• Nie Znaleziono Wyników

Precision measurement of the $\eta \rightarrow \pi^{+}\pi^{-}\pi^{0}$ Dalitz plot distribution with the KLOE detector

N/A
N/A
Protected

Academic year: 2022

Share "Precision measurement of the $\eta \rightarrow \pi^{+}\pi^{-}\pi^{0}$ Dalitz plot distribution with the KLOE detector"

Copied!
21
0
0

Pełen tekst

(1)

Pu b l i s h e d f o r SISSA b y Sp r i n g e r R e c e i v e d: January 27, 2016

R e v i s e d: March 24, 2016

A c c e p t e d: April 16, 2016

P u b l i s h e d: May 3, 2016

Precision measurement of the η → π + π − π 0 Dalitz plot distribution with the KLOE detector

T h e K L O E -2 collaboration

A. Anastasi,a ’ D. Babusci,’ G. Bencivenni,’ M . Berlowski,c C. Bloise,’ F. Bossi,’

P. Branchini,d A. Budano,e,d L. Caldeira Balkestahl,f B. Cao,f F. Ceradini,e,d P. Ciambrone,’ F. Curciarello,“,g,h E. Czerwiński,* G. D ’Agostini,J,fc E. Dane,’

V . De Leo,d E. De Lucia,’ A. De Santis,’ P. De Simone,’ A. Di Cicco,e,d

A. Di Domenico,-7'^ R. Di Salvo,1 D. Domenici,’ A. D ’Uffizi,’ A. Fantini,m1 G. Felici,’

S. Fiore,n,k A. Gajos,* P. Gauzzi,j,fc G. Giardina,a,g S. Giovannella,’ E. Graziani,d F. Happacher,’ L. Heijkenskjold,f W . Ikegami Andersson,f T . Johansson,f D. Kamińska,* W . Krzemien,c A. Kupsc,f S. Loffredo,e,d G. Mandaglio,o,p

M . M artini,’ ,q M . Mascolo,’ R. Messi,m1 S. M iscetti,’ G. Morello,’ D. Moricciani,1 P. Moskal,* M . Papenbrock,f A. Passeri,d V . Patera,r,k E. Perez del Rio,’ A. Ranieri,s P. Santangelo,’ I. Sarra,’ M . Schioppa,t,u M . Silarski,’ F. Sirghi,’ L. Tortora,d

G. Venanzoni,’ W . Wislickic and M . W olkef

aDipartimento di Fisica e Scienze della Terra dell’Universita di Messina, Messina, Italy bLaboratori Nazionali di Frascati dell’INFN, Frascati, Italy

cNational Centre fo r Nuclear Research, Warsaw, Poland dIN F N Sezione di Roma Tre, Roma, Italy

eDipartimento di Matematica e Fisica, dell’Universita “Roma Tre”, Roma, Italy f Department o f Physics and Astronomy, Uppsala University, Uppsala, Sweden g IN F N Sezione di Catania, Catania, Italy

hNovosibirsk State University, 630090 Novosibirsk, Russia 1 Institute of Physics, Jagiellonian University, Cracow, Poland j Dipartimento di Fisica, dell’Universita “Sapienza”, Roma, Italy kIN F N Sezione di Roma, Roma, Italy

1 IN F N Sezione di Roma Tor Vergata, Roma, Italy

m Dipartimento di Fisica, dell’Universita “Tor Vergata”, Roma, Italy n EN E A U T T M A T -IR R , Casaccia R.C ., Roma, Italy

o Dipartimento di Scienze Chimiche, Biologiche, Farmaceutiche ed Am bientali dell’Universita di Messina, Messina, Italy

p IN F N Gruppo collegato di Messina, Messina, Italy

qDipartimento di Scienze e Tecnologie applicate, Universita “Guglielmo Marconi”, Roma, Italy

O p e n A c c e s s, © T h e A u th o r s .

A r tic le f u n d e d b y S C O A P 3 . doi:10.1007/JHEP05(2016)019

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(2)

r Dipartimento di Scienze di Base ed Applicate per I’Ingegneria dell’Universita “Sapienza”, Roma, Italy

s IN F N Sezione di Bari, Bari, Italy

4Dipartimento di Fisica dell’Universita della Calabria,, Rende, Italy uIN F N Gruppo collegato di Cosenza, Rende, Italy

E -m a il: A n d r z e j .K u p s c @ p h y s i c s .u u .s e

Ab s t r a c t: U sing 1.6 fb- 1 of e + e - ^ ^ nY d a t a co llected w ith th e K L O E d e te c to r a t D A T N E , th e D a litz p lo t d is trib u tio n for th e η → π + π − π 0 d ecay is s tu d ie d w ith th e w o rld ’s la rg e st sam p le of ~ 4.7 ■ 106 ev en ts. T h e D a litz p lo t d e n sity is p a ra m e triz e d as a p o ly n o m ia l ex p a n sio n u p to cu b ic te rm s in th e n o rm alize d d im en sio n less v aria b les X a n d Y . T h e e x p e rim e n t is sen sitiv e to all ch a rg e c o n ju g a tio n co n se rv in g te rm s o f th e ex p a n sio n , in clu d in g a g X 2Y te rm . T h e s ta tis tic a l u n c e rta in ty of all p a ra m e te rs is im p ro v ed by a fa c to r tw o w ith re sp e c t to ea rlie r m ea su re m e n ts.

Ke y w o r d s: e + -e - E x p e rim e n ts , Q C D

ArXi y ePr i n t: 1601.06985

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(3)

C o n te n ts

1 I n t r o d u c t i o n 1

2 T h e K L O E d e t e c t o r 4

3 E v e n t s e l e c t i o n 5

4 D a l i t z p l o t 1 0

5 A s y m m e t r i e s 13

6 S y s t e m a t i c c h e c k s 13

7 D i s c u s s i o n 15

A A c c e p t a n c e c o r r e c t e d d a t a 1 7

1 I n t r o d u c t i o n

T h e isospin v io la tin g n ^ n + n - n0 d ecay c a n p ro ceed v ia e le c tro m a g n e tic in te ra c tio n s or v ia s tro n g in te ra c tio n s d u e to th e difference b etw e en th e m asses o f u an d d q u a rk s. T h e e le c tro m a g n e tic p a r t o f th e d ecay a m p litu d e is long k now n to be s tro n g ly su p p re sse d [1, 2].

T h e re cen t c a lc u la tio n s p erfo rm ed a t n e x t-to -le a d in g o rd e r (N L O ) o f th e ch ira l p e r tu r b a tio n th e o ry (C h P T ) [3 , 4] reaffirm t h a t th e d ecay a m p litu d e is d o m in a te d by th e isosp in v io la tin g p a r t of th e s tro n g in te ra c tio n .

D efining th e q u a rk m ass ra tio , Q , as

m 2 —n2 1

Q2 = —s---2 w ith — = - ( —d + m v) , (1.1)

—d - — U 2

th e d ecay a m p litu d e a t u p to N L O C h P T is p ro p o rtio n a l to Q- 2 [5]. T h e d e fin itio n in eq. (1.1) , n eg lec tin g — 2/ m 2, gives an ellipse in th e — s / m d , m u/ m d p la n e w ith m a jo r sem i­

axis Q [6]: a d e te rm in a tio n of Q p u ts a s trin g e n t c o n s tra in t o n th e ligh t q u a rk m asses. T h e p ro p o rtio n a lity fa c to r could be d e te rm in e d from C h P T c a lc u la tio n s in th e isosp in lim it.

U sin g D a s h e n ’s th e o re m [7] to ac c o u n t for th e e le c tro m a g n e tic effects, Q ca n b e d e te r ­ m in ed a t th e low est o rd e r from a c o m b in a tio n o f kaon a n d p io n m asses. W ith th is value o f Q = 24.2, th e C h P T re su lts for th e n ^ n + n - n0 d ecay w id th a t LO , r LO = 6 6eV , an d N L O , r NLO = 160 — 210 eV [8]. T h e c a lc u la tio n s sh o u ld b e c o m p a re d to th e p re se n t e x p e r­

im e n ta l value o f r exp = 300 ± 11 eV [9]. T h e e x p e rim e n t-th e o ry d isc re p a n c y could o rig in a te fro m h ig h er o rd e r c o n trib u tio n s to th e d ecay a m p litu d e o r from c o rre c tio n s to th e Q value.

To u n d e r s ta n d th e role o f th e h ig h er o rd e r c o n trib u tio n s a full N N L O C h P T c a lc u la tio n w as c a rrie d o u t a n d it gives r NNLO = 230 — 2 7 0 e V w ith in th e D a sh e n lim it [10]. T h e

-

1

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(4)

N N L O re su lt d e p e n d s o n th e values of a larg e n u m b e r o f th e co u p lin g c o n s ta n ts o f th e ch ira l la g ra n g ia n w hich are n o t know n precisely. O n th e o th e r h a n d it is kn ow n t h a t th e n n re s c a tte rin g play s a n im p o rta n t role in th e decay, givin g a b o u t h a lf o f th e c o rre c tio n from th e L O to th e N L O re su lt [8]. T h e re s c a tte rin g c a n b e a c c o u n te d for to all o rd e rs usin g d isp ersiv e in te g ra ls a n d precisely kn ow n n n p h a se shifts. In th e d isp ersiv e c a lc u la tio n s tw o ap p ro a c h e s a re possible. T h e first is to im p ro ve C h P T p re d ic tio n s s ta r tin g from th e N LO C h P T ca lc u la tio n s. In th e second a p p ro a c h on e c a n d e te rm in e th e p ro p o rtio n a lity fa c to r for th e Q -2 in th e n ^ n + n - n 0 d ecay a m p litu d e from fits to th e e x p e rim e n ta l D a litz p lo t d a t a a n d by m a tc h in g th e re su lts to th e L O a m p litu d e in th e reg ion w h ere it cou ld be co n sid ered a c c u ra te . B o th ap p ro a c h e s a re p u rsu e d by th re e th e o ry g ro up s: refs. [13- 15]. In th e first a p p ro a c h th e re lia b ility o f th e c a lc u la tio n s cou ld b e verified by a c o m p a riso n w ith th e e x p e rim e n ta l D a litz p lo t d a ta . C onversely, in th e second a p p ro a c h p recise e x p e rim e n ta l D a litz p lo t d is trib u tio n s cou ld b e used to d e te rm in e th e q u a rk ra tio Q w ith o u t re ly in g on th e h ig h er o rd e r C h P T ca lc u latio n s.

T w o o th e r re c e n t th e o re tic a l d e sc rip tio n s of th e n ^ 3n d ecay a m p litu d e in clu d e u n ita riz e d C h P T (U C h P T ) [11] a n d n o n -re la tiv is tic effective field th e o ry (N R F T ) [12].

U C h P T is a m odel d e p e n d e n t a p p ro a c h w hich uses re la tiv is tic co u p led ch a n n els a n d allow s fo r sim u lta n e o u s tr e a tm e n t of all h a d ro n ic n a n d n' decays. T h e N R F T fram ew o rk is used to s tu d y h ig h er o rd e r iso spin b re a k in g effects in th e final s ta te in te ra c tio n s .

F o r th e n ^ n + n - n 0 D a litz p lo t d is trib u tio n , th e n o rm alize d v aria b les X a n d Y are co m m o n ly used:

T* are k in e tic energies of th e pions in th e n re st fram e. T h e sq u a re d a m p litu d e of th e d ecay is p a ra m e triz e d by a p o ly n o m ia l ex p a n sio n a ro u n d (X , Y ) = (0, 0):

|A ( X ,Y ) |2 ~ N (1 + a Y + b Y 2 + c X + d X 2 + e X Y + f Y 3 + g X 2Y + h X Y 2 + I X 3 + . . . ) . (1.5) T h e D a litz p lo t d is trib u tio n c a n th e n b e fit u sin g th is fo rm u la to e x tr a c t th e p a ra m e te rs a, b, . . . , u su ally called th e D a litz p lo t p a ra m e te rs . N o te t h a t coefficients m u ltip ly in g o d d pow ers of X (c, e, h a n d l) m u st b e zero assu m in g ch a rg e c o n ju g a tio n in varian ce.

T h e e x p e rim e n ta l values o f th e D a litz p lo t p a ra m e te rs a re show n in ta b le 1 to g e th e r w ith th e p a r a m e triz a tio n of th e o re tic a l c a lc u la tio n s. T h e la st th re e m o st p recise m e a su re ­ m e n ts in clu d e th e 2008 an a ly sis from K L O E w hich w as b ase d on 1.34 ■ 106 ev e n ts [19].

T h e re is som e d isa g re e m e n t am o n g th e ex p e rim e n ts, sp ecially for th e b b u t also for th e a p a ra m e te r. B o th b a n d th e f p a ra m e te rs from th e o ry d e v ia te from th e e x p e rim e n ta l values. T h e new h ig h s ta tis tic s m e a su re m e n t p re se n te d in th is p a p e r c a n h elp to clarify th e te n s io n am o n g th e e x p e rim e n ta l re su lts, a n d c a n b e used as a m ore p recise in p u t for th e d isp ersiv e ca lc u latio n s.

( 1 .2)

(1.3) w ith

Qn — Tn+ + Tn- + Tn o — — 2mn+ — m no. (1.4)

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

X = -\/3 Tn+ T n - Q n Y _ 3Tn0 i Y _ o 7 - 1

(5)

E x p e r im e n t — a b d / - g

G orm ley(70) [16] 1.17 ± 0 .0 2 0.21 ± 0 .0 3 0.06 ± 0.04 - -

L ay te r(7 3 ) [17] 1.080 ± 0 .0 1 4 0.03 ± 0 .0 3 0.05 ± 0.03 - -

C B a rre l(9 8 ) [18] 1.22 ± 0 .0 7 0.22

±

0.11 0.06(fixed) - -

K L O E (0 8 ) [19] 1.090 ±0.005+o;oog 0.124 ± 0 .0 0 6 ± 0 .0 1 0 0.057 ± 0 . 0 0 6 1 S 0.14 ± 0 .0 1 ± 0 .0 2 - W A SA (14) [2 0 ] 1.144 ± 0 .0 1 8 0.219 ± 0 .0 1 9 ± 0 .0 4 7 0.086 ± 0 .0 1 8 ± 0 .0 1 5 0.115 ± 0 .0 3 7 - B E S III(1 5 ) [2 1] 1.128 ± 0 .0 1 5 ± 0 .0 0 8 0.153 ± 0 .0 1 7 ± 0 .0 0 4 0.085 ± 0 .0 1 6 ± 0 .0 0 9 0.173 ± 0 .0 2 8 ± 0 .0 2 1 - C a lc u la t io n s

C h P T LO [10] 1.039 0.27 0 0 -

C h P T N L O [10] 1.371 0.452 0.053 0.027 -

C h P T N N L O [10] 1.271 ± 0 .0 7 5 0.394 ± 0 .1 0 2 0.055 ± 0.057 0.025 ± 0.160 -

d isp ersiv e [2 2] 1.16 0.26 0.10 - -

sim plified d isp [5] 1.21 0.33 0.04 - -

N R E F T [12] 1.213 ± 0 .0 1 4 0.308 ± 0 .0 2 3 0.050 ± 0.003 0.083 ± 0 .0 1 9 0.039 ± 0 .0 0 2

U C h P T [ U ] 1.054 ± 0 .0 2 5 0.185 ± 0 .0 1 5 0.079 ± 0 .0 2 6 0.064 ± 0 .0 1 2 -

T a b le 1. Sum m ary of Dalitz plot param eters from experim ents and theoretical predictions.

JH EP

05 (2 01

6)

01

9

(6)

2 T h e K L O E d e t e c t o r

T h e K L O E d e te c to r a t th e D A $ N E e + e - co llider in F ra s c a ti co n sists o f a larg e c y lin d rica l D rift c h a m b e r (D C ) a n d a n e le c tro m a g n e tic c a lo rim e te r (E M C ) in a 0.52 T ax ial m a g n e tic field. T h e D C [23] is 4 m in d ia m e te r a n d 3.3 m long a n d is o p e ra te d w ith a h eliu m - is o b u ta n e gas m ix tu re (90% - 10% ). C h arg e d p a rtic le s are re c o n s tru c te d w ith a m o m e n tu m re so lu tio n o f & (p ± )/p ± — 0.4% .

T h e E M C [24] co n sists of a lte r n a tin g layers o f lead a n d s c in tilla tin g fibers covering 98% o f th e solid angle. T h e lead -fib er layers are a rra n g e d in ~ (4.4 x 4.4) c m2 cells, five in d e p th , a n d th e se a re re a d o u t a t b o th en d s. H its in cells close in tim e a n d sp ac e are g ro u p e d to g e th e r in c lu sters. C lu ste r en e rg y is o b ta in e d from th e signal a m p litu d e a n d has a re so lu tio n o f a ( E ) / E — 5 .7 % /^ /E ( G e V ) . C lu ste r tim e , Cluster, a n d p o s itio n are en erg y w eig h ted averages, w ith tim e re so lu tio n a ( t) — (57 p s ) / ^ / E ( G e V ) ® 100 ps. T h e c lu s te r p o sitio n alo n g th e fibers is o b ta in e d from tim e differences of th e signals.

T h e K L O E trig g e r [25] uses b o th E M C a n d D C in fo rm a tio n . T h e trig g e r co n d itio n s a re chosen to m inim ize b e a m b a c k g ro u n d . In th is an a ly sis, ev e n ts are selected w ith th e c a lo rim e te r trig g e r, re q u irin g tw o en e rg y d e p o sits w ith E > 5 0 M e V for th e b a rre l an d E > 150 M eV for th e en d c ap s. T h e trig g e r signal, t h a t is p h a se locked w ith th e clock com in g from D A $ N E ra d io freq u en c y (2.7 n s), c a n n o t b e used as th e tim e scale o rig in b ec au se of th e larg e sp re a d of a rriv a l tim e s of p ro d u c e d p a rtic le s (p h o to n s, kaons, e tc .). T h u s, th e in te r­

a c tio n tim e is o b ta in e d ev en t by ev en t fro m th e d a t a e x p lo itin g th e excellen t tim in g p e rfo r­

m an ces of th e c a lo rim e te r (230 ps for 50 M eV p h o to n s). A d is c re te sea rch o f d ifferen t b u n ch tim e s is d o n e by c o n stra in in g th e a rriv a l tim e o f p ro m p te s t clu ste rs w ith E > 50 M eV .

T h e an a ly sis is p erfo rm ed u sin g d a t a co llected a t th e 0 m eson p e a k w ith th e K L O E d e te c to r in 2004-2005, a n d c o rre sp o n d s to an in te g ra te d lu m in o sity of 1.6 fb 1. D u e to D A $ N E cro ssin g angle 0 m esons h ave a sm all h o riz o n ta l m o m e n tu m , o f a b o u t 1 3 M e V /c . T h e n m esons a re p ro d u c e d in th e ra d ia tiv e d ecay 0 ^ nY® T h e p h o to n from th e 0 ra d ia tiv e decay, 7^, h as an en e rg y E ~ 363 M eV . T h e d a t a sam p le used for th is a n a ly sis is in d e p e n d e n t a n d a b o u t fo u r tim e s la rg e r th a n th e o ne u sed in th e p rev io u s K L O E (0 8 ) n ^ n + n - n0 D a litz p lo t an aly sis [19].

T h e re c o n s tru c te d d a t a a re so rte d by a n ev en t classificatio n p ro c e d u re w h ich re je cts b e a m a n d cosm ic ra y b a c k g ro u n d s a n d sp lits th e ev e n ts in to s e p a ra te s tre a m s a c co rd in g to th e ir to p o lo g y [26]. T h e b e a m a n d b a c k g ro u n d c o n d itio n s a re m o n ito re d . T h e c o rre sp o n d ­ ing p a ra m e te rs are sto re d for each ru n a n d in clu d ed in th e G E A N T 3 b ase d M o n te C arlo (M C ) sim u la tio n of th e d e te c to r. T h e ev en t g e n e ra to rs for th e p ro d u c tio n a n d d ecays of th e 0 -m eso n in clu d e sim u la tio n o f in itia l s ta te ra d ia tio n . T h e final s ta te ra d ia tio n is in clu d ed for th e sim u la tio n of th e signal p rocess. T h e s im u la tio n of e + e - ^ w n0 p ro cess (a n im p o r­

t a n t b a c k g ro u n d in th is an a ly sis) assu m es a cross sec tio n of 8 nb. T h e sim u la tio n s of th e b a c k g ro u n d ch a n n els used in th is an a ly sis co rre sp o n d to th e in te g ra te d lu m in o sity of th e ex ­ p e rim e n ta l d a t a set, w hile th e signal sim u la tio n c o rre sp o n d s to te n tim e s la rg e r lu m ino sity .

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(7)

3 E v e n t s e l e c t i o n

T w o tra c k s of o p p o site c u rv a tu re a n d th re e n e u tra l c lu ste rs are e x p e c te d in th e final s ta te of th e c h a in e + e - ^ 0 ^ nY , ^ n + n - n ° y , ^ n + n - y y y , . S electio n ste p s are liste d below:

• A c a n d id a te ev en t h as a t least th re e p ro m p t n e u tra l c lu ste rs in th e E M C . T h e c lu ste rs are re q u ire d to have en e rg y a t le a st 1 0 M eV a n d p o la r angles 23° < 9 < 157°, w h ere 9 is c a lc u la te d from th e d is ta n c e of th e c lu s te r to th e b e a m cro ssin g p o in t (A cluster). T h e tim e of th e p ro m p t c lu ste rs shou ld be w ith in th e tim e w indow for m assless p artic le s,

|t cluster — R cluster / c | < 5 a ( t) , w hile n e u tra l c lu ste rs d o n o t have a n asso c ia te d tra c k in th e D C .

• A t least one of th e p ro m p t n e u tra l c lu ste rs h as en e rg y g re a te r th a n 250 M eV . T h e h ig h est en e rg y c lu ste r is a ssu m ed to o rig in a te from th e y , p h o to n .

• T h e tw o tra c k s w ith in a c y lin d rica l v olum e w ith ra d iu s 8 cm a n d ax ial p o sitio n ± 1 5 cm from th e b e a m crossing, a n d w ith o p p o s ite c u rv a tu re , are chosen. In th e follow ing th e se tra c k s a re a ssu m ed to b e d u e to ch a rg ed pions. D is c rim in a tio n a g a in s t elec tro n c o n ta m in a tio n from B h a b h a s c a tte rin g is achieved by m ean s of T im e O f F lig h t as discu ssed in th e following.

• P , , th e fo u r-m o m e n tu m o f th e 0 m eson, is d e te rm in e d u sin g th e b e a m -b e a m en erg y

t/ s a n d th e 0 tra n s v e rs e m o m e n tu m m e a su re d in B h a b h a s c a tte rin g ev en ts for each ru n .

• T h e y , d ire c tio n is o b ta in e d from th e p o s itio n o f th e E M C c lu s te r w hile its en ­ e r g y /m o m e n tu m is c a lc u la te d from th e tw o b o d y k in e m a tic s o f th e 0 ^ nY , decay:

2 2

= —

EY 2 { E , — |p , | cos 9 , , 7)

w h ere 9 ,,Y is th e angle b etw e en th e 0 a n d th e y , m o m e n ta . T h e fo u r-m o m e n tu m of th e n m eson is th e n : P n = P , — P YY.

• T h e n ° fo u r-m o m e n tu m is c a lc u la te d from th e m issin g fo u r-m o m e n tu m to n a n d th e ch a rg ed pions: P no = P n — P n+ — P n- .

• To re d u ce th e B h a b h a s c a tte rin g b ac k g ro u n d , th e follow ing tw o c u ts a re ap plied:

- a c u t in th e (9+Y,9-Y ) p la n e as show n in figure 1, w h ere 9+Y(9-Y ) is th e ang le b etw e en th e n + ( n - ) a n d th e closest p h o to n from n ° decay.

- a c u t in th e ( A t e, A t n ) p la n e as show n in figure 2, to d is c rim in a te e lec tro n s from pions, w h ere A t e , A t n a re c a lc u la te d for tra c k s w hich have a n asso c ia te d c lu ste r, A te /n = ttracke/n — tciuster, w h ere ttracke/n, is th e e x p e c te d a rriv a l tim e to E M C for e / n w ith th e m e a su re d m o m e n tu m , a n d t cluster th e m e a su re d tim e of th e E M C clu ster.

-

5

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(8)

Signal MC Bhabha MC

0.7 (rad)

F ig u r e 1. (Color online) 0+1 vs 0+1 angle plot. The three panels correspond to signal MC, B habha MC and the data. The three regions in the corners w ith borders marked by red lines represent the B habha rejection cut applied in th e analysis.

• To im prove th e a g re e m e n t b etw e en sim u la tio n a n d d a ta , a c o rre c tio n for th e re la tiv e yields of: (i) e + e - ^ w n°, a n d (ii) su m o f all o th e r b ac k g ro u n d s, w ith re sp e c t to th e signal is ap p lied . T h e c o rre c tio n fa c to rs a re o b ta in e d fro m a fit to th e d is trib u tio n of th e a z im u th a l an g le b etw e en th e n0 d ecay p h o to n s, in th e n0 re st fram e, 0*7 (figure 3) . T h e u n c e rta in tie s of th e c o rre c tio n fa c to rs a re ta k e n as h a lf of th e difference b etw een th e value o b ta in e d from th e co rre sp o n d in g fit to th e d is trib u tio n o f th e m issin g m ass sq u a re d , P^o (figure 4) .

• To f u r th e r re d u ce th e b a c k g ro u n d c o n ta m in a tio n , tw o m o re c u ts are ap plied :

- 0*7 > 165°, see figure 3 ;

- l|P no | — m no | < 15 M eV , see figure 4 ;

T h e overall signal efficiency is 37.6% a t th e en d o f th e an a ly sis c h a in a n d th e sig nal to b a c k g ro u n d ra tio is 133.

A s c a n be seen in figures 3 , 4 a n d 6 th e a g reem en t of sim u la tio n w ith th e e x p e rim e n ta l d a t a is good.

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(9)

F ig u re 2. (Color online) At e vs A tn plots for signal MC, B habha MC and the data. Events above the blue (dotted) line or above the black (full) line are rejected.

F ig u re 3. (Color online) Azimuthal angle difference between the n 0 decay photons in the n 0 rest frame, 0* , with the MC contributions scaled. The cut 0* > 165° is shown by the vertical line.

- 7 -

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(10)

F ig u re 4. (Color online) Missing mass squared, P%0, with the MC contributions scaled. The cut

||P n01 — m no | < 15 MeV is represented by the two vertical lines.

F ig u re 5. (Color online) The distributions of 0* (left) and P ^ 0 (right) after all the analysis cuts.

F ig u re 6. D istribution of the reconstructed m om entum of n 0 (left) and n (right) for the d a ta and MC.

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(11)

F ig u re 7. (Color online) Top: 0*7 angle distribution with the MC contributions scaled; the selected region is at the right of the vertical line. Bottom : missing mass squared,P^o, with the MC contributions scaled. The selected region is between the vertical lines. L eft/right: bin of the D alitz plot with the largest/sm allest num ber of entries, corresponding to (X, Y ) — (0.000, —0.850) and (X, Y ) — (—0.065,0.750), respectively.

F ig u re 8. (Color online) Resolution of the Dalitz plot variables X (left) and Y (right) from the signal Monte Carlo simulations. The full line approxim ates the sim ulated distribution by a sum of two G aussian functions; the dashed line represent the contribution of the broader Gaussian. The stan d ard deviation of the narrower G aussian is used in the discussion of the Dalitz plot bin width.

-

9

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(12)

F ig u r e 9. (Color online) The experim ental background subtracted Dalitz plot distribution repre­

sented by the two dimensional histogram w ith 371 bins. Only bins used for the Dalitz param eter fits are shown. The physical border is indicated by the red line.

4 D a l i t z p l o t

F o r th e D a litz p lo t, a tw o d im en sio n al h isto g ra m re p re s e n ta tio n is used . T h e bin w id th is d e te rm in e d b o th by th e re so lu tio n in th e X a n d Y v aria b les a n d th e n u m b e r o f ev e n ts in each bin, w hich sh o u ld be larg e e n o u g h to ju s tify x2 fittin g . T h e re so lu tio n o f th e X a n d Y v aria b les is e v a lu a te d w ith M C signal s im u la tio n (figure 8) . T h e d is trib u tio n o f th e differ­

ence b etw een th e tr u e a n d re c o n s tru c te d values is fit w ith a su m o f tw o G a u ssia n fu n c tio n s.

T h e s ta n d a r d d e v ia tio n s of th e n arro w er G a u ssia n s a re 5X = 0.021 a n d 5 y = 0.032. T h e ra n g e ( - 1 , 1 ) for th e X a n d Y v aria b les w as d iv id ed in to 31 a n d 20 bins, respectively. T h e re ­ fore th e b in w id th s co rre sp o n d to a p p ro x im a te ly th re e s ta n d a r d d e v ia tio n s. T h e m in im u m b in c o n te n t is 3.3 ■ 103 ev en ts. F ig u re 7 show s th e d is trib u tio n s o f th e 0*7 a n d th e P 2o v a ri­

ables for tw o bins in th e D a litz p lo t, o ne w ith th e la rg e st c o n te n t a n d on e w ith th e sm allest.

As c a n b e seen, th e signal a n d th e b a c k g ro u n d a re well re p ro d u c e d by th e sim u la tio n . F ig u re 9 show s th e e x p e rim e n ta l D a litz p lo t d is trib u tio n a fte r b a c k g ro u n d s u b tra c tio n , w hich is fit to th e a m p litu d e e x p a n sio n from eq. ( 1.5) to e x tra c t th e D a litz p lo t p a ra m e te rs.

O n ly n = 371 bins w hich are fully insid e th e k in e m a tic b o u n d a rie s are u sed a n d th e re are

~ 4.7 ■ 106 e n trie s in th e b a c k g ro u n d s u b tra c te d D a litz p lo t.

T h e fit is p erfo rm ed by m in im izin g th e x2 like fu n c tio n

x2 = £ ^ y ( 4, )

w here:

• N T ,j = / |A (X , Y ) |2d P h ( X , Y ) j , w ith |A (X , Y) | 2 given by eq. ( 1.5) . T h e in te g ra l is over X a n d Y in th e allow ed p h a se space for b in j . T h e su m over j bins in clud es all D a litz p lo t bins a t le a st p a r tly inside th e p h ysical b o rd e r, n T .

• N = Ndatay — A B j i — ^2Bi2 is th e b a c k g ro u n d s u b tra c te d c o n te n t of D a litz p lo t b in i, w h ere ^ 1>2 a re th e scaling fa cto rs, Bi1 is th e w n0 b a c k g ro u n d in th e b in i a n d Bi2

is th e sam e for th e re m a in in g b a c k g ro u n d .

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(13)

F i t / s e t # a b ■ 10 d 10 2 f ■ 10 g ■ 1 0 2 c, e, h , l X2/ d o f p -v a lu e (1) - 1 . 0 9 5 ± 0 .0 0 3 1 .4 5 4 ± 0 .0 3 0 8.11 ± 0.32 1.41 ± 0 .0 7 - 4 . 4 ± 0.9 free 3 5 4 /3 6 1 0 .6 0

(2) - 1 . 1 0 4 ± 0 .0 0 2 1 .5 3 3 ± 0 .0 2 8 6 .7 5 ± 0 .2 7 0 0 0 1 0 0 7 /3 6 7 0

(3) - 1 . 1 0 4 ± 0 .0 0 3 1 .4 2 0 ± 0 .0 2 9 7 .2 6 ± 0 .2 7 1 .5 4 ± 0.06 0 0 3 8 5 /3 6 6 0 .2 4 (4) - 1 . 0 3 5 ± 0 .0 0 2 1 .5 9 8 ± 0 .0 2 9 9 .1 4 ± 0 .3 3 0 - 1 1 . 7 ± 0.9 free 7 9 2 /3 6 2 0 (5) - 1 . 0 9 5 ± 0 .0 0 3 1 .4 5 4 ± 0 .0 3 0 8.11 ± 0 .3 3 1.41 ± 0 .0 7 - 4 . 4 ± 0.9 0 3 6 0 /3 6 5 0.56 (6) - 1 . 0 9 2 ± 0 .0 0 3 1.45 ± 0 .0 3 8.1 ± 0.3 1 .3 7 ± 0.06 - 4 . 4 ± 0.9 0 3 6 9 /3 6 5 0 .4 3

(7) - 1 . 1 0 1 ± 0 .0 0 3 1.41 ± 0 .0 3 7.2 ± 0.3 1 .5 0 ± 0.06 0 0 3 9 7 /3 6 6 0 .1 3

T a b le 2. Results for the Dalitz plot param eter fits. The m ain result corresponds to fit # 5 which includes b oth cubic param eters g and f , while fit # 3 , w ith g = 0, can be directly com pared to previous results. The fits # 6 and # 7 use the acceptance corrected d ata (see appendix A) .

• S ij is th e a c c e p ta n c e a n d sm earin g m a trix fro m bin j to b in i in th e D a litz p lo t. It is d e te rm in e d from signal M C by S ij = N rec,i;gen, j / N gen, j , w h ere N rec,i;gen,j d e n o te s th e n u m b e r of ev en ts re c o n s tru c te d in b in i w hich w ere g e n e ra te d in b in j a n d N gen,j d e n o te s th e to ta l n u m b e r o f ev e n ts g e n e ra te d in b in j .

• a i = a Ni + a2Sij is th e e rro r in b in i, w ith a2Sij = 1 N T,j ■ S ij ■( 1 - S i j ) / N gen,j.

T h e in p u t- o u tp u t te s t o f th e fit p ro c e d u re w as p erfo rm ed using sig nal M C g e n e ra te d w ith th e sam e s ta tis tic s as th e e x p e rim e n ta l d a ta . T h e e x tra c te d values for th e p a ra m e te rs w ere w ith in one s ta n d a r d d e v ia tio n w ith re sp e c t to th e in p u t.

T h e fit h as b ee n p erfo rm ed u sin g d ifferen t choices of th e free p a ra m e te rs in eq. ( 1.5) , w ith th e n o rm a liz a tio n N a n d th e p a ra m e te rs a, b a n d d alw ays let free. T h e m a in fit re su lts a re su m m a riz e d in ta b le 2 . T h e first row (set # 1 ) in clu des all p a ra m e te rs of th e cu b ic e x p a n sio n , eq. ( 1.5) . T h e fit values of th e ch a rg e c o n ju g a tio n v io la tin g p a ra m e te rs c , e , h a n d l are c o n siste n t w ith zero (c = (4 .3 ± 3 .4 )-1 0 -3, e = (2 .5 ± 3 .2 )-1 0 -3, h = (1 .1 ± 0 .9 )-1 0 -2, l = (1.1 ± 6.5) ■ 10-3) a n d a re o m itte d from th e ta b le . T h erefo re o u r m a in re su lts are o b ta in e d w ith th e ch a rg e c o n ju g a tio n v io la tin g p a ra m e te rs c, e, h a n d l set to zero. F it

# 2 w ith f = g = 0 d e m o n s tra te s t h a t it is n o t p o ssib le to d esc rib e th e e x p e rim e n ta l d is trib u tio n w ith o n ly q u a d r a tic te rm s . F it # 3 in clu d in g th e f p a r a m e te r a n d w ith g = 0 gives a re a so n a b le x2/ n d f value of 3 8 5 /3 6 6 . O n th e c o n tra ry th e c o m p le m e n ta ry selection o f th e cu b ic p a ra m e te rs f = 0 a n d g free (fit # 4 ) do es n o t p ro v id e a d e q u a te d e sc rip tio n o f th e d a ta . F in a lly fit # 5 w hich includ es b o th f a n d g p a ra m e te rs , gives th e g p a r a m e te r n e g a tiv e a n d d ifferen t from zero a t th e 4 .9 a level. T o co m p a re go o d n ess o f th e fit b etw een cases # 3 a n d # 5 one sh o u ld re m e m b e r t h a t th e p a ra m e te rs in th e tw o fits are th e sam e ex c e p t for one e x tr a p a r a m e te r in fit # 5 . T h erefo re if th e g p a r a m e te r is n o t significant we e x p e c t t h a t th e xSe t # 3 — x2et# 5 v aria b le will h ave chi sq u a re d d is trib u tio n w ith one deg ree of freedom . T h e d e te rm in e d valu e o f 25 allow s us to p re fer fit # 5 over # 3 . In case of u n c o rre la te d p a ra m e te rs one e x p e c ts th e chi sq u a re d ifference h as a n o n -c e n tra l chi sq u a re d d is trib u tio n w ith one deg ree of freed om a n d th e m e a n v alu e of ( g / a g)2 fully c o n s is te n t w ith th e d a ta . H ow ever, in th e f u r th e r d iscussion s we in clu d e also set # 3 w ith

-

11

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(14)

F ig u r e 10. (Color online) The experim ental background subtracted Dalitz plot data, N i , (points w ith errors), com pared to set # 5 fit results (red lines connecting bins with the same Y value). The row with lowest N i values corresponds to the highest Y value (Y = +0.75).

g = 0, since it en a b le s a m ore d ire c t co m p ariso n to th e p re v io u s e x p e rim e n ts (K L O E (0 8 ), W A SA (14) a n d B E S III(1 5 )). T h e c o rre la tio n m a tric e s for fits # 3 a n d # 5 are:

b d f

a —0.269 —0.365 —0.832

b + 0 .3 3 3 —0.139

d + 0 .0 8 9

b d f g

a 0.120 + 0 .0 4 4 —0.859 —0.534

b + 0 .3 8 9 0.201 —0.225

d —0.160 —0.557

f + 0 .4 0 8 .

T h e fit # 5 is co m p a re d to th e b a c k g ro u n d s u b tra c te d D a litz p lo t d a ta , Ni , in figure 10.

T h e red lines re p re se n t th e fit re su lt a n d co rre sp o n d to s e p a ra te slices in th e Y variab le.

F ig u re 11 show s th e d is trib u tio n of th e n o rm alize d re sid u a ls for th e fit # 5 : r i = (N i —

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(15)

E x p e r im e n t Al r x 10- 2 A q x 10- 2 A s x 10- 2 G orm ley (6 8 ) [27]

L a y te r(7 2 ) [28]

Ja n e (7 4 ) [29]

K L O E (0 8 ) [19]

K L O E (th is w ork)

+ 1 .5 ± 0.5 — 0.5 ± 0.5

—0.05 ± 0.22 —0.07 ± 0.22 0.10 ± 0.22

+ 0 .2 8 ± 0.26 —0.30 ± 0.25 0.20 ± 0.25

+ 0 .0 9 ± 0.10+0.09 —0.05 ± 0.010+0.03 0.08 ± 0.10+0.03

—0.050 ± 0.045+0.0fo 0.020 ± 0.045+0.028 0.004 ± 0.045+0.035 T a b le 3. Results on the asym m etry param eters.

+ j =1 S i j N T,j) / ^ j . T h e lo c a tio n of th e re sid u a ls ri > 1 a n d r i < —1 on th e D a litz p lo t is u n ifo rm . T h e fits # 6 a n d # 7 use th e a c c e p ta n c e c o rre c te d d a t a (see a p p e n d ix A ) .

5 A sy m m e tr ie s

W h ile th e e x tra c te d D a litz p lo t p a ra m e te rs are co n siste n t w ith c h a rg e c o n ju g a tio n sy m ­ m etry , th e u n b in n e d in te g ra te d ch a rg e a sy m m e trie s p ro v id e a m ore sensitiv e te s t. T h e le ft-rig h t (Al r), q u a d r a n t (Aq ) a n d s e x ta n t (As) a sy m m e trie s a re d efined in ref. [28]. T h e sam e b a c k g ro u n d s u b tra c tio n is a p p lie d as for th e D a litz p lo t p a r a m e te r an aly sis. F or each region in th e D a litz p lo t used in th e c a lc u la tio n of th e a sy m m e trie s, th e a c c e p ta n c e is c a lc u la te d from th e signal M C as th e ra tio b etw e en th e n u m b e r of th e re c o n s tru c te d an d th e g e n e ra te d events. T h e yields a re th e n c o rre c te d for th e co rre sp o n d in g efficiency. T h e p ro c e d u re w as te s te d u sin g sign al M C g e n e ra te d w ith th e sam e s ta tis tic s as th e e x p e ri­

m e n ta l d a ta . T h e re su lts for th e a sy m m e trie s a re p re se n te d in th e ta b le 3 a n d co m p a re d to o th e r ex p e rim e n ts. T h e s ta tis tic a l a c c u ra c y for all a sy m m e trie s in th e p re se n t analy sis is 4.5 ■ 10- 4 . T h e d iscu ssio n of th e sy ste m a tic a l u n c e rta in tie s is given in sec tio n 6 .

6 S y s te m a tic ch eck s

To q u a n tify a n d ac c o u n t for s y s te m a tic effects in th e re su lts, several checks have b een m ad e.

-

13

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

F ig u r e 11. (Color online) D istribution of the normalized residuals, r*, for fit # 5 .

(16)

• M in im u m p h o to n en e rg y c u t (E G m in ) is ch a n g ed from 10 M eV to 20 M eV (for co m ­ p a riso n th e E M C en e rg y re so lu tio n varies from 60% to 40% for th is en e rg y ra n g e).

T h e sy s te m a tic e rro r is ta k e n as h a lf o f th e difference.

• B ac k g ro u n d s u b tra c tio n (B kgS u b) is checked by d e te rm in in g th e b a c k g ro u n d scalin g fa c to rs for each b in (o r regio n for th e a sy m m e trie s) o f th e D a litz p lo t sep a rately . W ith th e sam e m e th o d as for th e w hole d a t a sam p le, u sin g th e a n d P2 d is trib u tio n s , b a c k g ro u n d scaling fa c to rs a re d e te rm in e d for each b in (o r regio n). T h e sy s te m a tic e rro r is ta k e n as h a lf th e difference w ith th e s ta n d a r d re su lt.

• C hoice of b in n in g (B IN ) is te s te d by v ary in g n u m b e r o f b in s of th e D a litz p lo t. F o r X a n d Y sim u ltan eo u sly , th e b in w id th is v aried from ~ 2£X,Y to ~ 55X,Y , in to ta l 10 co n fig u ratio n s. T h e s y s te m a tic u n c e rta in ty is given by th e s ta n d a r d d e v ia tio n of th e re su lts.

0+7,0 _ 7 c u t: th e a reas of th e th re e zones show n in figure 1 w ere s im u lta n e o u sly varied by ±1 0%.

• A t e , A t n c u t: th e offsets of th e h o riz o n ta l a n d d ia g o n a l lines show n in figure 2 w ere v aried by ±0 . 2 2 ns a n d ±0 . 2 1 ns, respectively.

• 0*7 c u t is varied by ± 3 ° , co rre sp o n d in g to ~ 1 a.

• M issing m ass c u t (M M ) is te s te d by v ary in g th e c u t by ± 2 .0 M eV , ~ 1a. F o r th is c u t a s tro n g e r d e p e n d e n c e of th e p a ra m e te rs o n th e c u t w as n o te d . T h is h as been fu r th e r in v e stig a te d by p e rfo rm in g th e D a litz p lo t p a r a m e te r fit for one p a r a m e te r a t a tim e , for each step , a n d k eepin g th e o th e r p a ra m e te rs fixed a t th e valu e for th e s ta n d a r d re su lt. Since th e d e p e n d e n c e w as re d u ced w h en v a ry in g j u s t one p a ra m e te r, we co n clu d e t h a t it is m o stly d u e to th e c o rre la tio n s b etw e en p a ra m e te rs .

• E v e n t classificatio n p ro c e d u re (E C L ) is in v e stig a te d by u sin g a p re scaled d a t a sam p le w ith o u t th e ev en t classificatio n b ias (co llected w ith p re scalin g fa c to r 1 /2 0 ). T h e fra c tio n of ev e n ts re m a in in g in each D a litz p lo t b in a fte r th e ev en t classificatio n c o n d itio n s varies b etw e en 94% a n d 80% for d ifferent b in s a n d it is v ery well d esc rib ed by th e M C w ith in th e erro rs. T h e an aly sis of th e p re scaled d a t a follows th e s ta n d a r d ch ain . T h e s y s te m a tic e rro r is e x tra c te d as h a lf th e difference b etw e en th e re su lts of th e an a ly sis w ith a n d w ith o u t th e ev en t classificatio n p ro c ed u re .

U nless s ta te d o th e rw ise th e sy s te m a tic e rro r is c a lc u la te d as th e difference b etw e en th e tw o te s ts a n d th e s ta n d a r d re su lt. If b o th differences have th e sam e sign, th e a sy m m e tric e rro r is ta k e n w ith one b o u n d a ry set a t zero a n d th e o th e r a t th e la rg e st of th e differences. T h e re s u ltin g s y s te m a tic e rro r c o n trib u tio n s fo r th e D a litz p lo t p a ra m e te rs for th e sets # 5 an d

# 3 are su m m a riz e d in ta b le 4 a n d ta b le 5 , resp ectiv ely . T h e s y s te m a tic e rro r c o n trib u tio n s fo r th e ch a rg e a sy m m e trie s a re s u m m a riz e d in ta b le 6.

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(17)

sy st. e rro r ( x1 04) A a Ab A d A f A g

E G m i n ± 6 ± 1 2 ± 1 0 ± 5 ± 1 6

B k g S u b ± 8 ± 7 ± 1 1 ± 6 ± 3 8

B I N ± 1 7 ± 1 3 ± 9 ± 3 6 ± 4 4

0+Y, 0 - Y c u t A t e c u t A t e — A t n c u t

+ 0 - 1

+ 6 - 1 1

± 0 + 0 - 2 + 1 2 - 1

+ 0 - 1

+ 2 - 2

+18

- 1

+3

- 1

+3

- 0

+3

- 8

± 0

+3

- 2

+26-54

+ 2 - 1

d*Y c u t M M

+ 14 - 5 + 8 - 1 0

+ 2 - 1

+46-43

+ 2 1 - 1 2

+49-45 + 5-25 +57-62

+26-38

+ 1 0 0

- 92

E C L ± 0 ± 8 ± 6 ± 9 ± 1 2

T O T A L +26

-25 +52

-48 +59

-50 +69

-77 +123

-129

T a b le 4. Sum m ary of the system atic errors for a, b, d, f , g param eters (fit # 5 ).

sy st. e rro r ( x1 0 4) A a A b A d A f

E G m i n ± 9 ± 1 0 ± 6 ± 0

B k g S u b ± 1 ± 5 ± 6 ± 8

B I N ± 9 ± 1 4 ± 9 ± 2 6

0+Y, 0-Y c u t + 0- 1 + 0- 2 + 1- 1 +4

- 0

A t e c u t + 0- 6 + 14

- 6

+7

- 0

+ 19 -15 A te — A tn c u t ± 0 + 0- 1

+3

- 0 ± 0

e*Y c u t + 6- 0 + 1- 1 +14

- 8 + 0

-13

M M + 1 0- 1 0 +39

-36 +31

-26 +28

-35

E C L ± 2 ± 9 ± 9 ± 1 3

T O T A L +18

-18 +46

-41 +38

-31 +45

-51

T a b le 5. Sum m ary of the system atic errors for a, b, d, f param eters (fit # 3 ).

7 D i s c u s s i o n

T h e final re su lts fo r th e D a litz p lo t p a ra m e te rs , in clu d in g s y s te m a tic effects, a re th ere fo re : a = - 1 .0 9 5 ± 0.003-0.002

b = + 0 .1 4 5 ± 0.003 ± 0.005 d = + 0 .0 8 1 ± 0.003-0.000 f = + 0 .1 4 1 ± 0.007-0.008 g = - 0 .0 4 4 ± 0.009-0.013

-

15

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(18)

sy st. e rro r ( x1 0 5) A Al r A Aq A As

E G m i n ± 1 ± 0 ± 4

B k g S u b ± 5 ± 3 ± 1 6

d-Y , Q-y c u t - 2- 0 - 0- 2 - 2- 0

A t e c u t -49

-92 -48

- 2 2

- 7 -15 A t e — A t n c u t - 0- 2 - 3

- 0

- 0 - 1

— c u t - 1

-57 - 3

- 4 - 0- 8

M M - 0-4 - 0- 1

- 1 - 2

E C L ± 9 ± 0 ± 2 5

T O T A L - 50

-109 -48

-23 -31

-35

T a b le 6. Sum m ary of the system atic errors for the asymmetries.

in clu d in g th e g p a ra m e te r. W ith g p a r a m e te r set to zero th e re su lts are:

a = - 1 .1 0 4 ± 0.003 ± 0.002 b = + 0 .1 4 2 ± 0.003-0.004 d = + 0 .0 7 3 ± 0.003-0.003 f = + 0 .1 5 4 ± 0.006-0:004.

T h ese re su lts co nfirm th e te n sio n w ith th e th e o re tic a l c a lc u la tio n s on th e b p a ra m e te r, a n d also th e need for th e f p a ra m e te r. In co m p a riso n to th e p re v io u s m e a su re m e n ts show n in ta b le 1, th e p re se n t re su lts are th e m o st p recise a n d th e first in clu d in g th e g p a ra m e te r.

T h e im p ro v em en t over K L O E (0 8 ) an aly sis com es from fo u r tim e s la rg e r s ta tis tic s an d im p ro v em en t in th e s y s te m a tic u n c e rta in tie s w h ich are in som e cases re d u ced b y fa c to r 2 — 3. T h e m a jo r im p ro v em en t in th e s y s te m a tic u n c e rta in tie s com es from th e an a ly sis of th e effect of th e E v e n t classificatio n w ith an u n b iased p re scaled d a t a sam p le.

T h e final values o f th e c h a rg e a sy m m e trie s are all co n siste n t w ith zero:

Al r = ( —5.0 ± 4.5— ) ■ 1 0-4

Aq = ( +1 . 8 ± 4.5— ■1 0-4

As = ( —0.4 ± 4.5— ■ 10-4.

T h e s y s te m a tic a n d s ta tis tic a l u n c e rta in tie s a re o f th e sam e size ex c e p t for th e Al r w hich is d o m in a te d by th e sy s te m a tic u n c e rta in ty d u e to th e d e s c rip tio n of th e B h a b h a b a c k g ro u n d .

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(19)

A c k n o w le d g m e n ts

W e w a rm ly th a n k o u r fo rm e r K L O E colleagues for th e access to th e d a t a co llected d u r ­ ing th e K L O E d a t a ta k in g ca m p a ig n . W e th a n k th e D A $ N E te a m for th e ir efforts in m a in ta in in g low b a c k g ro u n d ru n n in g c o n d itio n s a n d th e ir c o lla b o ra tio n d u rin g all d a t a ta k in g . W e w a n t to th a n k o u r te c h n ic a l staff: G .F . F o rtu g n o a n d F . S b o rzacch i for th e ir d e d ic a tio n in e n su rin g efficient o p e ra tio n of th e K L O E c o m p u tin g facilities; M. A nelli for his co n tin u o u s a tte n tio n to th e gas sy ste m a n d d e te c to r safety; A. B alla, M . G a tta , G. C o rra d i a n d G. P a p a lin o for elec tro n ics m a in te n a n c e ; M. S an to n i, G. P ao lu zzi an d R . R o sellini for g en e ral d e te c to r su p p o rt; C. P isc ite lli for his help d u rin g m a jo r m a in ­ te n a n c e p erio d s. T h is w ork w as s u p p o rte d in p a r t by th e E U In te g r a te d I n f ra s tru c tu r e In itia tiv e H a d ro n P h y sic s P ro je c t u n d e r c o n tra c t n u m b e r R II3 -C T - 2004-506078; by th e E u ro p e a n C om m ission u n d e r th e 7 th F ram ew o rk P ro g ra m m e th ro u g h th e ‘R esea rch In ­ f r a s tr u c tu r e s ’ a c tio n o f th e ‘C a p a c itie s ’ P ro g ra m m e , C all: F P 7 -IN F R A S T R U C T U R E S - 2008-1, G ra n t A g re em en t N o. 227431; by th e P o lish N a tio n a l S cience C e n tre th ro u g h th e G ra n ts N o. 2 0 1 1 /0 3 /N /S T 2 /0 2 6 5 2 , 2 0 1 3 /0 8 /M /S T 2 /0 0 3 2 3 , 2 0 1 3 /1 1 /B /S T 2 /0 4 2 4 5 , 2 0 1 4 /1 4 /E /S T 2 /0 0 2 6 2 , 2 0 1 4 /1 2 /S /S T 2 /0 0 4 5 9 .

A A c c e p ta n c e c o rr e cte d d a ta

W ith a sm earin g m a tr ix close to d ia g o n a l a n d th e sm earin g to a n d from n e a rb y bins sy m ­ m e tric a l, th e a c c e p ta n c e c o rre c te d d a t a ca n b e used in s te a d o f d e a lin g w ith th e sm earin g m a trix . T h is re p re s e n ta tio n h as th e a d v a n ta g e o f b ein g m u ch easier to co m p a re d ire c tly w ith th e o re tic a l c a lc u la tio n s. T h e a c c e p ta n c e c o rre c te d sig nal c o n te n t in each b in of th e D a litz p lo t is o b ta in e d by d iv id in g th e b ac k g ro u n d s u b tra c te d c o n te n t, Nj, by th e c o r­

re sp o n d in g ac c e p ta n c e , e». T h e a c c e p ta n c e is o b ta in e d from th e sig nal M C by d iv id in g th e n u m b e r of re c o n s tru c te d ev e n ts a llo c a te d to th e b in i by th e n u m b e r of g e n e ra te d (u n sm e a re d ) signal ev e n ts in t h a t bin.

T h e fit to e x tra c t th e D a litz p lo t p a ra m e te rs values is d o n e now by m in im izin g

w h ere th e sum includes o n ly bins c o m p letely in sid e th e D a litz p lo t b o u n d a rie s a n d N y,j — f f |A (X , Y ) |2d X i dYi . T h e s ta tis tic a l u n c e rta in ty a in clud es c o n trib u tio n s from th e e x p e r­

im e n ta l d a ta , th e b a c k g ro u n d e s tim a te d from M C a n d th e efficiency. T h e fitte d D a litz p lo t p a ra m e te rs using th e a c c e p ta n c e c o rre c te d d a t a a re p re se n te d in ta b le 2 as sets # 6 w ith g p a r a m e te r a n d # 7 w ith g — 0. T h e re su lts a re id e n tic a l w ith in s ta tis tic a l u n c e rta in tie s w ith th e values o b ta in e d usin g th e sm earin g m a trix . T h erefo re th e a c c e p ta n c e co rrec te d d a t a c a n b e u sed to re p re se n t th e m e a su re d D a litz p lo t d e n s ity if o ne neg lects s y s te m a tic a l u n c e rta in tie s. T h e ta b le c o n ta in in g D a litz p lo t a c c e p ta n c e c o rre c te d d a t a (n o rm a liz ed to th e c o n te n t of th e X c — 0.0, Y — 0.05 b in ), is p ro v id ed as a s u p p le m e n ta ry m a te ria l (file D P h i s t _ a c c c o r r .t x t ). T h e c o rre la tio n m a tr ix for th e fit # 6 reads:

(A .1)

- 17 -

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

2 f N i / e i — N T,i \ x = ^ { 1 = 1 * ---

(20)

b d f g a - 0 . 1 1 0 + 0 .0 0 6 - 0 .8 4 9 -0 .5 1 2

b + 0 .3 9 7 - 0 . 216 - 0 .2 3 9

d - 0 .1 3 3 - 0 .5 3 7

f + 0 .3 8 0 .

O p e n A c c e s s . T h is a rtic le is d is trib u te d u n d e r th e te rm s o f th e C re a tiv e C o m m on s A ttr ib u tio n L icense ( C C -B Y 4.0) , w hich p e rm its an y use, d is trib u tio n a n d re p ro d u c tio n in a n y m ed iu m , p ro v id ed th e o rig in al a u th o r(s ) a n d so urce are c re d ite d .

R e f e r e n c e s

[1] D.G. Sutherland, Current algebra and the decay n ^ 3n, Phys. Lett. 23 (1966) 384 [i nSPIRE].

[2] J.S. Bell and D.G. Sutherland, Current algebra and n ^ 3n, Nucl. Phys. B 4 (1968) 315 [i nSPIRE].

[3] R. Baur, J. Kam bor and D. Wyler, Electromagnetic corrections to the decays n ^ 3n, Nucl.

Phys. B 460 (1996) 127 [hep-ph/9 51 03 96 ] [i nSPIRE].

[4] C. Ditsche, B. Kubis and U.-G. Meifiner, Electromagnetic corrections in n ^ 3n decays, Eur.

Phys. J. C 60 (2009) 83 [a rX iv :0 8 1 2 .0 3 4 4 ] [i nSPIRE].

[5] J. Bijnens and J. Gasser, Eta decays at and beyond p 4 in chiral perturbation theory, Phys.

Scripta T 99 (2002) 34 [hep-ph/0 20 224 2] [i nSPIRE].

[6] H. Leutwyler, The ratios of the light quark masses, Phys. Lett. B 378 (1996) 313 [hep-ph/9602366] [i nSPIRE].

[7] R.F. Dashen, Chiral SU(3) x SU(3) as a sym m etry of the strong interactions, Phys. Rev. 183 (1969) 1245 [i nSPIRE].

[8] J. Gasser and H. Leutwyler, n ^ 3n to one loop, Nucl. Phys. B 250 (1985) 539 [i nSPIRE].

[9] Pa r t i c l e Da t a Gr o u p collaboration, K.A. Olive et al., Review of particle physics, Chin.

Phys. C 38 (2014) 090001 [i nSPIRE].

[10] J. Bijnens and K. Ghorbani, n ^ 3n at two loops in chiral perturbation theory, JH EP 11 (2007) 030 [a rX iv :0 7 0 9 .0 2 3 0 ] [i nSPIRE].

[11] B. Borasoy and R. Nissler, Hadronic n and n' decays, Eur. Phys. J. A 26 (2005) 383 [hep-ph/051038 4] [i nSPIRE].

[12] S.P. Schneider, B. Kubis and C. Ditsche, Rescattering effects in n ^ 3n decays, JH EP 02 (2011) 028 [a rX iv :1 0 1 0 .3 9 4 6 ] [i nSPIRE].

[13] K. Kampf, M. Knecht, J. Novotny and M. Zdrahal, Analytical dispersive construction of n ^ 3n amplitude: first order in isospin breaking, Phys. Rev. D 84 (2011) 114015 [a rX iv :1 1 0 3 .0 9 8 2 ] [i nSPIRE].

[14] G. Colangelo, S. Lanz, H. Leutwyler and E. Passem ar, D eterm ination of the light quark masses from n ^ 3n, PoS(EPS-HEP2011)304 [i nSPIRE].

[15] P. Guo et al., Three-body final state interaction in n ^ 3n, Phys. Rev. D 92 (2015) 054016 [a rX iv :1 5 0 5 .0 1 7 1 5 ] [i nSPIRE].

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

(21)

[16] M. Gormley et al., Experimental determ ination of the Dalitz-plot distribution of the decays n ^ n + n - n° and n ^ n + n - y and the branching ratio n ^ n + n - y /n ^ n+, Phys. Rev. D 2 (1970) 501 [i nSPIRE].

[17] J.G . Layter et al., Study of Dalitz-plot distributions of the decays n ^ n + n - n° and n ^ n + n - y, Phys. Rev. D 7 (1973) 2565 [i nSPIRE].

[18] Cr y s t a l Ba r r e l collaboration, A. Abele et al., M om entum dependence o f the decay n ^ n + n - n°, Phys. Lett. B 4 1 7 (1998) 197 [i nSPIRE].

[19] K L O E collaboration, F. Ambrosino et al., D eterm ination of n ^ n + n - n° Dalitz plot slopes and asymm etries with the K L O E detector, JH EP 05 (2008) 006 [a rX iv :0 8 0 1 .2 6 4 2 ]

[i nSPIRE].

[20] W ASA-AT-COSY collaboration, P. Adlarson et al., Measurement o f the n ^ n + n - n° Dalitz plot distribution, Phys. Rev. C 90 (2014) 045207 [a rX iv :1 4 0 6 .2 5 0 5 ] [i nSPIRE].

[21] B E S III collaboration, M. Ablikim et al., M easurement of the m atrix elements fo r the decays n ^ n + n - n° and p /p ' ^ n °n °n °, Phys. Rev. D 92 (2015) 012014 [a rX iv :1 5 0 6 .0 5 3 6 0 ]

[i nSPIRE].

[22] J. Kambor, C. W iesendanger and D. Wyler, Final state interactions and

Khuri-Treimanequations in n ^ 3n decays, Nucl. Phys. B 46 5 (1996) 215 [hep-p h/9 50 93 74 ] [i nSPIRE].

[23] M. Adinolfi et al., The tracking detector of the K L O E experiment, Nucl. Instrum . Meth. A 488 (2002) 51 [i nSPIRE].

[24] M. Adinolfi et al., The K L O E electromagnetic calorimeter, Nucl. Instrum . Meth. A 482 (2002) 364 [i nSPIRE].

[25] K L O E collaboration, M. Adinolfi et al., The trigger system of the K L O E experiment, Nucl.

Instrum. Meth. A 4 92 (2002) 134 [i nSPIRE].

[26] F. Ambrosino et al., Data handling, reconstruction and simulation fo r the K L O E experiment, Nucl. Instrum . Meth. A 534 (2004) 403 [p h y sic s/0 4 0 4 1 0 0 ] [i nSPIRE].

[27] M. Gormley et al., Experimental test of C invariance in n ^ n + n - n°, Phys. Rev. Lett. 21 (1968) 402 [i nSPIRE].

[28] J.G . Layter et al., Measurement of the charge asym m etry in the decay n ^ n + n - n°, Phys.

Rev. Lett. 29 (1972) 316 [i nSPIRE].

[29] M.R. Jane et al., A measurement of the charge asym m etry in the decay n ^ n + n - n°, Phys.

Lett. B 48 (1974) 260 [i nSPIRE].

-

19

-

J H E P 0 5 ( 2 0 1 6 ) 0 1 9

Cytaty

Powiązane dokumenty

The global efficiency, which ranges from 0.086 at 0.605 GeV to 0.27 at 0.975 GeV, has been obtained from a μ + μ − γ events gen- eration with PHOKHARA interfaced with the

Results of the fits to the analyzing power data in dependence of the deuteron scattering angle by use of eq.. Results of the fits to the analyzing power data in dependence of the π

In the ρ – ω region the systematic error is computed by adding in quadrature the contributions due to the theoretical uncertainty of the Monte Carlo generator (0. 5% [26]),

Note that the generated Monte Carlo events were scaled according to the fit to data after preselection and that the sum of all Monte Carlo events remaining after all cuts is equal to

Additionally, the upper limit of the preliminary total cross section was determined for the first time for the ( 4 He–η) bound production in dd → 3 Henπ 0 reaction [15]2. This

In the analysis pre- sented here we have produced an acceptance-corrected Dalitz plot and extracted experimental values for parameters describing the density distribution..

35 (a) Institute o f High Energy Physics, Chinese Academy o f Sciences, Beijing; (b) Department o f Modern Physics, University o f Science and Technology o f China,

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing; (b) Department of Modern Physics, University of Science and Technology of China, Anhui; (c) Department