7
3.58 3.60 3.62 3.64 3.66 3.68 3.70
M (GeV/c2)
K s0K±π±
)2c/VeG(
200.0
/
stnevE
4000
3500
η c(2S) → K S0K±π± m3C (a)
η(2S) → K0K±π± 4C
c S 3000 ψ(2S) → K0K±π± m3C S
ψ(2S) → K0K±π± 4C 2500 S
2000
1500
1000
500
0
3.58 3.60 3.62 3.64 3.66 3.68 3.70
M
K+K π0
(GeV/c2)
)2c/VeG(
200.0
/
stnevE
C. ISR and FSR events from e+e− annihilation
We use data collected at √s = 3.65 GeV with a luminosity of 401.00 4.01 pb−1 [15] to estimate the
backgrounds from th± e continuum processes e+e−
γ KK¯π and e+e− γ KK¯π. After event sele→ c- FSR ISR tion, we shift the mass→ of KK¯π (M ) to 3.686 GeV
shifted
by the rule:
M shifted =a ×(M KK¯π −m 0)+m 0, (1)
where a = (3.686 m )/(3.65 m ) with m being the
0 0 0 massthresholdfor− generatingK− K¯π. Wethennormalized
the number of continuum backgrounds according to the
crosssectionsandthe integratedluminositiesofthe data
samplesat√s=3.65GeV andattheψ(3686)peak[15].
4000
We determine the number of continuum events after the
η(2S) → K+K π0 m4C
3500 ηc (2S) → K+K π0 5C (b) selection in the ψ(3686) data sample to be 516 (360) in
c the γK0K±π∓ (γK+K−π0) final state.
3000 ψ(2S) → K+K π0 m4C S
ψ(2S) → K+K π0 5C
2500
2000 V. BRANCHING FRACTION
DETERMINATION
1500
1000 We perform a simultaneous fit to the mass spectra of
KK¯π in the range of (3.45 3.70) GeV/c2 to extract
500
−
the yield of signal events and the mass and the width of
0
the η (2S), as shown in Fig. 2. There are χ and χ c c1 c2
signals besides the η (2S) signals. We use the following
c
line-shape of the η (2S) produced by an M1 transition:
c
FIG.1. Acomparisonbetweenthe4C (5C)andthemodified (E γ3 ×BW(M KK¯π) ×f d(E γ) ×ε(M KK¯π)) ⊗DGaus, (2)
3C (4C) kinematic fits of the MC samples. (a) and (b) are
the invariant mass distributions of K S0K±π∓ and K+K−π0 where E γ = (m2 ψ(3686) −M K2 K¯π)/(2m ψ(3686)) is the en-
from ηc(2S) or ψ(3686) decays, respectively. ergy of the transition photon in the rest frame of the
ψ(3686), BW is a Breit-Wigner function with floating
width and mean, f (E ) = E2/(E E + (E E )2)
(1.53 0.05) and (1.34 0.12) from two different con- is a damping functid on γ proposed0 byγ th0 e KEDγ R− exp0 eri-
trol sa± mples. We tune± the ratio of ψ(3686) KK¯π ment[28]tosuppressthedivergingtailraisedbytheterm
c ψa on (rd 3d 6i 8ψ n 6g( )3 t6 o86 f () F γS→ R t )γ o KFS d KR ¯eK πte ,rK¯ m wπ hin icein hth wth e ile lM bM K eC K u¯π ss ei dm linu te ol -a→ s dt hi eo a sn p ce ria boc e- f o inf gE tγ3 hw ei mth eaE n0 e= ne( rm gy2 ψ( o3 f68 t6 h) e− tm ra2 η nc s( i2 tS i) o) n/( p2 hm otψ o(3 n6 ,86 ε) () Md Ken K¯o πt )-
→ FSR isthe efficiencyasafittedpolynomialfunctionofM KK¯π
the corresponding backgroundcontribution in the fit.
from the MC simulation, DGaus is a double Gaussian
function, i.e. f Gaus(m ,σ )+(1 f) Gaus(m ,σ ),
1 1 2 2
· − ·
that is utilized to describe the resolution. In fact, there
B. ψ(3686) π0KK¯π are two types of resolutions that need to be taken into
→
account. The first type is based on the detector resolu-
To account for ψ(3686) π0KK¯π backgrounds, we tion,whichisrepresentedbyadoubleGaussianfunction.
→
use the same data-drivenmethod as applied in Ref. [13]. The parameters of this function are directly determined
We first select ψ(3686) π0KK¯π events in data and throughMCsimulation. Thesecondtypeofresolutionis
→
then estimate their rate of contamination in the M KK¯π basedonthediscrepancybetweenthedataandMCsimu-
spectrum by exposing the selected events to the γKK¯π lation, and is represented by a single Gaussian function.
selection criteria and correcting with efficiencies deter- The parameters of this function are obtained through
mined from MC simulation. a linear extrapolation from those of χ . To consider
c1/2
This background contributes a smooth component both types of resolutions, a new double Gaussian func-
around the χ mass region with a small tail in the tion, DGaus, is constructed by convoluting the original
c1,2
η (2S) signal region. We fit these backgrounds with a double Gaussianfunction with the single Gaussianfunc-
c
Novosibirsk function [27], and fix its shape and size in tion. All parameters of DGaus are then determined and
the M KK¯π spectra fits. fixed during the fitting process.