Eu . Phys. J. C (2014) 74:3092
DOI 10.1140/epjc/s10052-014-3092-z
Regula A icle - Expe imen al Physics
S udy o χbmeson p oduc ion in pp collisions a √s=7and8TeV
and obse a ion o he decay χb(3P)→ϒ(3S)γ
The LHCb Collabo a ion
CERN, 1211 Gene a 23, Swi ze land
Recei ed: 30 July 2014 / Accep ed: 22 Sep embe 2014 / Published online: 8 Oc obe 2014
© CERN o he bene i o he LHCb collabo a ion 2014. This a icle is published wi h open access a Sp inge link.com
Abs ac A s udy o χbmeson p oduc ion a LHCb is
pe o med on p o on–p o on collision da a, co esponding
o 3.0 b−1o in eg a ed luminosi y collec ed a cen e-o -
mass ene gies √s= 7 and 8 TeV. The ac ion o ϒ(nS)
mesons o igina ing om χbdecays is measu ed as a unc-
ion o he ϒ ans e se momen um in he apidi y ange
2.0<yϒ<4.5. The adia i e ansi ion o he χb(3P)
meson o ϒ(3S)is obse ed o he i s ime. The χb1 (3P)
mass is de e mined o be
mχb1 (3P)=10 511.3±1.7±2.5MeV/c2,
whe e he i s unce ain y is s a is ical and he second is
sys ema ic.
1 In oduc ion
The p oduc ion o qua konia s a es in high-ene gy had on
collisions is desc ibed in he amewo k o non- ela i is ic
quan um ch omodynamics(NRQCD), as wo-s ep p ocess:
a hea y qua k–an iqua k pai is i s c ea ed pe u ba i ely
a sho dis ances, hen i e ol es non-pe u ba i ely in o
qua konium a long dis ances. The NRQCD amewo k
makes use o a combina ion o colou -single and colou -
oc e mechanisms [1–5]. Recen calcula ions [6–10] suppo
he leading ole o he colou -single mechanism. The com-
pa ison o expe imen al da a o p omp p oduc ion o S-
wa e qua konia, e.g. J/ψo ϒ(1S)mesons, wi h heo y p e-
dic ions equi es knowledge o eed-down con ibu ions om
P-wa e qua konia s a es, e.g. adia i e χb→ϒγdecays.
This con ibu ion could signi ican ly in luence he in e p e a-
ion o he measu ed pola iza ion o S-wa e ec o qua konia.
In addi ion, measu emen s o he ela i e p oduc ion a es o
P-wa e o S-wa e qua konia, as well as he enso - o- ec o
a ios, p o ide aluable in o ma ion on colou -oc e ma ix
elemen s [10–12].
The p oduc ion o P-wa e cha monia, join ly e e ed o
as χcs a es, has been s udied by he CDF [13], HERA-B [14],
e-mail: I [email p o ec ed]
LHCb [15–17], CMS [18], and ATLAS [19] collabo a ions;
measu emen s in ol ing χbs a es ha e been pe o med by
he CDF [20], ATLAS [21], CMS [22] and LHCb [23,24]
expe imen s.
This pape p esen s a measu emen o he ac ions
o ϒmesons o igina ing om adia i e decays o χb
mesons. Depending on he ela i e o ien a ion o he qua k
spins, he χbs a es can be ei he scala , ec o o en-
so mesons, deno ed by χbJ wi h o al angula momen um
J=0,1,2. The ac ions o ϒ(nS)decays o igina ing om
χb(mP)decays, whe e n and m a e adial quan um numbe s
o he bound s a es a e de ined as
Rχb(mP)
ϒ(nS)≡
σ(pp →χb1 (mP)X)
σ(pp →ϒ(nS)X)×B1
+
σ(pp →χb2 (mP)X)
σ(pp →ϒ(nS)X)×B2,(1)
whe e B1(2)deno es he b anching ac ion o he decay
χb1(2)(mP)→ϒ(nS)γ. Possible con ibu ions om χb0 (mP)
→ϒ(nS)γdecays a e neglec ed because o he small b anch-
ing ac ion o he co esponding adia i e decays [25].
The esul s p esen ed in his pape supe sede ea lie
LHCb measu emen s [23,24]. In pa icula , he ull da a sam-
ple collec ed by LHCb a √s=7 and 8 TeV has been
used and he measu ed ac ions Rχb(mP)
ϒ(nS)a e epo ed o all
six kinema ically allowed ansi ions: χb(1P)→ϒ(1S)γ,
χb(2P)→ϒ(1S)γ,χb(2P)→ϒ(2S)γ,χb(3P)→
ϒ(1S)γ,χb(3P)→ϒ(2S)γand χb(3P)→ϒ(3S)γin bins
o ans e se momen um o he ϒmesons in he apidi y
ange 2.0<y<4.5. The las ansi ion, which is usually no
conside ed in heo y p edic ions, is obse ed o he i s ime.
A p ecise measu emen o he mass o he χb1 (3P)meson,
which was ecen ly obse ed by he ATLAS [21], D0 [26]
and LHCb [24] collabo a ions, is also pe o med.
2 The LHCb de ec o and da a samples
The LHCb de ec o [27] is a single-a m o wa d spec-
ome e co e ing he pseudo apidi y ange 2 <η<5,
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3092 Page 2 o 13 Eu . Phys. J. C (2014) 74:3092
designed o he s udy o hea y- la ou ed pa icles. The
de ec o includes a high-p ecision acking sys em consis ing
o a silicon-s ip e ex de ec o su ounding he in e ac ion
egion, a la ge-a ea silicon-s ip de ec o loca ed ups eam
o a dipole magne wi h a bending powe o abou 4 Tm,
and h ee s a ions o silicon-s ip de ec o s and s aw d i
ubes placed downs eam o he magne . The combined ack-
ing sys em p o ides a momen um measu emen wi h a el-
a i e unce ain y ha a ies om 0.4 % a low momen-
um o 0.6 % a 100 GeV/c, and an impac pa ame e mea-
su emen wi h a esolu ion o 20 μm o cha ged pa i-
cles wi h la ge ans e se momen um, pT. Di e en ypes
o cha ged had ons a e dis inguished using in o ma ion
om wo ing-imaging Che enko de ec o s(RICH) [28].
Pho on, elec on and had on candida es a e iden i ied by
a calo ime e sys em consis ing o scin illa ing-pad(SPD)
and p eshowe (PS) de ec o s, an elec omagne ic calo ime-
e (ECAL) and a had onic calo ime e [29]. Muons a e iden-
i ied by a sys em composed o al e na ing laye s o i on
and mul iwi e p opo ional chambe s [30]. The igge [31]
consis s o a ha dwa e s age, based on in o ma ion om he
calo ime e and muon sys ems, ollowed by a so wa e s age,
which applies a ull e en econs uc ion.
Candida e e en s used in his analysis mus pass he ha d-
wa e igge , wi h he speci ic equi emen ha he p oduc o
he pTo wo muon candida es be g ea e han (1.3GeV/c)2
and (1.6GeV/c)2 o da a collec ed a √s=7 and 8 TeV,
espec i ely. The i s s age o he so wa e igge selec s
candida e e en s wi h wo well- econs uc ed acks wi h
hi s in he muon sys em, pTg ea e han 500 MeV/cand
momen um g ea e han 6 GeV/c o each ack. The wo
acks a e equi ed o o igina e om a common e ex and
o ha e an in a ian mass g ea e han 2.7 GeV/c2. E en s
a e equi ed o pass a second so wa e igge s age, whe e
he p e ious igge decision is con i med using imp o ed
ack econs uc ion algo i hms, and he equi emen ha he
in a ian mass o he dimuon pai exceeds 4.7 GeV/c2is
applied.
The da a samples used in his pape ha e been collec ed
by he LHCb de ec o in pp collisions a √s=7 and 8 TeV
wi h in eg a ed luminosi ies o 1.0 b−1and 2.0 b−1, espec-
i ely. Simula ed samples a e used o de e mine signal e i-
ciencies. In hese samples, ϒand χbmesons a e p oduced
unpola ized. The e ec o he unknown ini ial pola iza ion
on he e iciencies, and he e o e on he esul s, is aken
in o accoun as a sys ema ic unce ain y. In he simula ion,
pp collisions a e gene a ed using Py hia [32] wi h a speci ic
LHCb con igu a ion [33]. Decays o had ons a e desc ibed
by E Gen [34], in which inal-s a e adia ion is gene a ed
using Pho os [35]. The in e ac ion o he gene a ed pa -
icles wi h he de ec o and i s esponse a e implemen ed
using he Gean 4 oolki [36,37] as desc ibed in Re . [38].
A compa ison o he dis ibu ions o he ele an a iables
used in his analysis is pe o med on da a and simula ed
samples, in o de o assess he eliabili y o he simula-
ion in compu ing signal e iciencies and good ag eemen is
ound.
3 E en selec ion and signal ex ac ion
This analysis p oceeds h ough he econs uc ion o ϒ(nS)
candida es ia hei dimuon decays and hei subsequen pai -
ing wi h a pho on candida e o econs uc χb→ϒγdecays.
The ϒcandida es a e selec ed om pai s o opposi ely
cha ged acks iden i ied as muons and o igina ing om
a common e ex. The muons a e equi ed o ha e pTla ge
han 1 GeV/c. Good ack quali y is ensu ed by equi ing
aχ2pe deg ee o eedom, χ2/nd , o he ack i o be
less han 4 [39]. A mul i a ia e es ima o , based on in o -
ma ion om he acking, muon and RICH sys ems, as well
as compa ibili y wi h he hypo hesis o a minimum ioniz-
ing pa icle in he calo ime e sys em [40–42], is used o
imp o e he muon iden i ica ion pu i y. The iden i ica ion
e iciency o muons om ϒ→μ+μ−decays ises om
75 % o 98 % as he ans e se momen um o he muon
inc eases om 1 GeV/c o 3 GeV/c. A good quali y o
he wo-p ong common e ex is ensu ed by equi ing he p-
alue o he common e ex i o be g ea e han 0.5 %.
To imp o e he dimuon mass esolu ion and o supp ess com-
bina o ial backg ound om muons o igina ing in semilep-
onic decays o hea y- la ou ed had ons, he dimuon e ex
is e i ed using he posi ion o he econs uc ed pp collision
e ex as an addi ional cons ain [43]. The p- alue o his
i is equi ed o be la ge han 0.05 %. When se e al colli-
sion e ices a e econs uc ed in he e en , he one closes
o he dimuon e ex is used.
The in a ian mass dis ibu ions o selec ed dimuon can-
dida es in he kinema ic ange o ans e se momen um 6 <
pμ+μ−
T<40 GeV/cand apidi y 2.0<yμ+μ−<4.5a e
showninFig.1 o da a collec ed a √s=7 and 8 TeV. Th ee
clea peaks a e isible, co esponding o he ϒ(1S),ϒ(2S)
and ϒ(3S)signals(low-mass o high-mass). The yields o
he ϒ(nS)signals a e de e mined using an ex ended max-
imum likelihood i o he unbinned dimuon mass dis i-
bu ions. The i unc ion is pa ame e ised as he sum o
h ee signal componen s and combina o ial backg ound.
Each ϒsignal has been modelled wi h a modi ied Gaus-
sian unc ion wi h powe -law ails on bo h sides. The com-
bina o ial backg ound is modelled wi h an exponen ial unc-
ion. The ail pa ame e s o he signal unc ions a e ixed
using simula ed e en s, whe eas he mean and esolu ion a e
allowed o a y in he i . The i esul s a e supe imposed
in Fig. 1and i ed signal yields a e summa ized in Table 1.
The peak posi ions and mass esolu ions a e ound o be in
good ag eemen o he da a collec ed a √s=7 and 8 TeV,
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Eu . Phys. J. C (2014) 74:3092 Page 3 o 13 3092
91011
0
5000
10000
15000
20000
25000
30000
35000
40000
Candida es/(12 MeV/c2)
m
µ
+
µ
−
[GeV/c
2
]
LHCb
√s=7 TeV
91011
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
LHCb
√s= 8 TeV
m
µ
+
µ
−
[GeV/c
2
]
Candida es/(12 MeV/c2)
Fig. 1 In a ian mass dis ibu ions o selec ed dimuon candida es in
he kinema ic ange 6 <pμ+μ−
T<40 GeV/cand 2.0<yμ+μ−<4.5
o (le ) da a collec ed a √s=7 TeV and ( igh ) 8 TeV. The h ee
peaks on each plo co espond o he ϒ(1S),ϒ(2S)and ϒ(3S)sig-
nals(low-mass o high-mass). The esul o he i , desc ibed in he ex ,
is illus a ed wi h a ed solid line, while he backg ound componen is
shown wi h a blue dashed line
Table 1 Yields o ϒ(nS)mesons, de e mined by i ing he dimuon
in a ian mass in he ange 6 <pμ+μ−
T<40 GeV/cand 2.0<
yμ+μ−<4.5, o da a collec ed a √s=7 and 8 TeV. Only s a is-
ical unce ain ies a e shown
Signal yield √s=7TeV √s=8TeV
Nϒ(1S)326 300 ±638 747 610 ±969
Nϒ(2S)100 620 ±395 229 950 ±576
Nϒ(3S)57 613 ±312 129 450 ±459
and in ag eemen wi h he known ϒ(nS)masses [25] and
he esolu ions expec ed om simula ed samples.
Muon pai s wi h in a ian mass in he in e als 9310 <
mμ+μ−<9600 MeV/c2, 9860<mμ+μ−<10 155 MeV/c2
and 10 220 <mμ+μ−<10 520 MeV/c2a eusedasϒ(1S),
ϒ(2S)and ϒ(3S)candida es, espec i ely, when econ-
s uc ing χbpa icles. The selec ed ϒcandida es a e com-
bined wi h pho ons econs uc ed using he elec omagne ic
calo ime e and iden i ied using a likelihood-based es ima o ,
cons uc ed om a iables ha ely on calo ime e and ack-
ing in o ma ion [16,29,44,45]. Candida e pho on clus e s
mus no be associa ed wi h he posi ion o any econs uc ed
ack ex apola ed o he calo ime e . The pho on selec ion
is u he e ined by using in o ma ion om he PS and
SPD de ec o s. The pho on ans e se ene gy is equi ed o
be g ea e han 600 MeV.
The χbsignals a e sea ched o in he in a ian mass o
ϒγcombina ions. To imp o e he ϒ(nS)γmass esolu ion
and o emo e any esidual bias, he co ec ed mass
mϒ(nS)γ≡mμ+μ−γ−(mμ+μ−−mϒ(nS))(2)
is used, whe e mϒ(nS)is he known mass o he ϒ(nS)meson
[25]. The esolu ion imp o es by a ac o be ween wo and
ou wi h espec o he one ob ained by simply compu ing
he in a ian mass o he ϒγpai . The dis ibu ions o he co -
ec ed masses mϒ(nS)γa e shown in Fig. 2 o ϒ(1S),ϒ(2S)
and ϒ(3S)candida es in he ans e se momen um anges
14 <pϒ(1S)
T<40 GeV/c,18<pϒ(2S)
T<40 GeV/cand
24 <pϒ(3S)
T<40 GeV/c.
The yields o χb(mP)mesons a e de e mined om
an ex ended maximum likelihood i o he unbinned mϒ(nS)γ
dis ibu ions. The i model consis s o he sum o sig-
nal componen s o all kinema ically allowed χb(mP)→
ϒ(nS)γdecays and combina o ial backg ound. Neglec ing
a possible con ibu ion due o χb0 (mP)→ϒ(nS)γdecays,
he signal om each χb(mP)mul iple is pa ame e ised
as he sum o wo o e lapping C ys al Ball(CB) unc-
ions [46] wi h high-mass ails. The peak posi ions a e
sepa a ed by he known mass-spli ing be ween he en-
so and ec o s a es in he χb(1P)and χb(2P)mul i-
ple s [25]. Fo he χb(3P)mul iple he expec ed spli ing
o 10.5MeV/c2[47,48] is used. The ail pa ame e s o
he CB unc ions and he esolu ions a e ixed o he al-
ues de e mined using simula ed samples. The yield ac-
ions Nχb2 /Nχb1 o he enso and ec o s a es in each
χb(mP)mul iple a e assumed o be equal o 0.5 acco d-
ing o expec a ions om Re s. [11,47]. Fo he χb(1P)
and χb(2P)cases, his choice ag ees wi h di ec measu e-
men s o he ela i e p oduc ions o χb2 (1P)/ χb1 (1P)and
χb2 (2P)/ χb1 (2P)[22,49]. This assump ion is necessa y
o he de e mina ion o signal yields, since he χb1 and
χb2 s a es canno be esol ed gi en he limi ed in a ian
mass esolu ion o he ϒ(nS)γsys em. The impac o his
assump ion is quan i ied as a sys ema ic unce ain y. Wi h
his pa ame e isa ion o he wel e χbsignal componen s,
he ee pa ame e s a e he h ee masses o he χb1 s a es
and he six o e all yields o χb1 and χb2 signals. The com-
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3092 Page 4 o 13 Eu . Phys. J. C (2014) 74:3092
10 10.5
0
200
400
600
800
1000
1200
Candida es/(20 MeV/c
2
)
Candida es/(20 MeV/c
2
)
Candida es/(10 MeV/c
2
)
Candida es/(20 MeV/c
2
)
Candida es/(20 MeV/c
2
)
Candida es/(10 MeV/c
2
)
mΥ(1S)γ
LHCb
√s= 7 TeV
10 10.5
0
500
1000
1500
2000
2500
3000
mΥ(1S)γ
10.2 10.4 10.6 10.8 11
0
50
100
150
200
250
300
mΥ(2S)γ
10.2 10.4 10.6 10.8 11
0
100
200
300
400
500
600
700
mΥ(2S)γ
10.5 10.6 10.7
0
5
10
15
20
25
30
35
40
mΥ(3S)γ
10.5 10.6 10.7
0
10
20
30
40
50
60
70
80
90
mΥ(3S)γ
[GeV/c2]
[GeV/c2]
[GeV/c2]
[GeV/c2]
[GeV/c2]
[GeV/c2]
LHCb
√s= 8 TeV
LHCb
√s= 8 TeV
LHCb
√s= 8 TeV
LHCb
√s= 7 TeV
LHCb
√s= 7 TeV
Fig. 2 Dis ibu ions o he co ec ed mass mϒ(nS)γ o he selec ed
χbcandida es (black poin s) decaying in o ( op ow) ϒ(1S), (middle
ow) ϒ(2S)and (bo om ow) ϒ(3S), in he ans e se momen um
anges gi en in he ex , o (le ) √s=7 TeV and ( igh ) 8 TeV da a.
Each plo shows also he esul o he i (solid ed cu e), including
he backg ound (do ed blue cu e) and he signal (dashed g een and
magen a cu es) con ibu ions. The magen a dashed cu e co esponds
o he χb1 signal and he g een dashed cu e o he χb2 signal
bina o ial backg ound is pa ame e ised as he p oduc o
an exponen ial and polynomial unc ions up o he ou h
o de . The i esul s a e supe imposed on Fig. 2and he sig-
nal yields a e summa ized in Table 2.
To pe o m a p ecise measu emen o he χb1 (3P)mass,
he da a samples collec ed a √s=7 and 8 TeV a e com-
bined. A i o he combined sample o χb(3P)→ϒ(3S)γ
decays gi es
mχb1 (3P)=10 511.3±1.7MeV/c2,
whe e he unce ain y is s a is ical only.
Fo he de e mina ion o he χbsignal yields in pϒ
Tbins,
he masses o he χb1 s a es in he i s a e ixed o he al-
ues ob ained in he i s o he ull pT anges. Fo each pϒ
T
bin he ac ions Rχb(mP)
ϒ(nS), de ined by Eq. (1), a e calcula ed
sepa a ely o √s=7 and 8 TeV da a samples as
Table 2 Signal yields esul ing om i s o he co ec ed mass mϒ(nS)γ
dis ibu ions in he ans e se momen um anges 14 <pϒ(1S)
T<
40 GeV/c,18<pϒ(2S)
T<40 GeV/cand 24 <pϒ(3S)
T<40 GeV/c.
Only s a is ical unce ain ies a e shown
Decay mode √s=7TeV √s=8TeV
Nχb(1P)→ϒ(1S)γ1908 ±71 4608 ±115
Nχb(2P)→ϒ(1S)γ390 ±41 904 ±68
Nχb(3P)→ϒ(1S)γ133 ±31 196 ±50
Nχb(2P)→ϒ(2S)γ265 ±30 660 ±46
Nχb(3P)→ϒ(2S)γ48 ±17 73 ±26
Nχb(3P)→ϒ(3S)γ56 ±12 126 ±20
Rχb(mP)
ϒ(nS)=Nχb(mP)
Nϒ(nS)×εϒ(nS)
εχb(mP)
,(3)
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Eu . Phys. J. C (2014) 74:3092 Page 5 o 13 3092
whe e εχb(mP)and εϒ(nS)deno e he o al e iciencies, and
Nχb(mP)and Nϒ(nS)a e he i ed yields o he χb(mP)
and ϒ(nS)s a es o he espec i e pϒ
Tbin. The a io o
he e iciencies εχb(mP)and εϒ(nS)is la gely de e mined by
he econs uc ion e iciency o pho ons om χbdecays. I
is close o 25 % o χbmesons wi h ans e se momen um
la ge han 20 GeV/c, and i d ops o app oxima ely 10 %
o he lowes pTconside ed in his analysis. The domi-
nan sou ces o ine iciency a e he geome ical accep ance
o he elec omagne ic calo ime e , pho on con e sions in
he de ec o ma e ial, he acciden al o e lap o clus e s in
he ECAL and he selec ion equi emen on he pho on ans-
e se ene gy. The measu emen s a e pe o med in six bins o
pϒ(1S)
Tin he ange 6 <pϒ(1S)
T<40 GeV/c, i e bins o
pϒ(2S)
Tin he ange 18 <pϒ(2S)
T<40 GeV/cand wo bins
o pϒ(3S)
Tin he ange 24 <pϒ(3S)
T<40 GeV/c.
4 Sys ema ic unce ain ies
The sys ema ic unce ain ies on he ac ions Rχb(mP)
ϒ(nS), calcu-
la ed using Eq. (3), a e ela ed o he de e mina ion o he sig-
nal yields and he e alua ion o he e iciency a ios. The main
con ibu ions o he o me a e due o i modelling, whe eas
he pho on econs uc ion e iciency and he knowledge o
he ini ial s a e pola iza ion domina e he unce ain y on he
a ios o e iciencies εχb(mP)/εϒ(nS). The con ibu ions due
o o he e ec s la gely cancel in hese a ios.
Based on s udies om Re s. [23,50–52] he sys ema ic
unce ain y associa ed wi h he ϒsignal yields de e mina ion
is aken o be 0.7 % o all pϒ
Tbins.
In he χb i model se e al sou ces o unce ain y a e
aken in o accoun . The yield a io N(χb2)/N(χb1), which
is ixed in he i o be 0.5 as p edic ed by heo y, is a -
ied om 0.3 o 1.0. These limi s a e ob ained by ollowing
he p esc ip ion o Re . [11], whe e he expe imen ally mea-
su ed c oss-sec ion a io o χcmesons is escaled o p e-
dic he co esponding a io o χbmesons. The a io o
c oss-sec ions is hen con e ed o a a io o yields by ak-
ing in o accoun he χb1 and χb2 adia i e b anching ac-
ions and econs uc ion e iciencies. Fo he χb(1P)and
he χb(2P)mesons, he a ia ion ob ained ag ees wi hin
unce ain ies wi h he di ec measu emen s o ela i e p o-
duc ions o χb2 (1P)and χb1 (1P)mesons and χb2 (2P)and
χb1 (2P)mesons [49]. The co esponding sys ema ic unce -
ain y on Rχb(mP)
ϒ(nS) a ies be ween 0.1 % and 15 % ac oss
pϒ
Tbins. The sys ema ic unce ain y due o a sligh depen-
dence o he mass i esul s on pϒ
Tis es ima ed by aking
he minimum and he maximum alues o he χb1 masses,
epea ing he i and aking he maximum di e ence in
he yields. The assigned unce ain y a ies be ween 0.3 %
and 20 % o a ious pϒ
Tbins. The smalle alues co -
Table 3 Summa y o he ela i e sys ema ic unce ain ies o he ac-
ions Rχb(mP)
ϒ(nS)
Sou ce Unce ain y (%)
ϒ i model 0.7
χb i model
χb1 /χb2 a io 0.1–15
χb1 mass a ia ion 0.3–20
χbmass esolu ion 2.0–12
Backg ound model 2.0–10
mχb2 (3P)−mχb1 (3P)0.1–2
γ econs uc ion 3.0
χbpola iza ion 0.9–9
Table 4 Summa y o sys ema ic unce ain ies o mχb1 (3P)
Sou ce Unce ain y (MeV/c2)
χb i model
χbmass esolu ion 0.8
Backg ound model 0.3
mχb2 (3P)−mχb1 (3P)0.4
χb1 /χb2 a io 2.0
ECAL ene gy scale 1.0
ϒ(3S)mass unce ain y 0.5
esponds o he low-Q ansi ions: χb(1P)→ϒ(1S)γ,
χb(2P)→ϒ(2S)γand χb(3P)→ϒ(3S)γ. To assess
he sys ema ic unce ain y ela ed o possible mismodelling
o he mass esolu ion, he mass esolu ion is a ied by
±10 % a ound he alues ob ained using simula ed samples,
and he di e ence be ween he ob ained Rχb(mP)
ϒ(nS)is ea ed
as he co esponding sys ema ic unce ain y. The maximum
de ia ion in he esul s ob ained om a ying by ±1 he o de
o he polynomial unc ion used in he i model o desc ibe
he combina o ial backg ound, is assigned as he sys ema ic
unce ain y associa ed wi h he backg ound pa ame e isa-
ion. Fo he χb(3P)case, a sys ema ic unce ain y s ems
om he assump ion on he mass spli ing be ween χb2 (3P)
and χb1 (3P)s a es. This pa ame e is a ied in he ange
be ween 9 and 12 MeV/c2. The ob ained unce ain y o
Rχb(3P)
ϒ(3S)is ound o be much smalle han he one ob ained o
Rχb(3P)
ϒ(1S)and Rχb(3P)
ϒ(2S). The assigned unce ain y on Rχb(3P)
ϒ(nS)
a ies be ween 0.1 % and 2 %.
The unce ain y due o possible impe ec ions in he simu-
la ion in he de e mina ion o he pho on econs uc ion e i-
ciency is s udied by compa ing he ela i e yields be ween
da a and simula ion o B+→J/ψK∗+ and B+→
J/ψK+decays, whe e he K∗+ meson is econs uc ed using
he K+π0 inal s a e [23,45,53–55]. Acco ding o hese
s udies, a sys ema ic unce ain y o 3 % is assigned o
123
3092 Page 6 o 13 Eu . Phys. J. C (2014) 74:3092
Fig. 3 F ac ions Rχb(mP)
ϒ(nS)as unc ions o pϒ
T. Poin s wi h blue open
( ed solid) symbols co espond o da a collec ed a √s=7(8)TeV,
espec i ely. Fo be e isualiza ion he da a poin s a e sligh ly dis-
placed om he bin cen es. The inne e o ba s ep esen s a is ical
unce ain ies, while he ou e e o ba s indica e s a is ical and sys em-
a ic unce ain ies added in quad a u e
pho ons in he kinema ical ange conside ed in his anal-
ysis. This unce ain y is domina ed by he knowledge o
he a io o he b anching ac ions o B+→J/ψK∗+ and
B+→J/ψK+decays.
Ano he sou ce o sys ema ic unce ain y is associa ed
wi h he unknown pola iza ion o χband ϒs a es. The pola -
iza ion o ϒmesons o pϒ
T>10 GeV/cand in he cen-
al apidi y egion |yϒ|<1.2 has been ound o be small
by he CMS collabo a ion [56]. The e o e in his pape we
assume ze o pola iza ion o ϒmesons and no sys ema ic
unce ain y is assigned due o his e ec . The sys ema ic
unce ain y ela ed o he unknown pola iza ion o χbmesons
was es ima ed ollowing Re s. [14,17]. Fo each pϒ
Tbin,
he a ios o e iciencies εχb1 /εϒand εχb2 /εϒa e ecompu ed
using a ious possible pola iza ions scena ios o χb1 and
χb2 mesons. The maximum de ia ion o he e iciency a io
wi h espec o he one ob ained wi h unpola ized p oduc-
ion o χb1 and χb2 s a es is aken as he sys ema ic unce -
ain y. The assigned unce ain y on Rχb(mP)
ϒ(nS) a ies be ween
0.9 % and 9 % o a ious pϒ
Tbins.
Sys ema ic unce ain ies due o ex e nal expe imen al
inpu s, e.g. he ϒmass o he mass spli ing o χb(1P)and
χb(2P)mul iple s, a e negligible. The sys ema ic unce ain-
ies on he Rχb(mP)
ϒ(nS)measu emen s a e summa ized in Table 3.
Sys ema ic unce ain ies on he measu emen o he
χb1 (3P)mass a e due o he ECAL ene gy scale, he i
model and he ϒ(3S)mass [25]. The i s o hese is s ud-
ied by compa ing he econs uc ed in a ian mass o pho-
ons in π0→γγ decays wi h he known mass o he neu-
al pion [57–59], which gi es an unce ain y o 1.0 MeV/c2
in χb(3P)→ϒ(3S)γdecays. The e ec s o possible mis-
modelling o he mass esolu ion and backg ound mod-
els a e ound o be 0.8 MeV/c2and 0.3 MeV/c2, espec-
i ely. O he signi ican con ibu ions o he sys ema ic unce -
ain y a e ela ed o he assump ions on N(χb2)/N(χb1),
and o he mass spli ing be ween χbmul iple compo-
nen s. The e ec o he unknown alue o he mass-
spli ing is es ed by a ying mχb2 (3P)−mχb1 (3P)in he i
in a ange be ween 9 and 12 MeV/c2, p e e ed by he-
o y [47,48]; he ob ained de ia ion o 0.4 MeV/c2is assigned
123
Eu . Phys. J. C (2014) 74:3092 Page 7 o 13 3092
Table 5 F ac ions Rχb(mP)
ϒ(nS)in
bins o pϒ
T, measu ed o da a
collec ed a √s=7TeV.
The i s block co esponds o
Rχb(mP)
ϒ(1S), he second o Rχb(mP)
ϒ(2S)
and he hi d o Rχb(mP)
ϒ(3S).The
i s unce ain y is s a is ical and
he second sys ema ic
pϒ
T(GeV/c)Rχb(1P)
ϒ(nS)Rχb(2P)
ϒ(nS)Rχb(3P)
ϒ(nS)
ϒ(1S)6–8 14.8±1.2±1.33.3±0.6±0.2
8–10 17.2±1.0±1.45.2±0.6±0.3
10–14 21.3±0.8±1.44.0±0.5±0.31.7±0.5±0.1
14–18 24.4±1.3±1.25.2±0.8±0.41.8±0.6±0.2
18–22 27.2±2.1±2.15.5±1.0+0.4
−1.01.9±0.7±0.3
22–40 29.2±2.5±1.76.0±1.2+0.4
−0.72.9±1.0±0.4
ϒ(2S)18–20 31 ±6±4
20–22 30 ±9±3
22–24 33 ±10 ±5
24–28 28 ±9±3
28–40 29 ±8±3
18–40 4.4±1.6±0.5
ϒ(3S)24–29 44 ±12 ±10
29–40 36 ±14 ±8
Table 6 F ac ions Rχb(mP)
ϒ(nS)in
bins o pϒ
T, measu ed o da a
collec ed a √s=8TeV.
The i s block co esponds o
Rχb(mP)
ϒ(1S), he second o Rχb(mP)
ϒ(2S)
and he hi d o Rχb(mP)
ϒ(3S).The
i s unce ain y is s a is ical and
he second sys ema ic
pϒ
T(GeV/c)Rχb(1P)
ϒ(nS)Rχb(2P)
ϒ(nS)Rχb(3P)
ϒ(nS)
ϒ(1S)6–8 15.5±0.9±1.32.8±0.5±0.2
8–10 18.5±0.7±1.54.6±0.4±0.3
10–14 23.2±0.6±1.43.0±0.4±0.21.4±0.4±0.1
14–18 24.2±0.9±1.25.0±0.5±0.31.2±0.4±0.1
18–22 26.0±1.4±1.24.0±0.7±0.30.9±0.5±0.1
22–40 28.5±1.8±2.17.6±1.0±0.62.1±0.5+0.7
−0.2
ϒ(2S)18–20 31 ±4±4
20–22 30 ±5±3
22–24 30 ±6±3
24–28 37 ±5+4
−8
28–40 28 ±5±3
18–40 2.7±1.0±0.3
ϒ(3S)24–29 34 ±8±7
29–40 40 ±9+5
−14
as he co esponding sys ema ic unce ain y. The χb1 (3P)
mass exhibi s a linea dependence on he assumed ac ion o
χb1 decays and a ies om 10 509 o 10 513 MeV/c2, when
he χb2 /χb1 yield a io changes om 0.3 o 1.0. The de e -
mina ion o he χb1 (3P)mass is u he checked using
he la ge χb(1P)→ϒ(1S)γsignal, whe e he measu ed
χb1 (1P)mass ag ees wi h he known χb1 (1P)mass [25] o
be e han 0.5 MeV/c, sepa a ely o √s=7 and 8 TeV da a.
No addi ional sys ema ic unce ain y is assigned. The sys-
ema ic unce ain ies on he χb1 (3P)mass measu emen a e
summa ized in Table 4.
5 Resul s and conclusion
The measu ed ac ions Rχb(mP)
ϒ(nS)a e p esen ed in Fig. 3and
Tables 5and 6. The esul s a e domina ed by he s a is ical
unce ain ies, and show no dependence on he pp collision
ene gy. A measu emen o he Rχb(3P)
ϒ(3S) ac ion is pe o med
o he i s ime. The la ge alue o his ac ion impac s
he in e p e a ion o expe imen al da a on ϒp oduc ion and
pola iza ion. When da a on ϒp oduc ion and pola iza ion
a e compa ed wi h heo y p edic ions, as well as when di -
e en heo y p edic ions a e compa ed among hemsel es, i
is o en implici ly assumed ha he ac ion o ϒ(3S)mesons
p oduced by eed down om highe s a es is small. The la ge
measu ed alue o Rχb(3P)
ϒ(3S)indica es ha hese assump ions
need o be e isi ed.
In conclusion, he ac ions o ϒmesons o igina ing om
χb adia i e decays a e measu ed using a da a sample col-
lec ed by LHCb a cen e-o -mass ene gies o 7 and 8 TeV,
as a unc ion o he ϒ ans e se momen um in he kinema ic
ange 2.0<yϒ<4.5. The esul s p esen ed in his pape
123
3092 Page 8 o 13 Eu . Phys. J. C (2014) 74:3092
supe sede p e ious LHCb measu emen s [23] by inc easing
he s a is ical p ecision and exploi ing mo e decay modes
and highe ans e se momen um egions. The measu emen
o he ϒ(3S)p oduc ion ac ion due o adia i e χb(3P)
decays is pe o med o he i s ime.
Assuming he mass spli ing mχb2 (3P)−mχb1 (3P)=
10.5MeV/c2, he mass o χb1 (3P)s a e is measu ed o be
mχb1 (3P)=10 511.3±1.7±2.5MeV/c2,
whe e he i s unce ain y is s a is ical and he second sys-
ema ic. This esul is compa ible and signi ican ly mo e
p ecise han he e en yield a e age mass o χb1 (3P)and
χb2 (3P)s a es o 10 530 ±5±17 MeV/c2and 10 551 ±
14 ±17 MeV/c2, epo ed by he ATLAS [21] and D0 [26]
expe imen s, espec i ely.
Acknowledgmen s We hank K.-T. Chao, H. Han, V. G. Ka el-
ish ili, J.-P. Lansbe g A. K. Likhoded, A. V. Luchinsky, S. V. Posla sky
and H.-S. Shao o inspi ing and ui ul discussions on P-wa e bo -
omonia p oduc ion. We exp ess ou g a i ude o ou colleagues in he
CERN accele a o depa men s o he excellen pe o mance o he
LHC. We hank he echnical and adminis a i e s a a he LHCb
ins i u es. We acknowledge suppo om CERN and om he na ional
agencies: CAPES, CNPq, FAPERJ and FINEP (B azil); NSFC (China);
CNRS/IN2P3 (F ance); BMBF, DFG, HGF and MPG (Ge many); SFI
(I eland); INFN (I aly); FOM and NWO (The Ne he lands); MNiSW
and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Rus-
sia); MinECo (Spain); SNSF and SER (Swi ze land); NASU (Uk aine);
STFC (Uni ed Kingdom); NSF (USA). The Tie 1 compu ing cen es a e
suppo ed by IN2P3 (F ance), KIT and BMBF (Ge many), INFN (I aly),
NWO and SURF (The Ne he lands), PIC (Spain), G idPP (Uni ed King-
dom). We a e indeb ed o he communi ies behind he mul iple open
sou ce so wa e packages on which we depend. We a e also hank ul
o he compu ing esou ces and he access o so wa e R&D ools p o-
ided by Yandex LLC (Russia). Indi idual g oups o membe s ha e
ecei ed suppo om EPLANET, Ma ie Skłodowska-Cu ie Ac ions
and ERC (Eu opean Union), Conseil géné al de Hau e-Sa oie, Labex
ENIGMASS and OCEVU, Région Au e gne (F ance), RFBR (Russia),
Xun aGal and GENCAT (Spain), Royal Socie y and Royal Commission
o he Exhibi ion o 1851 (Uni ed Kingdom).
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