EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2013-181 LHCb-PAPER-2013-049 January 6, 2014

Search for the doubly charmed baryon $\Xi_{cc}^{+}$

The LHCb collaboration†††Authors are listed on the following pages.

A search for the doubly charmed baryon $\Xi_{cc}^{+}$ in the decay mode
$\Xi_{cc}^{+}\\!\rightarrow\mathchar 28931\relax_{c}^{+}K^{-}\pi^{+}$ is
performed with a data sample, corresponding to an integrated luminosity of
0.65$\mbox{\,fb}^{-1}$, of $pp$ collisions recorded at a centre-of-mass energy
of 7$\mathrm{\,Te\kern-1.00006ptV}$. No significant signal is found in the
mass range 3300–3800${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Upper limits
at the 95% confidence level on the ratio of the $\Xi_{cc}^{+}$ production
cross-section times branching fraction to that of the $\mathchar
28931\relax_{c}^{+}$, $R$, are given as a function of the $\Xi_{cc}^{+}$ mass
and lifetime. The largest upper limits range from $R<1.5\times 10^{-2}$ for a
lifetime of 100$\rm\,fs$ to $R<3.9\times 10^{-4}$ for a lifetime of
400$\rm\,fs$.

Published in JHEP, DOI: 10.1007/JHEP12(2013)090

© CERN on behalf of the LHCb collaboration, license CC-BY-3.0.

LHCb collaboration

R. Aaij40, B. Adeva36, M. Adinolfi45, C. Adrover6, A. Affolder51, Z.
Ajaltouni5, J. Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr24, S. Amato2, S. Amerio21, Y.
Amhis7, L. Anderlini17,f, J. Anderson39, R. Andreassen56, J.E. Andrews57, R.B.
Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov34, M. Artuso58,
E. Aslanides6, G. Auriemma24,m, M. Baalouch5, S. Bachmann11, J.J. Back47, A.
Badalov35, C. Baesso59, V. Balagura30, W. Baldini16, R.J. Barlow53, C.
Barschel37, S. Barsuk7, W. Barter46, Th. Bauer40, A. Bay38, J. Beddow50, F.
Bedeschi22, I. Bediaga1, S. Belogurov30, K. Belous34, I. Belyaev30, E. Ben-
Haim8, G. Bencivenni18, S. Benson49, J. Benton45, A. Berezhnoy31, R. Bernet39,
M.-O. Bettler46, M. van Beuzekom40, A. Bien11, S. Bifani44, T. Bird53, A.
Bizzeti17,h, P.M. Bjørnstad53, T. Blake37, F. Blanc38, J. Blouw10, S. Blusk58,
V. Bocci24, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi53, A.
Borgia58, T.J.V. Bowcock51, E. Bowen39, C. Bozzi16, T. Brambach9, J. van den
Brand41, J. Bressieux38, D. Brett53, M. Britsch10, T. Britton58, N.H. Brook45,
H. Brown51, A. Bursche39, G. Busetto21,q, J. Buytaert37, S. Cadeddu15, O.
Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, D.
Campora Perez37, A. Carbone14,c, G. Carboni23,k, R. Cardinale19,i, A.
Cardini15, H. Carranza-Mejia49, L. Carson52, K. Carvalho Akiba2, G. Casse51,
L. Castillo Garcia37, M. Cattaneo37, Ch. Cauet9, R. Cenci57, M. Charles8, Ph.
Charpentier37, S.-F. Cheung54, N. Chiapolini39, M. Chrzaszcz39,25, K. Ciba37,
X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M. Clemencic37, H.V. Cliff46,
J. Closier37, C. Coca28, V. Coco40, J. Cogan6, E. Cogneras5, P. Collins37, A.
Comerma-Montells35, A. Contu15,37, A. Cook45, M. Coombes45, S. Coquereau8, G.
Corti37, B. Couturier37, G.A. Cowan49, D.C. Craik47, M. Cruz Torres59, S.
Cunliffe52, R. Currie49, C. D’Ambrosio37, P. David8, P.N.Y. David40, A.
Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian11, J.M. De
Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach54, O. Deschamps5, F.
Dettori41, A. Di Canto11, H. Dijkstra37, M. Dogaru28, S. Donleavy51, F.
Dordei11, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F. Dupertuis38, P.
Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S. Easo48, U. Egede52,
V. Egorychev30, S. Eidelman33, D. van Eijk40, S. Eisenhardt49, U.
Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch. Elsasser39, A.
Falabella14,e, C. Färber11, C. Farinelli40, S. Farry51, D. Ferguson49, V.
Fernandez Albor36, F. Ferreira Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M.
Fiore16,e, C. Fitzpatrick37, M. Fontana10, F. Fontanelli19,i, R. Forty37, O.
Francisco2, M. Frank37, C. Frei37, M. Frosini17,37,f, E. Furfaro23,k, A.
Gallas Torreira36, D. Galli14,c, M. Gandelman2, P. Gandini58, Y. Gao3, J.
Garofoli58, P. Garosi53, J. Garra Tico46, L. Garrido35, C. Gaspar37, R.
Gauld54, E. Gersabeck11, M. Gersabeck53, T. Gershon47, Ph. Ghez4, V. Gibson46,
L. Giubega28, V.V. Gligorov37, C. Göbel59, D. Golubkov30, A. Golutvin52,30,37,
A. Gomes2, P. Gorbounov30,37, H. Gordon37, M. Grabalosa Gándara5, R. Graciani
Diaz35, L.A. Granado Cardoso37, E. Graugés35, G. Graziani17, A. Grecu28, E.
Greening54, S. Gregson46, P. Griffith44, L. Grillo11, O. Grünberg60, B. Gui58,
E. Gushchin32, Yu. Guz34,37, T. Gys37, C. Hadjivasiliou58, G. Haefeli38, C.
Haen37, S.C. Haines46, S. Hall52, B. Hamilton57, T. Hampson45, S. Hansmann-
Menzemer11, N. Harnew54, S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37,
T. Head37, V. Heijne40, K. Hennessy51, P. Henrard5, J.A. Hernando Morata36, E.
van Herwijnen37, M. Heß60, A. Hicheur1, E. Hicks51, D. Hill54, M. Hoballah5,
C. Hombach53, W. Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54, D.
Hutchcroft51, D. Hynds50, V. Iakovenko43, M. Idzik26, P. Ilten12, R.
Jacobsson37, A. Jaeger11, E. Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M.
John54, D. Johnson54, C.R. Jones46, C. Joram37, B. Jost37, M. Kaballo9, S.
Kandybei42, W. Kanso6, M. Karacson37, T.M. Karbach37, I.R. Kenyon44, T.
Ketel41, B. Khanji20, O. Kochebina7, I. Komarov38, R.F. Koopman41, P.
Koppenburg40, M. Korolev31, A. Kozlinskiy40, L. Kravchuk32, K. Kreplin11, M.
Kreps47, G. Krocker11, P. Krokovny33, F. Kruse9, M. Kucharczyk20,25,37,j, V.
Kudryavtsev33, K. Kurek27, T. Kvaratskheliya30,37, V.N. La Thi38, D.
Lacarrere37, G. Lafferty53, A. Lai15, D. Lambert49, R.W. Lambert41, E.
Lanciotti37, G. Lanfranchi18, C. Langenbruch37, T. Latham47, C. Lazzeroni44,
R. Le Gac6, J. van Leerdam40, J.-P. Lees4, R. Lefèvre5, A. Leflat31, J.
Lefrançois7, S. Leo22, O. Leroy6, T. Lesiak25, B. Leverington11, Y. Li3, L. Li
Gioi5, M. Liles51, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, S. Lohn37, I.
Longstaff50, J.H. Lopes2, N. Lopez-March38, H. Lu3, D. Lucchesi21,q, J.
Luisier38, H. Luo49, O. Lupton54, F. Machefert7, I.V. Machikhiliyan30, F.
Maciuc28, O. Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, J. Maratas5,
U. Marconi14, P. Marino22,s, R. Märki38, J. Marks11, G. Martellotti24, A.
Martens8, A. Martín Sánchez7, M. Martinelli40, D. Martinez Santos41,37, D.
Martins Tostes2, A. Martynov31, A. Massafferri1, R. Matev37, Z. Mathe37, C.
Matteuzzi20, E. Maurice6, A. Mazurov16,37,e, J. McCarthy44, A. McNab53, R.
McNulty12, B. McSkelly51, B. Meadows56,54, F. Meier9, M. Meissner11, M.
Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S. Monteil5, D.
Moran53, P. Morawski25, A. Mordà6, M.J. Morello22,s, R. Mountain58, I. Mous40,
F. Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B. Muster38, P. Naik45, T.
Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, S. Neubert37, N.
Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,o, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54, A. Novoselov34,
A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O.
Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,b, M. Palutan18, J. Panman37,
A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J. Parkinson52, G.
Passaleva17, G.D. Patel51, M. Patel52, G.N. Patrick48, C. Patrignani19,i, C.
Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pearce53, A. Pellegrino40, G.
Penso24,l, M. Pepe Altarelli37, S. Perazzini14,c, E. Perez Trigo36, A. Pérez-
Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen61,
G. Pessina20, K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste
Olloqui35, B. Pietrzyk4, T. Pilař47, D. Pinci24, S. Playfer49, M. Plo
Casasus36, F. Polci8, G. Polok25, A. Poluektov47,33, E. Polycarpo2, A.
Popov34, D. Popov10, B. Popovici28, C. Potterat35, A. Powell54, J.
Prisciandaro38, A. Pritchard51, C. Prouve7, V. Pugatch43, A. Puig Navarro38,
G. Punzi22,r, W. Qian4, B. Rachwal25, J.H. Rademacker45, B.
Rakotomiaramanana38, M.S. Rangel2, I. Raniuk42, N. Rauschmayr37, G. Raven41,
S. Redford54, S. Reichert53, M.M. Reid47, A.C. dos Reis1, S. Ricciardi48, A.
Richards52, K. Rinnert51, V. Rives Molina35, D.A. Roa Romero5, P. Robbe7, D.A.
Roberts57, A.B. Rodrigues1, E. Rodrigues53, P. Rodriguez Perez36, S. Roiser37,
V. Romanovsky34, A. Romero Vidal36, M. Rotondo21, J. Rouvinet38, T. Ruf37, F.
Ruffini22, H. Ruiz35, P. Ruiz Valls35, G. Sabatino24,k, J.J. Saborido Silva36,
N. Sagidova29, P. Sail50, B. Saitta15,d, V. Salustino Guimaraes2, B. Sanmartin
Sedes36, R. Santacesaria24, C. Santamarina Rios36, E. Santovetti23,k, M.
Sapunov6, A. Sarti18, C. Satriano24,m, A. Satta23, M. Savrie16,e, D.
Savrina30,31, M. Schiller41, H. Schindler37, M. Schlupp9, M. Schmelling10, B.
Schmidt37, O. Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B.
Sciascia18, A. Sciubba24, M. Seco36, A. Semennikov30, K. Senderowska26, I.
Sepp52, N. Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I.
Shapoval16,42,e, Y. Shcheglov29, T. Shears51, L. Shekhtman33, O. Shevchenko42,
V. Shevchenko30, A. Shires9, R. Silva Coutinho47, M. Sirendi46, N. Skidmore45,
T. Skwarnicki58, N.A. Smith51, E. Smith54,48, E. Smith52, J. Smith46, M.
Smith53, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro38, D. Souza45, B. Souza De
Paula2, B. Spaan9, A. Sparkes49, P. Spradlin50, F. Stagni37, S. Stahl11, O.
Steinkamp39, S. Stevenson54, S. Stoica28, S. Stone58, B. Storaci39, M.
Straticiuc28, U. Straumann39, V.K. Subbiah37, L. Sun56, W. Sutcliffe52, S.
Swientek9, V. Syropoulos41, M. Szczekowski27, P. Szczypka38,37, D. Szilard2,
T. Szumlak26, S. T’Jampens4, M. Teklishyn7, E. Teodorescu28, F. Teubert37, C.
Thomas54, E. Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41,
D. Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S.
Tourneur38, M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N.
Tuning40,37, M. Ubeda Garcia37, A. Ukleja27, A. Ustyuzhanin52,p, U. Uwer11, V.
Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez
Regueiro36, C. Vázquez Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,g,
G. Veneziano38, M. Vesterinen37, B. Viaud7, D. Vieira2, X. Vilasis-
Cardona35,n, A. Vollhardt39, D. Volyanskyy10, D. Voong45, A. Vorobyev29, V.
Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, C. Wallace47, R. Wallace12, S.
Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D.
Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48,
J. Wimberley57, J. Wishahi9, W. Wislicki27, M. Witek25, G. Wormser7, S.A.
Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3,
X. Yuan3, O. Yushchenko34, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L.
Zhang58, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A.
Zvyagin37.

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 Padova, Padova, Italy
22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), 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
40Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
50School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States
56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States
58Syracuse University, Syracuse, NY, United States
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
60Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
61Celal Bayar University, Manisa, Turkey, associated to 37

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
oHanoi University of Science, Hanoi, Viet Nam
pInstitute of Physics and Technology, Moscow, Russia
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy

##  1 Introduction

The constituent quark model [1, 2, 3] predicts the existence of multiplets of
baryon and meson states, with a structure determined by the symmetry
properties of the hadron wavefunctions. When considering $u$, $d$, $s$, and
$c$ quarks, the states form $SU(4)$ multiplets [4]. The baryon ground
states—those with no orbital or radial excitations—consist of a 20-plet with
spin-parity $J^{P}=1/2^{+}$ and a 20-plet with $J^{P}=3/2^{+}$. All of the
ground states with charm quantum number $C=0$ or $C=1$ have been discovered
[5]. Three weakly decaying $C=2$ states are expected: a $\Xi_{cc}$ isodoublet
($ccu,ccd$) and an $\Omega_{cc}$ isosinglet ($ccs$), each with
$J^{P}=1/2^{+}$. This paper reports a search for the $\Xi_{cc}^{+}$ baryon.
There are numerous predictions for the masses of these states (see, e.g., Ref.
[6] and the references therein, as well as Refs. [7, 8, 9, 10, 11]) with most
estimates for the $\Xi_{cc}^{+}$ mass in the range
3500–3700${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Predictions for its
lifetime range between 100 and 250$\rm\,fs$ [12, 13, 14].

Signals for the $\Xi_{cc}^{+}$ baryon were reported in the $\mathchar
28931\relax_{c}^{+}K^{-}\pi^{+}$ and $pD^{+}K^{-}$ final states by the SELEX
collaboration, using a hyperon beam (containing an admixture of $p$,
$\Sigma^{-}$, and $\pi^{-}$) on a fixed target [15, 16]. The mass was measured
to be $3519\pm 2$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, and the lifetime
was found to be compatible with zero within experimental resolution and less
than 33$\rm\,fs$ at the 90% confidence level (CL). SELEX estimated that 20% of
their $\mathchar 28931\relax_{c}^{+}$ yield originates from $\Xi_{cc}^{+}$
decays, in contrast to theory expectations that the production of doubly
charmed baryons would be suppressed by several orders of magnitude with
respect to singly charmed baryons [17]. Searches in different production
environments at the FOCUS, BaBar, and Belle experiments have not shown
evidence for a $\Xi_{cc}^{+}$ state with the properties reported by SELEX [18,
19, 20].

This paper presents the result of a search for the decay111The inclusion of
charge-conjugate processes is implied throughout.
$\Xi_{cc}^{+}\\!\rightarrow\mathchar 28931\relax_{c}^{+}K^{-}\pi^{+}$ with the
LHCb detector and an integrated luminosity of $0.65\mbox{\,fb}^{-1}$ of $pp$
collision data recorded at centre-of-mass energy
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$. Double charm production has been
observed previously at LHCb both in the $J/\psi\,J/\psi$ final state [21] and
in final states including one or two open charm hadrons [22]. Phenomenological
estimates of the production cross-section of $\Xi_{cc}$ in $pp$ collisions at
$\sqrt{s}=14\mathrm{\,Te\kern-1.00006ptV}$ are in the range 60–1800$\rm\,nb$
[17, 23, 24]; the cross-section at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$
is expected to be roughly a factor of two smaller. As is typical for charmed
hadrons, the production is expected to be concentrated in the low transverse
momentum ($p_{\rm T}$) and forward rapidity ($y$) kinematic region
instrumented by LHCb [24]. For comparison, the prompt $\mathchar
28931\relax_{c}^{+}$ cross-section in the range $0<\mbox{$p_{\rm
T}$}<8000$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ and $2.0<y<4.5$ at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ has been measured to be $(233\pm
26\pm 71\pm 14)$$\rm\,\upmu b$ at LHCb [25], where the uncertainties are
statistical, systematic, and due to the description of the fragmentation
model, respectively. Thus, the cross-section for $\Xi_{cc}^{+}$ production at
LHCb is predicted to be smaller than that for $\mathchar 28931\relax_{c}^{+}$
by a factor of order $10^{-4}$ to $10^{-3}$.

To reduce systematic uncertainties, the $\Xi_{cc}^{+}$ cross-section is
measured relative to that of the $\mathchar 28931\relax_{c}^{+}$. This has the
further advantage that it allows a direct comparison with previous
experimental results. The production ratio $R$ that is measured is defined as

$R\equiv\frac{\sigma(\Xi_{cc}^{+})\,{\cal
B}(\mbox{$\Xi_{cc}^{+}\\!\rightarrow\mathchar
28931\relax_{c}^{+}K^{-}\pi^{+}$})}{\sigma(\mathchar
28931\relax_{c}^{+})}=\frac{N_{\text{sig}}}{N_{\text{norm}}}\frac{\varepsilon_{\text{norm}}}{\varepsilon_{\text{sig}}},$
(1)

where $N_{\text{sig}}$ and $N_{\text{norm}}$ refer to the measured yields of
the signal ($\Xi_{cc}^{+}$) and normalisation ($\mathchar
28931\relax_{c}^{+}$) modes, $\varepsilon_{\text{sig}}$ and
$\varepsilon_{\text{norm}}$ are the corresponding efficiencies, ${\cal B}$
indicates a branching fraction, and $\sigma$ indicates a cross-section.
Assuming that ${\cal B}(\mbox{$\Xi_{cc}^{+}\\!\rightarrow\mathchar
28931\relax_{c}^{+}K^{-}\pi^{+}$})\approx{\cal B}(\mbox{$\mathchar
28931\relax_{c}^{+}\\!\rightarrow pK^{-}\pi^{+}$})\approx 5\%$ [5], the
expected value of $R$ at LHCb is of order $10^{-5}$ to $10^{-4}$. By contrast,
the SELEX observation [15] reported 15.9 $\Xi_{cc}^{+}$ signal events in a
sample of 1630 $\mathchar 28931\relax_{c}^{+}$ events with an efficiency ratio
of 11%, corresponding to $R=9\%$. For convenience, the single-event
sensitivity $\alpha$ is defined as

$\alpha\equiv\frac{\varepsilon_{\text{norm}}}{N_{\text{norm}}\,\varepsilon_{\text{sig}}}$
(2)

such that $R=\alpha N_{\text{sig}}$. For each candidate the mass difference
$\delta m$ is computed as

$\delta m\equiv m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}}K^{-}\pi^{+})-m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})-m(K^{-})-m(\pi^{+}),$ (3)

where $m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}}K^{-}\pi^{+})$ is the
measured invariant mass of the $\Xi_{cc}^{+}$ candidate,
$m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ is the measured invariant
mass of the $pK^{-}\pi^{+}$ combination forming the $\mathchar
28931\relax_{c}^{+}$ candidate, and $m(K^{-})$ and $m(\pi^{+})$ are the world-
average masses of charged kaons and pions, respectively [5].

Since no assumption is made about the $\Xi_{cc}^{+}$ mass, a wide signal
window of $380<\delta m<880$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is used
for this search, corresponding to approximately
$3300<m(\Xi_{cc}^{+})<3800$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. All
aspects of the analysis procedure were fixed before the data in this signal
region were examined. Limits on $R$ are quoted as a function of the
$\Xi_{cc}^{+}$ mass and lifetime, since the measured yield depends on $\delta
m$, and $\varepsilon_{\text{sig}}$ depends on both the mass and lifetime.

##  2 Detector and software

The LHCb detector [26] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector (VELO) surrounding the
$pp$ interaction region, a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\rm\,Tm}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream.
The combined tracking system provides a momentum measurement with relative
uncertainty that varies from 0.4% at 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$
to 0.6% at 100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and impact parameter
(IP) resolution of 20$\,\upmu\rm m$ for tracks with large transverse momentum.
Charged hadrons are identified using two ring-imaging Cherenkov detectors
[27]. Photon, electron, and hadron candidates are identified by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter, and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers [28]. The trigger [29] consists of a hardware stage, based on
information from the calorimeter and muon systems, followed by a software
stage, which applies a full event reconstruction.

In the simulation, $pp$ collisions are generated using Pythia 6.4 [30] with a
specific LHCb configuration [31]. A dedicated generator, Genxicc v2.0, is used
to simulate $\Xi_{cc}^{+}$ baryon production [32]. Decays of hadronic
particles are described by EvtGen [33], in which final state radiation is
generated using Photos [34]. The interaction of the generated particles with
the detector and its response are implemented using the Geant4 toolkit [35,
*Agostinelli:2002hh] as described in Ref. [37]. Unless otherwise stated,
simulated events are generated with
$m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, with
$\tau_{\Xi_{cc}^{+}}=333$$\rm\,fs$, and with the $\Xi_{cc}^{+}$ and $\mathchar
28931\relax_{c}^{+}$ decay products distributed according to phase space.

##  3 Triggering, reconstruction, and selection

The procedure to trigger, reconstruct, and select candidates for the signal
and normalisation modes is designed to retain signal and to suppress three
primary sources of background. These are combinations of unrelated tracks,
especially those originating from the same primary interaction vertex (PV);
mis-reconstructed charm or beauty hadron decays, which typically occur at a
displaced vertex; and combinations of a real $\mathchar 28931\relax_{c}^{+}$
with other tracks to form a fake $\Xi_{cc}^{+}$ candidate. The first two
classes generally have a smooth distribution in both
$m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ and $\delta m$; the third
peaks in $m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ but is smooth in
$\delta m$.

For both the $\Xi_{cc}^{+}$ search and the normalisation mode, $\mathchar
28931\relax_{c}^{+}$ candidates are reconstructed in the final state
$pK^{-}\pi^{+}$. To minimise systematic differences in efficiency between the
signal and normalisation modes, the same trigger requirements are used for
both modes, and those requirements ensure that the event was triggered by the
$\mathchar 28931\relax_{c}^{+}$ candidate and its daughter tracks. First, at
least one of the three $\mathchar 28931\relax_{c}^{+}$ daughter tracks must
correspond to a calorimeter cluster with a measured transverse energy
$\mbox{$E_{\rm T}$}>3500$$\mathrm{\,Me\kern-1.00006ptV}$ in the hardware
trigger. Second, at least one of the three $\mathchar 28931\relax_{c}^{+}$
daughter tracks must be selected by the inclusive software trigger, which
requires that the track have $\mbox{$p_{\rm
T}$}>1700{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ and $\chi^{2}_{\rm IP}>16$ with
respect to any PV, where $\chi^{2}_{\rm IP}$ is defined as the difference in
$\chi^{2}$ of a given PV reconstructed with and without the considered track.
Third, the $\mathchar 28931\relax_{c}^{+}$ candidate must be reconstructed and
accepted by a dedicated $\mathchar 28931\relax_{c}^{+}\\!\rightarrow
pK^{-}\pi^{+}$ selection algorithm in the software trigger. This algorithm
makes several geometric and kinematic requirements, the most important of
which are as follows. The three daughter tracks are required to have
$\mbox{$p_{\rm T}$}>500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, to have a
track fit $\chi^{2}/\rm{ndf}<3$, not to originate at a PV ($\chi^{2}_{\rm
IP}>16$), and to meet at a common vertex ($\chi^{2}/\rm{ndf}<15$, where
$\rm{ndf}$ is the number of degrees of freedom). The $\mathchar
28931\relax_{c}^{+}$ candidate formed from the three tracks is required to
have $\mbox{$p_{\rm T}$}>2500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, to
lie within the mass window $2150<m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})<2430$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, to be
significantly displaced from the PV (vertex separation $\chi^{2}>16$), and to
point back towards the PV (momentum and displacement vectors within
$1^{\circ}$). The software trigger also requires that the proton candidate be
inconsistent with the pion and kaon mass hypotheses. The $\mathchar
28931\relax_{c}^{+}$ trigger algorithm was only enabled for part of the data-
taking in 2011, corresponding to an integrated luminosity of
$0.65\mbox{\,fb}^{-1}$.

For events that pass the trigger, the $\mathchar 28931\relax_{c}^{+}$
selection proceeds in a similar fashion to that used in the software trigger:
three charged tracks are required to form a common vertex that is
significantly displaced from the event PV and has invariant mass in the range
$2185<m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})<2385$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Particle
identification (PID) requirements are imposed on all three tracks to suppress
combinatorial background and mis-identified charm meson decays. The same
$\mathchar 28931\relax_{c}^{+}$ selection is used for the signal and
normalisation modes.

The $\Xi_{cc}^{+}$ candidates are formed by combining a $\mathchar
28931\relax_{c}^{+}$ candidate with two tracks, one identified as a $K^{-}$
and one as a $\pi^{+}$. These three particles are required to form a common
vertex ($\chi^{2}/\rm{ndf}<10$) that is displaced from the PV (vertex
separation $\chi^{2}>16$). The kaon and pion daughter tracks are also required
to not originate at the PV ($\chi^{2}_{\rm IP}>16$) and to have $\mbox{$p_{\rm
T}$}>250$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. The $\Xi_{cc}^{+}$ candidate
is required to point back to the PV and to have $\mbox{$p_{\rm
T}$}>2000$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

A multivariate selection is applied only to the signal mode to further improve
the purity. The selector used is an artificial neural network (ANN)
implemented in the TMVA package [38]. The input variables are chosen to have
limited dependence on the $\Xi_{cc}^{+}$ lifetime. To train the selector,
simulated $\Xi_{cc}^{+}$ decays are used as the signal sample and $3.5\%$ of
the candidates from $\delta m$ sidebands of width
200${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ adjacent to the signal region
are used as the background sample. In order to increase the available
statistics, the trigger requirements are relaxed for these samples. In
addition to the training samples, disjoint test samples of equal size are
taken from the same sources. After training, the response distribution of the
ANN is compared between the training and test samples. Good agreement is found
for both signal and background, with Kolmogorov-Smirnov test $p$-values of 80%
and 65%, respectively. A selection cut on the ANN response is applied to the
data used in the $\Xi_{cc}^{+}$ search. In the test samples, the efficiency of
this requirement is $55.7\%$ for signal and $4.2\%$ for background.

The selection has limited efficiency for short-lived $\Xi_{cc}^{+}$. This is
principally due to the requirements that the $\Xi_{cc}^{+}$ decay vertex be
significantly displaced from the PV, and that the $\Xi_{cc}^{+}$ daughter kaon
and pion have a significant impact parameter with respect to the PV. As a
consequence, the analysis is insensitive to $\Xi_{c}$ resonances that decay
strongly to the same final state, notably the $\Xi_{c}(2980)^{+}$,
$\Xi_{c}(3055)^{+}$, and $\Xi_{c}(3080)^{+}$ [20, 39].

##  4 Yield measurements

To determine the $\mathchar 28931\relax_{c}^{+}$ yield, $N_{\text{norm}}$, a
fit is performed to the $pK^{-}\pi^{+}$ mass spectrum. The signal shape is
described as the sum of two Gaussian functions with a common mean, and the
background is parameterised as a first-order polynomial. The fit is shown in
Fig. 1. The selected $\mathchar 28931\relax_{c}^{+}$ yield in the full
$0.65\mbox{\,fb}^{-1}$ sample is $N_{\text{norm}}=(818\pm 7)\times 10^{3}$,
with an invariant mass resolution of around
6${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

Figure 1:  Invariant mass spectrum of $\mathchar
28931\relax_{c}^{+}\\!\rightarrow pK^{-}\pi^{+}$ candidates for 5$\%$ of the
data, with events chosen at random during preselection (due to bandwidth
limits for the normalisation mode). The dashed line shows the fitted
background contribution, and the solid line the sum of $\mathchar
28931\relax_{c}^{+}$ signal and background.

The $\Xi_{cc}^{+}$ signal yield is measured from the $\delta m$ distribution
under a series of different mass hypotheses. Although the methods used are
designed not to require detailed knowledge of the signal shape, it is
necessary to know the resolution with sufficient precision to define a signal
window. Since the $\Xi_{cc}^{+}$ yield may be small, its resolution cannot be
measured from data and is instead estimated with a sample of simulated events,
shown in Fig. 2. Fitting the candidates with the sum of two Gaussian
functions, the resolution is found to be approximately
4.4${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

Figure 2:  The distribution of the invariant mass difference $\delta m$,
defined in Eq. 3, for simulated $\Xi_{cc}^{+}$ events with a $\Xi_{cc}^{+}$
mass of 3500${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. The solid line shows
the fitted signal shape. In order to increase the available statistics, the
trigger and ANN requirements are not applied in this plot.

Two complementary procedures are used to estimate the signal yield given a
mass hypothesis $\delta m_{0}$. Both follow the same general approach, but use
different methods to estimate the background. In both cases, a narrow signal
window is defined as $2273<m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})<2303$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$\left|\delta m-\delta
m_{0}\right|<10$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, and the number of
candidates inside that window is taken as $N_{S+B}$. Candidates outside the
narrow window are used to estimate the expected background $N_{B}$ inside the
window. The signal yield is then $N_{S}=N_{S+B}-N_{B}$. This avoids any need
to model the signal shape beyond an efficiency correction for the estimated
signal fraction lost outside the window of width
20${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

The first method is an analytic, two-dimensional sideband subtraction in
$m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ and $\delta m$. A two-
dimensional region of width 80${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ in
$m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ and width
200${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ in $\delta m$ is centred around
the narrow signal window. A $5\times 5$ array of non-overlapping bins is
defined within this region, with the central bin identical to the narrow
signal window. It is assumed that the background consists of a combinatorial
component, which is described by a two-dimensional quadratic function, and a
$\mathchar 28931\relax_{c}^{+}$ component, which is described by the product
of a signal peak in $m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ and a
quadratic function in $\delta m$. Under this assumption, the background
distribution can be fully determined from the 24 sideband bins and hence its
integral within the signal box calculated. In this way the value of $N_{B}$
and the associated statistical uncertainty are determined. This method has the
advantage that it requires only minor assumptions about the background
distribution, given that part of that distribution cannot be studied prior to
unblinding. It is adopted as the baseline approach for this reason.

The second method, used as a cross-check, imposes a narrow window on all
candidates of $2273<m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})<2303$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ to reduce
the problem to a one-dimensional distribution in $\delta m$. Based on studies
of the $m([pK^{-}\pi^{+}]_{\mathchar 28931\relax_{c}})$ and $\delta m$
sidebands, it is found that the background can be described by a function of
the form

$f(\delta m)=\left\\{\begin{array}[]{ll}\phantom{a}L(\delta
m;\mu,\sigma_{L})&\delta m\leq\mu\\\ aL(\delta m;\mu,\sigma_{R})&\delta
m\geq\mu\\\ \end{array}\right.$ (4)

where $L(\delta m;\mu,\sigma)$ is a Landau distribution, $a$ is chosen such
that $L(\mu;\mu,\sigma_{L})=aL(\mu;\mu,\sigma_{R})$, and $\mu$, $\sigma_{L}$,
and $\sigma_{R}$ are free parameters. The data are fitted with this function
across the full range, $0<\delta
m<1500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, excluding the signal window
of width 20${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The fit function is
then integrated across the signal window to give the expected background
$N_{B}$.

##  5 Efficiency ratio

To measure $R$, it is necessary to evaluate the ratio of efficiencies for the
normalisation and signal modes,
$\varepsilon_{\text{norm}}/\varepsilon_{\text{sig}}$. The method used to
evaluate this ratio is described below. The signal efficiency depends upon the
mass and lifetime of the $\Xi_{cc}^{+}$, neither of which is known. To handle
this, simulated events are generated with
$m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$\tau_{\Xi_{cc}^{+}}=333$$\rm\,fs$ and the efficiency ratio is evaluated at
this working point. The variation of the efficiency ratio as a function of
$\delta m$ and $\tau_{\Xi_{cc}^{+}}$ relative to the working point is then
determined with a reweighting technique as discussed in Sec. 7. The kinematic
distribution of $\Xi_{cc}^{+}$ produced at the LHC is also unknown, but unlike
the mass and lifetime it cannot be described in a model-independent way with a
single additional parameter. Instead, the upper limits are evaluated assuming
the distributions produced by the Genxicc model.

The efficiency ratio may be factorised into several components as

$\frac{\varepsilon_{\text{norm}}}{\varepsilon_{\text{sig}}}=\frac{\varepsilon_{\text{norm}}^{\text{acc}}}{\varepsilon_{\text{sig}}^{\text{acc}}}\,\frac{\varepsilon_{\text{norm}}^{\text{sel}|\text{acc}}}{\varepsilon_{\text{sig}}^{\text{sel}|\text{acc}}}\,\frac{\varepsilon_{\text{norm}}^{\text{PID}|\text{sel}}}{\varepsilon_{\text{sig}}^{\text{PID}|\text{sel}}}\,\frac{1}{\varepsilon_{\text{sig}}^{\text{ANN}|\text{PID}}}\,\frac{\varepsilon_{\text{norm}}^{\text{trig}|\text{PID}}}{\varepsilon_{\text{sig}}^{\text{trig}|\text{ANN}}},$
(5)

where efficiencies are evaluated for the acceptance (acc), the reconstruction
and selection excluding PID and the ANN (sel), the particle identification
cuts (PID), the ANN selector (ANN) for the signal mode only, and the trigger
(trig). Each element is the efficiency relative to all previous steps in the
order given above.

In most cases the individual ratios are evaluated with simulated
$\Xi_{cc}^{+}$ and $\mathchar 28931\relax_{c}^{+}$ decays, taking the fraction
of candidates that passed the requirement in question. However, in some cases
the efficiencies need to be corrected for known differences between simulation
and data. This applies to the efficiencies for tracking, for passing PID
requirements, and for passing the calorimeter hardware trigger. Control
samples of data are used to determine these corrections as a function of track
kinematics and event charged track multiplicity, and the simulated events are
weighted accordingly. The data samples used are
$J/\psi\rightarrow\mu^{+}\mu^{-}$ for the tracking efficiency, and
$D^{*+}\rightarrow D^{0}(\rightarrow K^{-}\pi^{+})\pi^{+}$ and
$\varLambda\rightarrow p\pi^{-}$ for both the PID and calorimeter hardware
trigger requirements. The track multiplicity distribution is taken from data
for the $\mathchar 28931\relax_{c}^{+}$ sample, but for $\Xi_{cc}^{+}$ events
it is not known. It is modelled by taking a sample of events containing a
reconstructed $B^{0}_{s}$ decay, on the grounds that $B^{0}_{s}$ production
also requires two non-light quark-antiquark pairs.

The efficiency ratio obtained at this working point is
$\varepsilon_{\text{norm}}/\varepsilon_{\text{sig}}=20.4$. Together with the
value for $N_{\text{norm}}$ obtained in Sec. 4 and the definition in eq. 2,
this implies the single-event sensitivity $\alpha$ is $2.5\times 10^{-5}$ at
$m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
$\tau_{\Xi_{cc}^{+}}=333$$\rm\,fs$.

##  6 Systematic uncertainties

The statistical uncertainty on the measured signal yield is the dominant
uncertainty in this analysis, and the systematic uncertainties on $\alpha$
have very limited effect on the expected upper limits. As in the previous
section, they will be evaluated at the working point of
$m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$\tau_{\Xi_{cc}^{+}}=333$$\rm\,fs$, and their variation with mass and lifetime
hypothesis considered separately. Of the systematic uncertainties, the largest
($18.0\%$) is due to the limited sample size of simulated events used to
calculate the efficiency ratio. Beyond this, there are several instances where
the simulation may not describe the signal accurately in data. These are
corrected with control samples of data, with systematic uncertainties,
outlined below, assigned to reflect uncertainties in these corrections.

The IP resolution of tracks in the VELO is found to be worse in data than in
simulated events. To estimate the impact of this effect on the signal
efficiency, a test is performed with simulated events in which the VELO
resolution is artificially degraded to the same level. This is found to change
the efficiency of the reconstruction and non-ANN selection by $6.6\%$, and
that of the ANN by $6.7\%$. Taking these effects to be fully correlated, a
systematic uncertainty of $13.3\%$ is assigned.

A track-by-track correction is applied to the PID efficiency based on control
samples of data. There are several systematic uncertainties associated with
this correction. The first is due to the limited size of the control samples,
notably for high-$p_{\rm T}$ protons from the $\varLambda$ sample. The second
is due to the assumption that the corrections factorise between the tracks,
whereas in practice there are kinematic correlations. The third is due to the
dependence on the event track multiplicity. The fourth is due to limitations
in the method (e.g. the finite kinematic binning used) and is assessed by
applying it to samples of simulated events. The sum in quadrature of the above
gives an uncertainty of $11.8\%$.

Systematic uncertainties also arise from the tracking efficiency ($4.7\%$) and
from the hardware trigger efficiency ($3.3\%$). Additional systematic
uncertainties associated with candidate multiplicity, yield measurement, and
the decay model of $\Xi_{cc}^{+}\\!\rightarrow\mathchar
28931\relax_{c}^{+}K^{-}\pi^{+}$, which may proceed through intermediate
resonances, were considered but found to be negligible in comparison with the
total systematic uncertainty. The systematic uncertainties are summarised in
Table 1. Taking their sum in quadrature, the total systematic uncertainty is
$26\%$.

Table 1:  Systematic uncertainties on the single-event sensitivity $\alpha$.  Source | Size
---|---
Simulated sample size | $18.0\%$
IP resolution | $13.3\%$
PID calibration | $11.8\%$
Tracking efficiency | $4.7\%$
Trigger efficiency | $3.3\%$
Total uncertainty | $26.0\%$

##  7 Variation of efficiency with mass and lifetime

The efficiency to trigger on, reconstruct, and select $\Xi_{cc}^{+}$
candidates has a strong dependence upon the $\Xi_{cc}^{+}$ lifetime. The
efficiency also depends upon the $\Xi_{cc}^{+}$ mass, since this affects the
opening angles and the $p_{\rm T}$ of the daughters.

The simulated $\Xi_{cc}^{+}$ events are generated with a proper decay time
distribution given by an exponential function of average lifetime
$\tau_{\Xi_{cc}^{+}}=333$$\rm\,fs$. To test other lifetime hypotheses, the
simulated events are reweighted to follow a different exponential distribution
and the efficiency is recomputed. Most systematic uncertainties are
unaffected, but those associated with the limited simulated sample size and
with the hardware trigger efficiency increase at shorter lifetimes (the latter
due to kinematic correlations rather than direct dependence on the decay time
distribution). The values and uncertainties of the single-event sensitivity
$\alpha$ are given for several lifetime hypotheses in Table 2.

Table 2:  Single-event sensitivity $\alpha$ for different lifetime hypotheses $\tau$, assuming $m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. The uncertainties quoted include statistical and systematic effects, and are correlated between different lifetime hypotheses.  $\tau$ |  $\alpha$ ($\times 10^{-5}$)
---|---
100$\rm\,fs$ |  $63$ ± | $31$
150$\rm\,fs$ |  $15$ ± | $5$
250$\rm\,fs$ |  $4.1$ ± | $1.1$
333$\rm\,fs$ |  $2.5$ ± | $0.6$
400$\rm\,fs$ |  $1.9$ ± | $0.5$

To assess the effect of varying the $\Xi_{cc}^{+}$ mass hypothesis, large
samples of simulated events are generated for two other mass hypotheses,
$m(\Xi_{cc}^{+})=3300$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
3700${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, without running the Geant4
detector simulation. Two tests are carried out with these samples. First, the
detector acceptance efficiency is recalculated. Second, the $p_{\rm T}$
distributions of the three daughters of the $\Xi_{cc}^{+}$ in the main
$m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ sample are
reweighted to match those seen at the other mass hypotheses and the remainder
of the efficiency is recalculated. In both cases the systematic uncertainties
are also recalculated, though very little change is found. Significant
variations in individual components of the efficiency are seen—notably in the
acceptance, reconstruction, non-ANN selection, and hardware trigger
efficiencies—but when combined cancel almost entirely. This is shown in Table
3, which gives the value of $\alpha$ including the mass-dependent effects
discussed above but excluding the correction for the efficiency of the $\delta
m$ signal window described in Sec. 4 ($\alpha_{u}$), the correction for the
variation in resolution, and the combined value of $\alpha$. Because the
variation of $\alpha_{u}$ with mass is extremely small, a simple first-order
correction is sufficient. A straight line is fitted to the three points in the
table and used to interpolate the fractional variation in $\alpha_{u}$ between
the mass hypotheses. The resolution correction is then applied separately. Due
to the smallness of the mass-dependence, correlations between variation with
mass and with lifetime are neglected.

Table 3:  Variation in single-event sensitivity for different mass hypotheses $m(\Xi_{cc}^{+})$, assuming $\tau=333$$\rm\,fs$. The uncertainties quoted include statistical and systematic effects, and are correlated between different mass hypotheses. The variation is shown separately for all effects other than the efficiency of the $\delta m$ window ($\alpha_{u}$), for the correction due to the mass-dependent resolution, and for the combination ($\alpha$).  $m(\Xi_{cc}^{+})$ |  $\alpha_{u}$ ($\times 10^{-5}$) | Resolution correction |  $\alpha$ ($\times 10^{-5}$)
---|---|---|---
3300${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ |  $2.29$ ± | $0.61$ | 0.992 |  $2.30$ ± | $0.62$
3500${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ |  $2.38$ ± | $0.62$ | 0.957 |  $2.49$ ± | $0.65$
3700${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ |  $2.36$ ± | $0.63$ | 0.903 |  $2.61$ ± | $0.70$

As explained in Sec. 1, the value of $R$ at LHCb is not well known but is
expected to be of the order $10^{-5}$ to $10^{-4}$, while the SELEX
observation corresponds to $R=9\%$. Table 4 shows the expected signal yield,
calculated according to eq. 1, for various values of $R$ and lifetime
hypotheses. From studies of the sidebands in $m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})$ and $\delta m$, the expected background in the narrow
signal window is between 10 and 20 events. Thus, no significant signal excess
is expected if the value of $R$ at LHCb is in the range suggested by theory.
However, if production is greatly enhanced for baryon-baryon collisions at
high rapidity, as reported at SELEX, a large signal may be visible. The
procedure for determining the significance of a signal, or for establishing
limits on $R$, is discussed in the following section.

Table 4:  Expected value of the signal yield $N_{\text{sig}}$ for different values of $R$ and lifetime hypotheses, assuming $m(\Xi_{cc}^{+})=3500$${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. The uncertainties quoted are due to the systematic uncertainty on $\alpha$.  $\tau$ | $R=9\%$ | $R=10^{-4}$ | $R=10^{-5}$
---|---|---|---
100$\rm\,fs$ |  $140$ ± | $70$ |  $0.2$ ± | $0.1$ |  $0.02$ ± | $0.01$
150$\rm\,fs$ |  $600$ ± | $200$ |  $0.7$ ± | $0.2$ |  $0.07$ ± | $0.02$
250$\rm\,fs$ |  $2200$ ± | $600$ |  $2.4$ ± | $0.7$ |  $0.24$ ± | $0.07$
333$\rm\,fs$ |  $3600$ ± | $900$ |  $4.0$ ± | $1.0$ |  $0.40$ ± | $0.10$
400$\rm\,fs$ |  $4800$ ± | $1200$ |  $5.3$ ± | $1.4$ |  $0.53$ ± | $0.14$

##  8 Tests for statistical significance and upper limit calculation

Since $m(\Xi_{cc}^{+})$ is a priori unknown, tests for the presence of a
signal are carried out at numerous mass hypotheses, between $\delta
m=380$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and $\delta
m=880$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ inclusive in
1${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ steps for a total of 501 tests.
For a given value of $\delta m$, the signal and background yields and their
associated statistical uncertainties are estimated as described in Sec. 4.
From these the local significance $\mathscr{S}(\delta m)$ is calculated, where
$\mathscr{S}(\delta m)$ is defined as

$\mathscr{S}(\delta
m)\equiv\frac{N_{S+B}-N_{B}}{\sqrt{\sigma_{S+B}^{2}+\sigma_{B}^{2}}}$ (6)

and $\sigma_{S+B}$ and $\sigma_{B}$ are the estimated statistical
uncertainties on the yield in the signal window and on the expected
background, respectively. Since multiple points are sampled, the look
elsewhere effect (LEE) [40] must be taken into account. The procedure used is
to generate a large number of pseudo-experiments containing only background
events, with the amount and distribution of background chosen to match the
data (as estimated from sidebands). For each pseudo-experiment, the full
analysis procedure is applied in the same way as for data, and the local
significance is measured at all 501 values of $\delta m$. The LEE-corrected
$p$-value for a given $\mathscr{S}$ is then taken to be the fraction of the
pseudo-experiments that contain an equal or larger local significance at any
point in the $\delta m$ range.

The procedure established before unblinding is that if no signal with an LEE-
corrected significance of at least $3\sigma$ is seen, upper limits on $R$ will
be quoted. The $CL_{s}$ method [41, 42] is applied to determine upper limits
on $R$ for a particular $\delta m$ and lifetime hypothesis, given the observed
yield $N_{S+B}$ and expected background $N_{B}$ in the signal window obtained
as described in Sec. 4. The statistical uncertainty on $N_{B}$ and systematic
uncertainties on $\alpha$ are taken into account. The 95% CL upper limit is
then taken as the value of $R$ for which $CL_{s}=0.05$. Upper limits are
calculated at each of the 501 $\delta m$ hypotheses, and for five lifetime
hypotheses (100, 150, 250, 333, 400$\rm\,fs$).

##  9 Results

The $\delta m$ spectrum in data is shown in Fig. 3, and the estimated signal
yield in Fig. 4. No clear signal is found with either background subtraction
method. In both cases the largest local significance occurs at $\delta
m=513$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, with $\mathscr{S}=1.5\sigma$
in the baseline method and $\mathscr{S}=2.2\sigma$ in the cross-check.
Applying the LEE correction described in Sec. 8, these correspond to
$p$-values of 99% and 53%, respectively. Thus, with no significant excess
found above background, upper limits are set on $R$ at the 95% CL, shown in
Fig. 5 for the first method. These limits are tabulated in Table 9 for blocks
of $\delta m$ and the five lifetime hypotheses. The blocks are
50${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ wide, and for each block the
largest (worst) upper limit seen for a $\delta m$ point in that block is
given. Similarly, the largest upper limit seen in the entire
500${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ mass range is also given. A
strong dependence in sensitivity on the lifetime hypothesis is seen.

Figure 3:  Spectrum of $\delta m$ requiring $2273<m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})<2303$${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. Both plots
show the same data sample, but with different $\delta m$ ranges and binnings.
The wide signal region is shown in the right plot and indicated by the dotted
vertical lines in the left plot.

Figure 4:  Measured signal yields as a function of $\delta m$. The upper two
plots show the estimated signal yield as a dark line and the $\pm 1\sigma$
statistical error bands as light grey lines for (upper left) the baseline
method and (upper right) the cross-check method. The central values of the two
methods are compared in the lower plot and found to agree well.  Figure 5:
Upper limits on $R$ at the 95% CL as a function of $\delta m$, for five
$\Xi_{cc}^{+}$ lifetime hypotheses.  Table 5:  Largest values of the upper
limits (UL) on $R$ at the 95% CL in blocks of $\delta m$ for a range of
lifetime hypotheses, given in units of $10^{-3}$. The largest values across
the entire 500${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$ range are also shown.

|  $R$, largest 95% CL UL in range $\times 10^{3}$
---|---
$\delta m$ (MeV$/c^{2}$) | 100$\rm\,fs$ | 150$\rm\,fs$ | 250$\rm\,fs$ | 333$\rm\,fs$ | 400$\rm\,fs$
380–429 | 12.6 | 2.7 | 0.73 | 0.43 | 0.33
430–479 | 11.2 | 2.4 | 0.65 | 0.39 | 0.29
480–529 | 14.8 | 3.2 | 0.85 | 0.51 | 0.39
530–579 | 10.7 | 2.3 | 0.63 | 0.38 | 0.29
580–629 | 10.9 | 2.3 | 0.63 | 0.38 | 0.29
630–679 | 14.2 | 3.0 | 0.81 | 0.49 | 0.37
680–729 | 9.5 | 2.0 | 0.56 | 0.33 | 0.25
730–779 | 10.8 | 2.3 | 0.63 | 0.37 | 0.28
780–829 | 12.8 | 2.8 | 0.74 | 0.45 | 0.34
830–880 | 12.2 | 2.6 | 0.70 | 0.42 | 0.32
380–880 | 14.8 | 3.2 | 0.85 | 0.51 | 0.39

The decay $\Xi_{cc}^{+}\\!\rightarrow\mathchar
28931\relax_{c}^{+}K^{-}\pi^{+}$ may proceed through an intermediate
$\Sigma_{c}^{++}$ resonance. Such decays would be included in the yields and
limits already shown. Nonetheless, further checks are made with an explicit
requirement that the $\mathchar 28931\relax_{c}^{+}\pi^{+}$ invariant mass be
consistent with that of a $\Sigma_{c}^{++}$, since this substantially reduces
the combinatorial background. For $\Sigma_{c}(2455)^{++}$ and
$\Sigma_{c}(2520)^{++}$, the mass offsets $\left[m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}}\pi^{+})-m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})\right]$ are required to be within
4${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
15${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the world-average value,
respectively. The resulting $\delta m$ spectra are shown in Fig. 6. No
statistically significant excess is present.

Figure 6:  Mass difference spectrum requiring
$2273<m([pK^{-}\pi^{+}]_{\mathchar
28931\relax_{c}})<2303$${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$. Candidates
are also required to be consistent with (left) an intermediate
$\Sigma_{c}(2455)^{++}$, (right) an intermediate $\Sigma_{c}(2520)^{++}$.

##  10 Conclusions

A search for the decay $\Xi_{cc}^{+}\\!\rightarrow\mathchar
28931\relax_{c}^{+}K^{-}\pi^{+}$ is performed at LHCb with a data sample of
$pp$ collisions, corresponding to an integrated luminosity of
0.65$\mbox{\,fb}^{-1}$, recorded at a centre-of-mass energy of
7$\mathrm{\,Te\kern-1.00006ptV}$. No significant signal is found. Upper limits
on the $\Xi_{cc}^{+}$ cross-section times branching fraction relative to the
$\mathchar 28931\relax_{c}^{+}$ cross-section are obtained for a range of mass
and lifetime hypotheses, assuming that the kinematic distributions of the
$\Xi_{cc}^{+}$ follow those of the Genxicc model. The upper limit depends
strongly on the lifetime, varying from $1.5\times 10^{-2}$ for 100$\rm\,fs$ to
$3.9\times 10^{-4}$ for 400$\rm\,fs$. These limits are significantly below the
value of $R$ found at SELEX. This may be explained by the different production
environment, or if the $\Xi_{cc}^{+}$ lifetime is indeed very short ($\ll
100$$\rm\,fs$). Future searches at LHCb with improved trigger conditions,
additional $\Xi_{cc}$ decay modes, and larger data samples should improve the
sensitivity significantly, especially at short lifetimes.

## Acknowledgements

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 the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov
Institute” (Russia); MinECo, 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. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by
Yandex LLC (Russia), as well as to the communities behind the multiple open
source software packages that we depend on.

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figure table

# Soft x-ray detection for small satellites with a commercial CMOS sensor at
room temperature

Steve Tammes  Department of Physics and Astronomy, University of Iowa, Iowa
City, IA 52242, USA  Tyler Roth  Department of Physics and Astronomy,
University of Iowa, Iowa City, IA 52242, USA  Philip Kaaret  Department of
Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA  Casey
DeRoo  Department of Physics and Astronomy, University of Iowa, Iowa City, IA
52242, USA  Abdallah Elmaleh  Department of Physics and Astronomy, University
of Iowa, Iowa City, IA 52242, USA  Jessica L. McChesney  Argonne National
Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA  Fanny
Rodolakis  Argonne National Laboratory, 9700 South Cass Avenue, Argonne,
Illinois 60439, USA

###### Abstract

Recently CMOS (complementary metal-oxide-semiconductor) sensors have
progressed to a point where they may offer improved performance in imaging
x-ray detection compared to the CCDs often used in x-ray satellites. We
demonstrate x-ray detection in the soft x-ray band (250-1700 eV) by a
commercially available back-illuminated Sony IMX290LLR CMOS sensor using the
Advanced Photon Source at the Argonne National Laboratory. While operating the
device at room temperature, we measure energy resolutions (FWHM) of 48 eV at
250 eV and at 83 eV 1700 eV which are comparable to the performance of the
_Chandra_ ACIS and the _Suzaku_ XIS. Furthermore, we demonstrate that the
IMX290LLR can withstand radiation up to 17.1 krad, making it suitable for use
on spacecraft in low earth orbit.

###### keywords:

CMOS Image sensor, Back-side illuminated, x-rays spectroscopy, x-ray Imaging,
Silicon, Radiation Effects, Sensor performance

*Steve Tammes<EMAIL_ADDRESS>
*Tyler Roth<EMAIL_ADDRESS>
##  1 Introduction

The availability of low-cost small satellites for astrophysics drives a need
for low-cost detectors that place minimal demands on the limited spacecraft
resources available[1]. The charge-coupled device (CCD) detectors often used
for x-ray detection on space-based x-ray observatories have high cost and
require cooling to temperatures near -100 K.[2, 3, 4] Complementary Metal-
Oxide-Semiconductor (CMOS) sensors are designed for operation at room
temperature and many commercial devices are available at low cost. The active
pixel design of CMOS sensors enables lower power consumption, faster readout
rates, and comparable noise levels to CCDs[5].

Here, we investigate the candidacy of a low-cost commercial CMOS sensor as an
x-ray spectrometer in low earth orbit (LEO) for future small satellite
missions. In Sec. 2, we describe the selected CMOS sensor, initial results on
x-ray detection, and our x-ray event processing algorithm. We characterize the
soft x-ray performance of the sensor using measurements obtained at an x-ray
synchrotron beamline at the Argonne National Laboratory in Sec. 3. We then
discuss the electron noise (Sec. 4), radiation testing (Sec. 5), and our
conclusions (Sec. 6).

##  2 x-ray Detection And Event Processing

###  2.1 x-ray Detection

Back-illuminated (BI) sensors can provide superior performance for soft x-ray
detection because the photons do not pass through the passivation,
metallization, and inter-dielectric layers that form the pixel electronics. We
evaluated several candidate BI sensors and selected the Sony IMX290LLR CMOS
sensor for additional study due to its low electronic noise which is important
in achieving good spectral resolution for soft x-rays. The IMX290LLR contains
a 1936$\times$1096 array of 2.9 $\mu$m square back-side-illuminated pixels and
can achieve frame rates of up to 135 fps. To minimize development costs, we
used an IDS Imaging Development Systems (https://en.ids-imaging.com/)
UI-3860-LE-M-GL camera, that includes an IMX290 sensor and circuitry to
provide a USB interface, and the associated Software Development Kit (SDK).
For x-ray detection, we removed the coverglass designed to protect the
sensor’s surface.

Our initial x-ray tests were performed using an 55Fe radioactive source and an
x-ray tube fluorescing a teflon target and the walls of the vacuum chamber
where the sensor was mounted. This produces characteristic emission lines from
several elements including F, Cr, Mn, Fe, and bremsstraulung continuum
radiation. The chamber was evacuated to $\approx 10^{-2}$ Torr and the sensor
was mounted on a chiller plate maintained at a constant temperature of 21∘C.
We acquired 4,000 images each with 300 ms exposure under x-ray illumination
and 100 frames with no x-rays present for dark and bias measurements. Cutouts
of x-ray events taken from single frames are shown in Fig 1. x-rays produce
events in which charge is deposited in one, two, or multiple pixels.

To select an appropriate gain for the sensor, we collected a series of spectra
using the 55Fe radioactive source at different gain settings. We measured the
centroid of the pulse height distribution for the Mn K-$\alpha$ emission line
(corresponding to 1620 $e^{-}$ for an average hole-pair creation energy of
$w=3.64\rm\,eV$ in silicon at room temperature [6]) using the event processing
methodology outlined in Sec 2.2, and adopted settings producing a gain and
associated fitting error of 0.991 $\pm$ 0.006 ADU/e-. These gain settings were
used for all of the data described below.

Figure 1: Cutout images of the three types of events we consider for event
processing. Shown from left to right are single pixel, double pixel, and
extended pixel events. These events correspond to energies of 3.3 keV, 3.1
keV, and 5.4 keV respectively.

###  2.2 Event Processing

Individual x-rays may deposit charge in multiple pixels due to the finite
extent of the track traversed by primary photoelectron, the ejection of Auger
electrons, and charge diffusion. To cope with the variable spread of charge
across pixels, the event processing algorithms used for x-ray CCDs, such as
Chandra’s Advanced CCD imaging spectrometer (ACIS), search for pixels with
charge greater than the ‘event threshold’ and then record values in the
surrounding 3$\times$3 pixel grid. Pixels above the ‘split pixel threshold’
and sharing a side with the central pixel or in a 2$\times$2 square including
the central pixel are included in the sum used to reconstruct the energy of
the incident photon [3]. As shown in Fig. 1, the x-ray events from the IMX290
sometimes extend over a larger range of pixels. This is likely due to the
relatively small size of the pixels. We have developed an event processing
algorithm utilizing a 5$\times$5 grid of pixels.

Before processing the images, we first identified anomalous (hot) pixels. We
started by collecting 100 dark frames of the same exposure time as the data.
Setting a threshold equal to 2 standard deviations above the median value of
the 100 dark frames, we marked all pixels that are above the threshold in 10%
or more of the frames as hot. These pixels were excluded in further
processing. For the data described below, 0.47% of the pixels were marked as
hot. A master dark frame was compiled by taking the mean of the dark frames.
The master dark frame was subtracted from each of the x-ray frames.

The dark-subtracted x-ray frame is then scanned. For each pixel above the
event threshold, a surrounding 5$\times$5 grid is defined. The set of pixels
above the split pixel threshold (‘hit pixels’) that are connected to the
central pixel by a chain of adjoining hit pixels are included in the sum used
to estimate the photon energy and the position of the central pixel is
recorded as the x-ray position. The event and split pixel thresholds were
optimized by examining pulse height spectra for x-rays with energies between
250 eV and 1700 eV (see Sec. 3). The thresholds were adjusted to minimize the
width and skew of the pulse height distributions. We found an optimal event
threshold of 26 ADU and split pixel threshold of 5 ADU.

##  3 Argonne Data

(a)

(b)

Figure 2: (Left) The beamline used at APS for the experiment. (Right) Vacuum
chamber where the sensor was held. Arrows from left to right show the sensor
port, Si wafer, and beam direction.

###  3.1 Experimental Setup

In December 2019, we tested the sensor at the Intermediate Energy x-ray (IEX)
beamline 29-ID of the Advanced Photon Source (APS) at the Argonne National
Laboratory in Illinois. This beamline utilizes an electromagnetic, variably
polarizing undulator source followed by a monochromator and is capable of
producing monochromatic x-rays between 250-2500 eV[7]. Images of the
experimental setup are shown in Fig 2(a) and Fig 2(b). Our sensor is not
capable of handling the intensity of the direct beam in photon counting mode,
so it was mounted on a port at an angle 35∘ with respect to the incident beam.
A pump near the sensor maintained a high vacuum ($\approx 10^{-9}$ Torr). A Si
wafer was used to reflect the incident beam thereby reducing the beam flux
($\sim 10^{12}~{}\gamma$/s) to a level that could be handled by the camera
($<100~{}\gamma$/s). Some experimentation was required to focus the beam in
the center of the sensor and the optimal graze angle was 17.5∘.

With the beam centered on the sensor and the vacuum chamber covered to
minimize ambient light on the sensor, we accumulated sensor images with an
exposure time of 300 ms at energies from 250 eV to 1700 eV (see Table 1). At
each energy, we accumulated frames until at least 20,000 photon events were
registered. The sensor maintained an average temperature of 25∘C during this
continuous run. Both before and after taking beamline data, we turned off the
beam and acquired 100 dark frames with 300 ms exposure.

Figure 3: Example of a fitted spectrum from a beamline energy of 274 eV with
the best fit Gaussian model.

###  3.2 Spectral Fitting

Using the algorithm described in Sec. 2.2, x-ray events were extracted from
the sensor images. The list of x-ray events was then used to produce an energy
spectrum at each beam energy using a bin width of 2 ADU/bin. We fitted each
spectrum with a Gaussian model over a pulse height band covering the peak of
the Gaussian, as seen in the solid line in Fig 3.

The error on the counts in each pulse height bin was calculated as the
quadrature sum of the Gehrels variance function[8] and a linear term due to
differential non-linearity (DNL) proportional to the counts in each bin. The
same DNL factor was used for all spectra and was adjusted until the fits
produced $\chi^{2}_{\nu}\approx 1$ giving a value of 0.045. We interpret this
as the DNL of the analog-to-digital converters in the IMX290. Table 1 shows
the best fit parameters for each spectrum.

Energy | Centroid | FWHM | DoF | $\chi^{2}_{\nu}$
---|---|---|---|---
(eV) | (ADU) | (ADU) |  |
250.0 | 67.0 $\pm$ 0.1 | 12.4 $\pm$ 0.2 | 8 | 1.7
274.0 | 74.1 $\pm$ 0.1 | 12.5 $\pm$ 0.2 | 9 | 1.2
280.0 | 74.9 $\pm$ 0.1 | 12.6 $\pm$ 0.2 | 8 | 0.7
400.0 | 108.4 $\pm$ 0.1 | 14.7 $\pm$ 0.1 | 10 | 0.5
574.0 | 155.0 $\pm$ 0.1 | 15.2 $\pm$ 0.2 | 11 | 1.2
950.0 | 257.0 $\pm$ 0.1 | 16.7 $\pm$ 0.1 | 12 | 0.5
1200.0 | 325.2 $\pm$ 0.1 | 18.2 $\pm$ 0.1 | 13 | 0.5
1450.0 | 392.6 $\pm$ 0.1 | 20.0 $\pm$ 0.2 | 15 | 0.7
1700.0 | 459.7 $\pm$ 0.2 | 21.9 $\pm$ 0.4 | 18 | 2.5

Table 1: Summary of fit values obtained with a Gaussian plus a constant model.

###  3.3 Energy Calibration

We performed a linear regression of the best fitted Gaussian centroids versus
beam energy as shown in Fig. 4. We inverted the relation to find the pulse
height to energy calibration. We obtained a best fit slope of 3.6877 $\pm$
0.0008 eV/ADU and intercept of 1.840 $\pm$ 0.005 eV yielding the following
conversion function:

$\text{Energy (eV)}=\frac{{3.69}\text{\, eV}}{\text{ADU}}(\text{ADU
value}+{1.8}\ \text{eV}).\ $ (1)

The slope is equivalent to a camera gain of $0.9870\pm 0.0002\,{\rm
ADU}/e^{-}$. This is more accurately determined than our initial gain
calibration done with the radioactive 55Fe source and consistent within the
uncertainties of that measurement.
With active pixel technology, some variations of gain across the regions of
the sensor can be expected. To quantify the variations in gain across the
sensor, we divided the sensor area into a 5x5 grid, each grid 387 by 219
pixels. We then calculated the gain within each grid by fitting only the
events that occurred within the grid and performing the same linear regression
described above. We determined an average gain weighted by the slope error in
each grid region, which we find to be 3.686 $\pm$ 0.005 ADU/eV. The gain
varies by 0.14% across the sensor and we choose to use a single gain for the
whole sensor.

Figure 4: Best fit linear regression to the centroid of the Argonne IEX APS
lines with residuals plotted in the lower figure.

In Fig. 5 we display calibrated spectra from various beam energies on the same
plot. The Gaussians were normalized to have the same area under their curves.

Figure 5: Energy calibrated spectra with a y-axis normalization at beamline
energies of 274 eV, 950 eV, and 1700 eV. There are no significant counts below
400 eV and 1150 eV for the 950 eV and 1700 eV lines respectively. We do not
plot these spectra below these thresholds for visual clarity. Figure 6: Energy
resolution (FWHM) modeled by Eq 2.

###  3.4 Energy Resolution

The IEX resolving power is $10^{4}$; thus, the finite widths of the spectral
peaks are due to the sensor. Fig. 6 shows the energy resolution in terms of
the Gaussian full width half max (FWHM) as a function of beam energy. We
modeled the energy resolution as the quadrature sum of the Fano limited
Poisson fluctuations in the number of photoelectrons produced per photon and
the electronic noise per pixel,

$\text{FWHM}=2.355w\;\sqrt{N\sigma^{2}+\frac{fE}{w}}\ $ (2)

where $w=3.64$ eV is the average ionization energy of silicon, $f=0.115$ is
the Fano factor for silicon [9], $N$ is the number of pixels used to
calculated the pulse height sum for each event, and $\sigma$ is the root-mean-
square (RMS) electronic noise per pixel.

Figure 7: Mean number of summed pixels versus energy.

Fig. 7 shows the average number of pixels used in the pulse height summation
as a function of energy. The error bars indicate the standard deviation. We
attempted two different variations of $N$ for fitting, the first uses a
constant median $N$ value of 2 and the second uses the variable mean number of
pixels as a function of energy as shown in Fig. 5. We allowed the electronic
noise $\sigma$ parameter to vary and fit the two models to the resolution
curve in Fig. 7. We found best fit values of $3.64\pm 0.05\,e^{-}$ and
$3.59\pm 0.10\,e^{-}$ for the variable and constant pixel models,
respectively. Our FWHM resolution values of 48.1 eV at 274 eV and 75.6 eV at
1450 eV are competitive with the values of $\sim$50 eV and $\sim$70 eV near
0.3 keV and 1.5 keV, respectively, for the back-side illuminated CCDs aboard
the Suzaku x-ray Imaging Spectrometer [10, 4], and also with the resolution of
96 eV at 1.49 keV reported for the ACIS CCDs [11].

We fitted the Mn K-$\alpha$ and Mn K-$\beta$ lines in the spectrum mentioned
in Sec 2. The energy resolution values are larger than those estimated using
Eq 2 and the best fit noise for energies below 2 keV. The degradation of the
energy resolution above 2 keV may be due to incomplete charge collection.
Significant degradation of energy resolution at high energies has been found
in a front-illuminated sensor and attributed to a reduction in charge
collection efficiency for X-ray that penetrate into the $p^{+}$ substrate
beneath the epitaxial layer [12]. This preferentially occurs for higher energy
X-rays since they have longer absorption depth. The $p^{+}$ layer is absent in
back-illuminated devices, but incomplete charge collection may occur in the
pixel circuitry layer or the carrier wafer.

Figure 8: RMS noise distribution of the IMX290LLR chip at 300 ms. The
vertically and non-vertically dashed lines correspond to the mean and median
of the distribution respectively.

##  4 Noise Measurements

The sensor noise can be measured by examining the average variance in each
pixel when a sensor is subject to no light at short exposures. Due to the
construction of the CMOS pixel, namely that each pixel contains its own
circuitry, the RMS noise varies between pixels. This is different than a CCD
detector which traditionally has a single amplifier and analog-to-digital
converter for all pixels and therefore maintains uniform noise for all pixels.

We evaluated the noise of the IMX290 by taking a series of 100 frames with the
sensor in the dark in a vacuum chamber. Each image had an exposure 300 ms and
the sensor was held at a constant temperature of 21∘C. We constructed a master
dark frame by taking the mean ADU value in each pixel of the 100 images and
then subsequently subtracting the master image from each individual one.

We constructed a distribution of the per pixel noise by taking the RMS of the
100 master subtracted images (Fig. 8). We find mean and median read noise
values of $2.18\,e^{-}$ and $2.17\,e^{-}$, respectively. The tail extending to
large read noise of the distribution is well known for CMOS sensors and has
been characterized as Random Telegraph Signal (RTS) noise. RTS is generated
from defects within the silicon that lead to increased electron entrapment and
signal variance upon readout.[13] Fewer than 0.2% of the pixels have an RMS
noise greater than $4\,e^{-}$.

(a)

(b)

Figure 9: The IMX290LLR sensor at RadCORE. (Left) The sensor underneath the
Cs-137 sample. (Right) Close up of mount securing sensor

##  5 Radiation Testing

We irradiated a IMX290LLR sensor with gamma rays to study its performance in a
radiation environment. The testing was done at the RadCore facility at the
University of Iowa, see Fig.9. The camera was exposed to gamma-rays from
Cs-137 (main peak at 662 keV) at a rate of 0.054 krad(Si)/minute. We operated
the camera, recording 10 ms frames at the same gain settings as discussed
above, while monitoring the current drawn by the camera via its USB connection
from a radiation shielded location. While the camera was operating correctly,
the current was 0.16 A. We ended the test after the current dropped to 0.02 A
and the camera simultaneously ceased to function. The camera functioned
correctly while exposed to radiation for a total of 314.8 minutes, giving a
total exposure of 17.1 krad before failure. This is a lower bound on the
radiation tolerance of the sensor since some other component on the camera may
have failed.

Figure 10: Median ADU value versus accumulated dose

Fig. 10 shows the median ADU value versus accumulated dose. The ADU value at
the start of the test corresponds to charge deposition of $\sim
20,000\,e^{-}/{\rm s}$. The median ADU drops by $\approx 15\%$ during
accumulation of the first 6 krad, recovers by $\approx 4\%$ during a 13 minute
interval during which the irradiation was stopped, and then shows a more
gradual decrease during the remaining testing. The variations may be due to
ionization damage of the gate oxide in the active pixel circuity.[14] Such
damage anneals at room temperature, consistent with the recovery while
irradiation was stopped. Ionization damage depends on rate of irradiation
which was much higher during the test than expected in a typical low Earth
orbit (LEO), e.g. $\sim$ 5 krad over 2 years. Thus, testing at a low dose rate
would be of interest. We note that the sensor continued to operate as the
median ADU decreased. Thus, the sensor would likely continue to function,
although perhaps with some change in the energy calibration, over a moderate
duration mission of several years in LEO.

##  6 Conclusion

We have characterized the performance of a commercial Sony IMX290LLR CMOS
sensor as an imaging x-ray spectrometer intended for small satellites.
Radiation testing shows that the sensor and accompanying electronics is
operational for well beyond the radiation doses expected for missions of two
years duration in low Earth orbit. Testing at a synchrotron x-ray beamline
demonstrates the back-illuminated CMOS sensor operated at temperatures near
+20∘ C has an energy resolution competitive with the cooled CCD sensors on
current x-ray observatories, enabling use of such sensors in the resource-
limited environment of small spacecraft.

### Acknowledgments

We thank Amanda Kalen of RadCore for her assistance with the radiation
testing. This research was supported in part by the Iowa Space Grant
Consortium under NASA Award No. NNX16AL88H. This research used resources of
the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of
Science User Facility operated for the DOE Office of Science by Argonne
National Laboratory under Contract No. DE-AC02-06CH11357; additional support
by National Science Foundation under Grant No. DMR-0703406.

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