EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-PAPER-2011-016 CERN-PH-EP-2011-151

Measurements of the Branching fractions for $B_{(s)}\rightarrow
D_{(s)}\pi\pi\pi$ and $\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi\pi\pi$

The LHCb Collaboration 111Authors are listed on the following pages.

Branching fractions of the decays $H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-}$ relative to $H_{b}\rightarrow H_{c}\pi^{-}$ are
presented, where $H_{b}$ ($H_{c}$) represents $\bar{B}^{0}$ ($D^{+}$), $B^{-}$
($D^{0}$), $\bar{B}_{s}^{0}$ ($D_{s}^{+}$) and $\Lambda_{b}^{0}$
($\Lambda_{c}^{+}$). The measurements are performed with the LHCb detector
using 35 $\rm pb^{-1}$ of data collected at $\sqrt{s}=7$ TeV. The ratios of
branching fractions are measured to be

$\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-})}=2.38\pm
0.11\pm 0.21$ $\displaystyle{{\cal{B}}(B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(B^{-}\rightarrow
D^{0}\pi^{-})}=1.27\pm 0.06\pm 0.11$ $\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-})}=2.01\pm 0.37\pm 0.20$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-})}=1.43\pm
0.16\pm 0.13.$

We also report measurements of partial decay rates of these decays to excited
charm hadrons. These results are of comparable or higher precision than
existing measurements.

R. Aaij23, B. Adeva36, M. Adinolfi42, C. Adrover6, A. Affolder48, Z.
Ajaltouni5, J. Albrecht37, F. Alessio37, M. Alexander47, G. Alkhazov29, P.
Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2, Y. Amhis38, J. Anderson39,
R.B. Appleby50, O. Aquines Gutierrez10, F. Archilli18,37, L. Arrabito53, A.
Artamonov 34, M. Artuso52,37, E. Aslanides6, G. Auriemma22,m, S. Bachmann11,
J.J. Back44, D.S. Bailey50, V. Balagura30,37, W. Baldini16, R.J. Barlow50, C.
Barschel37, S. Barsuk7, W. Barter43, A. Bates47, C. Bauer10, Th. Bauer23, A.
Bay38, I. Bediaga1, K. Belous34, I. Belyaev30,37, E. Ben-Haim8, M. Benayoun8,
G. Bencivenni18, S. Benson46, J. Benton42, R. Bernet39, M.-O. Bettler17, M.
van Beuzekom23, A. Bien11, S. Bifani12, A. Bizzeti17,h, P.M. Bjørnstad50, T.
Blake49, F. Blanc38, C. Blanks49, J. Blouw11, S. Blusk52, A. Bobrov33, V.
Bocci22, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi47, A. Borgia52,
T.J.V. Bowcock48, C. Bozzi16, T. Brambach9, J. van den Brand24, J.
Bressieux38, D. Brett50, S. Brisbane51, M. Britsch10, T. Britton52, N.H.
Brook42, H. Brown48, A. Büchler-Germann39, I. Burducea28, A. Bursche39, J.
Buytaert37, S. Cadeddu15, J.M. Caicedo Carvajal37, O. Callot7, M. Calvi20,j,
M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, A. Carbone14, G.
Carboni21,k, R. Cardinale19,i,37, A. Cardini15, L. Carson36, K. Carvalho
Akiba23, G. Casse48, M. Cattaneo37, M. Charles51, Ph. Charpentier37, N.
Chiapolini39, K. Ciba37, X. Cid Vidal36, G. Ciezarek49, P.E.L. Clarke46,37, M.
Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V. Coco23, J. Cogan6, P.
Collins37, F. Constantin28, G. Conti38, A. Contu51, A. Cook42, M. Coombes42,
G. Corti37, G.A. Cowan38, R. Currie46, B. D’Almagne7, C. D’Ambrosio37, P.
David8, I. De Bonis4, S. De Capua21,k, M. De Cian39, F. De Lorenzi12, J.M. De
Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9, H.
Degaudenzi38,37, M. Deissenroth11, L. Del Buono8, C. Deplano15, O. Deschamps5,
F. Dettori15,d, J. Dickens43, H. Dijkstra37, P. Diniz Batista1, S. Donleavy48,
A. Dosil Suárez36, D. Dossett44, A. Dovbnya40, F. Dupertuis38, R.
Dzhelyadin34, C. Eames49, S. Easo45, U. Egede49, V. Egorychev30, S.
Eidelman33, D. van Eijk23, F. Eisele11, S. Eisenhardt46, R. Ekelhof9, L.
Eklund47, Ch. Elsasser39, D.G. d’Enterria35,o, D. Esperante Pereira36, L.
Estève43, A. Falabella16,e, E. Fanchini20,j, C. Färber11, G. Fardell46, C.
Farinelli23, S. Farry12, V. Fave38, V. Fernandez Albor36, M. Ferro-Luzzi37, S.
Filippov32, C. Fitzpatrick46, M. Fontana10, F. Fontanelli19,i, R. Forty37, M.
Frank37, C. Frei37, M. Frosini17,f,37, S. Furcas20, A. Gallas Torreira36, D.
Galli14,c, M. Gandelman2, P. Gandini51, Y. Gao3, J-C. Garnier37, J.
Garofoli52, J. Garra Tico43, L. Garrido35, C. Gaspar37, N. Gauvin38, M.
Gersabeck37, T. Gershon44,37, Ph. Ghez4, V. Gibson43, V.V. Gligorov37, C.
Göbel54, D. Golubkov30, A. Golutvin49,30,37, A. Gomes2, H. Gordon51, M.
Grabalosa Gándara35, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graugés35,
G. Graziani17, A. Grecu28, S. Gregson43, B. Gui52, E. Gushchin32, Yu. Guz34,
T. Gys37, G. Haefeli38, C. Haen37, S.C. Haines43, T. Hampson42, S. Hansmann-
Menzemer11, R. Harji49, N. Harnew51, J. Harrison50, P.F. Harrison44, J. He7,
V. Heijne23, K. Hennessy48, P. Henrard5, J.A. Hernando Morata36, E. van
Herwijnen37, E. Hicks48, W. Hofmann10, K. Holubyev11, P. Hopchev4, W.
Hulsbergen23, P. Hunt51, T. Huse48, R.S. Huston12, D. Hutchcroft48, D.
Hynds47, V. Iakovenko41, P. Ilten12, J. Imong42, R. Jacobsson37, A. Jaeger11,
M. Jahjah Hussein5, E. Jans23, F. Jansen23, P. Jaton38, B. Jean-Marie7, F.
Jing3, M. John51, D. Johnson51, C.R. Jones43, B. Jost37, S. Kandybei40, M.
Karacson37, T.M. Karbach9, J. Keaveney12, U. Kerzel37, T. Ketel24, A. Keune38,
B. Khanji6, Y.M. Kim46, M. Knecht38, S. Koblitz37, P. Koppenburg23, A.
Kozlinskiy23, L. Kravchuk32, K. Kreplin11, M. Kreps44, G. Krocker11, P.
Krokovny11, F. Kruse9, K. Kruzelecki37, M. Kucharczyk20,25,37, S. Kukulak25,
R. Kumar14,37, T. Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G.
Lafferty50, A. Lai15, D. Lambert46, R.W. Lambert37, E. Lanciotti37, G.
Lanfranchi18, C. Langenbruch11, T. Latham44, R. Le Gac6, J. van Leerdam23,
J.-P. Lees4, R. Lefèvre5, A. Leflat31,37, J. Lefran$c$cois7, O. Leroy6, T.
Lesiak25, L. Li3, L. Li Gioi5, M. Lieng9, M. Liles48, R. Lindner37, C. Linn11,
B. Liu3, G. Liu37, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-March38, J.
Luisier38, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc10, O. Maev29,37,
J. Magnin1, S. Malde51, R.M.D. Mamunur37, G. Manca15,d, G. Mancinelli6, N.
Mangiafave43, U. Marconi14, R. Märki38, J. Marks11, G. Martellotti22, A.
Martens7, L. Martin51, A. Martín Sánchez7, D. Martinez Santos37, A.
Massafferri1, Z. Mathe12, C. Matteuzzi20, M. Matveev29, E. Maurice6, B.
Maynard52, A. Mazurov32,16,37, G. McGregor50, R. McNulty12, C. Mclean14, M.
Meissner11, M. Merk23, J. Merkel9, R. Messi21,k, S. Miglioranzi37, D.A.
Milanes13,37, M.-N. Minard4, S. Monteil5, D. Moran12, P. Morawski25, R.
Mountain52, I. Mous23, F. Muheim46, K. Müller39, R. Muresan28,38, B. Muryn26,
M. Musy35, J. Mylroie-Smith48, P. Naik42, T. Nakada38, R. Nandakumar45, J.
Nardulli45, I. Nasteva1, M. Nedos9, M. Needham46, N. Neufeld37, C. Nguyen-
Mau38,p, M. Nicol7, S. Nies9, V. Niess5, N. Nikitin31, A. Oblakowska-Mucha26,
V. Obraztsov34, S. Oggero23, S. Ogilvy47, O. Okhrimenko41, R. Oldeman15,d, M.
Orlandea28, J.M. Otalora Goicochea2, P. Owen49, B. Pal52, J. Palacios39, M.
Palutan18, J. Panman37, A. Papanestis45, M. Pappagallo13,b, C. Parkes47,37,
C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49, S.K. Paterson49,
G.N. Patrick45, C. Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos Alvarez36,
A. Pellegrino23, G. Penso22,l, M. Pepe Altarelli37, S. Perazzini14,c, D.L.
Perego20,j, E. Perez Trigo36, A. Pérez-Calero Yzquierdo35, P. Perret5, M.
Perrin-Terrin6, G. Pessina20, A. Petrella16,37, A. Petrolini19,i, B. Pie
Valls35, B. Pietrzyk4, T. Pilar44, D. Pinci22, R. Plackett47, S. Playfer46, M.
Plo Casasus36, G. Polok25, A. Poluektov44,33, E. Polycarpo2, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell51, T. du Pree23, J. Prisciandaro38, V.
Pugatch41, A. Puig Navarro35, W. Qian52, J.H. Rademacker42, B.
Rakotomiaramanana38, M.S. Rangel2, I. Raniuk40, G. Raven24, S. Redford51, M.M.
Reid44, A.C. dos Reis1, S. Ricciardi45, K. Rinnert48, D.A. Roa Romero5, P.
Robbe7, E. Rodrigues47, F. Rodrigues2, P. Rodriguez Perez36, G.J. Rogers43, S.
Roiser37, V. Romanovsky34, J. Rouvinet38, T. Ruf37, H. Ruiz35, G.
Sabatino21,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail47, B. Saitta15,d,
C. Salzmann39, M. Sannino19,i, R. Santacesaria22, R. Santinelli37, E.
Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M.
Savrie16,e, D. Savrina30, P. Schaack49, M. Schiller11, S. Schleich9, M.
Schmelling10, B. Schmidt37, O. Schneider38, A. Schopper37, M.-H. Schune7, R.
Schwemmer37, A. Sciubba18,l, M. Seco36, A. Semennikov30, K. Senderowska26, I.
Sepp49, N. Serra39, J. Serrano6, P. Seyfert11, B. Shao3, M. Shapkin34, I.
Shapoval40,37, P. Shatalov30, Y. Shcheglov29, T. Shears48, L. Shekhtman33, O.
Shevchenko40, V. Shevchenko30, A. Shires49, R. Silva Coutinho54, H.P.
Skottowe43, T. Skwarnicki52, A.C. Smith37, N.A. Smith48, K. Sobczak5, F.J.P.
Soler47, A. Solomin42, F. Soomro49, B. Souza De Paula2, B. Spaan9, A.
Sparkes46, P. Spradlin47, F. Stagni37, S. Stahl11, O. Steinkamp39, S.
Stoica28, S. Stone52,37, B. Storaci23, M. Straticiuc28, U. Straumann39, N.
Styles46, V.K. Subbiah37, S. Swientek9, M. Szczekowski27, P. Szczypka38, T.
Szumlak26, S. T’Jampens4, E. Teodorescu28, F. Teubert37, C. Thomas51,45, E.
Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin39, S. Topp-Joergensen51,
M.T. Tran38, A. Tsaregorodtsev6, N. Tuning23, A. Ukleja27, P. Urquijo52, U.
Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez35, P. Vazquez Regueiro36,
S. Vecchi16, J.J. Velthuis42, M. Veltri17,g, K. Vervink37, B. Viaud7, I.
Videau7, X. Vilasis-Cardona35,n, J. Visniakov36, A. Vollhardt39, D. Voong42,
A. Vorobyev29, H. Voss10, K. Wacker9, S. Wandernoth11, J. Wang52, D.R. Ward43,
A.D. Webber50, D. Websdale49, M. Whitehead44, D. Wiedner11, L. Wiggers23, G.
Wilkinson51, M.P. Williams44,45, M. Williams49, F.F. Wilson45, J. Wishahi9, M.
Witek25,37, W. Witzeling37, S.A. Wotton43, K. Wyllie37, Y. Xie46, F. Xing51,
Z. Yang3, R. Young46, O. Yushchenko34, M. Zavertyaev10,a, L. Zhang52, W.C.
Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, E. Zverev31, A. Zvyagin 37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit,
Amsterdam, Netherlands
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Cracow, Poland
26Faculty of Physics & Applied Computer Science, Cracow, Poland
27Soltan Institute for Nuclear Studies, Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44Department of Physics, University of Warwick, Coventry, United Kingdom
45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
47School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oInstitució Catalana de Recerca i Estudis Avan$c$cats (ICREA), Barcelona,
Spain
pHanoi University of Science, Hanoi, Viet Nam

##  1 Introduction

Over the last two decades, a wealth of information has been accumulated on the
decays of $b$-hadrons. Measurements of their decays have been used to test the
CKM mechanism [1] for describing weak decay phenomena in the Standard Model,
as well as provide measurements against which various theoretical approaches,
such as HQET [2] and the factorization hypothesis, can be compared. While many
decays have been measured, a large number remain either unobserved or poorly
measured, most notably in the decays of $B^{0}_{s}$ mesons and
$\Lambda_{b}^{0}$ baryons. Among the largest hadronic branching fractions are
the decays $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$, where $H_{b}$
($H_{c}$) represents $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$
($D^{+}$), $B^{-}$ ($D^{0}$), $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ ($D_{s}^{+}$) and
$\Lambda_{b}^{0}$ ($\Lambda_{c}^{+}$). The first three branching fractions
were determined with only 30-40% accuracy, and the
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ branching
fraction was unmeasured.

Beyond improving our overall understanding of hadronic $b$ decays, these
decays are of interest because of their potential use in CP violation studies.
It is well known that the Cabibbo-suppressed decays $B^{-}\rightarrow DK^{-}$
[3, 4, 5] and $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{\pm}K^{\mp}$ [6, 7] provide clean measurements of the weak phase
$\gamma$ through time-independent and time-dependent rate measurements,
respectively. Additional sensitivity can be obtained by using $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ [8]
decays. As well as these modes, one can exploit higher multiplicity decays,
such as $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow DK^{*0}$,
$B^{-}\rightarrow DK^{-}\pi^{+}\pi^{-}$ [9] and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{\pm}K^{\mp}\pi^{\pm}\pi^{\mp}$. Moreover, the decay $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ has been used to measure $\Delta m_{s}$ [10],
and with a sufficiently large sample, provides a calibration for the flavor-
mistag rate for the time-dependent analysis of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{\pm}K^{\mp}\pi^{\pm}\pi^{\mp}$.

The first step towards exploiting these multi-body decays is to observe them
and quantify their branching fractions. The more interesting Cabibbo-
suppressed decays are $O(\lambda^{3})$ in the Wolfenstein parameterization
[11], and therefore require larger data samples. Here, we present measurements
of the Cabibbo-favored $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ decays.
The leading amplitudes contributing to these final states are shown in Fig. 1.
Additional contributions from annihilation and $W$-exchange diagrams are
suppressed and are not shown here. Note that for the $B^{-}$ and
$\Lambda_{b}^{0}$ decays, unlike the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$, there is potential for
interference between diagrams with similar magnitudes. In Ref. [12], it is
argued that this interference can explain the larger rate for
$B^{-}\rightarrow D^{0}\pi^{-}$ compared to $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$. Thus, it
is interesting to see whether this is also true when the final state contains
three pions.

Figure 1: Feynman diagrams for $H_{b}\rightarrow H_{c}\pi^{-}$ and
$H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ decays. Figs. (a) and (b) show
external tree diagrams, (c) and (d) show color-suppressed tree diagrams
($B^{-}$ and $\Lambda_{b}^{0}$ only), and (e) shows the Cabibbo-suppressed
external tree diagram, only accessible to $B^{0}$ meson.

In this paper, we report measurements of the $H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-}$ branching fractions, relative to $H_{b}\rightarrow
H_{c}\pi^{-}$. We also report on the partial branching fractions,
$H_{b}\rightarrow H_{c}^{*}\pi^{-},~{}H_{c}^{*}\rightarrow
H_{c}\pi^{+}\pi^{-}$, where $H_{b}$ is either $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$, $B^{-}$, or $\Lambda_{b}^{0}$,
and $H_{c}^{*}$ refers to $D_{1}(2420)^{+,0}$, $D_{2}^{*}(2460)^{0}$,
$\Lambda_{c}(2595)^{+}$, or $\Lambda_{c}(2625)^{+}$. We also present results
on the partial rates for
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}(2544)^{0,++}\pi^{\pm}\pi^{-}$. Charge
conjugate final states are implied throughout.

##  2 Detector and Trigger

The data used for this analysis were collected by the LHCb experiment during
the 2010 data taking period and comprise about 35 $\rm pb^{-1}$ of integrated
luminosity. LHCb has excellent capabilities to trigger on and reconstruct
bottom and charm hadrons. The most important element of the detector for this
analysis is a charged particle tracking system that covers the forward angular
region from about $15-350$ mrad and $15-250$ mrad in the horizontal and
vertical directions, respectively. It includes a 21 station, one-meter long
array of silicon strip detectors (VELO) that come within 8 mm of the LHC
beams, a 4 Tm dipole magnetic field, followed by three multi-layer tracking
stations (T-stations) downstream of the dipole magnet. Each T-station is
composed of a four layer silicon strip detector (IT) in the high occupancy
region near the beam pipe, an eight layer straw tube drift chamber (OT)
composed of 5 mm diameter straws outside this high occupancy region. Just
upstream of the dipole magnet is a four-layer silicon strip detector (TT).
Overall, the tracking system provides an impact parameter (IP) resolution of
$\sim 16\mu$m + 30$\mu$m/$p_{T}$ (transverse momentum, $p_{T}$ in GeV/$c$),
and a momentum resolution that ranges from $\sigma_{p}/p\sim 0.4\%$ at 3
GeV/$c$ to $\sim 0.6\%$ at 100 GeV/$c$. Two Ring Imaging Cherenkov Counters
(RICH) provide a kaon identification efficiency of $\sim$95% for a pion fake
rate of a few percent, integrated over the momentum range from 3$-$100
GeV/$c$. Downstream of the second RICH is a Preshower/Scintillating Pad
Detector (PS/SPD), and electromagnetic (ECAL) and hadronic (HCAL)
calorimeters. Information from the ECAL/HCAL is used to form the hadronic
triggers. Finally, a muon system consisting of five stations is used for
triggering on and identifying muons.

To reduce the 40 MHz crossing rate to about 2 kHz for permanent storage, LHCb
uses a two-level trigger system. The first level of the trigger, L0, is
hardware based and searches for either a large transverse energy cluster
($E_{T}>3.6$ GeV) in the calorimeters, or a single high $p_{T}$ or di-muon
pair in the muon stations. Events passing L0 are read out and sent to a large
computing farm, where they are analyzed using a software-based trigger. The
first level of the software trigger, called HLT1, uses a simplified version of
the offline software to apply tighter selections on charged particles based on
their $p_{T}$ and minimal IP to any primary vertex (PV), defined as the
location of the reconstructed $pp$ collision(s). The HLT1 trigger relevant for
this analysis searches for a single track with IP larger than 125 $\mu$m,
$p_{T}>1.8$ GeV/$c$, $p>12.5$ GeV/$c$, along with other track quality
requirements. Events that pass HLT1 are analyzed by a second software level,
HLT2, where the event is searched for 2, 3, or 4-particle vertices that are
consistent with $b$-hadron decays. Tracks are required to have $p>5$ GeV/$c$,
$p_{T}>0.5$ GeV/$c$ and IP $\chi^{2}$ larger than 16 to any PV, where the
$\chi^{2}$ value is obtained assuming the IP is equal to zero. We also demand
that at least one track has $p_{T}>1.5$ GeV/$c$, a scalar $p_{T}$ sum of the
track in the vertex exceed 4 GeV/$c$, and that the corrected mass222The
corrected mass is defined as $M_{\rm cor}=\sqrt{M^{2}+p_{\rm trans}^{2}}$,
where $M$ is the invariant mass of the 2, 3 or 4-track candidate (assuming the
kaon mass for each particle), and $p_{\rm trans}$ is the momentum imbalance
transverse to the direction of flight, defined by the vector that joins the
primary and secondary vertices. is between 4 and 7 GeV/$c^{2}$. These HLT
trigger selections each have an efficiency in the range of 80$-$90% for events
that pass typical offline selections for a large range of $B$ decays. A more
detailed description of the LHCb detector can be found in Ref. [13].

Events with large occupancy are known to have intrinsically high backgrounds
and to be slow to reconstruct. Therefore such events were suppressed by
applying global event cuts (GECs) to hadronically triggered decays. These GECs
included a maximum of 3000 VELO clusters, 3000 IT hits, and 10,000 OT hits. In
addition, hadron triggers were required to have less than 900 or 450 hits in
the SPD, depending on the specific trigger setting.

##  3 Candidate Reconstruction and Selection

Charged particles likely to come from a $b$-hadron decay are first identified
by requiring that they have a minimum IP $\chi^{2}$ with respect to any PV of
more than 9. We also require a minimum transverse momentum, $p_{T}>300$
MeV/$c$, except for $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ decays,
where we allow (at most) one track to have $200<p_{T}<300$ MeV/$c$. Hadrons
are identified using RICH information by requiring the difference in log-
likelihoods ($\Delta LL$) of the different mass hypotheses to satisfy $\Delta
LL(K-\pi)>-5$, $\Delta LL(p-\pi)>-5$ and $\Delta LL(K-\pi)<12$, for kaons,
protons and pions, respectively. These particle hypotheses are not mutually
exclusive, however the same track cannot enter more than once in the same
decay chain.

Charm particle candidates are reconstructed in the decay modes
$D^{0}\rightarrow K^{-}\pi^{+}$, $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$,
$D_{s}^{+}\rightarrow K^{+}K^{-}\pi^{+}$ and $\Lambda_{c}^{+}\rightarrow
pK^{-}\pi^{+}$. The candidate is associated to one of the PVs in the event
based on the smallest IP $\chi^{2}$ between the charm particle’s reconstructed
trajectory and all PVs in the event. A number of selection criteria are
imposed to reduce backgrounds from both prompt charm with random tracks as
well as purely combinatorial background. To reduce the latter, we demand that
each candidate is well separated from the associated PV by requiring that its
flight distance (FD) projected onto the $z$-axis is larger than 2 mm, the FD
$\chi^{2}>49$333This is the $\chi^{2}$ with respect to the FD=0 hypothesis.,
and that the distance in the transverse direction ($\Delta R$) is larger than
100 $\mu$m. Background from random track combinations is also suppressed by
requiring the vertex fit $\chi^{2}$/ndf$<8$, and $p_{T}>1.25$ GeV/$c$ (1.5
GeV/$c$ for $D^{+}_{(s)}$ in $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$.)
To reduce the contribution from prompt charm, we require that the charm
particle has a minimal IP larger than 80 $\mu$m and IP $\chi^{2}>12.25$ with
respect to its associated PV. For $D_{s}^{+}\rightarrow K^{+}K^{-}\pi^{+}$, we
employ tighter particle identification requirements on the kaons, namely
$\Delta LL(K-\pi)>0$, if the $K^{+}K^{-}$ invariant mass is outside a window
of $\pm$20 MeV/$c^{2}$ of the $\phi$ mass [15]. Lastly, we require the
reconstructed charm particles masses to be within 25 MeV/$c^{2}$ of their
known values.

The bachelor pion for $H_{b}\rightarrow H_{c}\pi^{-}$ is required to have
$p_{T}>0.5$ GeV/$c$, $p>5.0$ GeV/$c$ and IP $\chi^{2}>16$. For the 3$\pi$
vertex associated with the $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$
decays, we apply a selection identical to that for the charm particle
candidates, except we only require the $p_{T}$ of the $3\pi$ system to be
larger than 1 GeV/$c$ and that the invariant mass is in the range from
$0.8~{}{\rm GeV}/c^{2}<M(\pi\pi\pi)<3.0$ GeV/$c^{2}$.

Beauty hadrons are formed by combining a charm particle with either a single
pion candidate (for $H_{b}\rightarrow H_{c}\pi^{-}$) or a $3\pi$ candidate
(for $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$.) The $b$-hadron is
required to have a transverse momentum of at least 1 GeV/$c$. As with the
charm hadron, we require it is well-separated from its associated PV, with FD
larger than 2 mm, FD $\chi^{2}>49$ and $\Delta R>100$ $\mu$m. We also make a
series of requirements that ensure that the $b$-hadron candidate is consistent
with a particle produced in a proton-proton interaction. We require the
candidate to have IP$<$90 $\mu$m, IP $\chi^{2}<16$, and that the angle
$\theta$ between the $b$-hadron momentum and the vector formed by joining the
associated PV and the decay vertex satisfies $\cos\theta>0.99996$. To ensure a
good quality vertex fit, we require a vertex fit $\chi^{2}/$ndf$<6$ (8 for
$H_{b}\rightarrow H_{c}\pi^{-}$.)

To limit the timing to process high occupancy events, we place requirements on
the number of tracks444Here, tracks refer to charged particles that have
segments in both the VELO and the T-stations. in an event. For $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$,
the maximum number of tracks is 180, and for
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ and $B^{-}\rightarrow
D^{0}\pi^{-}$ it is 120. These selections are 99% and 95% efficient,
respectively, after the GECs. The $H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-}$ selection requires fewer than 300 tracks, and thus
is essentially 100% efficient after the GECs.

Events are required to pass the triggers described above. This alone does not
imply that the signal $b$-hadron decay was directly responsible for the
trigger. We therefore also require that one or more of the signal $b$-hadron
daughters is responsible for triggering the event. We thus explicitly select
events that Triggered On the Signal decay (TOS) at L0, HLT1 and HLT2. For the
measurements of excited charm states, where our yields are statistically
limited, we also make use of L0-triggers that Triggered Independently of the
Signal decay (TIS). In this case, the L0 trigger is traced to one or more
particles other than those in the signal decay.

Lastly, we note that in $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$
candidate events, between 4% and 10% have multiple candidates (mostly two) in
the same event. In such cases we choose the candidate with the largest
transverse momentum. This criterion is estimated to be $(75\pm 20)$% efficient
for choosing the correct candidate. For $H_{b}\rightarrow H_{c}\pi^{-}$
multiple candidates occur in less than 1% of events, from which we again
choose the one with the largest $p_{T}$.

###  3.1 Selection Efficiencies

Selection and trigger efficiencies are estimated using Monte Carlo (MC)
simulations. The MC samples are generated with an average number of
interactions per crossing equal to 2.5, which is similar to the running
conditions for the majority of the 2010 data. The $b$-hadrons are produced
using pythia [16] and decayed using evtgen [17]. The $H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-}$ decays are produced using a cocktail for the
$\pi\pi\pi$ system that is $\sim$2/3
$a_{1}(1260)^{-}\rightarrow\rho^{0}\pi^{-}$ and about 1/3 non-resonant
$\rho^{0}\pi^{-}$. Smaller contributions from $D_{1}^{0}(2420)\pi$ and
$D_{2}^{*0}(2460)\pi$ are each included at the 5% level to $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$ and 2% each for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$. For
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$, we include
contributions from $\Lambda_{c}(2595)^{+}$ and $\Lambda_{c}(2625)^{+}$, which
contribute 9% and 7% to the MC sample. The detector is simulated with geant4
[18], and the event samples are subsequently analyzed in the same way as data.

We compute the total kinematic efficiency, $\epsilon_{\rm kin}$ from the MC
simulation as the fraction of all events that pass all reconstruction and
selection requirements. These selected events are then passed through a
software emulation of the L0 trigger, and the HLT software used to select the
data, from which we compute the trigger efficiency ($\epsilon_{\rm trig}$).
The efficiencies for the decay modes under study are shown in Table 1. Only
the relative efficiencies are used to obtain the results in this paper.

Table 1: Summary of efficiencies for decay channels under study. Here, $\epsilon_{\rm kin}$ is the total kinematic selection efficiency, $\epsilon_{\rm trig}$ is the trigger efficiency, and $\epsilon_{\rm tot}$ is their product. The uncertainties shown are statistical only. Decay | $\epsilon_{\rm kin}$ | $\epsilon_{\rm trig}$ | $\epsilon_{\rm tot}$
---|---|---|---
| (%) | (%) | (%)
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}\pi^{+}\pi^{-}$ | $0.153\pm 0.003$ | $22.6\pm 0.5$ | $0.0347\pm 0.0011$
$B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$ | $0.275\pm 0.007$ | $27.4\pm 0.6$ | $0.0753\pm 0.0019$
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ | $0.137\pm 0.003$ | $24.9\pm 0.7$ | $0.0342\pm 0.0012$
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ | $0.110\pm 0.005$ | $24.0\pm 0.7$ | $0.0264\pm 0.0008$
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ | $0.882\pm 0.014$ | $20.8\pm 0.3$ | $0.184\pm 0.004$
$B^{-}\rightarrow D^{0}\pi^{-}$ | $1.54\pm 0.02$ | $27.4\pm 0.3$ | $0.421\pm 0.007$
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$ | $0.868\pm 0.010$ | $23.1\pm 0.2$ | $0.201\pm 0.003$
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ | $0.732\pm 0.015$ | $24.7\pm 0.4$ | $0.181\pm 0.004$

##  4 Reconstructed Signals in Data

The reconstructed invariant mass distributions are shown in Figs. 2 and 3 for
the signal and normalization modes, respectively. Unbinned likelihood fits are
performed to extract the signal yields, where the likelihood functions are
given by the sums of signal and several background components. The signal and
background components are shown in the figures. The signal contributions are
each described by the sum of two Gaussian shapes with equal means. The
relative width and fraction of the wider Gaussian shape with respect to the
narrower one are constrained to the values found from MC simulation based on
agreement with data in the large yield signal modes. This constraint is
included with a 10-12% uncertainty (mode-dependent), which is the level of
agreement found between data and MC simulation. The absolute width of the
narrower Gaussian is a free parameter in the fit, since the data shows a
slightly worse ($\sim$10%) resolution that MC simulation.

For $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ decays, there are peaking backgrounds from
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ and
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ just below the $B_{s}^{0}$ mass. We therefore fix
their core Gaussian widths as well, based on the resolutions found in data for
the kinematically similar $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ decays, scaled by 0.93, which is the ratio of
expected widths obtained from MC simulation.

Figure 2: Invariant mass distributions for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ (top left), $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$ (top right), $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ (bottom left), and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ (bottom
right). Fits showing the signal and background components are indicated, and
are described in the text.

Figure 3: Invariant mass distributions for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ (top
left), $B^{-}\rightarrow D^{0}\pi^{-}$ (top right), $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
(bottom left), and $\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ (bottom
right). Fits showing the signal and background components are indicated, and
are described in the text.

A number of backgrounds contribute to these decays. Below the $b$-hadron
masses there are generally peaking background structures due to partially
reconstructed $B$ decays. These decays include $B_{(s)}\rightarrow
D_{(s)}^{*}\pi(\pi\pi)$, with a missed photon, $\pi^{0}$ or $\pi^{+}$, as well
as $B_{(s)}\rightarrow D_{(s)}\rho^{-}$, where the $\pi^{0}$ is not included
in the decay hypothesis. For the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ and
$B^{-}\rightarrow D^{0}\pi^{-}$ decays, the shapes of these backgrounds are
taken from dedicated signal MC samples. The double-peaked background shape
from partially-reconstructed $D^{*}\pi$ decays is obtained by fitting the
background MC sample to the sum of two Gaussian shapes with different means.
The difference in their means is then fixed, while their average is a free
parameter in subsequent fits to the data. For $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ and $B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$,
the shape of the partially-reconstructed $D^{*}\pi\pi\pi$ background is not as
easily derived since the helicity amplitudes are not known. This low mass
background is also parametrized using a two-Gaussian model, but we let the
parameters float in the fit to the data. For $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
and $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$, we obtain the background shape from a large
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}X$
inclusive MC sample. Less is known about the $\Lambda_{b}^{0}$ hadronic decays
that would contribute background to the
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ invariant
mass spectra. For
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$, we see no
clear structure due to partially-reconstructed backgrounds. For
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$, there does appear to be
structure at about 5430 MeV/$c^{2}$, which may be due to
$\Lambda_{c}^{+}\rho^{-}$. The enhancement is described by a single Gaussian
above the combinatoric background, which, given the limited number of events,
provides a good description of this background.

There are also so-called reflection backgrounds, where fully reconstructed
signal decays from one $b$-hadron decay mode produce peaking structures in the
invariant mass spectra of other decay modes when one of the daughter particles
is misidentified. For $B\rightarrow D\pi^{-}(\pi^{+}\pi^{-})$, there are
reflections from $B\rightarrow DK^{-}(\pi^{+}\pi^{-})$ Cabibbo-suppressed
decays, where the kaon is misidentified as a pion. Due to the Cabibbo
suppression and the excellent RICH performance, their contributions are
limited to the 1% level. The shape of this misidentification background is
taken from MC simulation and is constrained to be $(1\pm 1)\%$ of the signal
yield.

For the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ decays, there are reflection backgrounds from
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ and
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ modes, when either of the $\pi^{+}$ from the
$D^{+}$ decay is misidentified as a $K^{+}$. This cross-feed background is
evaluated in two ways. First, we take our $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ ($\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$) data, which have very loose particle
identification (PID) requirements on the pions, and apply the kaon PID
selection to them. If either of the two pions pass, and the recomputed
($KK\pi$) mass is within the $D_{s}^{+}$ mass window, the candidate is counted
as a reflection background. Using this technique, we find $(5.3\pm 0.4)\%$
[$(6.3\pm 0.6)\%$] of $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ [$\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$] signal decays reflect into the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
[$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$] signal region. In the second method, we apply
a $\pi$-faking-$K$ misidentification matrix (in bins of $p$ and $p_{T}$),
obtained from a $D^{*+}$ data calibration sample to the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ (or $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$) signal MC sample, followed by the $D_{s}^{+}$
mass window requirement (after replacing the pion mass with the kaon mass.)
The results of this second procedure are $(4.4\pm 0.3)\%$ for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ and
$(5.2\pm 0.4)\%$ for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$, both of which are consistent with the first
method. We therefore constrain the peaking background from $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ ($\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$) into $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
($\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$) to be $(4.0\pm 1.5)\%$ ($(5.0\pm 2.0)\%$),
where the Gaussian constraint is conservatively assigned a 40% relative
uncertainty. The shape of this peaking background is obtained from MC
simulation and is well-described by a single Gaussian of mean 5350 MeV/$c^{2}$
and width 30 MeV/$c^{2}$. This shape is in good agreement with what is
observed in data.

The second reflection background to $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
($\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$) is
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$
($\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$), where the
proton from the $\Lambda_{c}$ decay is misidentified as a kaon. This is
similar to the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ reflection,
except here the $\Lambda_{b}^{0}$ yield is significantly smaller, obviating
the need for making an explicit $\Delta LL(K-p)$ requirement to reject
protons. The $\Lambda_{b}^{0}$ reflection background is evaluated using the
first technique as described above leading to reflection rates of $(15\pm
3)\%$ for $\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ into $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$
and $(20\pm 4)\%$ for
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ into $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$. We conservatively assign a 20% uncertainty on
this rate based on the agreement between data and MC simulation. The
asymmetric shape of this background is described by the simulation, which is
consistent with the shape observed in data. The combinatorial background is
modeled with an exponential distribution. The fits are superimposed on the
data in Figs. 2 and 3, and the fitted yields are summarized in Table 2.

The ratios of branching ratios are given by:

$\displaystyle{{\cal{B}}(H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(H_{b}\rightarrow
H_{c}\pi^{-})}={Y^{\rm sig}/\epsilon_{\rm tot}^{\rm sig}\over Y^{\rm
norm}/\epsilon_{\rm tot}^{\rm norm}}$

where the $Y$ factors are the observed yields in the signal and normalization
modes, and $\epsilon_{\rm tot}$ are the total selection efficiencies.

Table 2: Summary of yields for the branching fraction computation. Uncertainties are statistical only. Decay | Yield | Decay | Yield
---|---|---|---
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}\pi^{+}\pi^{-}$ | $1150\pm 43$ | $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$ | $2745\pm 66$
$B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$ | $950\pm 41$ | $B^{-}\rightarrow D^{0}\pi^{-}$ | $4244\pm 90$
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ | $138\pm 23$ | $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$ | $434\pm 32$
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ | $174\pm 18$ | $\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ | $853\pm 36$

##  5 Systematic Uncertainties

Several sources contribute uncertainty to the measured ratios of branching
fractions. Because we are measuring ratios of branching fractions, most, but
not all of the potential systematics cancel. Here, we discuss only the non-
cancelling uncertainties. With regard to the reconstruction of the
$H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ and $H_{b}\rightarrow
H_{c}\pi^{-}$ decays, the former has two additional pions which need to pass
our selections, and the $3\pi$ system needs to pass the various vertex-related
selection criteria. The track reconstruction efficiency and uncertainty are
evaluated by measuring the ratio of fully reconstructed $J/\psi$’s to all
$J/\psi$’s obtained from an inclusive single muon trigger, where only one of
the muons is required to be reconstructed. After reweighting the efficiencies
to match the kinematics of the signal tracks, the uncertainty is found to be
2% per track, which leads to a 4% uncertainty in the branching fraction
ratios. The IP resolution in data is about 20% worse than in the simulation,
leading to (i) a larger efficiency for tracks to pass the IP-related cuts (as
well as larger background), and (ii) a lower efficiency to pass the vertex
$\chi^{2}$ selections, for data relative to the value predicted by simulation.
The first of these is studied by reducing the IP $\chi^{2}$ requirement in
simulation by 20%, and the second by smearing the vertex $\chi^{2}$
distribution in simulation until it agrees with data. The combined correction
is found to be $1.02\pm 0.03$.

Another potential source of systematic uncertainty is related to the
production and decay model for producing the $H_{c}\pi\pi\pi$ final state. We
have considered that the $p_{T}$ spectrum of the pions in the 3$\pi$ system
may be different between simulation and data. To estimate the uncertainty, we
reweight the MC simulation to replicate the momentum spectrum of the lowest
momentum pion (amongst the pions in the $3\pi$ vertex.) We find that the total
efficiency using the reweighted spectra agrees with the unweighted spectra to
within 3%. We have also investigated the effect of differences in the $p_{T}$
spectra of the charm particle, and find at most a 1% difference. Our candidate
selection is limited to the mass region $M(\pi\pi\pi)<3$ GeV/$c^{2}$. Given
that the phase space population approaches zero as $M(\pi\pi\pi)\rightarrow
3.5$ GeV/$c^{2}$ (i.e., $M_{B}-M_{D}$) and that the simulation reasonably
reproduces the $\pi^{-}\pi^{+}\pi^{-}$ mass spectrum, we use the simulation to
assess the fraction of the $\pi\pi\pi$ mass spectrum beyond 3 GeV/$c^{2}$. We
find the fraction of events above 3 GeV/$c^{2}$ is $(3.5-4.5)$% for the decay
modes under study. We apply a correction of $1.04\pm 0.02$, where we have
assigned half the correction as an estimate of the uncertainty. In total, the
correction for production and decay models is $1.04\pm 0.04$.

As discussed in Sec. 3, we choose only one candidate per event. The efficiency
of this selection is estimated by comparing the signal yield in multiple-
candidate events before and after applying the best candidate selection. The
selection is estimated to be $(75\pm 20)\%$ efficient. In the
$H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ the multiple candidate rate
varies from 4% to 10%, so we have corrections that vary from 1.01 to 1.03. For
$H_{b}\rightarrow H_{c}\pi^{-}$, this effect is negligible. The corrections
for each mode are given in Table 3.

For the trigger efficiency, we rely on signal MC simulations to emulate the
online trigger. The stability of the relative trigger efficiency was checked
by reweighting the $b$-hadron $p_{T}$ spectra for both the signal and
normalization modes, and re-evaluating the trigger efficiency ratios. We find
maximum differences of 2% for L0, 1% for HLT1 and 1% for HLT2, (2.4% total)
which we assign as a systematic uncertainty.

Fitting systematics are evaluated by varying the background shapes and
assumptions about the signal parameterization for both the $H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-}$ and $H_{b}\rightarrow H_{c}\pi^{-}$ modes and re-
measuring the yield ratios. For the combinatorial background, using first and
second order polynomials leads to a 3% uncertainty on the relative yield.
Reflection background uncertainties are negligible, except for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{+}\pi^{-}$,
where we find deviations as large as 5% when varying the central value of the
constraints on the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$
reflections by $\pm$1 standard deviation. We have checked our sensitivity to
the signal model by varying the constraints on the width ratio and core
Gaussian area fraction by one standard deviation (2%). We also include a
systematic uncertainty of 1% for neglecting the small radiative tail in the
fit, which is estimated by comparing the yields between our double Gaussian
signal model and the sum of a Gaussian and Crystal Ball [20] line shape. Taken
together, we assign a 4% uncertainty to the relative yields. For the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ branching fraction ratio, the
total fitting uncertainty is 6.4%.

Another difference between the $H_{b}\rightarrow H_{c}\pi^{-}$ and
$H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ selection is the upper limit on
the number of tracks. The efficiencies of the lower track multiplicity
requirements can be evaluated using the samples with higher track multiplicity
requirements. Using this technique, we find corrections of $0.95\pm 0.01$ for
the $B^{-}$ and $\Lambda_{b}^{0}$ branching fraction ratios, and $0.99\pm
0.01$ for the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ branching fraction ratios.

We have also studied the PID efficiency uncertainty using a $D^{*+}$
calibration sample in data. Since the PID requirements are either common to
the signal and normalization modes, or in the case of the bachelor pion(s),
the selection is very loose, the uncertainty is small and we estimate a
correction of $1.01\pm 0.01$. We have also considered possible background from
$H_{b}\rightarrow H_{c}D_{s}^{-}$ which results in a correction of $0.99\pm
0.01$.

All of our MC samples have a comparable number of events, from which we incur
3-4% uncertainty in the efficiency ratio determinations. The full set of
systematic uncertainties and corrections are shown in Table 3. In total, the
systematic uncertainty is $\sim$9%, with correction factors that range from
1.01 to 1.07.

Table 3: Summary of corrections and systematic uncertainties to the ratio of branching fractions ${\cal{B}}(H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-})/{\cal{B}}(H_{b}\rightarrow H_{c}\pi^{-})$. Source | central value $\pm$ syst. error
---|---
| $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ | $B^{-}$ | $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ | $\Lambda_{b}$
Track Reconstruction | $1.00\pm 0.04$
IP/Vertex Resolution | $1.02\pm 0.03$
Production/Decay Model | $1.04\pm 0.04$
Best Cand. Selection | $1.02\pm 0.02$ | $1.01\pm 0.01$ | $1.02\pm 0.02$ | $1.03\pm 0.02$
Trigger Efficiency | $1.00\pm 0.02$
Fitting | $1.00\pm 0.04$ | $1.00\pm 0.04$ | $1.00\pm 0.06$ | $1.00\pm 0.04$
Cut on #Tracks | $0.99\pm 0.01$ | $0.95\pm 0.01$ | $0.99\pm 0.01$ | $0.95\pm 0.01$
PID | $1.01\pm 0.01$
$H_{c}D_{s}^{+}$ background | $0.99\pm 0.01$
MC Statistics | $1.00\pm 0.04$ |  $1.00\pm 0.03$ |  $1.00\pm 0.04$ | $1.00\pm 0.04$
Total Correction | 1.07 | 1.01 | 1.07 | 1.03
Total Systematic (%) | 8.8 | 8.4 | 10.1 | 9.2

##  6 Results for $\boldsymbol{H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}}$

The results for the ratios of branching ratios are

$\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-})}=2.38\pm
0.11\pm 0.21$ $\displaystyle{{\cal{B}}(B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(B^{-}\rightarrow
D^{0}\pi^{-})}=1.27\pm 0.06\pm 0.11$ (1) $\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-})}=2.01\pm 0.37\pm 0.20$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-})}=1.43\pm
0.16\pm 0.13,$

where the first uncertainty is statistical and the second is systematic. These
measurements are all substantially more precise than the current world average
values. Naively, one might have expected the four branching fraction ratios to
be nearly equal. The observed differences may be explained in terms of the
contributing Feynman diagrams. From Fig. 1, we see that the primary
contribution to $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}(\pi^{+}\pi^{-})$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}(\pi^{+}\pi^{-})$ is from a single decay diagram, an external
tree diagram. On the other hand the $B^{-}\rightarrow
D^{0}\pi^{-}(\pi^{+}\pi^{-})$ and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}(\pi^{+}\pi^{-})$ amplitudes
receive contributions from both external and color-suppressed tree diagrams.
This would suggest that the interference tends to be more constructive in
$B^{-}\rightarrow D^{0}\pi^{-}$ and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ than in $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$ and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ respectively.
The role of the various contributing topological amplitudes and the strong
phases in $B\rightarrow D\pi$ is discussed in the literature [12]. In general
we see the branching fractions for the $H_{c}\pi\pi\pi$ final states are at
least as large or even twice as large as the single-$\pi$ bachelor states.

##  7 Kinematic Distributions and Mass Spectra in the
$\boldsymbol{\pi^{-}\pi^{+}\pi^{-}}$ System

Since we rely on MC simulation to estimate signal efficiencies, we now compare
a few distributions between signal MC simulation and data. The higher signal
yield $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}$ and $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ decay modes are used, and for each we perform a
sideband subtraction, where the signal region includes candidates within 50
MeV/$c^{2}$ of the $B^{0}$ mass, ($m_{B^{0}}$) [15], and the sidebands
$60<|M-m_{B^{0}}|<110$ MeV/$c^{2}$. For both data and simulation, we require
events to pass any L0 trigger, and signal candidates must satisfy the HLT1 and
HLT2 triggers described in Sec. 2. Clearly, two of the most important
quantities used in our candidate selection are the $p_{T}$ and IP of the
daughters from the $D^{+}$ and the recoiling pion(s). Figure 4 compares the
$p_{T}$ and IP distributions of the $D^{+}$ daughters in data to those from
signal MC simulation. Figure 5 shows the corresponding comparisons for the
recoiling pion(s) in the respective $B$ decay. Overall, the agreement between
data and MC simulation is very good.

Figure 4: Comparisons of the $p_{T}$ and IP spectra for the daughters from the
$D^{+}$ in $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}$ [(a) and (b)], and from the $D^{+}$ in $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ [(c) and (d)]; Points with error bars are data and
the solid lines are simulation.

Figure 5: Comparisons of the $p_{T}$ and IP spectra for the bachelor pion in
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-}$
[(a) and (b)], and for the 3 pions in $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ [(c) and (d)]. Points with error bars are data and
the solid lines are simulation.

It is also interesting to examine the $\pi^{-}\pi^{+}\pi^{-}$ invariant mass
spectra for the four signal decay modes. Here, we use the sPlot method [19] to
obtain the underlying signal spectra, based on the event-by-event $b$-hadron
mass signal and background probabilities. The $\pi^{-}\pi^{+}\pi^{-}$ mass
spectra are shown in Fig. 6, along with signal MC shapes that are normalized
to the same yield as data. We also show several resonant contributions:
$D_{1}(2420)^{+}$ (2%), $D_{1}(2420)^{0}$ and $D_{2}^{*}(2460)^{0}$ (14% in
total), $\Lambda_{c}(2595)^{+}$ and $\Lambda_{c}(2625)^{+}$ (9% total), and
$\Sigma_{c}^{0}$ and $\Sigma_{c}^{++}$ (12% total), where the quantities in
parentheses are the normalizations relative to the total (see Sec. 8.) A
prominent structure at low mass, consistent with the $a_{1}(1260)^{-}$ is
evident for all decay modes, along with a long tail extending to 3
GeV/$c^{2}$. In all cases, the 3$\pi$ mass spectrum appears shifted toward
lower mass as compared to the MC simulation. The simulated value for the
$a_{1}(1260)^{-}$ mass is 1230 MeV/$c^{2}$, which is equal to the central
value given in the PDG [15] of $(1230\pm 40)$ MeV/$c^{2}$. Besides having a
large uncertainty, the mass as obtained by experiment may be process-
dependent, so it is difficult to draw any definitive conclusion from this
shift. Since both the reconstruction and trigger efficiency are flat through
this mass region, this small shift in mass does not introduce any significant
systematic uncertainty in the branching fraction measurement.

Figure 6: Invariant mass of the $3\pi$ system in $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ (top left), $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$ (top right), $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ (bottom left) and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ (bottom
right) decays. The data are the points with error bars and the simulations are
the solid lines and shaded regions.

We have also looked at the di-pion invariant masses within the 3$\pi$ system,
shown for $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$(a,b) and $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$(c,d) in Fig. 7. Contributions from the narrow
excited charm states, which are discussed in Sec. 8, are excluded. In all
cases, in the low $M(\pi^{-}\pi^{+}\pi^{-})$ mass region, we see a dominant
$\rho^{0}\pi^{-}$ contribution, consistent with the $a_{1}(1260)^{-}$
resonance. In the higher $M(\pi\pi\pi)$ regions there appears to be an
additional resonant structure, consistent with the $f_{2}(1270)$ state, in
addition to the $\rho^{0}$ contribution. Similar spectra are found for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-}$ and
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ (not shown.)
The $f_{2}(1270)$ has been previously seen in $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{*+}\pi^{-}\pi^{+}\pi^{-}$ [21]. The like-sign di-pion invariant mass
spectra do not show any resonant features.

Figure 7: $\pi^{+}\pi^{-}$ invariant mass (2 combinations per $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ candidate) in the $3\pi$ system
for $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ when (a) $M(\pi^{-}\pi^{+}\pi^{-})<1.5$
GeV/$c^{2}$ and (b) $M(\pi^{-}\pi^{+}\pi^{-})\geq 1.5$ GeV/$c^{2}$. The
corresponding plots for $B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$ are
shown in (c) and (d).

##  8 Contributions from Excited Charm Hadrons

Within the $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ final state, we
search for $D_{1}(2420)$, $D_{2}^{*}(2460)$, $\Lambda_{c}(2595)^{+}$,
$\Lambda_{c}(2625)^{+}$ and $\Sigma_{c}^{0,++}$, which may decay to $D$ or
$\Lambda_{c}^{+}$ with an accompanying $\pi^{\pm}$ or $\pi\pi$ pair. To search
for $H_{c}^{*}\rightarrow H_{c}\pi^{+}\pi^{-}$ intermediate states, we select
events in the $b$-hadron signal region ($\pm 60$ MeV/$c^{2}$ around the
nominal mass) and compute the invariant mass difference $\Delta
M_{\pi\pi}\equiv M(H_{c}\pi^{+}\pi^{-})-M(H_{c})$ (two combinations per
$b$-hadron candidate.) For the
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0,++}\pi^{\pm}\pi^{-},~{}\Sigma_{c}^{0,++}\rightarrow\Lambda_{c}^{+}\pi^{\pm}$,
we use $\Delta M_{\pi}\equiv M(H_{c}\pi^{\pm})-M(H_{c})$ in a similar way (one
(two) $\Sigma_{c}^{++}$ ($\Sigma_{c}^{0}$) candidates per $\Lambda_{b}^{0}$
decay.) We also have looked in the upper mass sidebands, and the $\Delta
M_{\pi\pi}$ and $\Delta M_{\pi}$ distributions are consistent with a smooth
background shape with no signal component. We look at all data, irrespective
of trigger, to establish signal significances, but for the branching fraction
measurement, we use the same trigger requirements described in Sec. 7. We
choose only one candidate per event using the same criteria as discussed
previously. We normalize the rates to the respective inclusive
$H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$ decay, using the same trigger
selection as above. We show only the $\Delta M_{\pi\pi}$ and $\Delta M_{\pi}$
distributions after the specified trigger, since the distributions before the
trigger are quite similar, except they typically have 25$-$30% larger yields
than the ones shown.

The $\Delta M_{\pi\pi}$ distributions for $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ and $B^{+}$ are shown in Fig. 8
and the $\Delta M_{\pi}$ for $\Lambda_{b}^{0}$ are shown in Fig. 9. For
$B_{s}^{0}$, the size of the data sample is insufficient to observe the
excited $D_{s}$ states in these hadronic decays.

Signal yields are determined using unbinned extended maximum likelihood fits.
Starting with $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ (Fig. 8(a)),
we see an excess at $\Delta M_{\pi\pi}\sim 560$ MeV/$c^{2}$, consistent with
the $D_{1}(2420)^{+}$. We fit the distribution to the sum of a signal Breit-
Wigner shape convoluted with a Gaussian resolution, and an exponential
background shape. The full width is fixed to 25 MeV/$c^{2}$ [15] and the mass
resolution is set to 7.5 MeV/$c^{2}$ based on simulation. The fitted yield is
$33\pm 8$ events and the fitted mean is $(562\pm 4)$ MeV/$c^{2}$, consistent
with the expected value. If the width is allowed to float, we find $(22.7\pm
8.0({\rm stat}))$ MeV/$c^{2}$, also in agreement with the world average. Prior
to applying the specific trigger selection, we find $40\pm 9$ signal events,
corresponding to a statistical significance of 6.8 standard deviations (for
one degree of freedom) as determined from the difference in log-likelihoods,
$\sqrt{-2\Delta LL}$, where the difference is taken between the signal yield
taken as a free parameter and fixed to zero.

Figure 8: Invariant mass difference $M(D\pi^{-}\pi^{+})-M(D)$, for (a) $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ signal candidates, (b) $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$ signal candidates, (c) $B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}$ through a $D^{*+}$ intermediate state, and (d)
$B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$ not through a $D^{*+}$
intermediate state. The signal components are the white region (and lightly
shaded regions for $B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$), and the
background component is the darker shaded region.

The $\Delta M_{\pi\pi}$ distributions for $B^{-}$ displayed in Fig. 8(b) show
not only the $D_{1}(2420)^{0}$, but also a shoulder at $\sim$600 MeV/$c^{2}$,
consistent with the $D_{2}^{*}(2460)^{0}$. Hence, we allow for both
$D_{1}(2420)^{0}$ and $D_{2}^{*}(2460)^{0}$ signal components, and fix their
full widths to the PDG values [15] of 20.4 MeV/$c^{2}$ and 42.9 MeV/$c^{2}$,
respectively. The means and yields are left as free parameters in the fit. The
fitted $D_{1}(2420)^{0}$ and $D_{2}^{*}(2460)^{0}$ yields are $124\pm 14$ and
$49\pm 12$, with masses that are consistent with the expected values. The
respective signal yields before the trigger requirement are $165\pm 17$ and
$63\pm 15$ events, with corresponding statistical significances of 10.5 and
5.5 standard deviations for the $D_{1}(2420)^{0}$ and $D_{2}^{*}(2460)^{0}$,
respectively. These $B^{0}$ and $B^{-}$ decays have also been observed by
Belle [22].

We have also measured the relative fractions of $D_{1}(2420)^{0}$ and
$D_{2}^{*}(2460)^{0}$ that do or do not decay through $D^{*+}$ by taking the
subset of candidates with $M(D^{0}\pi^{+})-M(D^{0})\leq 150$ MeV/$c^{2}$ or
$M(D^{0}\pi^{+})-M(D^{0})>150$ MeV/$c^{2}$, respectively. The corresponding
$\Delta M_{\pi\pi}$ distributions are shown in Fig. 8(c) and Fig. 8(d). A fit
is made to the data as discussed previously, and the yields are summarized in
Table 4.

For $\Lambda_{b}^{0}$ (see Fig. 9(a)), we find two well-separated peaks in the
$\Delta M_{\pi\pi}$ distribution, one at $\sim$307 MeV/$c^{2}$, and a second
at $\sim$340 MeV/$c^{2}$, consistent with the expected values for the
$\Lambda_{c}(2595)^{+}$ and $\Lambda_{c}(2625)^{+}$, respectively. The full
width of the $\Lambda_{c}(2595)^{+}$ is fixed to the PDG value of 3.6
MeV/$c^{2}$, and the mass resolution for each peak is fixed to 2.0
MeV/$c^{2}$, as determined from simulation. The fitted signal yields are
$9.7\pm 3.5$ and $9.3\pm 3.2$ for the $\Lambda_{c}(2595)^{+}$ and
$\Lambda_{c}(2625)^{+}$, respectively. Before the trigger, we find signal
yields of $10.6\pm 3.8$ for $\Lambda_{c}(2595)^{+}$ and $15.7\pm 4.1$ for
$\Lambda_{c}(2625)^{+}$, corresponding to statistical significances of 4.3 and
6.6 standard deviations. Thus we have evidence for
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}(2595)^{+}\pi^{-}$ and observation of
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}(2625)^{+}\pi^{-}$. The systematic
uncertainties do not change this conclusion. These decays have also been
reported by CDF [23], but are not yet published. The fitted $\Delta
M_{\pi\pi}$ values of $(306.7\pm 1.1)$ MeV/$c^{2}$ and $(341.7\pm 0.6)$
MeV/$c^{2}$, for the $\Lambda_{c}(2625)^{+}$ and $\Lambda_{c}(2625)^{+}$,
respectively, are consistent with the known mass differences [15] for these
excited states.

Figure 9: Intermediate resonances contributing to the
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ decay. Shown
are distributions for (a)
$M(\Lambda_{c}^{+}\pi^{-}\pi^{+})-M(\Lambda_{c}^{+})$, with
$\Lambda_{c}(2595)^{+}$ and $\Lambda_{c}(2625)^{+}$ contributions, (b)
$M(\Lambda_{c}^{+}\pi^{\pm})-M(\Lambda_{c}^{+})$ (3 combinations per
$\Lambda_{b}^{0}$ candidate) (c)
$M(\Lambda_{c}^{+}\pi^{-})-M(\Lambda_{c}^{+})$ (2 combinations per
$\Lambda_{b}^{0}$ candidate), and (d)
$M(\Lambda_{c}^{+}\pi^{+})-M(\Lambda_{c}^{+})$ (1 combination per
$\Lambda_{b}^{0}$ candidate), showing the intermediate $\Sigma_{c}$ states.
The line is a fit as described in the text, and the shaded region is the
fitted background.

We also observe the decays
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0,++}\pi^{\mp}\pi^{-}$, with
$\Sigma_{c}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}$ or
$\Sigma_{c}^{++}\rightarrow\Lambda_{c}^{+}\pi^{+}$. The $\Delta M_{\pi}$
distributions are shown in Fig. 9(b-d) for both $\Sigma_{c}^{0}$ and
$\Sigma_{c}^{++}$ candidates, $\Sigma_{c}^{0}$ candidates only (c), and (d)
$\Sigma_{c}^{++}$ candidates only. The data are fit to the sum of a Breit-
Wigner shape convolved with a Gaussian resolution function and a smooth
threshold function. The full width is fixed to 2.2 MeV/$c^{2}$ [15] in all
cases, and the $\Delta M_{\pi}$ resolution is fixed to 1 MeV/$c^{2}$ based on
simulation. The combined $\Sigma_{c}^{0}$ and $\Sigma_{c}^{++}$ signal has a
statistical significance of 6.0 standard deviations. The $\Sigma_{c}^{0}$ and
$\Sigma_{c}^{++}$ signals have statistical significances of 4.9 and 3.5,
respectively. These decays have also been seen by CDF [23].

Table 4 summarizes the yields for the various excited charm states for both
the full data sample and after the trigger selection as well as the yields in
the normalizing modes (after trigger selection.)

Table 4: Summary of yields for the signal and normalization modes. Below $D_{1}$ and $D_{2}^{*}$ refer to the $D_{1}(2420)$ and $D_{2}^{*}(2460)$ mesons, respectively. Decay |  $H_{c}^{*}\pi(\pi)$ Signal Yields | $H_{c}\pi^{-}\pi^{+}\pi^{-}$
---|---|---
| All | Trig. Sel | Trig. Sel
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D_{1}^{+}\pi^{-},~{}D_{1}^{+}\rightarrow D^{+}\pi^{-}\pi^{+}$ | $41\pm 8$ | $33\pm 7$ | $1741\pm 55$
$B^{-}\rightarrow D_{1}^{0}\pi^{-},~{}D_{1}^{0}\rightarrow D^{0}\pi^{-}\pi^{+}$ | $165\pm 17$ | $126\pm 14$ | $1386\pm 51$
$B^{-}\rightarrow D_{1}^{0}\pi^{-},~{}D_{1}^{0}\rightarrow D^{*+}\pi^{-}$ | $111\pm 14$ | $75\pm 12$ | $1386\pm 51$
$B^{-}\rightarrow D_{1}^{0}\pi^{-},~{}D_{1}^{0}\rightarrow D^{0}\pi^{-}\pi^{+},~{}{\rm non-}D^{*}$ | $57\pm 10$ | $52\pm 9$ | $1386\pm 51$
$B^{-}\rightarrow D_{2}^{*0}\pi^{-},~{}D_{2}^{*0}\rightarrow D^{0}\pi^{-}\pi^{+}$ | $66\pm 15$ | $49\pm 12$ | $1386\pm 51$
$B^{-}\rightarrow D_{2}^{*0}\pi^{-},~{}D_{2}^{*0}\rightarrow D^{*+}\pi^{-}$ | $46\pm 12$ | $34\pm 10$ | $1386\pm 51$
$B^{-}\rightarrow D_{2}^{*0}\pi^{-},~{}D_{2}^{*0}\rightarrow D^{0}\pi^{-}\pi^{+},~{}{\rm non-}D^{*}$ | $23\pm 9$ | $18\pm 8$ | $1386\pm 51$
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}(2595)^{+}\pi^{-}$ | $10.6\pm 3.8$ | $9.7\pm 3.5$ | $312\pm 23$
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}(2625)^{+}\pi^{-}$ | $15.7\pm 4.1$ | $9.3\pm 3.2$ | $312\pm 23$
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0,++}\pi^{\mp}\pi^{-}$ | $29.3\pm 7.0$ | $24.9\pm 6.2$ | $312\pm 23$
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0}\pi^{-}\pi^{+}$ | $19.6\pm 5.7$ | $16.2\pm 5.0$ | $312\pm 23$
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{++}\pi^{-}\pi^{-}$ | $10.1\pm 4.0$ | $9.3\pm 3.7$ | $312\pm 23$

The branching ratios for these modes are computed using:

${{\cal{B}}(H_{b}\rightarrow
H_{c}^{*}\pi(\pi))\times{\cal{B}}(H_{c}^{*}\rightarrow
H_{c}\pi(\pi))\over{\cal{B}}(H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-})}={N_{\rm signal}\over N_{\rm
norm}}\left(\epsilon_{\rm sel}^{\rm rel}\times\epsilon_{\rm trig|sel}^{\rm
rel}\right)^{-1}$ (2)

where $H_{c}^{*}$ refers to one of the observed excited charm states, $N_{\rm
signal}$ and $N_{\rm norm}$ are the number of reconstructed decays in the
signal and normalization modes after the trigger requirement, $\epsilon_{\rm
sel}^{\rm rel}$ is the reconstruction and selection efficiency relative to the
normalization mode, and $\epsilon_{\rm trig|sel}^{\rm rel}$ is the relative
trigger efficiency. All efficiencies are given for the mass region $0.8~{}{\rm
GeV}/c^{2}<M(\pi^{-}\pi^{+}\pi^{-})<3$ GeV/$c^{2}$.

The relative reconstruction, selection and trigger efficiencies, shown in
Table 5, are evaluated using MC simulations. The $D_{1}(2420)^{0}$ and
$D_{2}^{*}(2460)^{0}$ are each assumed to decay 70% through
$D^{*+}\pi^{-}\rightarrow D^{0}\pi^{+}\pi^{-}$ and 30% non-resonant
$D^{0}\pi^{+}\pi^{-}$. The $D_{1}(2420)^{+}$ is taken to be 100% non-resonant
$D^{+}\pi^{-}\pi^{+}$. The $\Lambda_{c}(2595)^{+}$ decay is simulated as 36%
$\Sigma_{c}^{0}\pi^{+}$, 36% $\Sigma_{c}^{++}\pi^{-}$ and 28% non-resonant
$\Lambda_{c}^{+}\pi^{-}\pi^{+}$. The $\Lambda_{c}(2625)^{+}$ decay is assumed
to be 100% non-resonant $\Lambda_{c}^{+}\pi^{-}\pi^{+}$. The
$\Sigma_{c}(2544)$ baryons are simulated non-resonant in phase space.

The relative efficiencies agree qualitatively with our expectations based on
the kinematics and proximity to threshold for these excited charm states. The
differences in the relative efficiency between the pairs of excited charm
states for a given $b$-hadron species are negligible compared to the
uncertainty from our limited MC event sample, and we use the average relative
efficiency for each pair of decays.

Table 5: Summary of the relative reconstruction and selection efficiencies ($\epsilon_{\rm sel}^{\rm rel}$) and trigger efficiencies ($\epsilon_{\rm trig|sel}^{\rm rel}$) for the excited charm hadron intermediate states with respect to the inclusive $H_{c}\pi^{-}\pi^{+}\pi^{-}$ final states. Below $D_{1}$ and $D_{2}^{*}$ refer to $D_{1}(2420)$ and $D_{2}^{*}(2460)$, respectively. The uncertainties shown are statistical only. Decay | $\epsilon_{\rm sel}^{\rm rel}$ | $\epsilon_{\rm trig|sel}^{\rm rel}$ | $\epsilon_{\rm total}^{\rm rel}$
---|---|---|---
| (%) | (%) | (%)
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D_{1}^{+}\pi^{-}$ | $0.83\pm 0.06$ | $1.05\pm 0.09$ | $0.87\pm 0.10$
$B^{-}\rightarrow(D_{1}^{0},~{}D_{2}^{*0})\pi^{-}$ | $0.70\pm 0.04$ | $1.24\pm 0.07$ | $0.86\pm 0.07$
$B^{-}\rightarrow(D_{1}^{0},~{}D_{2}^{*0})\pi^{-}({\rm via}~{}D^{*})$ | $0.66\pm 0.05$ | $1.29\pm 0.08$ | $0.84\pm 0.08$
$B^{-}\rightarrow(D_{1}^{0},~{}D_{2}^{*0})\pi^{-}({\rm non-}D^{*})$ | $0.78\pm 0.06$ | $1.15\pm 0.10$ | $0.91\pm 0.11$
$\Lambda_{b}^{0}\rightarrow(\Lambda_{c}(2595),~{}\Lambda_{c}(2625)^{+})\pi^{-}$ | $0.52\pm 0.03$ | $1.30\pm 0.07$ | $0.67\pm 0.06$
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0,++}\pi\pi,~{}\Sigma_{c}^{0,++}\rightarrow\Lambda_{c}^{+}\pi^{\mp}$ | $0.67\pm 0.05$ | $1.10\pm 0.13$ | $0.75\pm 0.10$

The dominant sources of systematic uncertainty are the limited MC sample sizes
and the fit model. Starting with the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$, the uncertainty due to limited MC
statistics is 11%. For the fit model, the largest source of uncertainty is
from a possible $D_{2}^{*}(2460)^{+}\pi^{-},~{}D_{2}^{*}(2460)^{+}\rightarrow
D^{+}\pi^{-}\pi^{+}$ contribution. If this contribution is included in the fit
using a Breit-Wigner shape with mean and width taken from the PDG [15], the
returned signal yield is $0^{+7}_{-0}$. If we assume isospin symmetry, and
constrain this fraction (relative to $D_{1}(2420)$) to be $(40\pm 11)\%$, the
ratio found for the $B^{-}$ decay, the fitted $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D_{1}(2420)^{+}\pi^{-},~{}D_{1}(2420)^{+}\rightarrow D^{+}\pi^{-}\pi^{+}$
signal yield is $26\pm 6$ events. We take this as a one-sided uncertainty of
${}^{+0\%}_{-21\%}$. Sensitivity to the background shape is estimated by using
a second order polynomial for the background (3%). The $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ mass sidebands, which have a
$D_{1}(2420)^{+}$ fitted yield of $2^{+3}_{-2}$ events from which we
conservatively assign as a one-sided systematic uncertainty of
${}^{+0\%}_{-6\%}$. For the signal decays, 4% of events have
$M(\pi^{-}\pi^{+}\pi^{-})>3$ GeV/$c^{2}$, whereas for the $D_{1}(2420)^{+}$,
we find a negligible fraction fail this requirement. We therefore apply a
correction of $0.96\pm 0.02$, where we have taken 50% uncertainty on the
correction as the systematic error. The systematic uncertainty on the yield in
the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}$ normalizing mode is 3%. We thus arrive at a total
systematic error on the $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$
branching fraction ratio of ${}^{+12}_{-25}\%$.

For the $B^{-}$, we have a similar set of uncertainties. They are as follows:
MC sample size (8%), background model (1%, 2%), $D_{1}(2420)^{0}$ width (2%,
4%), $D_{2}^{*}(2460)^{0}$ width (1%, 3%), where the two uncertainties are for
the ($D_{1}(2420)^{0}$, $D_{2}^{*}(2460)^{0}$) intermediate states. We have
not accounted for interference, and have assumed it is negligible compared to
other uncertainties. A factor of $0.98\pm 0.01$ is applied to correct for the
fraction of events with $M(\pi^{-}\pi^{+}\pi^{-})>3$ GeV/$c^{2}$. Including a
3% uncertainty on the $B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}$ yield, we
find total systematic errors of 9% and 10% for the $D_{1}(2420)^{0}$ and
$D_{2}^{*}(2460)^{0}$ intermediate states, respectively. For the $D^{*}$ sub-
decays, the total systematic uncertainties are 10% and 11% for
$B^{-}\rightarrow D_{1}(2420)^{0}\pi^{-},~{}D_{1}(2420)^{0}\rightarrow
D^{*+}\pi^{-}$ and $B^{-}\rightarrow
D_{2}^{*}(2460)^{0}\pi^{-},~{}D_{2}^{*}(2460)^{0}\rightarrow D^{*+}\pi^{-}$,
respectively. For final states not through $D^{*}$, we find a total systematic
uncertainty of 13% for both intermediate states. In all cases, the dominant
systematic uncertainty is the limited number of MC events.

For the $\Lambda_{b}^{0}$ branching fraction ratios, we attribute uncertainty
to limited MC sample sizes (8%), the $\Lambda_{c}^{+}(2595)$ width
(${}^{+9\%}_{-5\%}$),
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}$ signal yield
(3%), and apply a correction of $0.96\pm 0.02$ for the ratio of yields with
$M(\pi^{-}\pi^{+}\pi^{-})>3$ GeV/$c^{2}$. In total, the systematic
uncertainties on the $\Lambda_{c}^{+}(2595)^{+}$ and $\Lambda_{c}(2625)^{+}$
partial branching fractions are ${}_{-10\%}^{+13\%}$ and $\pm 10\%$,
respectively.

For the $\Sigma_{c}^{0,++}$ intermediate states, the systematic uncertainties
include 14% from finite MC statistics, and 4% from the $\Sigma_{c}^{0,++}$
width. For the $\Sigma_{c}^{0,++}$ simulation, 10% of decays have
$M(\pi^{-}\pi^{+}\pi^{-})>3$ GeV/$c^{2}$, compared to 4% for the normalizing
mode. We therefore apply a correction of $1.06\pm 0.03$ to the ratio of
branching fractions. All other uncertainties are negligible in comparison. We
thus arrive at a total systematic uncertainty of 16%.

The final partial branching fractions are

$\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D_{1}^{-}\pi^{+},~{}D_{1}^{-}\rightarrow D^{+}\pi^{-}\pi^{+})\over\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-}}$ $\displaystyle=(2.1\pm 0.5_{-0.5}^{+0.3})\%$
$\displaystyle{{\cal{B}}(B^{-}\rightarrow
D_{1}^{0}\pi^{+},~{}D_{1}^{0}\rightarrow D^{0}\pi^{-}\pi^{+})\over
B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}}$ $\displaystyle=(10.3\pm 1.5\pm
0.9)\%$ $\displaystyle{{\cal{B}}(B^{-}\rightarrow
D_{1}^{0}\pi^{+},~{}D_{1}^{0}\rightarrow D^{*+}\pi^{-})\over B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-}}$ $\displaystyle=(9.3\pm 1.6\pm 0.9)\%$
$\displaystyle{{\cal{B}}(B^{-}\rightarrow
D_{1}^{0}\pi^{+},~{}D_{1}^{0}\rightarrow D^{0}\pi^{-}\pi^{+})_{{\rm
non-}D^{*}}\over B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(4.0\pm 0.7\pm 0.5)\%$
$\displaystyle{{\cal{B}}(B^{-}\rightarrow
D_{2}^{*0}\pi^{+},~{}D_{2}^{*0}\rightarrow D^{0}\pi^{-}\pi^{+})\over
B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}}$ $\displaystyle=(4.0\pm 1.0\pm
0.4)\%$ $\displaystyle{{\cal{B}}(B^{-}\rightarrow
D_{2}^{*0}\pi^{+},~{}D_{2}^{*0}\rightarrow D^{*+}\pi^{-})\over
B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}}$ $\displaystyle=(3.9\pm 1.2\pm
0.4)\%$ $\displaystyle{{\cal{B}}(B^{-}\rightarrow
D_{2}^{*0}\pi^{+},~{}D_{2}^{*0}\rightarrow D^{0}\pi^{-}\pi^{+})_{{\rm
non-}D^{*}}\over B^{-}\rightarrow D^{0}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(1.4\pm 0.6\pm 0.2)\%$
$\displaystyle<3.0\%{\rm~{}at~{}90\%~{}C.L.}$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}(2595)^{+}\pi^{+},~{}\Lambda_{c}(2595)^{+}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+})\over\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(4.4\pm 1.7_{-0.4}^{+0.6})\%$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}(2625)^{+}\pi^{+},~{}\Lambda_{c}(2625)^{+}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+})\over\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(4.3\pm 1.5\pm 0.4)\%$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0,++}\pi^{\mp}\pi^{-},~{}\Sigma_{c}^{0,++}\rightarrow\Lambda_{c}^{+}\pi^{\mp})\over\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(11.4\pm 3.1\pm 1.8)\%$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0}\pi^{+}\pi^{-},~{}\Sigma_{c}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-})\over\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(7.4\pm 2.4\pm 1.2)\%$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{++}\pi^{-}\pi^{-},~{}\Sigma_{c}^{++}\rightarrow\Lambda_{c}^{+}\pi^{+})\over\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-}}$
$\displaystyle=(4.2\pm 1.8\pm 0.7)\%,$

where the first uncertainties are statistical and the second are systematic.
For the modes with $D^{*+}$, we include a factor ${\cal{B}}(D^{*+}\rightarrow
D^{0}\pi^{+})=(0.677\pm 0.005)$ [15] to account for unobserved $D^{*+}$
decays. The first four and the sixth of these decays have been previously
measured by Belle [22] with comparable precision. To compare our results to
those absolute branching fractions, we multiply them by the relative $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ [$B^{-}$] branching fractions in
Eq. 1, and then in turn by ${\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-})=(2.68\pm
0.13)\times 10^{-3}$ [${\cal{B}}(B^{-}\rightarrow D^{0}\pi^{-})=(4.84\pm
0.15)\times 10^{-3}$.] The resulting absolute branching fractions are

$\displaystyle{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D_{1}(2420)^{-}\pi^{+},~{}D_{1}(2420)^{-}\rightarrow
D^{+}\pi^{-}\pi^{+})=(1.3\pm 0.3_{-0.3}^{+0.2})\times 10^{-4}$
$\displaystyle{\cal{B}}(B^{-}\rightarrow
D_{1}(2420)^{0}\pi^{+},~{}D_{1}(2420)^{0}\rightarrow
D^{0}\pi^{-}\pi^{+})=(6.3\pm 0.9\pm 0.9)\times 10^{-4}$
$\displaystyle{\cal{B}}(B^{-}\rightarrow
D_{1}(2420)^{0}\pi^{+},~{}D_{1}(2420)^{0}\rightarrow D^{*+}\pi^{-})=(5.8\pm
1.0\pm 0.9)\times 10^{-4}$ $\displaystyle{\cal{B}}(B^{-}\rightarrow
D_{1}(2420)^{0}\pi^{+},~{}D_{1}(2420)^{0}\rightarrow
D^{0}\pi^{+}\pi^{-})_{{\rm non-}D^{*}}=(2.5\pm 0.4\pm 0.4)\times 10^{-4}$
$\displaystyle{\cal{B}}(B^{-}\rightarrow
D_{2}^{*}(2460)^{0}\pi^{+},~{}D_{2}^{*}(2460)^{0}\rightarrow
D^{*+}\pi^{-})=(2.5\pm 0.7\pm 0.4)\times 10^{-4}$

where the uncertainties are statistical and total systematic, respectively.
The corresponding values obtained by Belle are: $(0.89^{+0.23}_{-0.35})\times
10^{-4}$, $(6.5^{+1.1}_{-1.2})\times 10^{-4}$, $(6.8\pm 1.5)\times 10^{-4}$,
$(1.9^{+0.5}_{-0.6})\times 10^{-4}$, and $(1.8\pm 0.5)\times 10^{-4}$ [15,
22]. Our results are consistent with, and of comparable precision to, those
measurements.

Preliminary results on the
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}(2595)^{+}\pi^{-}$,
$\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}(2625)^{+}\pi^{-}$ and
$\Lambda_{b}^{0}\rightarrow\Sigma_{c}^{0,++}\pi^{\mp}\pi^{-}$ decays have been
reported by CDF [23]. Our values are consistent with these (unpublished)
results.

##  9 Summary

In summary, we have measured the branching fractions for $H_{b}\rightarrow
H_{c}\pi^{-}\pi^{+}\pi^{-}$ decays relative to $H_{b}\rightarrow
H_{c}\pi^{-}$. The ratio of branching fractions are measured to be

$\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow
D^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow D^{+}\pi^{-})}=2.38\pm
0.11\pm 0.21$ $\displaystyle{{\cal{B}}(B^{-}\rightarrow
D^{0}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(B^{-}\rightarrow
D^{0}\pi^{-})}=1.27\pm 0.06\pm 0.11$ $\displaystyle{{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{+}\pi^{-})}=2.01\pm 0.37\pm 0.20$
$\displaystyle{{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-}\pi^{+}\pi^{-})\over{\cal{B}}(\Lambda_{b}^{0}\rightarrow\Lambda_{c}^{+}\pi^{-})}=1.43\pm
0.16\pm 0.13.$

At low 3$\pi$ mass, these decays appear to be dominated by the $a_{1}(1260)$
resonance. We have also measured several partial decay rates through excited
charm states. The yields of $H_{b}\rightarrow H_{c}\pi^{-}\pi^{+}\pi^{-}$
relative to $H_{b}\rightarrow H_{c}\pi^{-}$ are in the range of 20$-$40%. If
the relative rates in the Cabibbo-suppressed decays, such as $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow
D_{s}^{\pm}K^{\mp}\pi^{\pm}\pi^{\mp}$ and $B^{-}\rightarrow
DK^{-}\pi^{+}\pi^{-}$ relative to $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow D_{s}^{\pm}K^{\mp}$
and $B^{-}\rightarrow DK^{-}$, respectively, are comparable, they could be
useful for measuring the weak phase $\gamma$.

## Acknowledgments

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at CERN and at the LHCb institutes, and acknowledge
support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI
(Ireland); INFN (Italy); FOM and NWO (Netherlands); SCSR (Poland); ANCS
(Romania); MinES of Russia and Rosatom (Russia); MICINN, XuntaGal and GENCAT
(Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United
Kingdom); NSF (USA). We also acknowledge the support received from the ERC
under FP7 and the Region Auvergne.

## References

  * [1] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).
  * [2] E. Eichten and B. R. Hill, Phys. Lett. B234, 511 (1990); N. Isgur and M. B. Wise, Phys.Lett. B232, 113 (1989); H. Georgi, Phys. Lett. B240, 447 (1990); E. Eichten and B. R. Hill, Phys. Lett. B243, 427 (1990); B. Grinstein, Nucl. Phys. B339, 253 (1990).
  * [3] I. Dunietz, Phys. Lett. B270, 75 (1991); I. Dunietz, Z. Phys. C56, 129 (1992); D. Atwood, G. Eilam, M. Gronau, and A. Soni, Phys. Lett. B341, 372 (1995); D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997).
  * [4] M. Gronau and D. London, Phys. Lett. B253, 483 (1991); M. Gronau and D. Tyler, Phys. Lett. B265, 172 (1991).
  * [5] A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D68 054018 (2003).
  * [6] R. Aleksan, I. Dunietz, and B. Kayser, Z. Phys. C54, 653 (1992).
  * [7] I. Dunietz, Phys. Rev. D52, 3048 (1995).
  * [8] C. S. Kim and S. Oh, Eur. Phys. J. C21, 495 (2001).
  * [9] M. Gronau, Phys. Lett. B557, 198-206 (2003).
  * [10] Measurement of $\Delta m_{s}$ in the Decay $B_{s}^{0}\rightarrow D_{s}^{-}((K^{-}K^{+}\pi^{-})(3)\pi$, [LHCb Collaboration], LHCb-CONF-2011-005 (2011).
  * [11] L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983).
  * [12] C.-W. Chiang and J. Rosner, Phys. Rev. F67, 074013 (2003); C. S. Kim et al , Phys. Lett B621, 259-268 (2004).
  * [13] A. A. Alves Jr. et al. [LHCb Collaboration], JINST 3, S08005 (2008).
  * [14] M. Williams et. al., LHCb Public Document, LHCb-PUB-2011-002.
  * [15] K. Nakamura et al., J. Phys. G37, 075021 (2010).
  * [16] T. Sj$\ddot{\rm o}$strand, S. Mrenna and P. Skands, JHEP 0605, 026 (2006).
  * [17] D. J. Lange, Nucl. Instrum. Meth. A462, 152 (2001).
  * [18] S. Agostinelli et al. [GEANT4 Collaboration], Nucl. Instrum. Meth. A506, 250 (2003).
  * [19] M. Pivk and F. Le Diberder, Nucl Instrum. Meth A555, 356 (2005).
  * [20] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances. PhD thesis, Institute of Nuclear Physics, Krakow, 1986. DESY-F31-86-02.
  * [21] D. Monorchio, Study of the properties of the $a_{1}$ meson produced in the $B\rightarrow D^{*-}a_{1}^{+}$ at the BABAR Experiment, PhD thesis, Universita Degli Studi Di Napoli, 2005.
  * [22] K. Abe et al. [Belle Collaboration] Phys. Rev. Lett. 94, 221805 (2005); Phys. Rev. D69, 112002 (2004).
  * [23] P. Azzurri et al. [CDF Collaboration], in Proceedings of Lepton Photon 2009 Conference, Hamburg, Germany, 17-22 Aug. 2009, p 434, edited by T. Behnke and J. Mnich [arXiv:0912.4380].