Recent results from NA48/2 and NA62 experiments at CERN

0.52 MB·

by  Nicolas Lurkin

Recent results from NA48/2 and NA62 experiments
at CERN
Nicolas Lurkin∗†on behalf of the NA48/2 and NA62 collaboration ‡
SchoolofPhysicsandAstronomy,UniversityofBirmingham
E-mail: [email protected]
The NA48/2 and NA62-R experiments at the CERN SPS collected a large sample of charged
K
kaon decays in flight. NA62-R was running in 2007–08 with a highly efficient minimum bias
K
7 trigger for decays into electrons. A preliminary measurement of the electromagnetic transition
1 form factor slope of the π0 from 1.05×106 fully reconstructed π0 Dalitz decays is presented.
0
2 Theobtainedvaluea=(3.70±0.53stat±0.36syst)×10−2representsa5.8σ observationofanon-

n zeroslopeinthetime-likeregionofmomentumtransfer. Anupperlimitontherateofalepton
a numberviolatingdecayK±→π∓µ±µ± isreportedfrom∼1.6×1011K± decaysatNA48/2in
J
2003–04: B <8.6×10−11 at 90% CL. Searches for heavy sterile neutrino N and inflaton χ
4 4
2 resonances in K± →πµµ decays are reported. No signal is observed and upper limits on the

products B(K± → µ±N )B(N →π∓µ±) and B(K± →π±χ)B(χ → µ+µ−) are set in the
] 4 4
x
range 10−10–10−9for resonance lifetimes up to 100ps. The result of a search for dark photon
e
- withthesamesampleofdecaysisalsoreported. Intheabsenceofobservedsignal,thelimitson
p
e themixingparameterε2intherange9–70MeV/c2areimproved.
h
[ XIIIInternationalConferenceonHeavyQuarksandLeptons

1 22-27May,2016
v Blacksburg,Virginia,USA
9
7
9 ∗Speaker.
6
†SupportedbyERCStartingGrant336581
0
. ‡F.Ambrosino,A.Antonelli,G.Anzivino,R.Arcidiacono,W.Baldini,S.Balev,J.R.Batley,M.Behler,S.Bifani,
1
C.Biino,A.Bizzeti,B.Bloch-Devaux,G.Bocquet,V.Bolotov,F.Bucci,N.Cabibbo,M.Calvetti,N.Cartiglia,A.Cec-
0
7 cucci, P. Cenci, C. Cerri, C. Cheshkov, J.B. Chèze, M. Clemencic, G. Collazuol, F. Costantini, A. Cotta Ramusino,
1 D.Coward,D.Cundy,A.Dabrowski,G.D’Agostini,P.Dalpiaz,C.Damiani,H.Danielsson,M.DeBeer,G.Dellacasa,
: J. Derré, H. Dibon, D. Di Filippo, L. DiLella, N. Doble, V. Duk, J. Engelfried, K. Eppard, V. Falaleev, R. Fantechi,
v
i M.Fidecaro,L.Fiorini,M.Fiorini,T.FonsecaMartin,P.L.Frabetti,A.Fucci,S.Gallorini,L.Gatignon,E.Gersabeck,
X
A. Gianoli, S. Giudici, A. Gonidec, E. Goudzovski, S. Goy Lopez, E. Gushchin, B. Hallgren, M. Hita-Hochgesand,
r M.Holder,P.Hristov,E.Iacopini,E.Imbergamo,M.Jeitler,G.Kalmus,V.Kekelidze,K.Kleinknecht,V.Kozhuharov,
a
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.Polenke-
vich,I.Popov,Yu.Potrebenikov,M.Raggi,B.Renk,F.Retière,P.Riedler,A.Romano,P.Rubin,G.Ruggiero,A.Sala-
mon, 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)underthetermsoftheCreativeCommons
Attribution-NonCommercial-NoDerivatives4.0InternationalLicense(CCBY-NC-ND4.0). http://pos.sissa.it/
RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
1. TheNA48/2andNA62-R setup
K
TheNA48/2experimentoperatingin2003–04,anditssuccessorNA62-R phasein2007–08,
K
collectedchargedkaondecaysinflightattheCERNSPS.TheaimofNA48/2wasthemeasurement
ofdirectCPviolation[1]withtheworld’slargestsampleofchargedkaonsdecays,whileNA62-R
K
aimedatmeasuringtheleptonuniversalityinthekaondecay[2]withaminimumbiasdatasample.
Inbothcasestheamountofstatisticsrecordedallowedustostudyotherprocesses. Leptonnumber
violatingdecaysandresonancesearchesinK±→πµµ anddarkphotonsearcheswithNA48/2are
reported,aswellastheπ0 electromagnetictransitionformfactorwithNA62-R .
K
The beam line described in detail in [1] was designed to provide simultaneous K+ and K−
beams. They were extracted from the 400GeV/c SPS proton beam impinging on a 40cm long
berylliumtarget. Thefinalbeammomentumof(60±3)GeV/c(NA48/2)and(74.0±1.4)GeV/c
(NA62-R ) was selected using a system of dipole magnets and a momentum-defining slit incor-
K
porated into a beam dump. This 3.2m thick copper/iron block provided the possibility to block
eitheroftheK+ orK− beams. Thebeamswerefocusedandcollimatedbeforeenteringthe114m
long cylindrical vacuum tank containing the fiducial decay volume. The beam contained mainly
pions but included approximately 6% of kaons. The simultaneous K+/K− beams provided about
6.2×107particlesperspillof4.8sforNA48/2,whileNA62-R wasalsousingasinglemodebeam
K
withanintensity∼10timeslower,alternatingperiodswithK+,periodswithK−,andperiodswith
both.
The principal subdetectors in use were the same in both cases and a detailed description is
given in [3]. The momenta of the charge particles were measured by a spectrometer housed in
a tank separated from the decay volume and filled with helium. It was composed of four drift
chambers(DCH)andadipolemagnetbetweenthesecondandthirdones. Themagnetprovideda
horizontal transverse momentum kick of 120MeV/c in NA48/2 and 265MeV/c in NA62-R . A
K
hodoscope(HOD)composedoftwoplanesofplasticscintillatorwasplacedafterthespectrometer
toprovideprecisetimingofthechargedparticlesandgeneratefasttriggersignalsforthelow-level
trigger. A127cmthickquasi-homogeneouselectromagneticcalorimeterfilledwithliquidkrypton
(LKr) was located downstream and used both as a photon detector and for particle identification.
Thevolumeisdividedinto13248cellsof∼2×2cm2 crosssectionwithoutlongitudinalsegmen-
√
(cid:0) (cid:1)
tation. The energy resolution is σ /E = 3.2/ E⊕9/E⊕0.42 % and the position resolution is
√ E
(cid:0) (cid:1)
σ = σ = 4.2/ E⊕0.6 mmwheretheparticleenergyE isgiveninGeV. Amuonvetosys-
x y
tem (MUV) was installed behind the LKr and consisted of three planes of scintillator orthogonal
to the beam axis, each one preceded by a 80cm thick iron wall. They were made of 2.7m long
and2cmthickstripsalternativelyarrangedhorizontallyandvertically. Thewidthofthestripswas
25cminthefirsttwoplanesand45cminthelastone. Thecentralstripsweredividedintwohalves
to accommodate the beam pipe in a 22×22cm2 central hole. The detection efficiency was above
99%forsinglemuonevents,withatimeresolutionof350ps.
The NA48/2 main trigger, used in the presented results, was optimised for three-track vertex
topologies. Coincidence of hits in the two HOD planes was required in at least two of the 16
segments, or at least one segment accompanied by at least two clusters of energy deposition in
the LKr. Fast algorithms were run to reconstruct tracks from the DCH hits and accept events
with a three-track closest distance of approach below 5cm. Alternatively, the track assumed to
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RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
be a π±, should have an energy E∗ <230MeV in the 60GeV/c K± rest frame. This condition
suppressed the K± →π±π0 (E∗ =248MeV) while keeping the K± →π±π0π0. For NA62-R
K
the trigger operating in minimum-bias mode was optimised for decays into electrons: at least one
coincidence of hits in the HOD, bounds on the hits multiplicity in the DCH, at least 10GeV of
energy deposit in the LKr and at least one track with E/p>0.6 and p∈(5–90)GeV/c (with the
energyE reconstructedintheLKrandthemomentum preconstructedintheDCH).
2. π0 electromagnetictransitionformfactorslopeattheNA62-R experiment
K
As the π0 is produced in four of the main K± decays, with about 2×1010collected kaon
decays NA62-R is an ideal experiment to study the neutral pion. The Dalitz decay π0 →γe+e−
K D
[4] has a branching fraction of B =(1.174±0.035)% [5] and proceeds through the π0γγ vertex
withoneoff-shellphoton. Thecommonlyusedkinematicvariablesdefinedintermsoftheparticle
four-momentaare:
(cid:18)M (cid:19)2 (p +p )2 2p ·(p −p )
x= ee = e+ e− , y= π0 e+ e− ,
m m2 m2 (1−x)
π0 π0 π0
where p ,p ,p are respectively the π0 and e± four-momenta, m is the mass of the π0, and
π0 e+ e− π0
M isthee+e− invariantmass. Thephysicalregionisgivenby
ee
(cid:18)2m (cid:19)2 (cid:114) r2
r2= e ≤x≤1, |y|≤ 1− .
m x
π0
Theπ0 differentialdecaywidthnormalisedtotheπ0 →γγ decaywidthreads:
D 2γ
1 d2Γ(π0) α (1−x)3(cid:18) r2(cid:19)
D = 1+y2+ (1+δ(x,y)) |F(x)|2 ,
Γ(π0 ) dxdy 4π x x
2γ
whereF(x)isthesemi-off-shellelectromagnetictransitionformfactor(TFF)oftheπ0andδ(x,y)
encodestheradiativecorrections.
The TFF is usually expanded as F(x)=1+ax where a is the form factor slope parameter.
This approximation is justified by the smallness of this parameter. It has been studied first in the
vectormesondominance(VMD)model[6]whereitisdominatedbytheρ andω mesons,resulting
(cid:16) (cid:17)
inavaluea≈m2 m−2+m−2 /2≈0.03. FurtherstudiesextendingtheVMDmodel[7],orusing
π0 ρ ω
differentframeworks[8,9,10,11]areinagreementwiththeoriginalvalue.
Another crucial aspect is the inclusion of the radiative corrections in the differential rate as
they are of the same size as the TFF. The total radiative corrections have been first studied in
[12], butthefirststudyofthecorrectionsonthedifferentialrateisdonein[13]inthesoft-photon
approximation. Ithasbeenlaterextendedin[14]. Themostrecentcontribution[15],triggeredby
thiswork,includesnewcontributionsandacodeimplementedattheMCeventgeneratorlevelfor
thegenerationofradiativephotonfromtheinternalbremsstrahlungcontribution.
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RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
2.1 Eventselection
The selection is tuned to select a pure Dalitz decay sample from the dominant K± →π+π0
D
decaychain(K ),featuringtwosame-signtracks,oneopposite-signtrackandaphoton. Exactly
2πD
one three-track vertex must be reconstructed within the fiducial decay region and no additional
track is allowed. The impact point of the three tracks should be in the acceptance of the DCH
chambers and separated by at least 2cm in the first one. The momenta are required to be in the
range (2–74)GeV/c. A single cluster of energy deposition with more than 2GeV of energy, and
separatedbyatleast20cmfromthesame-signtracksand10cmfromtheremainingtrackisallowed
intheevent. Itisusedtoreconstructaphotoncandidateassumingitoriginatesfromthevertex. The
totalreconstructedmomentumofthethreetracksandthephotoncandidateshouldbeintherange
(70–78)GeV/candthesquaredtotaltransversemomentumwithrespecttothenominalbeamaxis
p2<5×10−4(GeV/c)2. Themassassignmenttothetracksisdoneusingthekinematicproperties
t
of this decay chain. The opposite-sign track is assigned an electron mass and two hypotheses
are built for the possible mass assignments of the same-sign tracks. Only events with at most
one of the hypotheses satisfying the following conditions on the reconstructed π0 and K± masses
andx,ykinematicvariablesareselected: M ∈(115–145)MeV/c2, M ∈(465–510)MeV/c2,
eeγ π±π0
and x,|y|<1. The trigger conditions described in section 1 must be reproduced, but with tighter
criteria to eliminate edge effects due to different resolution between online and offline analysis.
ThetotalLKrelectromagneticenergyshouldbehigherthan14GeVandatleastoneofthetracksis
requiredtohave p>5.5GeV/candE/p>0.6. Duetotheacceptancenotbeingwellreproduced
in the simulation for events with low x, the signal region is defined as x > 0.01, equivalent to
M >13.5MeV/c2.
ee
The final selected sample amounts to 1.1×106 events. The acceptances, evaluated from
Monte-Carlosimulations,are1.81%forK and0.02%forK±→π0µ±ν (K ).
2πD D µ3D
2.2 Preliminaryresult
A χ2 fitofthexdistributionofdataandsimulationisusedtoextracttheTFFslopevalue. An
equipopulous binning is used. The different hypotheses are tested by reweighing the MC events
simulated with a known slope a = 0.032. The main systematic uncertainties arise from the
sim
simulation of the beam spectrum and from the calibration of the spectrometer global momentum
scale.
Thepreliminaryresultobtainedis:
a=(3.70±0.53 ±0.36 )×10−2,
stat syst
with χ2/ndf=52.5/49, which has a p-value of 0.34. This measurement represents a significant
measurement of a positive π0 electromagnetic TFF slope of more than 5σ in the time-like region
of momentum transfer. An illustration of the best fit result and the comparison with previous
measurementsfromπ0 DalitzareshowninFig. 1.
3. SearchesforleptonnumberviolationandresonancesinK± →πµµ atthe
NA48/2experiment
Lepton number violation has never been observed. However heavy Majorana neutrinos are
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RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
Ratio1.05 Data / MC(a=0) Geneva-Saclay (1978)
C Form factor: best fit Fischer et al. 30k events
M1.04 Form factor: – 1s band
a / Saclay (1989)
at1.03 Fonvieille et al.
D 32k events
1.02 SINDRUM I @ PSI (1992)
Meijer Drees et al. 54k events
1.01
TRIUMF (1992)
Farzanpay et al. 8k events
1
0.99 NA62 (2016) 1.1M events
10-2 10-1 1 - 0.1 - 0.05 0 0.05 0.1
x p 0 TFF slope
Figure1: (a)Illustrationofthefitresultshowingtheratiodata/MC,withtheMCsampleweighted
toobtaina=0. Theeventsaredividedinto20equipopulousbinswiththepointsatthebarycentre
of each bin. The solid line represents the TFF function with a slope value equal to the fit central
value. Dashedlinesindicatethe1σ band. (b)Comparisonofthisresultwithpreviousexperiments
measuringtheTFFslopefromπ0 decays.
D
possiblemediatorsforsuchprocesses. TheνMSMmodel[16]introducesthreeheavysterileneu-
trinosN. ThelightestoneN hasamassofO(keV/c2)andisalsoacandidatefordarkmatter. The
i 1
twoothershavemassesrangingfrom100MeV/c2 tofewGeV/c2. Themodelcanexplainbaryon
asymmetrythroughCP-violatingsterileneutrinooscillationsandmixingwiththeactiveneutrinos,
and the low neutrino masses through see-saw mechanism. Effective vertices with theW±,Z and
the SM leptons can be built, with a mixing matrix U describing the mixing between sterile and
SM neutrinos. A simple extension of this model with a real scalar field (inflaton χ) [17] can also
explainthehomogeneityandisotropyoftheuniverseonlargescalesandtheexistenceofstructures
onsmallerscales.
The particular case of the lepton number violating (LNV) decay K± →π∓µ±µ± is investi-
gated, with the data sample of NA48/2 containing ∼1.6×1011 K± decays in vacuum. It can be
mediatedbythesterileneutrinosiftheyareproducedinthekaondecayasK± →µ±N, thensub-
sequently decay as N →π∓µ±. For a neutrino produced as a resonance (indicated as N ) with a
4
mass m , the possible mass range is m +m <m <m −m . The total branching fraction for
4 π µ 4 K µ
thischannelwouldbe:
B(K±→π∓µ±µ±)=B(K±→µ±N)×B(N →π∓µ±)∼(cid:12)(cid:12)Uµ4(cid:12)(cid:12)4 ,
where U is the mixing matrix element corresponding to the resonant sterile neutrino and the
µ4
muon neutrino. The current limit on this branching ratio is B <1.1×10−9 at 90% CL [5]. The
same neutrino can also be seen in the lepton number conserving (LNC) channel K± →π±µ±µ∓
if it decays as N →π±µ∓. The inflaton in the mass range 2m <m <m −m can appear in a
µ χ K π
similar way in the decay K± →π±χ and subsequently decays into a muon pair. The production
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RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
branchingfractionisgivenby[18]:
(cid:114) 
(cid:16) (cid:17)2
m2 −m2 −m2 −4m2m2
B(K±→π±χ)=1.3×10−3 K π χ π χθ2,
 m2 
K
whereθ istheinflatonmixingwiththeHiggsboson.
3.1 Eventselection
TheselectionisdevelopedbasedontheMCsimulationofK± →π∓µ±µ±,K± →π±µ±µ∓
and K± →π±π+π− (K ) decays. This last channel is the main background when π± are mis-
3π
identifiedas µ±. Sincetheeventtopologyissimilar,thesystematiceffectsduetotriggerefficien-
ciescancelatfirst-order. Theselectionisbasedonathree-trackvertextopology,wherethevertex
is reconstructed inside the decay volume. The total reconstructed momentum of the three tracks
must be compatible with the nominal beam momentum and with no transverse momentum with
respecttothenominalbeamdirection. Contrarytotheselectiondescribedinsection2, theπ,µ,e
separationisdoneusingthemeasuredE/pratioofthetracks,thusrequiringthetrackimpactpoints
ontheLKrplanetobeintheacceptance. Toobtainanadditionalseparationfactor,the µ± arere-
quiredtohaveassociatedhitsintheMUV1andMUV2whiletheπ±cannotbeassociatedwithany
pairofhitsfromdifferentMUVplanes.
For the LNV channel, the muons are required to have the same sign, with an opposite sign
pion. A blind analysis is performed and the tuning of the selection is done based on the control
regiondefinedasM <480MeV/c2,whereM isthereconstructedinvariantmassofthepion
πµµ πµµ
andthetwomuons. Thesignalregionisdefinedas|M −m |<5MeV/c2.
πµµ K
Conversely, for the LNC channel the muons tracks are requested to have opposite sign. The
signalregionisdefinedas|M −m |<8MeV/c2. Atotalof3489candidateeventsareselected
πµµ K
withabackgroundestimatedat(0.36±0.10)%.
3.2 UpperlimitontheleptonnumberviolatingdecayK±→π∓µ±µ±
After the final selection, a single event is observed in the signal region while the expected
numberofbackgroundeventsisN =1.163±0.867 ±0.021 ±0.116 . Theobtainedupper
exp stat ext syst
limitat90%CLonthebranchingfractionis
N
B(K±→π∓µ±µ±)= est B(K )<8.6×10−11,
3π
N A
K sig
whereN istheupperlimitonthenumberofsignalevents,N isthetotalnumberofreconstructed
est K
K± decaysinthefiducialdecayregionandA =(20.62±0.01)%istheacceptanceforthesignal
sig
estimated from the MC simulation. The upper limit at 90% CL on N is computed using the
est
Rolke-Lopezstatisticaltreatment[19,20]fromthenumberofobservedeventsinthesignalregion,
thenumberofbackgroundeventsexpectedfromtheMCsimulationandtheassociateduncertainty.
This limit represents an improvement by a factor of 10 with respect to the previous measurement
[5].
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RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
3.3 Searchfortwo-bodyresonances
A scan for a resonance of mass M in the reconstructed π±µ∓ invariant mass M of both
res πµ
LNV and LNC channels, and in the µ±µ∓ invariant mass M of the LNC channel is done. The
µµ
stepandwidthofthesearchwindowsaredeterminedbythemassresolutionσ(M )atthetested
res
value. The mass step between two mass hypotheses is 0.5σ(M ) and the window centered on
res
M hasawidthof2σ(M ). Asthewindowisfourtimeslargerthanthemassstep,theresultfor
res res
neighbouring mass hypotheses is highly correlated. The upper limit at 90% CL on the product of
branchingfractionsiscomputedas
N
UL(B(K±→ p X)B(X → p p ))= est ,
1 2 3
N A
K sig
where(p ,p ,p )→(µ±π∓µ±,µ±π±µ∓,π±µ+µ−)andN istheupperlimitat90%CLonthe
1 2 3 est
number of signal events in the mass window. This is again estimated by the Rolke-Lopez method
from the number of observed events and the number of expected background events in each mass
window. As a result of the three-track vertex requirement, the acceptance depends also on the
lifetime of the resonance τ and drops to zero as the distance travelled from the initial vertex by
res
theresonantparticleincreases.
A total of 284 mass hypotheses are tested on the LNV M spectrum to search for K± →
πµ
µ±N ; N →π∓µ±decays. InthiscasetwochoicesarepossibletobuildM ,selectingoneofthe
4 4 πµ
muons or the other. The possibility closest to M is chosen. No signal is observed and an upper
res
limit of O(10−10) is set on the product of the branching ratios for heavy Majorana neutrinos with
τ < 100ps. TheLNCM spectrumistestedwith280hypothesesandnoK± →µ±N ; N →
N4 πµ 4 4
π±µ∓ signalisobserved. TheupperlimitisO(10−9)forsterileneutrinoswithτ <100ps. The
N
4
lastscandoneontheM spectrumoftheLNCchanneltosearchforK± →π±χ; χ →µ±µ∓ is
µµ
done with 267 hypotheses and no signal is observed. The upper limit is O(10−9) for an inflaton
with τ <100ps. The ULs as a function of the resonance mass are shown in Fig. 2 for several
χ
lifetimevaluesupto100ns.
4. DarkphotonsearchesattheNA48/2experiment
An extra U(1) symmetry is the simplest hidden sector model that can be introduced as an
explanationoftheexcessofpositronsobservedincosmicrays[22,21,23],orthemuongyromag-
neticratio(g−2)anomaly[24]. ItgivesrisetothedarkphotonA(cid:48),anewvectorgaugebosonthat
interacts with the visible sector through kinetic mixing with QED [25] and couples to the quarks
andleptonsinthesameway,withacouplingconstantε.
The same NA48/2 data sample is used to search for dark photons generated in π0 decays in
association with a SM photon. The expected branching ratio depending on ε and the dark photon
massm is[26]:
A(cid:48)
(cid:32) (cid:33)3
m2
B(π0→γA(cid:48))=2ε2 1− A(cid:48) B(π0→γγ). (4.1)
m2
π0
The sensitivity decreases as the dark photon mass approaches the π0 mass due to the kinematic
suppression factor and limits the mass range for this analysis. In such case, the dark photon is
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RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
L L
% C 10-5 % C 10-5
0 0
9 9
at at
µ±) 10-6 µ) ± 10-6 τ = 100 ns
π± π±
→ →
N4 N4
BR( 10-7 τ = 100 ns BR( 10-7 τ = 10 ns
× ×
) N4 ) N4
µ± µ± τ = 1 ns
→ 10-8 τ = 10 ns → 10-8
± K ± K
R( R( τ = 100 ps
B B
on 10-9 τ = 1 ns on 10-9
UL UL τ < 10 ps
τ = 100 ps
10-10 10-10
τ < 10 ps
260 280 300 320 340 360 380 260 280 300 320 340 360 380
Assumed N mass, MeV/c2 Assumed N mass, MeV/c2
4 4
L
% C 10-5
0
9
at
−µ) 10-6 τ = 100 ns
µ+
→
X
R( τ = 10 ns
B 10-7
×
X)
π→± 10-8 τ = 1 ns
± K
BR( τ = 100 ps
L on 10-9
U
τ < 10 ps
10-10
220 240 260 280 300 320 340
Assumed X mass, MeV/c2
Figure2: Obtainedupperlimitsat90%CLontheproductofbranchingfractionsasafunctionof
theresonancemassfordifferentlifetimeoftheresonantparticle. (a)B(K± →µ±N )×B(N →
4 4
π∓µ±)(b)B(K±→µ±N )×B(N →π±µ∓)(c)B(K±→π±N )×B(N →µ±µ∓).
4 4 4 4
belowthresholdforalldecaysintochargedSMfermionsandtheonlyaccessibleoneisA(cid:48)→e+e−.
Theexpectedtotaldecaywidththenreads[27]:
(cid:115)
1 4m2(cid:18) 2m2(cid:19)
Γ ≈Γ(A(cid:48)→e+e−)= αε2m 1− e 1+ e .
A(cid:48) 3 A(cid:48) m2 m2
A(cid:48) A(cid:48)
If ε2 > 10−7 and m > 10MeV/c2 the mean free path does not exceed 10cm and can be ne-
A(cid:48)
glected, and the dark photon is assumed to decay promptly. The searched decay chain is then
K± →π±π0 ,π0 →γA(cid:48) ,A(cid:48) →e+e− and the final state is therefore similar to the Dalitz decay of
theπ0,whichrepresentsanirreduciblebackground. Asecondselectionfocusedonthedecaychain
startingwiththeK±→π0µ±ν (K )decayisalsobuilt.
µ3
7
RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
4.1 Eventselection
Thelogicoftheeventsselectionissimilartotheπ0 onepresentedinsection2withonenotable
D
difference: the E/p based particle separation method is used and therefore all tracks should be in
theLKracceptanceandwellseparatedontheLKrplane. ThedistanceD betweenthetrackimpact
ij
points on the LKr are requested to be D >10cm for electron candidates and D >25cm for
ee eπ/µ
(cid:12) (cid:12)
electron to pion/muon candidates. The reconstructed masses should also satisfy (cid:12)Meeγ−mπ0(cid:12)<
8MeV/c2and|M −m |<20MeV/c2. FortheK therequirementonthetotalinvariantmass
π±π0 K µ3
is replaced by |M2 |<0.01(GeV/c2)2, where M2 =(P −P −P )2 is the squared missing
miss miss K µ π0
mass, P and P are the reconstructed momenta of the µ± and π0, and P is the nominal beam
µ π0 K
momentum.
Thetotalselectedsampleamountsto1.67×107fullyreconstructedπ0 candidates. Theoverall
D
acceptancesare3.82%forK and4.20%forK .
2π µ3
4.2 Searchfordarkphotonresonance
ThesamemassscanframeworkusingtheRolke-Lopezmethodasinsection3isusedtosearch
for narrow peaks in the reconstructed e+e− invariant mass spectrum M . The steps and width of
ee
the search windows are determined by the resolution σ(M ), which has been estimated from a
ee
K MCsampleandisapproximatelygivenbyσ(M )≈0.011×M . Themassstepforthescan
2πD ee ee
is set to 0.5σ(M ) rounded to the nearest multiple of 0.02MeV/c2. The window is centered on
ee
the searched dark photon mass with a width equal to 3σ(M ). A total of 404 m hypotheses are
ee A(cid:48)
testedintherange9MeV/c2≤m ≤120MeV/c2.
A(cid:48)
The90%CLlimitsareobtainedfromtherelation
B(π0→γA(cid:48))= NA(cid:48) (cid:2)B(K )A(K )+B(K )A(K )(cid:3)−1 ,
2π 2π µ3 µ3
N
K
where N is the number of dark photon candidates, N is the total number of kaon decays in the
A(cid:48) K
fiducial region, and B(K ),A(K ),B(K ) and A(K ) are the branching fraction and accep-
2π 2π µ3 µ3
tances of the K and K decays respectively. The largest uncertainty (3%) comes from the π0
2π µ3 D
branching fraction entering in the computation of N and is neglected. The 90% CL upper limits
K
ontheε2 mixingparameterarecalculatedfromeq. 4.1.
Nodarkphotonsignalisobservedinthescannedrange. Itconstitutesanimprovementonthe
existing limits in the range m ∈(9–70)MeV/c2. The sensitivity is limited by the irreducible π0
A(cid:48) D
background and the upper limits are 2–3 orders of magnitude above the single event sensitivity.
Theresultingexclusionlimitsassociatedtoconstraintsfromotherexperiments,asshowninFig.3,
completely rules out the dark photon as an explanation for the muon (g−2) problem within the
theoreticalassumptionsmadeintheanalysis.
Conclusions
The preliminary measurement of the electromagnetic transition form factor slope of the π0
using1.05×106π0→e+e−γ decaycollectedattheNA62experimentin2007–08isreported. The
obtainedresulta=(3.70±0.53 ±0.36 )×10−2isasignificantmeasurementofmorethan5σ
stat syst
ofapositiveslopeinthetime-liketransfermomentumregion.
8
RecentresultsfromNA48/2andNA62experimentsatCERN NicolasLurkin
ε2 KLOE
WASA
σ)
(3
−2)e
g
10-5 (
HADES X
E
P
(g−2) A
µ A1
10-6
BaBar
E774
NA48/2
10-7 E141
10 102
m (MeV/c2)
A’
Figure3: Upperlimitsat90%CLonthemixingparameterε2foreachdarkphotonmasshypothesis
comparedwithexclusionlimitssetbypreviousexperiments.
SearchesfortheLNVK±→π∓µ±µ± decayandresonancesinK±→πµµ decaysusingthe
2003–04 data sample collected at NA48/2 are also presented. No signals are observed. An upper
limitonthebranchingratiooftheLNVchannelissetat8.6×10−11,improvingthepreviousbest
limitbyanorderofmagnitude. UpperlimitsaresetontheproductsofbranchingratiosB(K±→
µ±N )B(N → π∓µ±), B(K± → µ±N )B(N → π±µ∓) and B(K± → π±χ)B(χ → µ+µ−)
4 4 4 4
as functions of the resonance mass and lifetime. These limits are in the range 10−9–10−10 for
resonancelifetimesbelow100ps.
Usingthesamedatasample,upperlimitsaresetonthemixingparameterε2 ofadarkphoton
A(cid:48). The dark photon is assumed to be produced in the decay π0 →γA(cid:48) and decays only into an
e+e− pair. Thelimitsareoftheorderof10−6 inthemassrangem ∈(9–70)MeV/c2, excluding
A(cid:48)
thisdarkphotonasanexplanationforthemuon(g−2)anomaly.
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9