Measurement of the branching fractions of D-s(+) -> eta ' X and D-s(+) -> eta 'rho(+) in e(+)e(-) -> Ds+Ds-

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

branching

fractions

of

D

+

_s

→

η

X and

D

+

_s

→

η

ρ

+

in

e

+

e

−

→

D

+

_s

D

−

_s

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

6

,

X.C. Ai

a

,

O. Albayrak

e

,

M. Albrecht

d

,

D.J. Ambrose

av

,

A. Amoroso

az

,

bb

,

F.F. An

a

,

Q. An

aw

,

1

,

J.Z. Bai

a

,

R. Baldini Ferroli

t

,

Y. Ban

ag

,

D.W. Bennett

s

,

J.V. Bennett

e

,

M. Bertani

t

,

D. Bettoni

v

,

J.M. Bian

au

,

F. Bianchi

az

,

bb

,

E. Boger

y

,

4

,

I. Boyko

y

,

R.A. Briere

e

,

H. Cai

bd

,

X. Cai

a

,

1

,

O. Cakir

ap

,

2

,

A. Calcaterra

t

,

G.F. Cao

a

,

S.A. Cetin

aq

,

J.F. Chang

a

,

1

,

G. Chelkov

y

,

4

,

5

,

G. Chen

a

,

H.S. Chen

a

,

H.Y. Chen

b

,

J.C. Chen

a

,

M.L. Chen

a

,

1

,

S.J. Chen

ae

,

X. Chen

a

,

1

,

X.R. Chen

ab

,

Y.B. Chen

a

,

1

,

H.P. Cheng

q

,

X.K. Chu

ag

,

G. Cibinetto

v

,

H.L. Dai

a

,

1

,

J.P. Dai

aj

,

A. Dbeyssi

n

,

D. Dedovich

y

,

Z.Y. Deng

a

,

A. Denig

x

,

I. Denysenko

y

,

M. Destefanis

az

,

bb

,

F. De Mori

az

,

bb

,

Y. Ding

ac

,

C. Dong

af

,

J. Dong

a

,

1

,

L.Y. Dong

a

,

M.Y. Dong

a

,

1

,

S.X. Du

bf

,

P.F. Duan

a

,

E.E. Eren

aq

,

J.Z. Fan

ao

,

J. Fang

a

,

1

,

S.S. Fang

a

,

X. Fang

aw

,

1

,

Y. Fang

a

,

L. Fava

ba

,

bb

,

F. Feldbauer

x

,

G. Felici

t

,

C.Q. Feng

aw

,

1

,

E. Fioravanti

v

,

M. Fritsch

n

,

x

,

C.D. Fu

a

,

Q. Gao

a

,

X.Y. Gao

b

,

Y. Gao

ao

,

Z. Gao

aw

,

1

,

I. Garzia

v

,

C. Geng

aw

,

1

,

K. Goetzen

j

,

W.X. Gong

a

,

1

,

W. Gradl

x

,

M. Greco

az

,

bb

,

M.H. Gu

a

,

1

,

Y.T. Gu

l

,

Y.H. Guan

a

,

A.Q. Guo

a

,

L.B. Guo

ad

,

Y. Guo

a

,

Y.P. Guo

x

,

Z. Haddadi

aa

,

A. Hafner

x

,

S. Han

bd

,

Y.L. Han

a

,

X.Q. Hao

o

,

F.A. Harris

at

,

K.L. He

a

,

Z.Y. He

af

,

T. Held

d

,

Y.K. Heng

a

,

1

,

Z.L. Hou

a

,

C. Hu

ad

,

H.M. Hu

a

,

J.F. Hu

az

,

bb

,

T. Hu

a

,

1

,

Y. Hu

a

,

G.M. Huang

f

,

G.S. Huang

aw

,

1

,

H.P. Huang

bd

,

J.S. Huang

o

,

X.T. Huang

ai

,

Y. Huang

ae

,

T. Hussain

ay

,

Q. Ji

a

,

Q.P. Ji

af

,

X.B. Ji

a

,

X.L. Ji

a

,

1

,

L.L. Jiang

a

,

L.W. Jiang

bd

,

X.S. Jiang

a

,

1

,

X.Y. Jiang

af

,

J.B. Jiao

ai

,

Z. Jiao

q

,

D.P. Jin

a

,

1

,

S. Jin

a

,

T. Johansson

bc

,

A. Julin

au

,

N. Kalantar-Nayestanaki

aa

,

X.L. Kang

a

,

X.S. Kang

af

,

M. Kavatsyuk

aa

,

B.C. Ke

e

,

P. Kiese

x

,

R. Kliemt

n

,

B. Kloss

x

,

O.B. Kolcu

aq

,

9

,

B. Kopf

d

,

M. Kornicer

at

,

W. Kühn

z

,

A. Kupsc

bc

,

J.S. Lange

z

,

M. Lara

s

,

P. Larin

n

,

C. Leng

bb

,

C. Li

bc

,

C.H. Li

a

,

Cheng Li

aw

,

1

,

D.M. Li

bf

,

F. Li

a

,

1

,

G. Li

a

,

H.B. Li

a

,

J.C. Li

a

,

Jin Li

ah

,

K. Li

m

,

K. Li

ai

,

Lei Li

c

,

P.R. Li

as

,

T. Li

ai

,

W.D. Li

a

,

W.G. Li

a

,

X.L. Li

ai

,

X.M. Li

l

,

X.N. Li

a

,

1

,

X.Q. Li

af

,

Z.B. Li

an

,

H. Liang

aw

,

1

,

Y.F. Liang

al

,

Y.T. Liang

z

,

G.R. Liao

k

,

D.X. Lin

n

,

B.J. Liu

a

,

C.X. Liu

a

,

F.H. Liu

ak

,

Fang Liu

a

,

Feng Liu

f

,

H.B. Liu

l

,

H.H. Liu

p

,

H.H. Liu

a

,

H.M. Liu

a

,

J. Liu

a

,

J.B. Liu

aw

,

1

,

J.P. Liu

bd

,

J.Y. Liu

a

,

K. Liu

ao

,

K.Y. Liu

ac

,

L.D. Liu

ag

,

P.L. Liu

a

,

∗

,

1

,

Q. Liu

as

,

S.B. Liu

aw

,

1

,

X. Liu

ab

,

X.X. Liu

as

,

Y.B. Liu

af

,

Z.A. Liu

a

,

1

,

Zhiqiang Liu

a

,

Zhiqing Liu

x

,

H. Loehner

aa

,

X.C. Lou

a

,

1

,

8

,

H.J. Lu

q

,

J.G. Lu

a

,

1

,

R.Q. Lu

r

,

Y. Lu

a

,

Y.P. Lu

a

,

1

,

C.L. Luo

ad

,

M.X. Luo

be

,

T. Luo

at

,

X.L. Luo

a

,

1

,

M. Lv

a

,

X.R. Lyu

as

,

F.C. Ma

ac

,

H.L. Ma

a

,

L.L. Ma

ai

,

Q.M. Ma

a

,

T. Ma

a

,

X.N. Ma

af

,

X.Y. Ma

a

,

1

,

F.E. Maas

n

,

M. Maggiora

az

,

bb

,

Y.J. Mao

ag

,

Z.P. Mao

a

,

S. Marcello

az

,

bb

,

J.G. Messchendorp

aa

,

J. Min

a

,

1

,

T.J. Min

a

,

R.E. Mitchell

s

,

X.H. Mo

a

,

1

,

Y.J. Mo

f

,

C. Morales Morales

n

,

K. Moriya

s

,

N.Yu. Muchnoi

i

,

6

,

H. Muramatsu

au

,

Y. Nefedov

y

,

F. Nerling

n

,

I.B. Nikolaev

i

,

6

,

Z. Ning

a

,

1

,

S. Nisar

h

,

S.L. Niu

a

,

1

,

X.Y. Niu

a

,

S.L. Olsen

ah

,

Q. Ouyang

a

,

1

,

S. Pacetti

u

,

P. Patteri

t

,

M. Pelizaeus

d

,

H.P. Peng

aw

,

1

,

K. Peters

j

,

J. Pettersson

bc

,

J.L. Ping

ad

,

R.G. Ping

a

,

R. Poling

au

,

V. Prasad

a

,

Y.N. Pu

r

,

M. Qi

ae

,

S. Qian

a

,

1

,

C.F. Qiao

as

,

L.Q. Qin

ai

,

N. Qin

bd

,

X.S. Qin

a

,

Y. Qin

ag

,

Z.H. Qin

a

,

1

,

J.F. Qiu

a

,

K.H. Rashid

ay

,

C.F. Redmer

x

,

H.L. Ren

r

,

M. Ripka

x

,

G. Rong

a

,

Ch. Rosner

n

,

X.D. Ruan

l

,

http://dx.doi.org/10.1016/j.physletb.2015.09.059

(2)

V. Santoro

v

,

A. Sarantsev

y

,

7

,

M. Savrié

w

,

K. Schoenning

bc

,

S. Schumann

x

,

W. Shan

ag

,

M. Shao

aw

,

1

,

C.P. Shen

b

,

P.X. Shen

af

,

X.Y. Shen

a

,

H.Y. Sheng

a

,

W.M. Song

a

,

X.Y. Song

a

,

S. Sosio

az

,

bb

,

S. Spataro

az

,

bb

,

G.X. Sun

a

,

J.F. Sun

o

,

S.S. Sun

a

,

Y.J. Sun

aw

,

1

,

Y.Z. Sun

a

,

Z.J. Sun

a

,

1

,

Z.T. Sun

s

,

C.J. Tang

al

,

X. Tang

a

,

I. Tapan

ar

,

E.H. Thorndike

av

,

M. Tiemens

aa

,

M. Ullrich

z

,

I. Uman

aq

,

G.S. Varner

at

,

B. Wang

af

,

B.L. Wang

as

,

D. Wang

ag

,

D.Y. Wang

ag

,

K. Wang

a

,

1

,

L.L. Wang

a

,

L.S. Wang

a

,

M. Wang

ai

,

P. Wang

a

,

P.L. Wang

a

,

S.G. Wang

ag

,

W. Wang

a

,

1

,

X.F. Wang

ao

,

Y.D. Wang

n

,

Y.F. Wang

a

,

1

,

Y.Q. Wang

x

,

Z. Wang

a

,

1

,

Z.G. Wang

a

,

1

,

Z.H. Wang

aw

,

1

,

Z.Y. Wang

a

,

T. Weber

x

,

D.H. Wei

k

,

J.B. Wei

ag

,

P. Weidenkaff

x

,

S.P. Wen

a

,

U. Wiedner

d

,

M. Wolke

bc

,

L.H. Wu

a

,

Z. Wu

a

,

1

,

L.G. Xia

ao

,

Y. Xia

r

,

D. Xiao

a

,

Z.J. Xiao

ad

,

Y.G. Xie

a

,

1

,

Q.L. Xiu

a

,

1

,

G.F. Xu

a

,

L. Xu

a

,

Q.J. Xu

m

,

Q.N. Xu

as

,

X.P. Xu

am

,

L. Yan

aw

,

1

_,

_{W.B. Yan}

aw

,

1

_,

_{W.C. Yan}

aw

,

1

_,

_{Y.H. Yan}

r

_,

_{H.J. Yang}

aj

_,

_{H.X. Yang}

a

_,

L. Yang

bd

,

Y. Yang

f

,

Y.X. Yang

k

,

H. Ye

a

,

M. Ye

a

,

1

,

M.H. Ye

g

,

J.H. Yin

a

,

B.X. Yu

a

,

1

,

C.X. Yu

af

,

H.W. Yu

ag

,

J.S. Yu

ab

,

C.Z. Yuan

a

,

W.L. Yuan

ae

,

Y. Yuan

a

,

A. Yuncu

aq

,

3

,

A.A. Zafar

ay

,

A. Zallo

t

,

Y. Zeng

r

,

B.X. Zhang

a

,

B.Y. Zhang

a

,

1

,

C. Zhang

ae

,

C.C. Zhang

a

,

D.H. Zhang

a

,

H.H. Zhang

an

,

H.Y. Zhang

a

,

1

,

J.J. Zhang

a

,

J.L. Zhang

a

,

J.Q. Zhang

a

,

J.W. Zhang

a

,

1

,

J.Y. Zhang

a

,

J.Z. Zhang

a

,

K. Zhang

a

,

L. Zhang

a

,

S.H. Zhang

a

,

X.Y. Zhang

ai

,

Y. Zhang

a

,

Y.N. Zhang

as

,

Y.H. Zhang

a

,

1

,

Y.T. Zhang

aw

,

1

,

Yu Zhang

as

,

Z.H. Zhang

f

,

Z.P. Zhang

aw

,

Z.Y. Zhang

bd

,

G. Zhao

a

,

J.W. Zhao

a

,

1

_,

_{J.Y. Zhao}

a

_,

_{J.Z. Zhao}

a

,

1

_,

_{Lei Zhao}

aw

,

1

_,

_{Ling Zhao}

a

_,

M.G. Zhao

af

,

Q. Zhao

a

,

Q.W. Zhao

a

,

S.J. Zhao

bf

,

T.C. Zhao

a

,

Y.B. Zhao

a

,

1

,

Z.G. Zhao

aw

,

1

,

A. Zhemchugov

y

,

4

,

B. Zheng

ax

,

J.P. Zheng

a

,

1

,

W.J. Zheng

ai

,

Y.H. Zheng

as

,

B. Zhong

ad

,

L. Zhou

a

,

1

,

Li Zhou

af

,

X. Zhou

bd

,

X.K. Zhou

aw

,

1

,

X.R. Zhou

aw

,

1

,

X.Y. Zhou

a

,

K. Zhu

a

,

K.J. Zhu

a

,

1

,

S. Zhu

a

,

X.L. Zhu

ao

,

Y.C. Zhu

aw

,

1

,

Y.S. Zhu

a

,

Z.A. Zhu

a

,

J. Zhuang

a

,

1

,

L. Zotti

az

,

bb

,

B.S. Zou

a

,

J.H. Zou

a

a_Institute_of_High_Energy_Physics,_Beijing_100049,_People’s_Republic_of_China b_Beihang_University,_Beijing_100191,_People’s_Republic_of_China

c_Beijing_Institute_of_{Petrochemical}_Technology,_Beijing_102617,_People’s_Republic_of_China d_Bochum_{Ruhr-University,}_D-44780_Bochum,_Germany

e_Carnegie_Mellon_University,_Pittsburgh,_{PA 15213,}_USA

f_Central_China_Normal_University,_Wuhan_430079,_People’s_Republic_of_China

g_China_Center_of_Advanced_Science_and_Technology,_Beijing_100190,_People’s_Republic_of_China

h_COMSATS_Institute_of_Information_Technology,_Lahore,_Defence_Road,_Off_Raiwind_Road,₅₄₀₀₀_Lahore,_Pakistan i_G.I._Budker_Institute_of_Nuclear_Physics_SB_RAS_(BINP),_Novosibirsk_630090,_Russia

j_GSI_{Helmholtzcentre}_for_Heavy_Ion_Research_GmbH,_D-64291_Darmstadt,_Germany k_Guangxi_Normal_University,_Guilin_541004,_People’s_Republic_of_China

l_GuangXi_University,_Nanning_530004,_People’s_Republic_of_China

m_Hangzhou_Normal_University,_Hangzhou_310036,_People’s_Republic_of_China n_Helmholtz_Institute_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany o_Henan_Normal_University,_Xinxiang_453007,_People’s_Republic_of_China

p_Henan_University_of_Science_and_Technology,_Luoyang_471003,_People’s_Republic_of_China q_Huangshan_College,_Huangshan_245000,_People’s_Republic_of_China

r_Hunan_University,_Changsha_410082,_People’s_Republic_of_China s_Indiana_University,_Bloomington,_{IN 47405,}_USA

t_INFN_Laboratori_Nazionali_di_Frascati,_I-00044,_Frascati,_Italy u_INFN_and_University_of_Perugia,_I-06100,_Perugia,_Italy v_INFN_Sezione_di_Ferrara,_I-44122,_Ferrara,_Italy w_University_of_Ferrara,_I-44122,_Ferrara,_Italy

x_Johannes_Gutenberg_University_of_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany y_Joint_Institute_for_Nuclear_Research,₁₄₁₉₈₀_Dubna,_Moscow_region,_Russia

z_Justus_Liebig_University_Giessen,_II._{Physikalisches}_Institut,_{Heinrich-Buff-Ring}_16,_D-35392_Giessen,_Germany aa_KVI-CART,_University_of_Groningen,_NL-9747_AA_Groningen,_The_Netherlands

ab_Lanzhou_University,_Lanzhou_730000,_People’s_Republic_of_China ac_Liaoning_University,_Shenyang_110036,_People’s_Republic_of_China ad_Nanjing_Normal_University,_Nanjing_210023,_People’s_Republic_of_China ae_Nanjing_University,_Nanjing_210093,_People’s_Republic_of_China af_Nankai_University,_Tianjin_300071,_People’s_Republic_of_China ag_Peking_University,_Beijing_100871,_People’s_Republic_of_China ah_Seoul_National_University,_Seoul,_{151-747, Republic}_of_Korea ai_Shandong_University,_Jinan_250100,_People’s_Republic_of_China

aj_Shanghai_Jiao_Tong_University,_Shanghai_200240,_People’s_Republic_of_China ak_Shanxi_University,_Taiyuan_030006,_People’s_Republic_of_China

al_Sichuan_University,_Chengdu_610064,_People’s_Republic_of_China am_Soochow_University,_Suzhou_215006,_People’s_Republic_of_China an_Sun_Yat-Sen_University,_Guangzhou_510275,_People’s_Republic_of_China ao_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China ap_Istanbul_Aydin_University,₃₄₂₉₅_Sefakoy,_Istanbul,_Turkey aq_Dogus_University,₃₄₇₂₂_Istanbul,_Turkey

(3)

ar_Uludag_University,₁₆₀₅₉_Bursa,_Turkey

as_University_of_Chinese_Academy_of_Sciences,_Beijing_100049,_People’s_Republic_of_China at_University_of_Hawaii,_Honolulu,_{HI 96822,}_USA

au_University_of_Minnesota,_Minneapolis,_{MN 55455,}_USA av_University_of_Rochester,_Rochester,_{NY 14627,}_USA

aw_University_of_Science_and_Technology_of_China,_Hefei_230026,_People’s_Republic_of_China ax_University_of_South_China,_Hengyang_421001,_People’s_Republic_of_China

ay_University_of_the_Punjab,_Lahore_54590,_Pakistan az_University_of_Turin,_I-10125,_Turin,_Italy

ba_University_of_Eastern_Piedmont,_I-15121,_Alessandria,_Italy bb_INFN,_I-10125,_Turin,_Italy

bc_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden bd_Wuhan_University,_Wuhan_430072,_People’s_Republic_of_China be_Zhejiang_University,_Hangzhou_310027,_People’s_Republic_of_China bf_Zhengzhou_University,_Zhengzhou_450001,_People’s_Republic_of_China

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received30June2015

Receivedinrevisedform22September 2015

Accepted23September2015 Availableonline30September2015 Editor:L.Rolandi

Keywords:

BESIII

Ds

Branchingfractions

We study D+s decays to ﬁnal states involving the

η

with a 482 pb−1 data sample collected at

√

s=4.009 GeV with the BESIII detector at the BEPCIIcollider. We measure the branching fractions

B(D+_s _→

η

X)= (8.8_±1.8_±0.5)% and_B(D+_s _→

η

ρ

+)= (5.8_±1.4_±0.4)% wheretheﬁrstuncertainty isstatisticalandthesecondissystematic.Inaddition,weestimateanupperlimitonthenon-resonant branchingratio B(D+s →

η

π

+

π

0)<5.1% atthe90% conﬁdencelevel.Ourresults areconsistentwith

CLEO’s recentmeasurements and helptoresolvethe disagreementbetweenthetheoretical prediction andCLEO’spreviousmeasurementofB(D+s →

η

ρ

+).

1. Introduction

Hadronic weak decays of charmedmesons provide important

informationon ﬂavormixing, CP violation,andstrong-interaction effects [1]. There are several proposed QCD-derived theoretical

approaches to handle heavy meson decays [2–6]. However, in

contrast to B mesons, theoretical treatment of charmed mesons suffers from large uncertainties since the c quark mass is too lightforgoodconvergenceoftheheavy quark expansionbutstill much too massive for chiral perturbative theory to be applica-ble. Currently, theoretical results for the partial decay widths of ground-state charmed mesons agree fairly well with experimen-tal results. However, there exists a contradiction concerning the branching fraction

B(

D+_s

→

η

ρ

+

)

. CLEO reported

(

12

.

5

±

2

.

2

)

%

[7],while ageneralizedfactorizationmethod[8]predictsa factor offour less,

(

3

.

0

±

0

.

5

)

%. Summing the large experimental value of

B(

D+_s

→

η

ρ

+

)

with other exclusive rates involving

η

gives

B(

D+_s

→

η

X

)

= (

18

.

6

±

2

.

3

)

% [9], while the measured inclusive decayrate

B(

D+_s

→

η

X

)

ismuchlower,

(

11

.

7

±

1

.

8

)

%[10],where

X denotes all possible combinations of states. Therefore, further

experimental studyofthe

η

decaymodesis ofgreatimportance forresolvingthisconﬂict.

*

Correspondingauthor.

E-mailaddress:liupl@ihep.ac.cn(P.L. Liu).

1 _Also _at _State _Key _Laboratory _of _Particle _Detection _and _Electronics, _Beijing 100049,Hefei230026,People’sRepublicofChina.

2 _Also_at_Ankara_University,₀₆₁₀₀_Tandogan,_Ankara,_Turkey. 3 _Also_at_Bogazici_University,₃₄₃₄₂_Istanbul,_Turkey.

4 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia. 5 _Also_at_the _Functional_Electronics_Laboratory,_Tomsk _State_University,_Tomsk, 634050,Russia.

6 _Also_at_the_Novosibirsk_State_University,_Novosibirsk,_630090,_Russia. 7 _Also_at_the_NRC_“Kurchatov_{Institute”,}_PNPI,_188300,_Gatchina,_Russia. 8 _Also_at_University_of_Texas_at_Dallas,_Richardson,_{TX 75083,}_USA. 9 _Currently_at_Istanbul_Arel_University,₃₄₂₉₅_Istanbul,_Turkey.

Recently, CLEO reportedan updated measurementof

B(

D+_s

→

η

π

+

π

0

₎

_{= (}

₅

_.

₆

_±

₀

_.

₅

_±

₀

_.

₆

₎

_% _[11]_; _this _includes _the _resonant

process

η

ρ

+.This is much smaller than the previous result [7]. In thispaper, we report the measurements of the inclusiverate

B(

D+_s

→

η

X

)

andtheexclusiverate

B(

D+_s

→

η

ρ

+

)

attheBESIII experiment.

2. Datasampleanddetector

The analysis is carried out using a sample of 482 pb−1 [12] e+e−collisiondatacollectedwiththeBESIIIdetectoratthecenter ofmassenergy

√

s

=

4

.

009 GeV.

TheBESIIIdetector,asdescribedindetailinRef.[13],hasa geo-metricalacceptanceof93%ofthesolidangle.Asmall-cell helium-basedmaindriftchamber(MDC)immersedina1 Tmagneticﬁeld measures the momentum of charged particles with a resolution of0.5%at1 GeV

/

c.Theelectromagneticcalorimeter(EMC)detects photons with a resolution of 2.5% (5%) at an energy of 1 GeV in the barrel (end cap) region. A time-of-flight system(TOF) as-sistsinparticleidentification(PID)withatimeresolutionof80 ps (110 ps)inthebarrel(endcap)region.OurPIDmethodscombine the TOF information with the specific energy loss (dE

/

dx) mea-surements of charged particles in the MDC to forma likelihood

L(

h

)(

h

=

π

,

K

)

foreachhadron(h)hypothesis.

A geant4-based [14] Monte Carlo (MC) simulation software, whichincludesthegeometricdescriptionoftheBESIIIdetectorand thedetectorresponse,isusedtooptimizetheeventselection cri-teria, determinethedetectioneﬃciencyandestimatebackground contributions.Thesimulationincludesthebeamenergyspreadand initial-state radiation (ISR), implemented with kkmc [15].

Allow-ing for a maximum ISR photon energy of 72 MeV, open charm

processes are simulated from D+_sD−_s threshold at 3.937 GeV to the center-of-mass energy 4.009 GeV. Cross sections have been takenfromRef.[16].Forbackgroundcontributionstudiesandthe validation oftheanalysisprocedure, aninclusiveMC sample cor-responding to an integrated luminosity of 10 fb−1 is analyzed.

(4)

In addition to the open charm modes, this sample includes ISR production, continuum light quark production and QED events.

The known decay modes are generated with evtgen [17] with

branching fractions setto the world average values [9], and the remainingunknowneventsaregeneratedwith lundcharm[18]. 3. Dataanalysis

3.1.Measurementof

B(

D+_s

→

η

X

)

Fordatatakenat4.009 GeV,energyconservationprohibitsany additionalhadronsaccompanyingtheproductionofa D+_sD−_s pair. Followingatechnique ﬁrstintroducedby theMARK III Collabora-tion

[19]

, theinclusivedecayrateof D+s

→

η

X ismeasured. We

selectsingletag(ST)eventsinwhichatleastone D+_s orD−_s can-didateisreconstructed,anddoubletag(DT)eventsinwhichboth

D+_s and D−_s are reconstructed.To illustrate themethod, we take theSTmode D−_s

→

α

andthesignal mode D+_s

→

η

X for exam-ple.The

η

candidates inthesignal modeare reconstructedfrom thedecaymode

η

→

π

+

π

−

η

withthe

η

subsequentlydecaying into

γ γ

.TheSTyieldsaregivenas

yα_ST

=

N_D+

sD−s

B

(

D

−

s

→

α

)

ε

αST

,

(1)

whereN_D+

sD−s is thenumberofproduced D

+

s D−s pairsand

ε

STα is

the detectioneﬃciency of reconstructing D−_s

→

α

. Similarly, the DTyieldsaregivenas

yα_DT

=

N_D+

sD−s

B

(

D

−

s

→

α

)

B

(

D+s

→

η

X

)

B

ηPDG

ε

DTα

,

(2)

where

B

PDG_η istheproduct branchingfractions

B(

η

→

π

+

π

−

η

)

· B(

η

→

γ γ

)

,

ε

α

DT is the detection eﬃciency of reconstructing D−_s

→

α

and D+_s

→

η

X atthesame time.With

ε

α

ST and

ε

αDT

es-timatedfrom MC simulations, theratio of yα_DT to yα_ST provides a measurementof

B(

D+_s

→

η

X

)

,

B

(

D+_s

→

η

X

)

B

PDG_η

=

yα_DT yα_ST

· ε

_STα

ε

α DT

.

(3)

WhenmultipleSTmodesareused,thebranchingfractionis deter-minedas

B

(

D+_s

→

η

X

)

B

PDG_η

=

αyαDT

αyαST

·

εDTα εα ST

=

yDT αyαST

·

εαDT εα ST

,

(4)

whereyDT

=

_{α y}α_DTisthetotalnumberofDTevents.

Inthisanalysis, theSTeventsare selectedby reconstructinga

D−_s inninedifferentdecaymodes:K0

SK−,K+K−

π

−,K+K−

π

−

π

0,

K0_SK+

π

−

π

−,

π

+

π

−

π

−,

π

−

η

,

π

−

η

(

η

→

π

+

π

−

η

)

,

π

−

η

(

η

→

ρ

0

_γ

_,

_ρ

0

_→

_π

+

_π

−

₎

_, _and

_π

−

_π

0

_η

_. _The _DT _events _are _selected _by

further reconstructing an

η

among the remaining particles not used in the ST reconstruction. Throughout the paper, charged-conjugatemodesarealwaysimplied.

Foreachchargedtrack(exceptforthoseusedforreconstructing

K0_S decays),thepolarangleintheMDCmustsatisfy

|

cos

θ

|

<

0

.

93, andthe point of closest approach to the e+e− interaction point (IP)mustbewithin

±

10 cm along thebeamdirectionandwithin 1 cmintheplane perpendiculartothebeamdirection.Acharged

K

(

π

)

mesonisidentiﬁedbyrequiringthePIDlikelihoodtosatisfy

L(

K

)

>

L(

π

)

(

L(

π

)

>

L(

K

)

).

Showersidentiﬁed as photon candidates must satisfy the fol-lowingrequirements.ThedepositedenergyintheEMCisrequired to be larger than 25 MeV in the barrel region (

|

cos

θ|

<

0

.

8) or largerthan50 MeVinthe endcapregion (0

.

86

<

|

cos

θ

|

<

0

.

92). Tosuppresselectronicnoise andenergydepositsunrelatedtothe event,theEMCtimedeviationfromtheeventstarttimeisrequired

Table 1

Requirementson E forSTD−s candidates.

ST modeα Data (GeV) MC (GeV)

K0 SK− (−0.027,0.021) (−0.025,0.021) K+K−π− (−0.032,0.023) (−0.031,0.024) K+K−π−π0 (−0.041,0.022) (−0.041,0.022) K0 SK+π−π− (−0.035,0.024) (−0.032,0.026) π+π−π− (−0.036,0.023) (−0.033,0.025) π−η (−0.038,0.037) (−0.041,0.032) π−ηπ π η (−0.035,0.027) (−0.034,0.028) π−ηργ (−0.035,0.022) (−0.035,0.021) π−π0_η ₍₋₀_.₀₅₃_,₀_.₀₃₀₎ ₍₋₀_.₀₅₃_,₀_.₀₂₈₎

tobe 0

≤

T

≤

700 ns.Photoncandidatesmustbe separatedby at least 10 degrees from the extrapolated positions of any charged tracksintheEMC.

The K0_S candidatesareformedfrompairsofoppositelycharged tracks.Forthesetwotracks,thepolaranglesintheMDCmust sat-isfy

|

cos

θ|

<

0

.

93,andthepointofclosestapproachtotheIPmust be within

±

20 cm alongthe beamdirection. No requirementson thedistanceofclosestapproachinthetransverseplaneoron par-ticleidentiﬁcationcriteriaareappliedtothetracks.Theirinvariant massisrequiredtosatisfy0

.

487

<

M

(

π

+

π

−

)

<

0

.

511 GeV

/

c2_._The

twotracksareconstrainedtooriginatefromacommondecay ver-tex, which is required to be separated from the IP by a decay lengthofatleasttwicethevertexresolution.

The

π

0 _and

_η

_candidates _are _{reconstructed} _from _photon

pairs. Theinvariant massis requiredtosatisfy 0

.

115

<

M

(

γ γ

)

<

0

.

150 GeV

/

c2 for

π

0_, _and₀

_.

₅₁₀

_<

_M

₍

_{γ γ}

₎

_<

₀

_.

_{570 GeV}

_/

_c2 _for

_η

_.

Toimprovethemassresolution,a mass-constrainedﬁttothe nom-inal mass of

π

0 _or

_η

_[9] _is _applied _to _the _photon _pairs. _For

_η

candidates, the invariant mass must satisfy 0

.

943

<

M

(

η

_{π π η}

)

<

0

.

973 GeV

/

c2 _and ₀

_.

₉₃₂

_<

_M

₍

_η

ργ

)

<

0

.

980 GeV

/

c2. For the

η

_ργ candidates, we additionally require 0

.

570

<

M

(

π

+

π

−

)

<

0

.

970 GeV

/

c2 _to _reduce _{contributions} _from _{combinatorial}

back-ground.

Wedeﬁne theenergydifference,

E

≡

E

−

E0,where E isthe total measured energy ofthe particles in the D−_s candidate and

E0 isthebeamenergy.The D−s candidatesarerejectediftheyfail

topass

E requirements correspondingto3timestheresolution,

as given in Table 1. To reduce systematic uncertainty, we apply differentrequirementson

E fordataandMCsamples.Ifthereis morethanone D−_s candidateinaspeciﬁcSTmode,thecandidate withthesmallest

|

E

|

iskeptforfurtheranalysis.

ToidentifySTsignals, thebeam-constrainedmassMBCisused. ThisisthemassoftheD−s candidatecalculatedbysubstitutingthe

beam energy E0 forthe measured energy of the D−s candidate:

M2

BCc4

≡

E20

−

p2c2,where p isthe measured momentum of the D−_s candidate.True D−_s

→

α

single-tagspeakatthe nominal D−_s

massinMBC.

We ﬁt the MBC distribution of each mode

α

to obtain yαST.

Backgroundcontributionsforeachmodearewelldescribedbythe ARGUS function [20],asverified withMC simulations.The signal distributionsaremodeledbyaMC-derivedsignalshapeconvoluted withaGaussianfunctionwhoseparametersareleftfreeinthefit. The Gaussian function compensatesthe resolution difference be-tween data andMC simulation. Fig. 1shows thefits to the MBC

distributionsindata;theﬁttedSTyields arepresentedin

Table 2

alongwiththedetectioneﬃcienciesestimatedbasedonMC simu-lations.

Toselecteventswherethe D+_s decaysto

η

X ,we requirethat theDTeventscontainan

η

candidateamongtheparticles recoil-ing against theST candidate. As mentioned above, the

η

candi-dates are reconstructed in the decay

η

→

π

+

π

−

η

, with the

η

(5)

Fig. 1. FitstotheMBCdistributionsfortheSTDscandidates.Ineachplot,thepointswitherrorbarsaredata,thedashedcurveisthebackgroundcontributionandthesolid lineshowsthetotalﬁt.

Table 2

ThedetectioneﬃcienciesandthedatayieldsoftheSTandDTevents.The eﬃcien-ciesdonotincludetheintermediatebranchingfractionsfor π0_→_{γ γ,}_η_→_{γ γ,} K0

S→π+π−,η→π+π−ηandη→ρ0γ.Alluncertaintiesarestatisticalonly.

ST modeα εα ST(%) yαST εDTα (%) yDT K0SK− 47.89±0.35 1088±40 13.75±0.14 K+K−π− 44.16±0.18 5355±118 12.46±0.14 K+K−π−π0 _13.25_±_0.22 ₁₉₇₂_±₁₄₅ _4.32_±_0.08 K0 SK+π−π− 24.27±0.37 595±50 6.05±0.09 π+π−π− 60.26±0.90 1657±143 17.18±0.16 68±14 π−η 48.39±0.70 843±54 14.82±0.16 π−ηπ π η 29.48±0.52 461±41 7.91±0.11 π−ηργ 43.11±0.88 1424±147 11.96±0.13 π−π0_η _26.02_±_0.32 ₂₂₆₀_±₁₅₆ _7.90_±_0.11

subsequently decaying into

γ γ

. All particles used in the

η

re-constructionmustsatisfytherequirementsdetailedabove.Ifthere ismore thanone

η

candidate, theone withthesmallest

M

≡

|

M

(

η

_{π π η}

)

−

m

(

η

)

|

iskept,wherem

(

η

)

isthenominal

η

mass[9]. Thedecaymode

η

→

ρ

0

_γ

_is_not_used_due_to_large_{contributions}

fromcombinatorialbackground.

There are peakingbackground contributions in M

(

η

_{π π η}

)

pro-ducedbyeventsinwhichthereisawrongly-reconstructed D−_s tag accompanied by areal

η

in the restofthe event. To obtainthe DTyields,wethereforeperformatwo-dimensionalunbinnedﬁtto thevariables MBC

(

α

)

and M

(

η

_{π π η}

)

.For MBC

(

α

)

,theﬁtfunctions arethesameasthoseusedintheextractionofyα_ST.ForM

(

η

_{π π η}

)

, thesignal isdescribed bythe convolutionofa MC-derivedsignal shapeandaGaussianfunctionwithparametersleftfreeintheﬁt. BackgroundcontributionsinM

(

η

_{π π η}

)

consistof(a) D+_sD−_s events inwhich D−_s decays tothe desiredST modes,but the D+_s decay does not involve an

η

; (b) other (non-ST signal) decays of D−_s

andalso non-D+_sD−_s processes.Component (a) isdescribed with aﬁrst-orderpolynomialfunction.Component(b) ismodeledwith the sum of two Gaussian functions plus a quadratic polynomial function.ThemeansofthetwoGaussiansareﬁxedtothe

η

nom-inalmass[9].Otherparametersandalltheamplitudesareleftfree in theﬁt. The ARGUS function of MBC

(

α

)

helpsto constrain the descriptionofM

(

η

_{π π η}

)

incomponent(b).Thistreatmenton back-groundcontributions has been veriﬁed in MC simulations. There

is no obvious correlation between MBC

(

α

)

and M

(

η

_{π π η}

)

, so the probability densityfunctions(PDFs)ofthesetwo variablesare di-rectly multiplied.We obtainthecombinedDTyield yDTfromthe unbinned fit shown in Fig. 2. Table 2 gives the total yields of DT in dataand thecorresponding DT efficiencies. Combining the yields and efficiencies, we obtain

B(

D+_s

→

η

X

)

= (

8

.

8

±

1

.

8

)

% withEq.(4).

3.2. Measurementof

B(

D+_s

→

η

ρ

+

)

Inordertoimprovethestatisticalprecision,we determinethe branching fraction for D+_s

→

η

ρ

+ using STs. As a standalone measurement, this doesnot beneﬁt fromcancellationof system-atic uncertainties as inthe double-tag method.However, a simi-lar cancellationcan be achievedby measuring the signal relative to asimilar, alreadywell-measured ﬁnalstate. Thus, we measure

B(

D+_s

→

η

ρ

+

)

relativeto

B(

D+_s

→

K+K−

π

+

)

,using

B

(

D+_s

→

η

ρ

+

)

B

PDG_ρ+

B

PDG_η

B

(

D+_s

→

K+K−

π

+

)

=

yη_STρ+ y_STK+K−π+

· ε

K+K−π+ ST

ε

η_STρ+

,

(5) where

B

PDG_ρ+

=

B(

ρ

+

→

π

+

π

0

)B(

π

0

→

γ γ

)

.

Thedecay D+_s

→

K+K−

π

+ isreconstructedinthesame man-ner asreportedabove intheSTmode.OurMCsimulationofthis mode includes a full treatment of interfering resonances in the Dalitz plot [21]. The decay D+_s

→

η

ρ

+ is reconstructed via the decays

η

→

π

+

π

−

η

and

ρ

+

→

π

+

π

0_,_where

_η

₍

_π

0

₎

_→

_{γ γ}

_._We

apply thesamecriteriatoﬁnd

π

0 _and

_η

_candidates_as_were_used

in the analysis of D+_s

→

η

X . We do not requirePID criteria on the chargedtracks, but instead assume them all to be pions. In the reconstruction of

ρ

+ and

η

,the

π

+ are randomlyassigned. Theinvariant mass,M

(

π

+

π

0

₎

_,_of_the

_ρ

+ _candidate_is_required_to

be within

±

0

.

170 GeV

/

c2 _of _the _nominal

_ρ

+ _mass, _and _the

in-variant mass of the

η

candidate, M

(

η

_{π π η}

)

, is requiredto lie in the interval

(

0

.

943

,

0

.

973

)

GeV

/

c2.Additionally requiring1

.

955

<

MBC

<

1

.

985 GeV

/

c2 to enrich signal events, the M

(

π

+

π

0

₎

dis-tribution of D+_s

→

η

ρ

+ ininclusive MC simulationsand datain

Fig. 3 show good agreement. The small difference visible in the

M

(

η

_{π π η}

)

distributionwillbetakenintoaccountinthesystematic uncertainties.

(6)

Fig. 2. Projections of the two-dimensional unbinned ﬁt to DT events from data onto MBC(left) and M(η_π+π−η)(right).

Fig. 3. ComparisonoftheM(π+π0₎_(left)_and_M₍_η

π π η)(right)distributionsinSTeventsofD+s →ηρ+indata(points)andinclusiveMC(solidline).Thearrowsshowthe signalregion.

Fig. 4. Projectionplotsofthetwo-dimensional unbinnedﬁtontoMBC(left)andcosθπ+ (right).Thesignaleventsareenrichedbyrequiring1.955<MBC<1.985 GeV/c2in therightplot.

If multiple

η

ρ

+ candidates are found in an event, only the one with the smallest

|

E

|

is kept. We require

−

0

.

035

<

E

<

0

.

023 GeV fordataand

−

0

.

037

<

E

<

0

.

029 GeV forMC.Fitsto theMBCdistributionsareusedtoextractsignalyields.Toseparate thethree bodyprocess D+_s

→

η

π

+

π

0 _from_the _two _body_decay D+_s

→

η

ρ

+,thehelicityangle

θ

π+ isusedtoextractthe

ρ

+ com-ponent,where

θ

π+ istheanglebetweenthemomentumofthe

π

+

fromthe

ρ

+decayandthedirectionopposite tothe D+s

momen-tuminthe

ρ

+restframe.ThesignalD+_s

→

η

ρ

+isdistributedas cos2

_θ

π+,whilethethreebodyprocessisﬂatincos

θ

π+.

Weperformatwo-dimensional unbinnedmaximumlikelihood

ﬁttothedistributionofMBCversuscos

θ

π+ todeterminetheyield

yη_STρ+.ThesignalmodelofMBC isthesameasthatintheanalysis of D+_s

→

η

X . Forcos

θ

π+,the signal shapesof D+s

→

η

ρ

+ and

D+s

→

η

π

+

π

0 are determined based on MC simulations.

Back-ground contributions in MBC are modeled withan ARGUS

func-tion, while background contributions in cos

θ

π+ are taken from the events in the MBC sidebands 1

.

932

<

MBC

<

1

.

950 GeV

/

c2

and1

.

988

<

MBC

<

1

.

997 GeV

/

c2_._There_is_no_obvious_correlation

between MBC and cos

θ

π+, so the PDFsused for thesetwo

vari-ables are directlymultiplied. Fig. 4 showsthe projections of the two-dimensional ﬁt results in data. In the rightplot, we further require1

.

955

<

MBC

<

1

.

985 GeV

/

c2 to enrichsignal events.The ﬁtreturns yη_STρ+

=

210

±

50, and y_STηπ+π0

= −

13

±

56, which in-dicates that no signiﬁcant non-resonant D+s

→

η

π

+

π

0 signal is

observed. Anupper limit of

B(

D+_s

→

η

π

+

π

0

₎

_at_the _90%

conﬁ-dencelevelisevaluatedto be5.1%,afteraprobability scan based on 2000 separate toy MC simulations, taking into account both

(7)

Fig. 5. MBCdistributions with the requirement of|cosθπ+| <0.5 (left) or|cosθπ+| >0.5 (right).

Table 3

Summaryofrelativesystematicuncertaintiesinpercent.Thetotaluncertaintyis takenasthesuminquadratureoftheindividualcontributions.

Source B(D+s →ηX) B(D+s →ηρ+) MDC track reconstruction 2.0 PID 2.0 3.0 π0_detection _2.4 ηdetection 2.7 3.5 E requirement 1.0 1.4 M(ηπ π η)requirement 2.0 M(ηπ π η)backgrounds 1.5 Peaking backgrounds in ST 0.3 MBCsignal shape 1.0 0.6 MBCﬁt range 1.7 0.5 cosθπ+backgrounds 2.9 Uncertainty of eﬃciency 1.6 0.5

Quoted branching fractions 1.7 3.8

Total 5.3 7.5

thestatisticalandsystematicuncertainties.Asshownin

Fig. 5

,we seeobvious D+_s signalsinthe MBC distribution withthe require-ment of

|

cos

θ

π+

|

>

0

.

5, while it is not the casewhen requiring

|

cos

θ

π+

|

<

0

.

5. This indicates that the three body process is not

signiﬁcant.

We study the MBC distributions for events in

ρ

+ and

η

sidebands. The

ρ

+ sideband region is chosen as M

(

π

+

π

0

₎

_<

0

.

500 GeV

/

c2, and the

η

sidebands are 0

.

915

<

M

(

η

_{π π η}

)

<

0

.

925 GeV

/

c2 and0

.

990

<

M

(

η

_{π π η}

)

<

1

.

000 GeV

/

c2. No D+s

sig-nalisvisibleinthesidebandevents,furthersubstantiatingthatthe non-resonantprocesses D+_s

→

η

π

+

π

0 _and_D+

s

→

ηπ

+

π

−

ρ

+are

negligible.Asimulationstudyshowsthatthepotentialbackground contributionfrom

η

→

ρ

0

_γ

_is_negligible.

Thedetectioneﬃciency

ε

_STηρ+ isestimatedtobe

(

9

.

80

±

0

.

04

)

%. Combinedwiththeresultsforthenormalizationmode K+K−

π

+, asgivenin

Table 2

, weobtain fromEq.(5)theratioof

B(

D+_s

→

η

ρ

+

)

relative to

B(

D+_s

→

K+K−

π

+

)

as 1

.

04

±

0

.

25. Taking the mostprecise measurement of

B(

D+s

→

K+K−

π

+

)

= (

5

.

55

±

0

.

19

)

% from CLEO [11] as input, we obtain

B(

D+_s

→

η

ρ

+

)

=

(

5

.

8

±

1

.

4

)

%.

3.3. Systematicuncertainties

In the measurement of

B(

D+_s

→

η

X

)

,many uncertainties on theST side mostly cancelinthe eﬃciencyratios inEq.(4). Sim-ilarly, for D+_s

→

η

ρ

+, the uncertainty in the tracking eﬃciency cancelsto anegligiblelevel bytakingtheratioto the normaliza-tionmode D+_s

→

K+K−

π

+ inEq.(5).The followingitems, sum-marizedin

Table 3

,aretakenintoaccountassourcesofsystematic uncertainty.

a. MDCtrackreconstructioneﬃciency. Thetrackreconstruction ef-ﬁciencyisstudiedusingacontrolsample ofD+

→

K−

π

+

π

+

inthedatasampletakenat

√

s

=

3

.

773 GeV.Thedifferencein the trackreconstruction eﬃciencies between dataand MC is found to be 1.0%per charged pionandkaon.Therefore, 2.0% istakenasthesystematicuncertaintyoftheMDCtrack recon-structioneﬃciencyforD+_s

→

η

X .

b. PIDefficiency. We study the PID efficiencies using the same control sampleasinthetrackreconstructionefficiencystudy. ThedifferenceinPIDefficienciesbetweendataandMCis de-termined to be 1.0% per charged pion or kaon. Hence, 2.0% (3.0%) is takenasthe systematic uncertaintyof the PID effi-ciencyforD+_s

→

η

X (D+_s

→

η

ρ

+).

c.

π

0_and

_η

_{detection. The}

_π

0 _{reconstruction} _eﬃciency,

includ-ing the photon detection eﬃciency, is studied using a con-trol sample of D0

→

K−

π

+

π

0 _in _the _data _sample _taken _at

√

s

=

3

.

773 GeV. After weighting the systematic uncertainty inthemomentumspectraof

π

0_,_2.8%_is_taken_as_the

system-aticuncertaintyforthe

π

0_eﬃciency_in_D+

s

→

η

ρ

+.Similarly,

the systematicuncertainty forthe

η

eﬃciencyin D+_s

→

η

X

(D+s

→

η

ρ

+) is determined to be 2.7% (3.5%) by

assum-ingdata-MCdifferenceshavethesamemomentum-dependent valuesasfor

π

0 _detection. _The_systematic_{uncertainties}_were

setconservativelyusingthecentralvalue ofthedata-MC dis-agreements plus 1.0(1.64) standarddeviations for

π

0 ₍

_η

_),_as

appropriate fora 68% (95%)conﬁdencelevel.Here we inﬂate the

η

uncertainty,becausetheuncertaintyofthe

η

detection isestimatedreferringto

π

0_.

d.

E requirement. Differences in detector resolutions between

dataandMCmayleadtoadifferenceintheeﬃcienciesofthe

E requirements.In ourstandardanalysisprocedure,we

ap-plydifferent

E requirements ondataandMC,toreducethe systematicuncertainties. To be conservative,we examine the relative changesoftheeﬃciencies byusingthesame

E

re-quirementsforMCasfordata.Weassignthesechanges,1.0% forD+_s

→

η

X and1.4%forD+_s

→

η

ρ

+,asthesystematic un-certaintiesonthe

E requirement.

e. M

(

η

_{π π η}

)

requirement. In the right plot in Fig. 3, the resolu-tionofthe

η

peakinMCisnarrowerthandata.Wetakethe change in eﬃciency of 2.0%, after using a Gaussian function tocompensateforthisresolutiondifference,asthesystematic uncertaintyoftheM

(

η

_{π π η}

)

requirementforD+_s

→

η

ρ

+.

f. M

(

η

_{π π η}

)

background contributions. In the measurement of

B(

D+s

→

η

X

)

, a two-dimensional ﬁt is performed to the

MBC

(

ST

)

and M

(

η

π π η

)

distributions. The uncertainty due to

the description of the M

(

η

_{π π η}

)

background contributions is estimated by repeating the ﬁt with higher orderpolynomial functions. We take the maximum relative change of 1.5% in