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 Introduction
Fractional 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 distribution
with 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 fit
2001 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 section
fixed
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 correction
Standard 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 correction
up to 30%
correction

10. Line shape fit: results
Mf= 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 effect
Final 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 radiation
Correction 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 radiation
MC – data
comparison
at 1025 MeV
radiative return to f
events

16. MK single event resolution
Solve: 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 energy
Stable 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 uncertainties
Momentum 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 uncertainties
W 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 error
Statistical 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)