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
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
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
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
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
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
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
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
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
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
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.
-
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J H E P 0 5 ( 2 0 1 6 ) 0 1 9
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
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
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J H E P 0 5 ( 2 0 1 6 ) 0 1 9
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
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.
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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 .
• 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
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
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15-
J H E P 0 5 ( 2 0 1 6 ) 0 1 9
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
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 * ---
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 .
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