JHEP06(2021)177
Published o SISSA by Sp inge
Recei ed:May 7, 2021
Accep ed:June 3, 2021
Published:June 29, 2021
Angula analysis o B0→D∗−D∗+
swi h D∗+
s→D+
sγ
decays
The LHCb collabo a ion
E-mail: [email p o ec ed]
Abs ac : The i s ull angula analysis o he B0→D∗−D∗+
sdecay is pe o med us-
ing 6 b−1o pp collision da a collec ed wi h he LHCb expe imen a a cen e-o -mass
ene gy o 13 TeV. The D∗+
s→D+
sγand D∗− →D0π− ec o meson decays a e used
wi h he subsequen D+
s→K+K−π+and D0→K+π−decays. All helici y ampli udes
and phases a e measu ed, and he longi udinal pola isa ion ac ion is de e mined o be
L= 0.578±0.010±0.011 wi h wo ld-bes p ecision, whe e he i s unce ain y is s a is i-
cal and he second is sys ema ic. The pa e n o helici y ampli ude magni udes is ound o
align wi h expec a ions om qua k-helici y conse a ion in Bdecays. The a io o b anch-
ing ac ions [B(B0→D∗−D∗+
s)×B(D∗+
s→D+
sγ)]/B(B0→D∗−D+
s)is measu ed o be
2.045 ±0.022 ±0.071 wi h wo ld-bes p ecision. In addi ion, he i s obse a ion o he
Cabibbo-supp essed Bs→D∗−D+
sdecay is made wi h a signi icance o se en s anda d de-
ia ions. The b anching ac ion a io B(Bs→D∗−D+
s)/B(B0→D∗−D+
s)is measu ed o
be 0.049 ±0.006 ±0.003 ±0.002, whe e he hi d unce ain y is due o limi ed knowledge
o he a io o agmen a ion ac ions.
Keywo ds: Bphysics, B anching ac ion, Had on-Had on sca e ing (expe imen s), Po-
la iza ion
A Xi eP in : 2105.02596
Open Access, Copy igh CERN,
o he bene i o he LHCb Collabo a ion.
A icle unded by SCOAP3.
h ps://doi.o g/10.1007/JHEP06(2021)177
JHEP06(2021)177
Con en s
1 In oduc ion 1
2 Angula decay a e o malism 3
3 LHCb de ec o and simula ion 3
4 E en selec ion 5
5 Measu emen o Land b anching ac ion a ios 6
5.1 Fi componen s 7
5.2 Resul s 10
6 In a ian -mass i o B0→D∗−D∗+
sdecays 11
7 Angula accep ance unc ions 12
7.1 Accep ance unc ions o cos θDand cos θX13
7.2 Accep ance unc ion o χ14
8 Angula i o da a 15
9 Sys ema ic unce ain ies 16
10 Resul s and conclusion 18
A Rela ionship be ween m(D∗−D+
s)and cos θX20
The LHCb collabo a ion 24
1 In oduc ion
The B0→D∗−D∗+
sdecay in ol es he p oduc ion o wo ec o cha m mesons om a
pseudoscala B0pa en . This p ocess exhibi s a pola isa ion s uc u e, whe e h ee complex
helici y ampli udes H0,H+, and H−con ibu e o he o al decay a e. These ampli udes
co espond o he ela i e o ien a ion o he linea pola isa ion ec o s o he wo ec o
mesons. Pa i y-e en (k) and pa i y-odd (⊥) ans e si y ampli udes can also be de ined
in e ms o H+and H−, namely Ak,⊥= (H+±H−)/√2. The helici y ampli udes can
in e e e, wi h in e e ence go e ned by he s ong phases o he ans e se componen s,
φ+and φ−, ela i e o he phase o he longi udinal componen , φ0, which is con en ionally
aken o be equal o ze o. The e o e, i e pa ame e s in o al de e mine he decay a e:
•|H0|, he magni ude o he longi udinal ampli ude;
•|H+|and |H−|, he magni udes o he wo ans e se ampli udes;
•φ+and φ−, he phases o he ans e se ampli udes ela i e o H0.
– 1 –
JHEP06(2021)177
In o de o no malise he o al decay a e, |H0|2+|H+|2+|H−|2= L+ T= 1 is equi ed,
whe e L≡ |H0|2is he longi udinal pola isa ion ac ion and T≡ |H+|2+|H−|2is he
ans e se pola isa ion ac ion. The cu en wo ld a e age o Lis 0.52 ±0.05 [1,2],
while heo e ical p edic ions co e a simila ange [3–6]; he ans e se helici y ampli udes
ha e no been measu ed p e iously. The no malisa ion condi ion educes he o al numbe
o independen obse ables o ou , whe e he addi ional obse able is abso bed in o he
absolu e b anching ac ion o he decay which is no measu ed. Measu ing he ela i e
magni udes o he helici y ampli udes o e s a es o qua k-helici y conse a ion in his
ee-le el decay in ol ing a b→cqua k ansi ion. In such decays, a |H0|>|H+|>|H−|
hie a chy is expec ed [7], whe e he V−Ana u e o he weak in e ac ion causes he
longi udinal componen o domina e.
The B0→D∗−D∗+
sdecay has a la ge b anching ac ion,
B(B0→D∗−D∗+
s) = (1.77 ±0.14)% [2], and is hus a p ominen backg ound in
B0→D∗−τ+ντanalyses ha exploi he had onic h ee-p ong τ+→π+π+π−¯ντmode
in o de o measu e he a io R(D∗)≡ B(B0→D∗−τ+ντ)/B(B0→D∗−`+ν`)[8] o he
angula coe icien s o he B0→D∗−τ+ντdecay [9]. Such a backg ound a ises when he
neu al pa icle p oduced in he D∗+
sdecay is no econs uc ed, and he D+
smeson decays
o h ee pions plus addi ional non- econs uc ed pa icles.
Using da a co esponding o an in eg a ed luminosi y o 6 b−1collec ed a a cen e-o -
mass ene gy o 13 TeV wi h he LHCb expe imen be ween 2015 and 2018, B0→D∗−D∗+
s
wi h D∗+
s→D+
sγdecays a e econs uc ed ia he D∗− →(D0→K+π−)π−and
D+
s→K+K−π+channels; he inclusion o cha ge-conjuga e p ocesses is implied h ough-
ou . Pa ially econs uc ed decays, whe e he pho on is no conside ed in he in a ian -
mass calcula ion, a e used in a i o he m(D∗−D+
s)dis ibu ion o measu e L. Fully
econs uc ed decays a e hen conside ed in a subsequen angula analysis o measu e he
emaining helici y obse ables. Measu emen s a e pe o med unde he assump ion ha
bo h he D0π−and D+
sγsys ems a e pu e ec o , as no e idence o a scala con ibu ion
is ound in he m(D0π−)dis ibu ion in da a and no scala componen is pe mi ed in
m(D+
sγ)due o he pho on angula momen um. The analysis includes an imp o ed mea-
su emen o Land i s measu emen s o he ans e se helici y ampli ude magni udes and
phases.
The da a sample is also used o measu e he a io o b anching ac ions
R ≡ [B(B0→D∗−D∗+
s)×B(D∗+
s→D+
sγ)]/B(B0→D∗−D+
s), whe e he cu en alue o
R= 2.07±0.33 is calcula ed using wo ld-a e age b anching ac ions aken om e . [2]. In
addi ion, a measu emen o he p e iously unobse ed Cabibbo-supp essed B0
s→D∗−D+
s
decay is pe o med and he a io o b anching ac ions B(B0
s→D∗−D+
s)/B(B0→D∗−D+
s)
de e mined.
The o malism adop ed is desc ibed in sec ion 2, essen ial de ails o he LHCb de ec o
and simula ion a e gi en in sec ion 3, and he e en selec ion is ou lined in sec ion 4.
The longi udinal pola isa ion ac ion and a ios o b anching ac ions a e measu ed in
sec ion 5, and he emaining helici y obse ables a e measu ed in sec ions 6–8. Sys ema ic
unce ain ies a e de e mined in sec ion 9, and inal esul s and conclusions a e p esen ed
in sec ion 10.
– 2 –
JHEP06(2021)177
2 Angula decay a e o malism
The B0→D∗−D∗+
sdecay a e is a unc ion o h ee decay angles, θD,θX, and χ, whe e
θDis he angle be ween he D0meson and he di ec ion opposi e he B0momen um ec o
in he D∗− es ame, θXis he angle be ween he D+
smeson and he di ec ion opposi e
he B0momen um ec o in he D∗+
s es ame, and χis he angle be ween he wo decay
planes as de ined in he B0 es ame. The angles a e illus a ed in igu e 1, and a e
explici ly de ined as ollows
cos θD=ˆp(D∗− )
D0·ˆp(B0)
D∗− =ˆp(D∗− )
D0·−ˆp(D∗− )
B0,
cos θX=ˆp(D∗+
s)
D+
s·ˆp(B0)
D∗+
s=ˆp(D∗+
s)
D+
s·−ˆp(D∗+
s)
B0,
cos χ=ˆp(B0)
D+
s׈p(B0)
γ·ˆp(B0)
D0׈p(B0)
π−,(2.1)
sin χB0=−hˆp(B0)
D+
s׈p(B0)
γ׈p(B0)
D0׈p(B0)
π−i·ˆp(B0)
D∗− ,
sin χB0= +hˆp(B0)
D−
s׈p(B0)
γ׈p(B0)
D0׈p(B0)
π−i·ˆp(B0)
D∗+,
whe e he ˆp(Y)
Xa e uni ec o s desc ibing he di ec ion o a pa icle Xin he es ame
o he sys em Y. In he B0 es ame, he angula de ini ion o he B0decay is a cha ge-
pa i y (CP) ans o ma ion o ha o he B0decay. The sign o sin χis nega i e o B0
candida es and posi i e o B0candida es, whe e he B-meson la ou is agged by he
D∗-meson cha ge. This o malism is he same as ha adop ed in o he LHCb angula
analyses such as ha o B→K∗µ+µ−decays [10,11].
The ull h ee-dimensional di e en ial decay a e exp essed in e ms o he helici y
ampli udes is gi en by [3]
d3Γ
dcos θDdcos θXdχ ∝9
8cos2θDsin2θX|H0|2+1
4sin2θD1 + cos2θX|H+|2+|H−|2
−1
2sin2θDsin2θXcos 2χRe H+H∗
−−sin 2χIm H+H∗
− (2.2)
−1
4sin 2θDsin 2θX[cos χRe (H+H∗
0+H−H∗
0)−sin χIm (H+H∗
0−H−H∗
0)] .
3 LHCb de ec o and simula ion
The LHCb de ec o [12,13] is a single-a m o wa d spec ome e co e ing he pseudo apidi y
ange 2< η < 5, designed o he s udy o pa icles con aining b- o c-qua ks. 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 pp 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 acking sys em p o-
ides a measu emen o he momen um, p, o cha ged pa icles wi h a ela i e unce ain y
ha a ies om 0.5% a low momen um o 1.0% a 200 GeV/c. The minimum dis ance o
– 3 –
JHEP06(2021)177
D*−D*+
sB0
χ
¯
D0
¯
D0
π−D+
s
γ
D+
s
γ
π−
pB0
pB0
θX
θD
es ame es ame es ame
Figu e 1. Illus a ion o he B0→D∗−D∗+
sdecay angles.
a ack o a p ima y pp collision e ex (PV), he impac pa ame e (IP), is measu ed wi h
a esolu ion o (15 + 29/pT)µm, whe e pTis he componen o he momen um ans e se
o he beam, in GeV/c. 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. Pho ons, elec ons and had ons a e
iden i ied by a calo ime e sys em consis ing o scin illa ing-pad and p eshowe de ec o s,
an elec omagne ic and a had onic calo ime e . 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.
The online e en selec ion is pe o med by a igge , which 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. A he ha dwa e igge s age, e en s a e
equi ed o ha e a muon wi h high pTo a had on, pho on o elec on wi h high ans e se
ene gy in he calo ime e s. Fo had ons, he ans e se ene gy h eshold is 3.5 GeV. The
so wa e igge equi es a wo-, h ee- o ou - ack seconda y e ex wi h a signi ican
displacemen om any p ima y pp in e ac ion e ex. A leas one cha ged pa icle mus
ha e a ans e se momen um pT>1.6GeV/cand be inconsis en wi h o igina ing om any
PV. A mul i a ia e algo i hm is used o he iden i ica ion o seconda y e ices consis en
wi h he decay o a bhad on. In he o line selec ion, igge in o ma ion is associa ed
wi h econs uc ed pa icles. Selec ion equi emen s can he e o e be made on he igge
selec ion i sel and on whe he he decision was due o he signal candida e, o he pa icles
p oduced in he pp collision, o an o e lap o bo h.
Simula ion is equi ed o model he e ec s o he de ec o accep ance and he imposed
selec ion equi emen s. In he simula ion, pp collisions a e gene a ed using Py hia [14]
wi h a speci ic LHCb con igu a ion [16]. Decays o uns able pa icles a e desc ibed by
E Gen [17], in which inal-s a e adia ion is gene a ed using Pho os [18]. 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 [19] as desc ibed in e . [21]. The unde lying pp in e ac ion is eused
mul iple imes, wi h an independen ly gene a ed signal decay o each [22]. In addi ion,
he m(D∗−D+
s)dis ibu ions o pu e longi udinal and ans e se pola ised B0→D∗−D∗+
s
– 4 –
JHEP06(2021)177
decays a e s udied using as -simula ed samples gene a ed wi h he RapidSim package [23],
whe e an LHCb momen um esolu ion con igu a ion is used o smea he gene a ed ou -
momen a. The same ool is used o s udy he m(D∗−D+
s)dis ibu ions o a ious back-
g ound con ibu ions om decays in ol ing highe -exci ed cha m mesons.
4 E en selec ion
Candida e B0→D∗−D+
sdecays a e econs uc ed h ough he D∗− →(D0→K+π−)π−
and D+
s→K+K−π+channels. The acks o he inal-s a e pa icles a e equi ed o ha e
a good quali y, ul il loose pa icle iden i ica ion (PID) c i e ia, and ha e a high χ2
IP alue
wi h espec o any PV, whe e χ2
IP is de ined as he di e ence in he e ex- i χ2o a
gi en PV econs uc ed wi h and wi hou he pa icle being conside ed. The econs uc ed
masses o he D0and D+
scandida es a e equi ed o lie inside mass windows o ±20 MeV/c2
a ound hei known alues [2]. The D∗− candida e mass is equi ed o be wi hin ±40 MeV/c2
o he known alue [2], while he di e ence in mass be ween he D∗− and D0candida es
is equi ed o be in he ange 140–150 MeV/c2. In combina ion wi h he ack PID cu s,
hese na ow mass windows educe po en ial backg ounds om misiden i ied decays such
as B0→D∗−D+ o negligible le els.
The B0candida e is econs uc ed by combining he D∗− and D+
scandida es o o m
a common e ex. I mul iple PVs a e econs uc ed in he same e en , he PV o which
he B0candida e has he lowes χ2
IP is assigned as he associa ed PV. The pTo he
B0candida e is equi ed o be la ge han 5 GeV/c, and he χ2
IP o he B0candida e
o he associa ed PV is equi ed o be small. To supp ess combina o ial backg ound
and backg ound om decays in ol ing he p oduc ion o a D∗− and h ee p omp acks,
he ligh dis ance o he D+
scandida e along he beam axis is equi ed o be di e en
om ze o by mo e han one s anda d de ia ion, conside ing bo h he o igin and decay-
e ex unce ain ies o he D+
scandida e. To supp ess combina o ial backg ound om
combina ions o acks o igina ing om he PV, he decay ime o he B0candida e is
equi ed o be la ge han 0.2 ps. To imp o e he in a ian -mass esolu ion, a kinema ic i is
pe o med o he decay chain [24], he B0candida e is cons ained o o igina e om he PV
and he D+
sand D0masses a e cons ained o hei known alues. Candida es a e e ained
i he esul ing in a ian mass o he D∗−D+
scombina ion alls wi hin he 4900–5500 MeV/c2
ange, which includes he egion occupied by pa ially econs uc ed B0→D∗−D∗+
sdecays
when he neu al pa icle p oduced in he D∗+
sdecay is no econs uc ed. This sample is
conside ed in sec ion 5, whe e a i o he m(D∗−D+
s)dis ibu ion o candida es is used o
measu e L.
A subsample o ully econs uc ed B0→D∗−D∗+
scandida es is selec ed by combin-
ing D+
scandida es om he abo e da ase wi h pho ons. The di e ence be ween he D∗+
s
and D+
scandida e masses is equi ed o be in he ange 120–180 MeV/c2, and he pho on
is equi ed o ha e a pTla ge han 500 MeV/c. Each D∗+
scandida e is hen ecombined
wi h he co esponding D∗− candida e om he abo e da ase o o m a B0candida e,
whe e candida es in he in a ian -mass ange 5150–5500 MeV/c2a e e ained. Fully econ-
s uc ed candida es wi h m(D∗−D+
s) alues g ea e han 5240 MeV/c2a e e oed o emo e
– 5 –
JHEP06(2021)177
B0→D∗−D+
sdecays whe e a andom pho on is combined wi h he D+
scandida e. This
da ase is used in sec ion 8 o measu e he emaining helici y obse ables in an angula
analysis.
5 Measu emen o Land b anching ac ion a ios
The longi udinal pola isa ion ac ion, L, de e mines he ac ional con ibu ion o he H0
helici y ampli ude o he o al B0→D∗−D∗+
sdecay a e. The longi udinal and ans e se
ampli udes con ibu e o he one-dimensional di e en ial decay a e in cos θXas ollows,
dΓ
dcos θX∝3
4|H0|2(1 −cos2θX) + 1
2(|H+|2+|H−|2)(1 + cos2θX)
=3
4 L(1 −cos2θX) + (1 − L)
2(1 + cos2θX),(5.1)
which is ob ained om eq. (2.2) ia a de ini e in eg al o e cos θDand χ. Expe imen ally,
he in eg al o e cos θDand χmus also include he accep ance in hese angles. Howe e ,
he accep ance is p edominan ly linea o bo h angles, as shown in igu es 4and 5, such
ha no signi ican esidual dependence emains a e he in eg a ion. Due o a common
dependence on pho on kinema ics, he angle cos θXand he in a ian mass o he D∗−D+
s
sys em a e s ongly nega i ely co ela ed, as illus a ed in appendix Ain igu e 7. Mo e
posi i e alues o cos θXco espond o highe momen um pho ons and hus lowe alues
o m(D∗−D+
s). As a esul , he di e en cos θXshapes o longi udinal and ans e se
pola ised B0→D∗−D∗+
sdecays mani es in co esponding m(D∗−D+
s)dis ibu ions wi h
di e en pa abolic o ms, as shown in appendix Ain igu e 8. This ea u e enables L o be
measu ed using a binned maximum-likelihood i o he m(D∗−D+
s)dis ibu ion in da a,
whe e he o al B0→D∗−D∗+
scon ibu ion is modelled by he sum o p obabili y densi y
unc ions (PDFs) o he longi udinal and ans e se componen s wi h ela i e ac ions
Land 1− L. De e mining L ia an m(D∗−D+
s) i enables pa ially econs uc ed
B0→D∗−D∗+
sdecays o be used, which inc eases he sample size by a oiding e iciency
losses due o he limi ed pho on econs uc ion e iciency o he LHCb de ec o .
Due o he p esence o B0→D∗−D+
sdecays in he same sample, a measu emen o
he b anching ac ion a io
R ≡ B(B0→D∗−D∗+
s)×B(D∗+
s→D+
sγ)
B(B0→D∗−D+
s)(5.2)
can also be made. Expe imen ally, his quan i y is de ined as
R=N(B0→D∗−(D∗+
s→D+
sγ))
N(B0→D∗−D+
s)×(B0→D∗−D+
s)
(B0→D∗−(D∗+
s→D+
sγ))
=N(B0→D∗−(D∗+
s→D+
sγ))
N(B0→D∗−D+
s)×ξ , (5.3)
whe e Ndeno es he yields o each decay mode, and ξis he a io o hei o al econ-
s uc ion and selec ion e iciencies. In he case o B0→D∗−D∗+
sdecays, he yields and
– 6 –
JHEP06(2021)177
e iciencies co espond o hose o pa ially econs uc ed signal. The e iciency a io is
de e mined using simula ed samples o B0→D∗−D∗+
sand B0→D∗−D+
sdecays, and is
ound o be ξ= 1.142 ±0.034, whe e he unce ain y quo ed accoun s only o he use o
ini e simula ed samples and po en ial a ia ion in he e iciency ac oss da a- aking yea s.
This unce ain y is conside ed as a sou ce o sys ema ic unce ain y on R.
A con ibu ion om Cabibbo-supp essed B0
s→D∗−D+
sdecays is also conside ed in
he m(D∗−D+
s) i , enabling a measu emen o he b anching ac ion a io
(B0
s)≡B(B0
s→D∗−D+
s)
B(B0→D∗−D+
s)(5.4)
o be made. Expe imen ally, (B0
s)is de ined as
(B0
s) = d
s×N(B0
s→D∗−D+
s)
N(B0→D∗−D+
s)×(B0→D∗−D+
s)
(B0
s→D∗−D+
s)
= d
s×N(B0
s→D∗−D+
s)
N(B0→D∗−D+
s)×ξ(B0
s),(5.5)
whe e Ndeno es he yields o each decay mode, and s/ d= 0.2539 ±0.0079 is he a io o
agmen a ion ac ions a √s= 13 TeV as measu ed inside he LHCb accep ance [25]. The
ela i e e iciency ξ(B0
s)is assumed o be uni y, wi h a 5% ela i e sys ema ic unce ain y
assigned o accoun o po en ial a ia ion in e iciency due o mass and li e ime di e ences.
5.1 Fi componen s
The m(D∗−D+
s)dis ibu ion o selec ed candida es is shown in igu e 2, and is domina ed by
he na ow signal due o ully econs uc ed B0→D∗−D+
sdecays and a b oad s uc u e
due o B0→D∗−D∗+
sdecays wi h missing a pho on o π0 om he D∗+
sdecay. The
dis ibu ion is modelled as a sum o se e al componen s which a e desc ibed below.
B0→D∗−D+
sdecays. Fully econs uc ed B0→D∗−D+
sdecays a e modelled using
he sum o wo C ys al Ball PDFs [26] wi h a eely a ying common mean and wid h,
and a ela i e yield ac ion ha is Gaussian-cons ained acco ding o simula ion. The
componen PDF ails a e modelled on opposi e sides, and he ail pa ame e s a e Gaussian-
cons ained om simula ion. The b anching ac ion a io Ris measu ed di ec ly in he
i , such ha he yield o he B0→D∗−D+
scomponen is ela ed o he yield o he
B0→D∗−(D∗+
s→D+
sγ)componen ia a eely a ying pa ame e Rand he ixed
ela i e e iciency a io ξ.
B0→D∗−(D∗+
s→D+
sγ)decays. The pa ially econs uc ed B0→D∗−(D∗+
s→D+
sγ)
signal is modelled using he sum o a longi udinal componen and a ans e se componen ,
whe e a eely a ying pa ame e Lde e mines he ela i e p opo ion o he longi udinal
componen . To de i e in a ian -mass PDFs o each componen , i s a e pe o med o simu-
la ed samples o pu e longi udinal and ans e se pola ised decays as shown in appendix A
in igu e 9. The m(D∗−D+
s)dis ibu ions a e modelled wi h pa abolas con ol ed wi h
Gaussian esolu ion unc ions, whe e he pa abolas a e based on he cos θXdependence in
– 7 –
JHEP06(2021)177
4900 5000 5100 5200 5300 5400
m(D∗−D+
s) [MeV/c2]
500
1000
1500
2000
2500
Candida es / (2.0 MeV/c2)
LHCb
6 b−1
Da a
To al i
B0→D∗−(D∗+
s→D+
sγ), L
B0→D∗−(D∗+
s→D+
sγ), T
B0→D∗−(D∗+
s→D+
sπ0), L
B0→D∗−(D∗+
s→D+
sπ0), T
B0→D∗−D+
s
B0
s→D∗−D(∗)+
s
B→D∗(∗)D∗(∗)
s
Combina o ial
5325 5350 5375 5400 5425 5450 5475
m(D∗−D+
s) [MeV/c2]
10
20
30
40
50
Candida es / (2.0 MeV/c2)
LHCb
6 b−1
Figu e 2. (Top) Dis ibu ion o m(D∗−D+
s) o selec ed candida es in da a, wi h he i o e laid.
Whe e indica ed, L(T) ep esen s longi udinally ( ans e se) pola ised decays. (Bo om) Re-
s ic ed o egion o candida es wi h m(D∗−D+
s)>5325 MeV/c2, whe e he Cabibbo-supp essed
B0
s→D∗−D+
scon ibu ion is isible.
eq. (5.1). This app oach closely ollows he me hod used in e s. [27] and [28] o CP iola-
ion s udies o pa ially econs uc ed B−→D∗0h−wi h D∗0→Dγ/π0decays, whe e h−
is a pion o a kaon and he neu al pa icle p oduced in he D∗0decay is no econs uc ed.
The o al yield o he B0→D∗−(D∗+
s→D+
sγ)componen , N(B0→D∗−(D∗+
s→D+
sγ)),
a ies eely and is used along wi h Rand ξ o se he B0→D∗−D+
scomponen yield.
All PDF pa ame e s o he B0→D∗−(D∗+
s→D+
sγ)componen a e ixed in he da a i ,
and a e a ied wi hin hei unce ain ies o de e mine he sys ema ic unce ain ies on L,
R, and (B0
s).
– 8 –
JHEP06(2021)177
−π−π
20π
2π
χ[ ad]
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Densi y / (0.63)
LHCb
Reco. LHCb simula ion
Gene a ed sample
−π−π
20π
2π
χ[ ad]
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Accep ance
LHCb
Reco. LHCb simula ion / Gene a ed a io
Polynomial i
Figu e 5. Compa ison o econs uc ed χdis ibu ion in a ully-simula ed B0→D∗−D∗+
ssample
and he gene a ed χdis ibu ion in a RapidSim sample p oduced wi h he same helici y ampli ude
model (le ). The a io is i ed wi h a second-o de polynomial o de e mine he accep ance unc ion
o use in he da a i ( igh ).
hei unce ain ies o de e mine he sys ema ic unce ain ies on he helici y pa ame e s.
In his p ocedu e, he co ela ions be ween he polynomial coe icien s a e accoun ed o
using he accep ance i co a iance ma ix.
8 Angula i o da a
To measu e |H−|,φ−, and φ+, an unbinned maximum-likelihood i o he h ee-dimensional
angula dis ibu ion o signal-weigh ed da a is pe o med using z i [30]. Fo he i , he
B0→D∗−(D∗+
s→D+
sγ)candida es om he m(D∗−D∗+
s) i in sec ion 6a e used wi h
pe -candida e signal weigh s assigned. The longi udinal pola isa ion ampli ude, H0, is
assigned a ixed magni ude |H0|using he alue o Lmeasu ed in sec ion 5, and i s phase
is se o he a bi a y alue φ0= 0. The pa ame e |H+|is ully de e mined by he
no malisa ion o he helici y ampli udes o uni y. The signal densi y a each poin in
angula phase space is desc ibed using eq. (2.2) mul iplied by accep ance unc ions in each
o he decay angles. To de e mine he s a is ical unce ain ies o he obse ables, he i
applies an asymp o ic co ec ion o he co a iance ma ix as de ailed in e . [31], which
co ec ly accoun s o he use o signal-weigh ed da a. The dis ibu ions o each decay
angle a e shown in igu e 6, wi h he one-dimensional i p ojec ions o e laid.
S udies wi h pseudoexpe imen s a e pe o med o de e mine he le el o bias p esen
in he esul s, whe e pull dis ibu ions o mean µx
Pand wid h σx
Pa e cons uc ed o each
obse able x. The pull dis ibu ions o each helici y obse able a e ound o ollow Gaus-
sian dis ibu ions closely, whe e σ|H−|
Pis consis en wi h uni y. Howe e , σφ+
P= 1.14 ±0.02
and σφ−
P= 1.12 ±0.02, indica ing ha he de aul i unce ain ies o hese obse ables
a e unde es ima ed. The mean alues o he pulls o he ans e se phases a e consis en
wi h ze o, bu µ|H−|
P=−0.14 ±0.02. These biases a e aced o he ini e size o he i ed
– 15 –
JHEP06(2021)177
−1.0−0.5 0.0 0.5 1.0
cos θD
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Candida e densi y / (0.07)
LHCb
6 b−1
−0.5 0.0 0.5 1.0
cos θX
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Candida e densi y / (0.06)
LHCb
6 b−1
−π−π
20π
2π
χ[ ad]
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Candida e densi y / (0.21 ad)
LHCb
6 b−1
Figu e 6. Decay-angle dis ibu ions o signal-weigh ed B0→D∗−D∗+
scandida es in da a, wi h
he one-dimensional angula i p ojec ions o e laid.
da ase , and a e ound o esol e when pseudoexpe imen da ase s con aining mo e e en s
han a e p esen in da a a e gene a ed. The alues o µx
Pand σx
Pa e used o co ec he
de aul i esul s x±σxas ollows
xc=x−µx
P×σx(8.1)
σc
x=σx
P×σx(8.2)
whe e xc±σc
xa e he co ec ed i esul s. In sec ion 10, he esul s o |H−|,φ+, and φ−
a e quo ed a e his co ec ion p ocedu e.
9 Sys ema ic unce ain ies
The alues o R, (B0
s), and Lmeasu ed in sec ion 5a e subjec o sys ema ic unce ain-
ies due o limi ed knowledge o he shape pa ame e s, b anching ac ions, and ela i e
e iciency co ec ions used in he i . To de e mine hese sys ema ic unce ain ies, he
– 16 –
JHEP06(2021)177
Sys ema ic unce ain y R R(B0
s) L
Fixed PDF shape pa ame e s 0.030 0.00197 0.0074
Fixed b anching ac ions 0.016 0.00004 0.0080
E iciency co ec ions 0.062 0.00253 0.0001
To al 0.071 0.00320 0.0109
Table 1. Sys ema ic unce ain ies on he b anching ac ion a ios and Las measu ed in he
m(D∗−D+
s) i .
Sys ema ic unce ain y |H−|φ+φ−
Fixed Lin angula i and cos(θX/D)accep ance 0.0005 0.0007 0.005
Use o sWeigh ed da a 0.0003 0.0011 0.002
S a is ical unce ain y o accep ance unc ions 0.0034 0.0132 0.044
m(D∗D∗
s) i backg ound model 0.0319 0.0156 0.025
To al 0.0321 0.0205 0.051
Table 2. Sys ema ic unce ain ies on he helici y pa ame e s measu ed in he unbinned angula i .
m(D∗−D+
s) i o da a is pe o med many imes wi h he pa ame e s andomly a ied
wi hin hei p esc ibed unce ain ies acco ding o Gaussian dis ibu ions. This p ocedu e
is pe o med sepa a ely o he shape pa ame e s, b anching ac ions, and e iciency co -
ec ions, and he o al sys ema ic unce ain ies calcula ed as he sum in quad a u e o
hese con ibu ions. The sys ema ic unce ain ies a e summa ised in able 1.
The obse ables |H−|,φ+, and φ−measu ed in he angula i a e subjec o se e al
sys ema ic unce ain ies. Fi s ly, he angula analysis is pe o med a a ixed alue o
L, which is used as inpu in he cos θDand cos θXaccep ance i s and also o se he
alue o |H0|in he angula i . To de e mine he sys ema ic unce ain y, he angula
analysis is epea ed many imes wi h L a ied wi hin i s o al unce ain y; he s anda d
de ia ions o he helici y obse able esul s a e aken as he sys ema ic unce ain ies. In
his p ocedu e, he a ied L alue used in he accep ance i s is sha ed wi h he angula i
o ensu e consis ency. A small sys ema ic unce ain y is also assigned o he use o signal-
weigh ed da a, whe e he angula i is un many imes while a ying he signal weigh s
wi hin he signal yield unce ain ies om he m(D∗−D∗+
s) i . To de e mine he sys ema ic
unce ain y om he use o ini e samples o ob ain he accep ance unc ions, he accep ance
coe icien s a e a ied wi hin hei unce ain ies acco ding o he accep ance i co a iance
ma ices. Finally, he angula analysis is epea ed wi h an al e na i e backg ound model
in he m(D∗−D∗+
s) i , and he di e ences in cen al alue o each helici y obse able
a e assigned as a sys ema ic unce ain y. The con ibu ing sys ema ic unce ain ies a e
summa ised in able 2.
– 17 –
JHEP06(2021)177
10 Resul s and conclusion
Using a i o he m(D∗−D+
s)dis ibu ion o de e mine he p ope ies o pa ially econ-
s uc ed B0→D∗−(D∗+
s→D+
sγ)decays, he longi udinal pola isa ion ac ion is mea-
su ed o be
L= 0.578 ±0.010 ±0.011,
whe e he i s unce ain y is s a is ical and he second is sys ema ic. The co esponding
magni ude o he longi udinal helici y ampli ude, gi en by |H0|=√ L, is
|H0|= 0.760 ±0.007 ±0.007.
This in o ma ion is used o measu e he emaining helici y obse ables in an angula i o
ully econs uc ed B0→D∗−(D∗+
s→D+
sγ)decays, ob aining
|H−|= 0.195 ±0.022 ±0.032,
|H+|= 0.620 ±0.011 ±0.013,
φ+=−0.046 ±0.102 ±0.020,
φ−= 0.108 ±0.170 ±0.051,
whe e he quo ed alue and unce ain ies o |H+|a e ully de e mined by he no malisa ion
o he h ee helici y ampli udes o uni y. The measu emen o Lis consis en wi h and mo e
p ecise han he cu en wo ld a e age, L= 0.52 ±0.05 [1,2]. The ans e se ampli ude
magni udes and phases a e measu ed o he i s ime, whe e bo h phases a e consis en
wi h ze o bu he magni udes di e om each o he a he le el o nine s anda d de ia ions.
I is no ed ha |H0|>|H+|>|H−|, which is expec ed om qua k-helici y conse a ion in
Bdecays in ol ing a b→cqua k ansi ion. In such decays, he V−Ana u e o he weak
in e ac ion causes he longi udinal componen o domina e. The inequali y is s onge o
decays in ol ing ligh ec o mesons [7], bu also appea s o be sa is ied in B0→D∗−D∗+
s
decays whe e wo ec o cha m mesons a e p oduced. This helici y hie a chy is no obse ed
in decays domina ed by penguin ampli udes such as B0→φK∗0, whe e he longi udinal
and ans e se componen s a e ound o ha e oughly equal ampli udes [32–35].
The b anching ac ion a io o B0→D∗−(D∗+
s→D+
sγ)decays ela i e o B0→D∗−D+
s
decays is measu ed o be
R= 2.045 ±0.022 ±0.071,
whe e he i s unce ain y is s a is ical and he second is sys ema ic. This esul is
in ag eemen wi h, bu conside ably mo e p ecise han, he cu en wo ld-a e age alue
R= 2.07 ±0.33 [2]. The b anching ac ion a io o he Cabibbo-supp essed B0
s→D∗−D+
s
decay ela i e o he B0→D∗−D+
sdecay is measu ed o be
(B0
s)=0.049 ±0.006 ±0.003 ±0.002,
whe e he i s unce ain y is s a is ical, he second is sys ema ic, and he hi d accoun s
o he use o an ex e nal alue o s/ d[25]. This measu emen cons i u es he i s
– 18 –
JHEP06(2021)177
obse a ion o he Cabibbo-supp essed B0
s→D∗−D+
sdecay wi h a signi icance o se en
s anda d de ia ions.
In conclusion, an angula analysis o B0→D∗−D∗+
swi h D∗+
s→D+
sγdecays is pe -
o med using 6 b−1o da a collec ed wi h he LHCb expe imen a √s= 13 TeV in o -
de o measu e a comple e se o helici y ampli ude obse ables. Pa ially econs uc ed
candida es a e used in a i o he m(D∗−D+
s)dis ibu ion o measu e he longi udinal
pola isa ion ac ion L=|H0|2. This knowledge is hen used in a subsequen angula i
o ully econs uc ed da a in o de o measu e he emaining helici y obse ables. The
measu emen o Lis consis en wi h and mo e p ecise han he cu en wo ld-a e age
alue, while he magni udes and phases o he ans e se helici y ampli udes a e measu ed
o he i s ime. The pa e n o helici y ampli ude magni udes is ound o align wi h
expec a ions om qua k-helici y conse a ion o ee-le el Bdecays in ol ing a b→c
ansi ion. The B0→D∗−D∗+
sdecay is a la ge backg ound in B0→D∗−τ+ντanalyses,
pa icula ly when he τ+decays had onically. Analyses aiming o measu e angula ob-
se ables in B0→D∗−τ+ντdecays mus con ol he angula dis ibu ions o p ominen
had onic backg ounds such as B0→D∗−D∗+
s, and he esul s p esen ed he ein will help
o signi ican ly educe backg ound model unce ain ies in u u e measu emen s.
Acknowledgmen s
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); MOST and NSFC (China); CNRS/IN2P3
(F ance); BMBF, DFG and MPG (Ge many); INFN (I aly); NWO (Ne he lands); MNiSW
and NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MICINN (Spain); SNSF and
SER (Swi ze land); NASU (Uk aine); STFC (U.K.); DOE NP and NSF (U.S.A.). We
acknowledge he compu ing esou ces ha a e p o ided by CERN, IN2P3 (F ance), KIT
and DESY (Ge many), INFN (I aly), SURF (Ne he lands), PIC (Spain), G idPP (U.K.),
RRCKI and Yandex LLC (Russia), CSCS (Swi ze land), IFIN-HH (Romania), CBPF
(B azil), PL-GRID (Poland) and NERSC (U.S.A.). We a e indeb ed o he communi ies
behind he mul iple open-sou ce so wa e packages on which we depend. Indi idual g oups
o membe s ha e ecei ed suppo om ARC and ARDC (Aus alia); A H Founda ion
(Ge many); EPLANET, Ma ie Skłodowska-Cu ie Ac ions and ERC (Eu opean Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Au e gne-Rhône-Alpes (F ance);
Key Resea ch P og am o F on ie Sciences o CAS, CAS PIFI, CAS CCEPP, Fundamen-
al Resea ch Funds o he Cen al Uni e si ies, and Sci. & Tech. P og am o Guangzhou
(China); RFBR, RSF and Yandex LLC (Russia); GVA, Xun aGal and GENCAT (Spain);
he Le e hulme T us , he Royal Socie y and UKRI (U.K.).
– 19 –
JHEP06(2021)177
4950 5000 5050 5100 5150 5200 5250
m(D∗−D+
s) [MeV/c2]
−1.00
−0.75
−0.50
−0.25
0.00
0.25
0.50
0.75
1.00
cos θX
LHCb simula ion
0
20
40
60
80
100
120
140
Figu e 7. Rela ionship be ween m(D∗−D+
s)and cos θXin a sample o ully econs uc ed
B0→D∗−(D∗+
s→D+
sγ)simula ed decays. The colou scale indica es he numbe o candida es in
each bin.
A Rela ionship be ween m(D∗−D+
s)and cos θX
In igu e 7, he ela ionship be ween m(D∗−D+
s)and cos θXis shown o ully econs uc ed
B0→D∗−(D∗+
s→D+
sγ)simula ed decays. A s ong nega i e co ela ion is e iden , due
o a common dependence on he kinema ics o he pho on p oduced in he D∗+
sdecay. The
one-dimensional decay a e as a unc ion o cos θXis gi en by eq. (5.1), whe e sepa a e
ans e se and longi udinal componen s con ibu e; hese componen s a e illus a ed in
igu e 8. Due o he co-dependence o m(D∗−D+
s)and cos θX, he di e en angula o ms
o ans e se and longi udinal signal gi e ise o di e en m(D∗−D+
s)dis ibu ions. This
is illus a ed in igu e 9, whe e RapidSim samples o ans e se and longi udinal signal a e
shown. The i s used o de i e shape pa ame e s o he m(D∗−D+
s) i a e o e laid.
– 20 –
JHEP06(2021)177
−1.0−0.5 0.0 0.5 1.0
cos θX
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Densi y
LHCb
To al
Longi udinal
T ans e se
Figu e 8. T ans e se and longi udinal con ibu ions o he one-dimensional decay a e shown as
a unc ion o cos θX.
4900 5000 5100 5200 5300
m(D∗−D+
s) [MeV/c2]
500
1000
1500
Candida es / (2.0 MeV/c2)
LHCb
Fi
RapidSim simula ion
4950 5000 5050 5100 5150 5200
m(D∗−D+
s) [MeV/c2]
500
1000
1500
2000
Candida es / (2.0 MeV/c2)
LHCb
Fi
RapidSim simula ion
Figu e 9. In a ian -mass dis ibu ions o (le ) pu e ans e se and ( igh ) longi udinal
B0→D∗−(D∗+
s→D+
sγ)simula ed decays. Fi s o he dis ibu ions a e o e laid, om which shape
pa ame e s o use in he m(D∗−D+
s)da a i a e de i ed.
– 21 –
JHEP06(2021)177
Open Access. This a icle is dis ibu ed unde he e ms o he C ea i e Commons
A ibu ion License (CC-BY 4.0), which pe mi s any use, dis ibu ion and ep oduc ion in
any medium, p o ided he o iginal au ho (s) and sou ce a e c edi ed.
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The LHCb collabo a ion
R. Aaij32, C. Abellán Be e a50, T. Acke nley60, B. Ade a46, M. Adinol i54, H. A sha nia9,
C.A. Aidala86, S. Aiola25, Z. Ajal ouni9, S. Aka 65, J. Alb ech 15, F. Alessio48, M. Alexande 59,
A. Al onso Albe o45, Z. Aliouche62, G. Alkhazo 38, P. Al a ez Ca elle55, S. Ama o2, Y. Amhis11,
L. An48, L. Ande lini22, A. And eiano 38, M. And eo i21, F. A chilli17, A. A amono 44,
M. A uso68, K. A zyma o 42, E. Aslanides10, M. A zeni50, B. Audu ie 12, S. Bachmann17,
M. Bachmaye 49, J.J. Back56, P. Balad on Rod iguez46, V. Balagu a12, W. Baldini21,
J. Bap is a Lei e1, R.J. Ba low62, S. Ba suk11, W. Ba e 61, M. Ba olini24, F. Ba yshniko 83,
J.M. Basels14, G. Bassi29, B. Ba sukh68, A. Ba ig15, A. Bay49, M. Becke 15, F. Bedeschi29,
I. Bediaga1, A. Bei e 68, V. Bela in42, S. Belin27, V. Bellee49, K. Belous44, I. Belo 40,
I. Belyae 41, G. Benci enni23, E. Ben-Haim13, A. Be ezhnoy40, R. Be ne 50, D. Be ningho 17,
H.C. Be ns ein68, C. Be ella48, A. Be olin28, C. Be ancou 50, F. Be i48, Ia. Bezshyiko50,
S. Bhasin54, J. Bhom35, L. Bian73, M.S. Bieke 15, S. Bi ani53, P. Billoi 13, M. Bi ch61,
F.C.R. Bishop55, A. Bi adze62, A. Bizze i22,k, M. Bjø n63, M.P. Blago48, T. Blake56, F. Blanc49,
S. Blusk68, D. Bobulska59, J.A. Boelhau e15, O. Boen e Ga cia46, T. Boe che 65, A. Boldy e 82,
A. Bonda 43, N. Bonda 38,48, S. Bo ghi62, M. Bo isyak42, M. Bo sa o17, J.T. Bo suk35,
S.A. Bouchiba49, T.J.V. Bowcock60, A. Boye 48, C. Bozzi21, M.J. B adley61, S. B aun66,
A. B ea Rod iguez46, M. B odski48, J. B odzicka35, A. B ossa Gonzalo56, D. B undu27,
A. Buonau a50, C. Bu 48, A. Bu sche72, A. Bu ke ich39, J.S. Bu e 32, J. Buy ae 48,
W. Byczynski48, S. Cadeddu27, H. Cai73, R. Calab ese21, , L. Cale ice15,13, L. Cale o Diaz23,
S. Cali23, R. Calladine53, M. Cal i26,j , M. Cal o Gomez85, P. Cama go Magalhaes54,
A. Camboni45,85, P. Campana23, A.F. Campo e de Quezada6, S. Capelli26,j , L. Cap io i20,d,
A. Ca bone20,d, G. Ca boni31, R. Ca dinale24, A. Ca dini27, I. Ca li4, P. Ca ni i26,j, L. Ca us14,
K. Ca alho Akiba32, A. Casais Vidal46, G. Casse60, M. Ca aneo48, G. Ca alle o48, S. Celani49,
J. Ce asoli10, A.J. Chadwick60, M.G. Chapman54, M. Cha les13, Ph. Cha pen ie 48,
G. Cha zikons an inidis53, C.A. Cha ez Ba ajas60, M. Che de ille8, C. Chen3, S. Chen4,
A. Che no 35, V. Chobano a46, S. Cholak49, M. Ch zaszcz35, A. Chubykin38, V. Chuliko 38,
P. Ciamb one23, M.F. Cicala56, X. Cid Vidal46, G. Cieza ek48, P.E.L. Cla ke58, M. Clemencic48,
H.V. Cli 55, J. Closie 48, J.L. Cobbledick62, V. Coco48, J.A.B. Coelho11, J. Cogan10,
E. Cogne as9, L. Cojoca iu37, P. Collins48, T. Colombo48, L. Congedo19,c, A. Con u27, N. Cooke53,
G. Coombs59, G. Co i48, C.M. Cos a Sob al56, B. Cou u ie 48, D.C. C aik64, J. C ko ská67,
M. C uz To es1, R. Cu ie58, C.L. Da Sil a67, E. Dall’Occo15, J. Dalseno46, C. D’Amb osio48,
A. Danilina41, P. d’A gen 48, A. Da is62, O. De Aguia F ancisco62, K. De B uyn79,
S. De Capua62, M. De Cian49, J.M. De Mi anda1, L. De Paula2, M. De Se io19,c, D. De Simone50,
P. De Simone23, J.A. de V ies80, C.T. Dean67, D. Decamp8, L. Del Buono13, B. Delaney55,
H.-P. Dembinski15, A. Dendek34, V. Denysenko50, D. De kach82, O. Deschamps9, F. Desse11,
F. De o i27,e, B. Dey77, P. Di Nezza23, S. Didenko83, L. Dies e Ma onas46, H. Dijks a48,
V. Dobishuk52, A.M. Donohoe18, F. Do dei27, A.C. dos Reis1, L. Douglas59, A. Do bnya51,
A.G. Downes8, K. D eimanis60, M.W. Dudek35, L. Du ou 48, V. Duk78, P. Du an e48,
J.M. Du ham67, D. Du a62, A. Dziu da35, A. Dzyuba38, S. Easo57, U. Egede69, V. Ego yche 41,
S. Eidelman43, , S. Eisenha d 58, S. Ek-In49, L. Eklund59,w, S. Ely68, A. Ene37, E. Epple67,
S. Esche 14, J. Eschle50, S. Esen13, T. E ans48, A. Falabella20, J. Fan3, Y. Fan6, B. Fang73,
S. Fa y60, D. Fazzini26,j, M. Féo48, A. Fe nandez P ie o46, J.M. Fe nandez- enllado A ibas45,
A.D. Fe nez66, F. Fe a i20,d, L. Fe ei a Lopes49, F. Fe ei a Rod igues2, S. Fe e es Sole32,
M. Fe illo50, M. Fe o-Luzzi48, S. Filippo 39, R.A. Fini19, M. Fio ini21, , M. Fi lej34,
K.M. Fische 63, D.S. Fi zge ald86, C. Fi zpa ick62, T. Fiu owski34, F. Fleu e 12, M. Fon ana13,
F. Fon anelli24,h, R. Fo y48, V. F anco Lima60, M. F anco Se illa66, M. F ank48, E. F anzoso21,
– 24 –
