1 Measurement of the neutral kaon mass Using Ks-> p+p- events*M. Antonelli M. Dreucci 2nd KLOE Physics workshop (Otranto) Introduction center-of-mass energy determination kaon mass measurement systematics conclusions *approval for publication
2 DM = W -2 MK ~ Mf - 2 MK ~ 26 MeV IntroductionFractional accuracy on MK ~ 6 x (PDG) not easy to achieve with invariant mass reconstruction But… if the center-of-mass energy W ~ EKL+EKS ~ 2EK is precisely determined MK2=W2/4- PK2 momentum calibration less important dMK/MK ~ b2 dPK/PK ~ DM dPK/PK ~ 0.05 dPK/PK DM = W -2 MK ~ Mf - 2 MK ~ 26 MeV
3 2001 energy scan Introduction 2 Center-of-mass energy:bhabha events (e+e- invariant mass) calibration with f mass from line shape fit to e+e- -> f -> KLKS 2001 energy scan ISR effect: KLKS invariant mass WKK(MK) W WKK f(W) =W f(W) from theory (QED)
4 Determination of W e+ e- invariant mass distributionwith 60o < qmin< 90o Fit with numerical function from BHABHAYAGA Typical accuracy ~ 2 – 50 keV 3 50 nb-1 q cut stability studied
5 Calibration of W: line-shape fit2001 energy scan: about 500 nb energy points (1014 – 1025) MeV KLKS cross section from KS -> p+p- Luminosity from VLAB
6 { r term f term w term Theoretical cross sectionfixed Phase space: Propagator: Gv(s) energy dependent width
7 s/s(no V) Theoretical cross section: r w terms V= r,w Up to 10%contributions W(MeV)
8 Initial state radiation correctionStandard method: Radiator Radiator from Nicrosini et al. 2nd DAFNE handbook numerical integration with VEGAS Fadeav radiator used for comparison (no differences) other integration codes used REMT and Capon code
9 Initial state radiation correctionup to 30% correction
10 Line shape fit: resultsMf= 0.011 MeV/c2 W -> W Mf(CMD-2)/ Mf Mf(CMD-2)= 0.011 MeV/c2
11 Measurement of WKK KLKS invariant mass WKK(MK) from KS-> p+ p- events WKK =( 2MK2 + 2EKSEKL –2PKLPKS)1/2 PKS from pion momenta; EKS=(PKS2+MK2)1/2 PKL= Pf-PKS ; EKS=(PKS2+MK2)1/2 Run by run average Pf from bhabha * * About 122/10002 correction
12 Measurement of WKK MK(MeV) Calibration constant about 2 W(MeV)
13 g by fK(W) ( W dependence trough s(w)) Initial state radiation effectFinal state KL g Undetected radiated photon (mostly collinear to beams) KS Center-of-mass energy W reduced to WKK by fK(W) ( W dependence trough s(w)) + additional “beam energy spread” Evaluated with: s(s) + H(s,s’) + beam energy spread convolution full MC simulation: all above + radiation from both beams + detector effects
14 Initial state radiationCorrection function fK(W)=W/WKK Very small below f peak ~40 KeV (~20 for MK) full simulation simple convolution Larger above f (radiative return events) ~ 200 KeV +/- half correction
15 Initial state radiationMC – data comparison at 1025 MeV radiative return to f events
16 MK single event resolutionSolve: WKK(MK)fK(W)=W Event by event MC prediction: ~370 KeV PK resolution ~220 KeV beam energy spread ~100 KeV ISR spread
17 MK run by run results vs center-of-mass energyStable vs W but just above Mf (rad. returns) Average for W< 1025 MeV (smaller ISR corrections) MK= 0.005 normalized RMS=1.3
18 Systematic uncertaintiesMomentum calibration: evaluated by forcing a dp/p in the analysis dMK/MK = 0.06dp/p (very close to the expected) p calibration at about 2x dMK ~ 6 keV ISR correction: full a2 correction included higher order terms < a2 constant (W) terms dMK ~ 7 keV Checks with other radiators + MK(above f) consistent with MK(below f) + correction is small (below f) - 20 keV
19 dMf(CMD-2)=0.011 0.033 MeV/c2 Systematic uncertaintiesW calibration error: arises from dMf= MeV/c2 dMf(CMD-2)=0.011 MeV/c2 dMK ~ 18 keV Error treated as uncorrelated dMK(tot) = 20 keV MK= 0.005 0.020
20 Comparison with other measurements
21 Conclusions K0 mass measurement with competitive errorStatistical error not a problem: many events + amazing resolution ~400 keV Systematic error dominated by W calibration ~20 keV 3 measurements with about 30 keV errors in ~100 keV MK ?
22 f mass in PDG Dominated by a masurements by a fixed target experiment (invariant mass reconstruction)