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Measurement of the neutral kaon mass Using Ks-> p + p - events*. M. Antonelli M. Dreucci 2 nd KLOE Physics workshop (Otranto). Introduction center-of-mass energy determination kaon mass measurement systematics conclusions. *approval for publication. Introduction.

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slide1

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

slide2

Introduction

Fractional accuracy on MK ~ 6 x 10-5 (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 ~ b2dPK/PK ~ DM dPK/PK ~ 0.05 dPK/PK

DM = W -2 MK ~ Mf - 2 MK ~ 26 MeV

slide3

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)
slide4

Determination of W

e+ e- invariant mass distribution

  • e+ e- invariant mass
  • with 60o < qmin< 90o
  • Fit with numerical
  • function
  • from BHABHAYAGA
  • Typical accuracy
  • ~ 2 – 50 keV
  • 3 keV @ 50 nb-1

q cut stability studied

slide5

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

Calibration of W: line-shape fit

  • 2001 energy scan:
  • about 500 nb-1 11 energy points (1014 – 1025) MeV
  • KLKS cross section from KS -> p+p-
  • Luminosity from VLAB
slide6

Theoretical cross section

r term

f term

w term

{

fixed

Phase space:

Propagator:

Gv(s) energy dependent width

slide7

Theoretical cross section: r w terms

s/s(no V)

V= r,w

Up to 10%

contributions

W(MeV)

slide8

Initial state radiation correction

Standard method:

Radiator

  • Radiator from Nicrosini et al. 2ndDAFNE handbook
  • numerical integration with VEGAS
  • Fadeav radiator used for comparison (no differences)
  • other integration codes used REMT and Capon code
slide10

Line shape fit: results

Mf= 1019.3290.011 MeV/c2

W -> W Mf(CMD-2)/ Mf

Mf(CMD-2)=

1019.504 0.011  0.033 MeV/c2

slide11

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

slide12

Measurement of WKK

MK(MeV)

Calibration constant

about 2

W(MeV)

slide13

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
slide14

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

slide15

Initial state radiation

MC – data

comparison

at 1025 MeV

radiative return to f

events

slide16

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

slide17

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=497.5830.005

normalized RMS=1.3

slide18

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 2x10-4 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(belowf)

+ correction is small (below f) - 20 keV

slide19

Systematic uncertainties

W calibration error:

arises from

dMf= 0.011 MeV/c2

dMf(CMD-2)=0.011  0.033 MeV/c2

dMK ~ 18 keV

Error treated as uncorrelateddMK(tot)= 20 keV

MK=497.583 0.005 0.020

slide21

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?

slide22

f mass in PDG

Dominated by a masurements by a fixed target experiment (invariant mass reconstruction)