was s p =(1.02
p ⊕
0.044 p)% (p in Gev/c). The spectrometer was followed by a scintillator hodoscope with a time
·
resolution of 1˜50 ps, whose fast signals were used to trigger the readout of events with a charged
track.
A Liquid Krypton calorimeter (LKr), located behind the hodoscope, was used to measure
the energy of electrons and photons. It is an almost homogeneous ionization chamber with an
active volume of7 m3 of liquid krypton 27X deep, segmented transversally into projective cells,
0
2 2cm2each. Transversepositionofisolatedshowerwasmeasuredwithaspatialresolutions =
x
×
s =(0.42/√E 0.06)cm. Energyresolution forphotons andelectrons wass /E =(3.2/√E
y E
⊕ ⊕
9.0/E 0.42)%(EinGeV).
⊕
2
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
p + f
+
q e
p q
+
e
K
n
p -
Figure2:TopologyofK (+ )decays.
e4
−
An aluminium beam pipe of 16 cm outer diameter and 1.1 mm thickness was traversing the
centres of all the detector elements, providing the path in vacuum for undecayed beam particles
andformuonsfrombeamp decays.
±
2. K+ decay
e4−
Kinematics of the K p +p e n (K+ (+ )) decay is defined by five variables [4]: the
± → − ± e4− −
squared invariant masses of dipion (Sp )and dilepton (Se), the angle q p of p ± indipion rest frame
withrespecttotheflightdirectionofdipioninthekaoncenterofmasssystem,thesimilarangleq
e
ofe indilepton restframe,andtheanglef betweendipionanddilepton planes(seeFig. 2).
±
K decay amplitude is a product of the leptonic weak current and (V-A) hadronic current,
e4
described in terms of three (F,G,R)axial-vector and one (H) vector complex form factors. Sensi-
tivityofK decaymatrixelementtoRformfactorisnegligible duetothesmallmassofelectron.
e4
Form-factors maybedeveloped inapartialwaveexpansion:
F =Fseid fs+Fpeid fpcosq p +Fdeid fdcos2q p +...
G=Gpeidgp+Gdeidgdcosq p +...
H =Hpeidhp+Hdeidhdcosq p +... (2.1)
Limiting the expansion to S- and P-waves and considering a unique phase d for all P-wave
p
form factors in absence of CP violating weak phases, one will obtain the decay probability, that
depends only on the real form factor magnitudes F,F ,G ,H , a single phase shift d =d d
s p p p s p
−
and kinematic variables. The partial wave form factors can be developed in a series expansion of
the dimensionless invariants q2 = (Sp /4m2p ) 1 and Se/4m2p [5]. Two slope and one curvature
−
terms are sufficient to describe the F form factor variation within the available statistics (F/f =
s s s
1+(fs′/fs)q2+(fs′′/fs)q4+(fe′/fs)Se/4m2p ), whiletwotermsare enough to describe theGp form
factor(G /f =g /f +(g /f )q2),andtwoconstants –todescribe theF andH formfactors.
p s p s ′p s p p
Hadronic form factors for the S- and P-waves have been obtained by NA48/2 concurrently
with the phase difference between the S- and P-wave states of pp system, leading to the precise
determination ofa0 anda0,theI=0andI=2S-wavepp scattering lengths [7].
0 2
3
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
AhighprecisionmeasurementofK+ formfactorsandbranchingfractionhasbeenpublished
e4−
byNA48/2fewyearslater[8,9]. K+ decayratewasmeasuredrelativetoK p +p p (K+ )
e4− ±→ − ± 3p−
normalization channel.
Forthe selection in this analysis atrack of charged particle witha momentum p>2.75 GeV
and 0.9<E/p<1.1 was identified as e , while the track with p>5 GeV and E/p<0.8 was
±
regarded as p . A dedicated linear discriminant variable based on shower properties has been
±
applied to reject events with one misidentified pion. To suppress K+ background, the vertex
3p−
invariant mass M3p in the p +p −p ± hypothesis and its transverse momentum pt were required to
beoutside anellipsecentered atPDGkaonmass[10]andzerotransversal momentum, withsemi-
axesof20MeV/c2 and35MeV/c,respectively.
The squared missing mass was required to be >0.04 (Gev/c2)2 to reject p p 0 decays with
±
a subsequent p 0 e+e g process. The invariant mass of e+e system was required to be >
− −
→
0.03GeV/c2 inordertorejectphoton conversions.
For the normalization channel K3+p− the M3p and pt were inside a smaller ellipse with semi-
axes12MeV/c2 and25MeV/c,respectively. Asampleofabout1.11millionK+ candidates and
e4−
about19millionsofprescaled K3p candidates wereselected fromdatarecorded in2003-2004.
Twomain background sources for this modeare known: K p +p p decays withsubse-
± − ±
→
quentp en decayorapionmis-identified asanelectron;andK p 0(p 0)p withsubsequent
± ±
→ →
p 0 e+e g decaywithundetected photonsandanelectronmis-identifiedasapion. Theiradmix-
−
→
tureinthesignaleventsisestimated tobebelow1%.
A detailed GEANT3-based [11] Monte Carlo simulation was used to take into account full
detector geometry, DCHalignment, localinefficiencies andbeamproperties.
TheresultingK+ branchingfraction[9]BR(K+ )=(4.257 0.004 0.016 0.031 )10 5
e4− e4− ± stat± syst± ext −
is 3 times more precise than available PDG value [10] . It has been used to extract the common
normalization formfactor f [9].
s
3. K00 decay
e4
The K00 rate is measured relative to the K p 0p 0p (K00) normalization channel. These
e4 ± → ± 3p
twomodesarecollected usingthesametriggerandwithasimilareventselections. Theseparation
betweenthemoccursonlyatalaterstage.
Events with at least four g , detected by LKr, and at least one track, reconstructed from spec-
trometer data, were regarded as K00 or K00 candidates. Every combination of 4 reconstructed g
e4 3p
withenergiesE >3GeVwasconsidered asapossiblepairofp 0 decays. Reconstructed longitudi-
nalpositionsZ andZ ofbothp 0 2g decaycandidateswererequiredtocoincidewithin500cm,
1 2
→
withtheiraverageposition Z =(Z +Z )/2insidethefiducialvolume106mlong.
n 1 2
Decaylongitudinal position Z ,assigned tothetrack, wasdefinedbytheclosest distance ap-
ch
proachbetweenthetrackandthebeamaxis. Combinedvertex,composedoffourLKrclustersand
one charged track with momentum p>5GeV, was required to have the difference Z Z less
n ch
| − |
than 800 cm. If several combinations satisfy the vertex criteria, the case of minimum (Z1 Z2)2+
s−
n
(Zn Zch)2 has been chosen, where s and s are the Z -dependent widths of corresponding distri-
−s n c n
c
butions.
4
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
Figure 3: Reconstructed (M3p ,pt) plane for the normalization(a) and signal (b) candidates. Plot (a) is a
zoominsidethesmallerellipse whichdefinesthe normalizationsample. Crossescorrespondtotheellipse
centers(M3p =MK; pt =5MeV/c).
A track was preliminarily identified as e , if it has an associated LKr cluster with E/p be-
±
tween 0.9and 1.1, otherwise p wasassumed atthefirststage. Further suppression ofpions mis-
±
identified aselectrons isobtained bymeansofdiscriminant variablewhichisalinearcombination
ofE/p,showerwidthandenergy weightedtrack-to-cluster distanceatLKrfrontface.
Ke040 and K30p0 decays were discriminated by means of elliptic cuts in the (Mp 0p 0p ,pt) plane,
±
where M is the invariant mass of combined vertex in the K0 hypothesis, and p is the
p 0p 0p 3p t
±
transversal momentum (see Fig. 3). Elliptic cut separates about 94 million K00 normalization
3p
events from about 65000 K00 candidates. Residual fake-electron background is about 0.65% of
e4
K00 amount. Background fromK00 withthesubsequent p e n is0.12%ofthesignal,andthe
e4 3p ±→ ±
accidental-related background isabout0.23%. Itgivesintotal1%ofbackground admixture.
For the case of K p 0p 0e n (K00) decay, due to the presence of two identical particles
± → ± e4
in dipion, it cannot be in antisymmetric l=1 state, so form factors do not include P-terms. In first
approximation, only S-wave contributes, and matrix element is parametrized in terms of the only
formfactor Fs, that may depend on Sp and Se. Form factor Fs was extracted from the fit of events
distribution on(Se,Sp )plane,takingintoaccounttheacceptance, calculated fromMCsimulation.
Thefollowingempiricalparameterization hasbeenused:
Fs/fs =1+(fs′/fs)q2+(fs′′/fs)q4+(fe′/fs)Se/4m2p for q2>0;
Fs/fs =1+dqq2/(1+q2) +(fe′/fs)Se/4mp2 forq2<0. (3.1)
| |
Theresultsareinagreement withNA48/2K+ analysis described above:
e4−
f /f =0.149 0.033 0.014 ,
s′ s stat syst
± ±
f /f = 0.070 0.039 0.013 ,
s′′ s stat syst
− ± ±
5
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
Figure 4: K00 normalized form factor squared as a function of q2. The line corresponds to the adopted
e4
empiricalfit. Thearrowpointstothe2mp threshold.
f /f =0.113 0.022 0.007 ,
e′ s stat syst
± ±
d= 0.256 0.049 0.016 .
syst
− ± ±
The obtained form factor was used to obtain the final result of branching fraction measure-
ment: Br(K00)=(2.552 0.010 0.010 0.032 )10 5. It is 10 times more precise, than
e4 ± stat ± syst± ext −
PDGcorresponding value[10]. Systematicerrorincludesthecontributions frombackground, sim-
ulation statistical error, sensitivity toformfactor, radiation correction, trigger efficiency andbeam
geometry. Externalerrorcomesfromuncertainty ofnormalizationchannelK00 branchingfraction.
3p
Below the threshold of Sp =(2mp ±)2 the measured Ke040 decay form factor shows a deficit of
events, that is well described by the present empirical parameterization (Fig. 4). It is similar to
theeffect ofp +p p 0p 0 rescattering inK p 0p 0p decay (cuspeffect [6]), investigated by
− ± ±
→ →
NA48/2collaboration earlier[7]onthebasisofChPTformulations.
4. K p gg decay
± ±
→
In the ChPT framework, the K p gg decay receives twonon-interfering contributions at
± ±
→
lowestnon-trivialorderO(p4): thepionandkaonloopamplitudedepending onanunknownO(1)
constant cˆrepresenting thetotalcontribution ofthecounterterms, andthepoleamplitude [12].
New measurements of this decay have been performed using data collected during a 3-day
special NA48/2 run in 2004 and a 3-month NA62 run in 2007. The Kpgg decay rate has been
measured withrespecttothenormalization decaychain: K p p 0 decayfollowedbyp 0 gg
± ±
→ →
(Fig. 5).
Both for signal and normalization modes only one reconstructed charged particle track with
the closest distance of approach (CDA) to beam axis less than 3.5 cm and with the momentum p
between 8and50GeV/cwasrequired. Theratio ofcorresponding LKrcluster energy tothetrack
momentum, measured by means of spectrometer was E/p<0.8. TwoLKrclusters with energies
E >3GeV/cintimewiththetrack( 15ns),butseparatedbyatleast25cmfromthetrackimpact
±
6
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
Figure 5: Reconstructedinvariantmass distributionsof p gg (a) and p p 0 (normalizationchannel)can-
± ±
didates. Filled circles: NA62(R stage) experimentaldata; histograms: simulated signalandbackground
K
components.Signalregionsareindicatedwitharrows.
Figure6: Reconstructedz=(mgg /mK)2 spectrumforselectedKpgg candidatescomparedtothesimulated
signalandbackgrounddistributions.Signalregionisindicstedwithverticalarrows.
7
ChPTtestsattheNA48andNA62experimentsatCERN DmitryMADIGOZHIN
point on LKr front plane were considered as g candidates. An energy-dependent upper limit was
imposedontheclusterlateralwidthtosuppress thecontribution ofcaseswithclustermerging.
Signal events are selected in the region of z = (mgg /mK)2 > 0.2 to reject the K± p ±p 0
→
background peaking at z = 0.075 (see Fig. 6). For K2p as a normalization channel, 0.064 <
z <0.086 was required. 149 (232) decays candidates are observed in the 2004 (2007) data set,
withbackgrounds contaminations of10.4%(7.5%)fromK p p 0(p 0)(g )decayswithmerged
± ±
→
photon clustersintheelectromagnetic calorimeter.
The values of cˆ in the frameworks of the ChPT O(p4) and O(p6) parameterizations [13] as
well asbranching ratio have been measured using likelihood fitsto the data. Themainsystematic
effect isdue tothe background uncertainty. Uncertainties related totrigger, particle identification,
acceptanceandaccidentaleffectsfoundtobenegligible. Thefinalcombinedresultsbasedon2004
and 2007 runs data [14, 15] are: cˆ for O(p4) fit = 1.72 0.20 0.06 ; cˆ for O(p6) fit =
stat syst
± ±
1.86 0.23stat 0.11syst;branchingfractionBr(Kpgg )forO(p6)fit=(1.003 0.056) 10−6. The
± ± ± ×
model-independent branchingratioforz>0.2isequalto(0.965 0.063) 10 6. Newresultsare
−
± ×
inagreementwiththeearlier(basedon31events)BNLE787[16]ones.
References
[1] J.R.Batley,etal.,Eur.Phys.J.C52(2007)875–891.
[2] G.Anelli,etal.,CERN-SPSC-2005-013.
[3] V.Fanti,etal.,Nucl.Instrum.Meth.A574(2007)433–471.
[4] N.Cabibbo,A.Maksymowicz,Phys.Rev.137(1965)B438–B443.
[5] G.Amoros,J.Bijnens,J.Phys.GG25(1999)1607–1622.
[6] N.Cabibbo,Phys.Rev.Lett.93(2004)121801.
[7] J.Batley,etal.,Eur.Phys.J.C64(2009)589–608.
[8] J.Batley,etal.,Eur.Phys.J.C70(2010)635–657.
[9] J.Batley,etal.,Phys.Lett.B715(2012)105–115.
[10] J.Beringer,etal.,Phys.Rev.D86(2012)010001.
[11] R.Brun,F.Carminati,S.Giani,CERN-W-5013.
[12] G.Ecker,A.PichandE.deRafael,Nucl.Phys.B303(1988)665.
[13] G.D’AmbrosioandJ.Portolés,Phys.Lett.B386(1996)403.
[14] J.Batley,etal.,Phys.Lett.B730(2014)141.
[15] J.Batley,etal.,Phys.Lett.B732(2014)65.
[16] P.Kitchingetal.,Phys.Rev.Lett.79(1997)4079.
8