EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-363 LHCb-PAPER-2012-036 21 January 2013

Measurement of the cross-section for $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ production in pp collisions at
$\sqrt{s}=7$$\mathrm{\,Te\kern-2.07413ptV}$

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

A measurement of the cross-section for $\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ is presented using data at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ corresponding to an integrated
luminosity of 0.94$\mbox{\,fb}^{-1}$. The process is measured within the
kinematic acceptance $\mbox{$p_{\rm
T}$}>20$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2<\eta<4.5$ for the
daughter electrons and dielectron invariant mass in the range
60–120${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The cross-section is
determined to be

$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-})=76.0\pm 0.8\pm 2.0\pm 2.6\rm\,pb$

where the first uncertainty is statistical, the second is systematic and the
third is the uncertainty in the luminosity. The measurement is performed as a
function of Z rapidity and as a function of an angular variable which is
closely related to the Z transverse momentum. The results are compared with
previous LHCb measurements and with theoretical predictions from QCD.

Submitted to Journal of High Energy Physics

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

LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C.
Adrover6, A. Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M.
Alexander48, S. Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves
Jr22,35, S. Amato2, Y. Amhis7, L. Anderlini17,f, J. Anderson37, R.
Andreassen57, R.B. Appleby51, O. Aquines Gutierrez10, F. Archilli18, A.
Artamonov 32, M. Artuso53, E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J.
Back45, C. Baesso54, V. Balagura28, W. Baldini16, R.J. Barlow51, C.
Barschel35, S. Barsuk7, W. Barter44, A. Bates48, Th. Bauer38, A. Bay36, J.
Beddow48, I. Bediaga1, S. Belogurov28, K. Belous32, I. Belyaev28, E. Ben-
Haim8, M. Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, A.
Berezhnoy29, R. Bernet37, M.-O. Bettler44, M. van Beuzekom38, A. Bien11, S.
Bifani12, T. Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36,
C. Blanks50, J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N.
Bondar27, W. Bonivento15, S. Borghi51, A. Borgia53, T.J.V. Bowcock49, E.
Bowen37, C. Bozzi16, T. Brambach9, J. van den Brand39, J. Bressieux36, D.
Brett51, M. Britsch10, T. Britton53, N.H. Brook43, H. Brown49, A. Büchler-
Germann37, I. Burducea26, A. Bursche37, J. Buytaert35, S. Cadeddu15, O.
Callot7, M. Calvi20,j, M. Calvo Gomez33,n, A. Camboni33, P. Campana18,35, A.
Carbone14,c, G. Carboni21,k, R. Cardinale19,i, A. Cardini15, H. Carranza-
Mejia47, L. Carson50, K. Carvalho Akiba2, G. Casse49, M. Cattaneo35, Ch.
Cauet9, M. Charles52, Ph. Charpentier35, P. Chen3,36, N. Chiapolini37, M.
Chrzaszcz 23, K. Ciba35, X. Cid Vidal34, G. Ciezarek50, P.E.L. Clarke47, M.
Clemencic35, H.V. Cliff44, J. Closier35, C. Coca26, V. Coco38, J. Cogan6, E.
Cogneras5, P. Collins35, A. Comerma-Montells33, A. Contu15, A. Cook43, M.
Coombes43, G. Corti35, B. Couturier35, G.A. Cowan36, D. Craik45, S.
Cunliffe50, R. Currie47, C. D’Ambrosio35, P. David8, P.N.Y. David38, I. De
Bonis4, K. De Bruyn38, S. De Capua51, M. De Cian37, J.M. De Miranda1, L. De
Paula2, W. De Silva57, P. De Simone18, D. Decamp4, M. Deckenhoff9, H.
Degaudenzi36,35, L. Del Buono8, C. Deplano15, D. Derkach14, O. Deschamps5, F.
Dettori39, A. Di Canto11, J. Dickens44, H. Dijkstra35, P. Diniz Batista1, M.
Dogaru26, F. Domingo Bonal33,n, S. Donleavy49, F. Dordei11, A. Dosil Suárez34,
D. Dossett45, A. Dovbnya40, F. Dupertuis36, R. Dzhelyadin32, A. Dziurda23, A.
Dzyuba27, S. Easo46,35, U. Egede50, V. Egorychev28, S. Eidelman31, D. van
Eijk38, S. Eisenhardt47, U. Eitschberger9, R. Ekelhof9, L. Eklund48, I. El
Rifai5, Ch. Elsasser37, D. Elsby42, A. Falabella14,e, C. Färber11, G.
Fardell47, C. Farinelli38, S. Farry12, V. Fave36, D. Ferguson47, V. Fernandez
Albor34, F. Ferreira Rodrigues1, M. Ferro-Luzzi35, S. Filippov30, C.
Fitzpatrick35, M. Fontana10, F. Fontanelli19,i, R. Forty35, O. Francisco2, M.
Frank35, C. Frei35, M. Frosini17,f, S. Furcas20, E. Furfaro21, A. Gallas
Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y. Gao3, J. Garofoli53,
P. Garosi51, J. Garra Tico44, L. Garrido33, C. Gaspar35, R. Gauld52, E.
Gersabeck11, M. Gersabeck51, T. Gershon45,35, Ph. Ghez4, V. Gibson44, V.V.
Gligorov35, C. Göbel54, D. Golubkov28, A. Golutvin50,28,35, A. Gomes2, H.
Gordon52, M. Grabalosa Gándara5, R. Graciani Diaz33, L.A. Granado Cardoso35,
E. Graugés33, G. Graziani17, A. Grecu26, E. Greening52, S. Gregson44, O.
Grünberg55, B. Gui53, E. Gushchin30, Yu. Guz32, T. Gys35, C. Hadjivasiliou53,
G. Haefeli36, C. Haen35, S.C. Haines44, S. Hall50, T. Hampson43, S. Hansmann-
Menzemer11, N. Harnew52, S.T. Harnew43, J. Harrison51, P.F. Harrison45, T.
Hartmann55, J. He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando
Morata34, E. van Herwijnen35, E. Hicks49, D. Hill52, M. Hoballah5, C.
Hombach51, P. Hopchev4, W. Hulsbergen38, P. Hunt52, T. Huse49, N. Hussain52,
D. Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12, J. Imong43, R.
Jacobsson35, A. Jaeger11, E. Jans38, F. Jansen38, P. Jaton36, F. Jing3, M.
John52, D. Johnson52, C.R. Jones44, B. Jost35, M. Kaballo9, S. Kandybei40, M.
Karacson35, T.M. Karbach35, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A.
Keune36, B. Khanji20, O. Kochebina7, I. Komarov36,29, R.F. Koopman39, P.
Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M.
Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, M. Kucharczyk20,23,j, V.
Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G.
Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35, G.
Lanfranchi18,35, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J.
van Leerdam38, J.-P. Lees4, R. Lefèvre5, A. Leflat29,35, J. Lefrançois7, O.
Leroy6, Y. Li3, L. Li Gioi5, M. Liles49, R. Lindner35, C. Linn11, B. Liu3, G.
Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33, N. Lopez-March36, H.
Lu3, J. Luisier36, H. Luo47, A. Mac Raighne48, F. Machefert7, I.V.
Machikhiliyan4,28, F. Maciuc26, O. Maev27,35, S. Malde52, G. Manca15,d, G.
Mancinelli6, N. Mangiafave44, U. Marconi14, R. Märki36, J. Marks11, G.
Martellotti22, A. Martens8, L. Martin52, A. Martín Sánchez7, M. Martinelli38,
D. Martinez Santos34, D. Martinez Santos39, D. Martins Tostes2, A.
Massafferri1, R. Matev35, Z. Mathe35, C. Matteuzzi20, M. Matveev27, E.
Maurice6, A. Mazurov16,30,35,e, J. McCarthy42, R. McNulty12, B. Meadows57,52,
F. Meier9, M. Meissner11, M. Merk38, D.A. Milanes13, M.-N. Minard4, J. Molina
Rodriguez54, S. Monteil5, D. Moran51, P. Morawski23, R. Mountain53, I. Mous38,
F. Muheim47, K. Müller37, R. Muresan26, B. Muryn24, B. Muster36, P. Naik43, T.
Nakada36, R. Nandakumar46, I. Nasteva1, M. Needham47, N. Neufeld35, A.D.
Nguyen36, T.D. Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, R. Niet9, N.
Nikitin29, T. Nikodem11, S. Nisar56, A. Nomerotski52, A. Novoselov32, A.
Oblakowska-Mucha24, V. Obraztsov32, S. Oggero38, S. Ogilvy48, O. Okhrimenko41,
R. Oldeman15,d,35, M. Orlandea26, J.M. Otalora Goicochea2, P. Owen50, B.K.
Pal53, A. Palano13,b, M. Palutan18, J. Panman35, A. Papanestis46, M.
Pappagallo48, C. Parkes51, C.J. Parkinson50, G. Passaleva17, G.D. Patel49, M.
Patel50, G.N. Patrick46, C. Patrignani19,i, C. Pavel-Nicorescu26, A. Pazos
Alvarez34, A. Pellegrino38, G. Penso22,l, M. Pepe Altarelli35, S.
Perazzini14,c, D.L. Perego20,j, E. Perez Trigo34, A. Pérez-Calero Yzquierdo33,
P. Perret5, M. Perrin-Terrin6, G. Pessina20, K. Petridis50, A. Petrolini19,i,
A. Phan53, E. Picatoste Olloqui33, B. Pie Valls33, B. Pietrzyk4, T. Pilař45,
D. Pinci22, S. Playfer47, M. Plo Casasus34, F. Polci8, G. Polok23, A.
Poluektov45,31, E. Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A.
Powell52, J. Prisciandaro36, V. Pugatch41, A. Puig Navarro36, W. Qian4, J.H.
Rademacker43, B. Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, N.
Rauschmayr35, G. Raven39, S. Redford52, M.M. Reid45, A.C. dos Reis1, S.
Ricciardi46, A. Richards50, K. Rinnert49, V. Rives Molina33, D.A. Roa Romero5,
P. Robbe7, E. Rodrigues51, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35,
V. Romanovsky32, A. Romero Vidal34, J. Rouvinet36, T. Ruf35, H. Ruiz33, G.
Sabatino22,k, J.J. Saborido Silva34, N. Sagidova27, P. Sail48, B. Saitta15,d,
C. Salzmann37, B. Sanmartin Sedes34, M. Sannino19,i, R. Santacesaria22, C.
Santamarina Rios34, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C.
Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina28,29, P. Schaack50, M.
Schiller39, H. Schindler35, S. Schleich9, M. Schlupp9, M. Schmelling10, B.
Schmidt35, O. Schneider36, A. Schopper35, M.-H. Schune7, R. Schwemmer35, B.
Sciascia18, A. Sciubba18,l, M. Seco34, A. Semennikov28, K. Senderowska24, I.
Sepp50, N. Serra37, J. Serrano6, P. Seyfert11, M. Shapkin32, I. Shapoval40,35,
P. Shatalov28, Y. Shcheglov27, T. Shears49,35, L. Shekhtman31, O.
Shevchenko40, V. Shevchenko28, A. Shires50, R. Silva Coutinho45, T.
Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K. Sobczak5, M.D.
Sokoloff57, F.J.P. Soler48, F. Soomro18,35, D. Souza43, B. Souza De Paula2, B.
Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37,
S. Stoica26, S. Stone53, B. Storaci37, M. Straticiuc26, U. Straumann37, V.K.
Subbiah35, S. Swientek9, V. Syropoulos39, M. Szczekowski25, P. Szczypka36,35,
T. Szumlak24, S. T’Jampens4, M. Teklishyn7, E. Teodorescu26, F. Teubert35, C.
Thomas52, E. Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39,
D. Tonelli35, S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S.
Tourneur36, M.T. Tran36, M. Tresch37, A. Tsaregorodtsev6, P. Tsopelas38, N.
Tuning38, M. Ubeda Garcia35, A. Ukleja25, D. Urner51, U. Uwer11, V. Vagnoni14,
G. Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J.
Velthuis43, M. Veltri17,g, G. Veneziano36, M. Vesterinen35, B. Viaud7, D.
Vieira2, X. Vilasis-Cardona33,n, A. Vollhardt37, D. Volyanskyy10, D. Voong43,
A. Vorobyev27, V. Vorobyev31, C. Voß55, H. Voss10, R. Waldi55, R. Wallace12,
S. Wandernoth11, J. Wang53, D.R. Ward44, N.K. Watson42, A.D. Webber51, D.
Websdale50, M. Whitehead45, J. Wicht35, D. Wiedner11, L. Wiggers38, G.
Wilkinson52, M.P. Williams45,46, M. Williams50,p, F.F. Wilson46, J. Wishahi9,
M. Witek23, W. Witzeling35, S.A. Wotton44, S. Wright44, S. Wu3, K. Wyllie35,
Y. Xie47,35, F. Xing52, Z. Xing53, Z. Yang3, R. Young47, X. Yuan3, O.
Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang53, W.C.
Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov28, L. Zhong3, A. Zvyagin35.

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
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
24AGH University of Science and Technology, Kraków, Poland
25National Center for Nuclear Research (NCBJ), Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
32Institute for High Energy Physics (IHEP), Protvino, Russia
33Universitat de Barcelona, Barcelona, Spain
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain
35European Organization for Nuclear Research (CERN), Geneva, Switzerland
36Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
37Physik-Institut, Universität Zürich, Zürich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
45Department of Physics, University of Warwick, Coventry, United Kingdom
46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
48School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
56Institute of Information Technology, COMSATS, Lahore, Pakistan, associated
to 53
57University of Cincinnati, Cincinnati, OH, United States, associated to 53

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
pMassachusetts Institute of Technology, Cambridge, MA, United States

##  1 Introduction

The measurement of vector boson production permits a number of tests of
electroweak physics and of quantum chromodynamics (QCD) to be performed. In
particular, the angular acceptance of LHCb, roughly $2<\eta<5$ in the case of
the main tracking system where $\eta$ denotes pseudorapidity, complements that
of the general purpose detectors ATLAS and CMS. LHCb measurements provide
sensitivity to the proton structure functions at very low Bjorken $x$ values
where the parton distribution functions (PDFs) are not particularly well
constrained by previous data from HERA (see for example Ref. [1]).

The most straightforward decay modes in which the $\mathrm{W}^{\pm}$ and Z
bosons can be studied using the LHCb data are the muonic channels, $\rm
Z\rightarrow\upmu^{+}\upmu^{-}$ and
$\mathrm{W}^{+}\rightarrow\upmu^{+}\upnu_{\mu}$. Measurements of $\rm
Z\rightarrow\upmu^{+}\upmu^{-}$ and of $\rm Z\rightarrow\uptau^{+}\uptau^{-}$
using the LHCb data at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ have already
been presented [2, 3]. To complement these studies, the electron channels $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ and
$\mathrm{W}^{+}\rightarrow\mathrm{e}^{+}\upnu_{e}$, which offer statistically
independent samples with different sources of systematic uncertainties, are
examined.

The main difficulty with electron111The term “electron” is used generically to
refer to either $\mathrm{e}^{+}$ or $\mathrm{e}^{-}$. reconstruction in LHCb
is the energy measurement. A significant amount of material is traversed by
the electrons before they reach the momentum analysing magnet, and their
measured momenta are therefore liable to be reduced by bremsstrahlung. For low
energy electrons, the bremsstrahlung photons can frequently be identified in
the electromagnetic calorimeter and their energies added to the measured
momentum of the electron. However, in the case of $\mathrm{W}^{\pm}$ and Z
decays, the electrons are of high momentum and transverse momentum ($p_{\rm
T}$), so that the bremsstrahlung photons often overlap with the electrons. The
LHCb calorimeters were designed so as to optimise the the measurement of
photons and $\uppi^{0}$s from heavy flavour decays, whose transverse energy
($E_{\rm T}$) values are generally well below 10 GeV. As a consequence,
individual calorimeter cells saturate at $E_{\rm T}$ around
10$\mathrm{\,Ge\kern-1.00006ptV}$, so it is not possible to substitute the
calorimeter energy for the momentum measured using the spectrometer. We
therefore have a situation in which the electron directions are well
determined, but their energies are underestimated by a variable amount,
typically around 25%. Nevertheless, the available information can be used to
study certain interesting variables.

In this paper, we present a measurement of the cross-section for
$\mathrm{p}\mathrm{p}\rightarrow\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$
using the data recorded by LHCb in 2011 at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$. Throughout this paper we use $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ to refer to the process $\rm
Z/\gamma^{*}\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ where either a virtual
photon or a $\rm Z$ boson is produced and decays to
$\mathrm{e}^{+}\mathrm{e}^{-}$. For consistency, the measurement is presented
in the same kinematic region as the recent measurement of $\rm
Z\rightarrow\upmu^{+}\upmu^{-}$ using the 2010 LHCb data at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ [2]: $2<\eta<4.5$ and $\mbox{$p_{\rm
T}$}>20{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ for the leptons and
$60<M<120$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ for the dileptons where
$M$ is the invariant mass. Since the rapidity of the Z boson can be determined
to a precision of $\sim$0.05, the rapidity distribution will be presented.
However, the $p_{\rm T}$ of the Z boson is poorly determined and its
distribution will not be discussed. A similar problem was encountered by the
D0 collaboration [4], who employed a new variable proposed in Ref. [5]
depending only on track angles

$\mbox{$\phi^{*}$}\equiv\tan\left(\frac{\phi_{\mathrm{acop}}}{2}\right)\left/\cosh\left(\frac{\Delta\eta}{2}\right)\approx\frac{\mbox{$p_{\rm
T}$}}{Mc}\,,\right.$ (1)

where $M$ and $p_{\rm T}$ refer to the lepton pair, $\Delta\eta$ and
$\Delta\phi$ are the differences in pseudorapidity and azimuthal angles
respectively between the leptons, and the acoplanarity angle is
$\phi_{\mathrm{acop}}=\pi-|\Delta\phi|$. The $p_{\rm T}$ of the Z boson is
correlated with $\phi^{*}$, and the resolution on $\phi^{*}$ is excellent,
with a precision better than 0.001. The measurement of $\phi^{*}$ presented
here therefore largely accesses the same physics as a measurement of the Z
$p_{\rm T}$ distribution. The measurement of the distribution of Z rapidity
(denoted $y_{\rm Z}$) is expected to show sensitivity to the choice of PDFs,
while $\phi^{*}$ is likely to be more sensitive to higher order effects in the
QCD modelling.

After a brief description of the detector, Sect. 3 describes the event
selection, and Sect. 4 outlines the determination of the cross-section. The
results are given in Sect. 5 followed by a short summary.

##  2 LHCb detector

The LHCb detector [6] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed primarily for the study of particles
containing $\mathrm{b}$ or $\mathrm{c}$ quarks. The detector includes a high
precision tracking system consisting of a silicon-strip vertex detector
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 has a momentum
resolution $\Delta p/p$ that varies from 0.4% at
5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ to 0.6% at
100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ for hadrons and muons, and an impact
parameter resolution of 20$\,\upmu\rm m$ for tracks with high transverse
momentum. Charged hadrons are identified using two ring-imaging Cherenkov
detectors. Photon, electron and hadron candidates are identified by a
calorimeter system consisting of scintillating-pad (SPD) and preshower (PRS)
detectors, an electromagnetic calorimeter (ECAL) and a hadronic calorimeter
(HCAL). The acceptance of the calorimeter system is roughly $1.8<\eta<4.3$.
Muons are identified by a system composed of alternating layers of iron and
multiwire proportional chambers.

The trigger [7] consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage which applies full
event reconstruction. A significant improvement to the trigger was implemented
during August 2011 which affected the trigger efficiency for $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$. The data samples before and after
this change are treated separately and will be referred to as data sample I
and data sample II. These correspond to integrated luminosities of $581\pm
20$$\mbox{\,pb}^{-1}$ and $364\pm 13$$\mbox{\,pb}^{-1}$ respectively, yielding
a total of $945\pm 33$$\mbox{\,pb}^{-1}$.

##  3 Event selection

The $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ sample is initially
selected by single-electron triggers, which require electrons to have an
$E_{\rm T}$ above a given threshold between 10 and
15$\mathrm{\,Ge\kern-1.00006ptV}$ depending on the data-taking period and
specific trigger. The $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ selection
starts from a sample of $\mathrm{e}^{+}\mathrm{e}^{-}$ candidates with high
invariant mass, which is refined by requiring the following selection
criteria:

  * •

At least one of the candidate electrons must be selected by a high-$E_{\rm T}$
electron trigger.

  * •

The electrons are both required to have $\mbox{$p_{\rm
T}$}>20$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and pseudorapidity in the range
$2.0<\eta<4.5$. The invariant mass of the $\mathrm{e}^{+}\mathrm{e}^{-}$ pair
should be greater than 40${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

  * •

Requirements on calorimeter information are imposed to provide particle
identification (PID) of electrons. The particle must satisfy
$E_{\mathrm{ECAL}}/pc>0.1$, where $p$ is the particle momentum, with
bremsstrahlung correction if available, and $E_{\mathrm{ECAL}}$ is the ECAL
energy associated with the particle. The particle is required to lie within
the HCAL acceptance and to satisfy $E_{\mathrm{HCAL}}/pc<0.05$, where
$E_{\mathrm{HCAL}}$ is the HCAL energy associated with the particle. The
energy in the preshower detector associated with the particle is required to
satisfy $E_{\mathrm{PRS}}>50$$\mathrm{\,Me\kern-1.00006ptV}$. These
requirements impose an electromagnetic shower profile, while being loose
enough to maintain a high electron efficiency despite the effects of
calorimeter saturation and bremsstrahlung.

  * •

If more than one $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ candidate
satisfies the above requirements in an event, just one candidate is used,
chosen at random. This only affects around 0.5% of cases, and in all instances
the multiple candidates share one daughter.

A sample of same-sign $\mathrm{e}^{\pm}\mathrm{e}^{\pm}$ combinations, subject
to the same selection criteria, is used to provide a data-based estimate of
background. The main background is expected to arise from hadrons that shower
early in the ECAL and consequently fake the signature of an electron. These
will contribute approximately equally to same-sign and opposite-sign pairs.
The contribution from semileptonic heavy flavour decays should be similar to
the small level ($\sim 0.2\%$) estimated for the $\rm
Z\rightarrow\upmu^{+}\upmu^{-}$ channel [2]; in any case, subtracting the
same-sign contribution should account for most of this effect.

Simulated event samples of $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ with
$M(\mathrm{e}^{+}\mathrm{e}^{-})>40$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$
are also used to assess some efficiencies as discussed below. Simulated
samples of $\rm Z\rightarrow\uptau^{+}\uptau^{-}$ and of
$\mathrm{t}\overline{}\mathrm{t}$ are used to assess possible background
contributions. For the simulation, pp collisions are generated using Pythia
6.4 [8] with a specific LHCb configuration [9] and the CTEQ6L1 PDF set [10].
The interaction of the generated particles with the detector and its response
are implemented using the Geant4 toolkit [11, *Agostinelli:2002hh] as
described in Ref. [13]. Simulated samples based on different versions of GEANT
and of the detector model are employed, which allows the reliability of the
simulation to be assessed. The simulated events are then reconstructed in the
same way as the data, including simulation of the relevant trigger conditions.

The invariant mass distribution of the selected candidates is shown in Fig. 1.
The distribution falls off abruptly above the Z mass and is spread to lower
masses by bremsstrahlung. Good agreement in shape is observed between data and
the simulation sample used in the data correction; this will be further
discussed below. The background estimated from same-sign events amounts to
4.5% of the total number of $\mathrm{e}^{+}\mathrm{e}^{-}$ candidates. The
backgrounds from $\uptau^{+}\uptau^{-}$ and $\mathrm{t}\overline{}\mathrm{t}$
events are estimated to be around 0.1% and are neglected.

Figure 1: Invariant mass distribution of $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ candidates. The data are shown as
points with error bars, the background obtained from same-sign data is shown
in red (dark shading), to which the expectation from signal simulation is
added in yellow (light shading). The $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ simulated distribution has been
normalised to the (background-subtracted) data.

##  4 Cross-section determination

In a given bin of Z rapidity or $\phi^{*}$, the cross-section is calculated
using

$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-})=\frac{N(\mathrm{e}^{+}\mathrm{e}^{-})-N(\mathrm{e}^{\pm}\mathrm{e}^{\pm})}{\epsilon_{\mathrm{GEC}}\cdot\epsilon_{\mathrm{trig}}\cdot\epsilon_{\mathrm{track}}\cdot\epsilon_{\mathrm{kin}}\cdot\epsilon_{\mathrm{PID}}\cdot\int\mathcal{L}\mathrm{d}t}\cdot
f_{\mathrm{FSR}}\cdot f_{\mathrm{MZ}}\;\;,$ (2)

where $N(\mathrm{e}^{+}\mathrm{e}^{-})$ is the number of Z candidates selected
in data, $N(\mathrm{e}^{\pm}\mathrm{e}^{\pm})$ is the background estimated
from the number of same-sign candidates and $\int\mathcal{L}\mathrm{d}t$ is
the integrated luminosity. The cross-section
$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-})$ denotes the product of the
inclusive production cross-section for the $\rm Z$ or $\gamma^{*}$ and the
branching ratio to $\mathrm{e}^{+}\mathrm{e}^{-}$. The meaning and estimation
of the other factors are described below. The values obtained for each,
averaged over the acceptance, are summarised in Table 1.

Table 1: Quantities entering into the cross-section determination, averaged over the range of Z rapidity used.  | Data sample I | Data sample II
---|---|---
$\int\mathcal{L}\mathrm{d}t\;[\mbox{\,pb}^{-1}]$ | $581\pm 20$ | $364\pm 13$
$\epsilon_{\mathrm{GEC}}$ | $0.947\pm 0.004$
$\epsilon_{\mathrm{trig}}$ | $0.715\pm 0.021$ | $0.899\pm 0.003$
$\epsilon_{\mathrm{track}}$ | $0.913\pm 0.015$
$\epsilon_{\mathrm{kin}}$ | $0.500\pm 0.007$
$\epsilon_{\mathrm{PID}}$ | $0.844\pm 0.011$
$f_{\mathrm{FSR}}$ | $1.049\pm 0.005$
$f_{\mathrm{MZ}}$ | $0.967\pm 0.001$

The luminosity is determined as described in Ref. [14] and has an uncertainty
of $3.5\%$. The factor $f_{\mathrm{FSR}}$ accounts for the effects of final-
state electromagnetic radiation, correcting the measurement to the Born level.
As in the $\rm Z\rightarrow\upmu^{+}\upmu^{-}$ analysis [2] it is determined
using Photos [15] interfaced to Pythia [8], with Horace [16] used as a cross-
check. An overall systematic uncertainty of 0.5% is assigned to this
correction [17]. The factor $f_{\mathrm{MZ}}$ corrects for
$\mathrm{e}^{+}\mathrm{e}^{-}$ events outside the mass range
$60<M(\mathrm{e}^{+}\mathrm{e}^{-})<120$$\mathrm{\,Ge\kern-1.00006ptV}$ which
pass the event selection, and is estimated from simulation by examining the
true mass for selected events.

The probability for a $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ event to
satisfy the trigger and selection requirements is given by the product of the
efficiency factors, $\epsilon$, as described below.

  * •

Global event cuts (GEC) are applied in the trigger in order to prevent very
large events from dominating the processing time. Their efficiency for
selecting signal events is given by $\epsilon_{\mathrm{GEC}}$. In the $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ case, the most important requirement
is on the multiplicity of SPD hits, $N_{\mathrm{SPD}}\leq 600$. This is
strongly correlated with the number of primary vertices reconstructed in the
event. The inefficiency is assessed by comparing with $\rm
Z\rightarrow\upmu^{+}\upmu^{-}$ candidates recorded in the same running period
using a dimuon trigger for which a less stringent requirement of 900 hits is
imposed. A correction is made for the small difference in the numbers of SPD
hits associated with the electrons and muons themselves. This procedure is
adopted for each number of reconstructed primary vertices and the results are
combined to obtain the overall efficiency.

  * •

The trigger efficiency for events passing the final selection,
$\epsilon_{\mathrm{trig}}$, is determined from data. A sample of events
triggered independently of the $\mathrm{e}^{+}$ is identified and used to
determine the efficiency for triggering the $\mathrm{e}^{+}$, and likewise for
the $\mathrm{e}^{-}$. Using the total numbers of candidates for which the
single electron trigger is satisfied at each stage by the $\mathrm{e}^{+}$
($N^{+}$), by the $\mathrm{e}^{-}$ ($N^{-}$) and by both ($N^{+-}$), the
efficiency for triggering the $\mathrm{e}^{+}$ is given by
$\varepsilon^{+}=N^{+-}/N^{-}$. The overall efficiency is then taken to be
$\varepsilon^{-}+\varepsilon^{+}-\varepsilon^{-}\varepsilon^{+}$ assuming that
the $\mathrm{e}^{+}$ and $\mathrm{e}^{-}$ are triggered independently. The
procedure is validated on simulated events. The determination is performed
separately in each bin of Z rapidity and $\phi^{*}$. In all cases, the
statistical uncertainty on the efficiency is taken as a contribution to the
systematic uncertainty on the measurement.

  * •

The track-finding efficiency, $\epsilon_{\mathrm{track}}$, represents the
probability that both of the electrons are successfully reconstructed. The
simulation is used to determine the track-finding efficiency, in bins of Z
rapidity and $\phi^{*}$, by calculating the probability that, in a $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ event whose generated electrons lie
within the kinematic acceptance, both of the electrons are associated with
reconstructed tracks that satisfy the track quality requirements, but not
necessarily the kinematic requirements. Its statistical precision is
propagated as a contribution to the systematic uncertainty.
This efficiency is checked in data using a tag-and-probe approach. One
electron is tagged using the standard requirements, and a search is made for
an accompanying cluster of electromagnetic energy having a high $E_{\rm T}$
and forming a high invariant mass with the tag electron. If such a cluster has
no associated track it provides evidence of a failure to reconstruct the other
electron. This sample contains significant background, which can be
discriminated by examining the $p_{\rm T}$ distribution of the tag electron
for cases where the photon candidate is and is not isolated. The $p_{\rm T}$
distribution of the electrons in signal events in data displays a clear
shoulder extending to $\sim$ 45${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ while
that for background falls monotonically, as shown in Fig. 2. The number of
signal-like events in which a cluster is not associated with a track can be
used to estimate a tracking efficiency, and the ratio of efficiencies between
data and simulation is applied as a correction to the tracking efficiency. The
precision of the test is taken to define a systematic uncertainty, assumed to
be fully correlated between bins of rapidity and $\phi^{*}$.

Figure 2:  Distribution of $p_{\rm T}$ for the “tag” electron in cases where
an isolated cluster of energy of high $E_{\rm T}$ is found in the
electromagnetic calorimeter. This is fitted with two components obtained from
data, the $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ signal whose shape is
taken from those candidates where the cluster is associated with an identified
electron track, and background whose shape is obtained from candidates where
the cluster is not isolated.

  * •

The kinematic efficiency, $\epsilon_{\mathrm{kin}}$, represents the
probability that, in a $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ event
whose generated electrons lie within the kinematic acceptance and are
associated with reconstructed tracks, both tracks pass the kinematic selection
requirements $2<\eta<4.5$ and $\mbox{$p_{\rm
T}$}>20$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The efficiency is estimated
from simulation, with its statistical precision being treated as a
contribution to the systematic uncertainty.
This determination relies on a correct simulation, which can be tested using
data. For example, underestimation of the amount of material in the simulation
would cause a discrepancy between data and simulation in the $p_{\rm T}$
distributions of the electrons or the reconstructed mass spectrum shown in
Fig. 1. By comparing the shapes of the reconstructed mass spectrum and other
kinematic distributions in data with different simulation samples, a
systematic uncertainty on the momentum scale and hence on the kinematic
efficiency is assigned. This is combined with the statistical uncertainty
mentioned above, with the systematic contribution taken to be fully correlated
between bins of rapidity and $\phi^{*}$.

  * •

The PID efficiency, $\epsilon_{\mathrm{PID}}$, represents the probability
that, in a $\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ event with
reconstructed electron tracks satisfying the kinematic requirements, both
tracks fulfil the calorimeter energy requirements for identified electrons.
This includes the probability that the tracks are within the calorimeter
acceptance and have been successfully associated with calorimeter information.
Because of the acceptance contribution, the efficiency has a strong dependence
on the Z rapidity. This dependence is taken from simulation, while the overall
normalisation of the PID efficiency is estimated directly from data, using a
tag-and-probe method.
Starting from a sample which requires just one high $p_{\rm T}$ electron,
events are selected by applying the usual criteria except that only one of the
$\mathrm{e}^{+}$ and $\mathrm{e}^{-}$ (the “tag”) is required to pass the
calorimeter-based electron identification requirements. The other track is
used as a “probe” to test the PID efficiency. The requirement of only one
identified electron admits a significant level of background, which is
assessed similarly to the tracking efficiency by examining the $p_{\rm T}$
distribution of the tag or alternatively the $p_{\rm T}$ of the probe electron
or the invariant mass of the two particles. The size of the signal component
can be used to define the number of Z events which fail the PID, and hence to
determine the PID efficiency and its uncertainty.

A systematic uncertainty is also assigned to the same-sign background
subtraction. The assumption that same-sign $\mathrm{e}^{\pm}\mathrm{e}^{\pm}$
combinations model background in $\mathrm{e}^{+}\mathrm{e}^{-}$ events is
tested by selecting events which satisfy all criteria except that one of the
particles fails the calorimeter energy requirements. This sample should be
dominated by background, and shows an excess of $\sim$8% of opposite-sign
events over same-sign events. Accordingly a systematic uncertainty amounting
to 8% of the number of same-sign events is assigned to the measurements.

##  5 Results

Using the efficiencies described above, the event yields detailed in Table 2
and Eq. (2) separate cross-section measurements for the two data-taking
periods are obtained. Since these are in good agreement, the results are
combined using a weighted average, and assuming their uncertainties are fully
correlated apart from the statistical contribution and the uncertainty in the
trigger efficiency. Data sample II has a smaller integrated luminosity but a
higher and more precisely estimated trigger efficiency. The weighting of the
two samples is chosen to minimise the total uncertainty on the cross-section
integrated over Z rapidity. The values of the differential cross-sections
obtained are given in Table 2. Correlation matrices may be found in the
Appendix. The bin $4.25<y_{\rm Z}<4.5$ is empty in data, and is expected to
have close to zero detection efficiency since the calorimeter acceptance
extends only slightly beyond 4.25. Hence no measurement is possible. However,
the QCD calculations discussed below predict a cross-section below
$\sim$0.01$\rm\,pb$ in this bin, which is negligibly small, so comparisons
with the Z$\rightarrow$ $\upmu^{+}\upmu^{-}$ results or with theoretical
calculations in the range $2<y_{\rm Z}<4.5$ are still meaningful.

The cross-section integrated over Z rapidity is obtained by summing the cross-
sections of all bins of $y_{\rm Z}$, taking the uncertainties associated with
the GEC and the luminosity to be fully correlated between bins, along with
parts of the tracking, kinematic and PID efficiencies, and treating the other
contributions as uncorrelated. The cross-section is measured to be

$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-})=76.0\pm 0.8\,(\mathrm{stat.})\pm
2.0\,(\mathrm{syst.})\pm 2.6\,(\mathrm{lumi.})\pm 0.4\,(\mathrm{FSR})\rm\,pb,$

where the first uncertainty is statistical, the second is the experimental
systematic uncertainty, the third is the luminosity uncertainty and the last
represents the uncertainty in the FSR correction. Since the results have been
corrected to the Born level using the factor $f_{\mathrm{FSR}}$, it is
possible to compare this measurement with that found in the Z$\rightarrow$
$\upmu^{+}\upmu^{-}$ analysis [2] using 37$\mbox{\,pb}^{-1}$ of data, namely
$76.7\pm 1.7\,(\mathrm{stat.})\pm 3.3\,(\mathrm{syst.})\pm
2.7\,(\mathrm{lumi.})$ pb. Accounting for correlated uncertainties, the ratio
of cross-sections is

$\frac{\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-})}{\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\upmu^{+}\upmu^{-})}=0.990\pm 0.024\,(\mathrm{stat.})\pm
0.044\,(\mathrm{syst.}).$

This may be regarded as a cross-check of the analyses. Assuming lepton
universality, the two cross-sections can be combined in a weighted average so
as to minimise the total uncertainty, yielding

$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\ell^{+}\ell^{-})=76.1\pm 0.7\,(\mathrm{stat.})\pm
1.8\,(\mathrm{syst.})\pm 2.7\,(\mathrm{lumi.})\pm 0.4\,(\mathrm{FSR})\rm\,pb.$

A recent measurement in $\rm Z\rightarrow\uptau^{+}\uptau^{-}$ decays which
has a larger statistical uncertainty [3] can also be combined with the
electron and muon channels, yielding

$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\ell^{+}\ell^{-})=75.4\pm 0.8\,(\mathrm{stat.})\pm
1.7\,(\mathrm{syst.})\pm 2.6\,(\mathrm{lumi.})\pm 0.4\,(\mathrm{FSR})\rm\,pb.$

Table 2: Event yields and measurements for the differential cross-section of
$\mathrm{p}\mathrm{p}\rightarrow\rm Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$
at $\sqrt{s}=$7 TeV as a function of Z rapidity, $y_{\rm Z}$, and of
$\phi^{*}$. The first uncertainty is statistical, the second and third are the
uncorrelated and correlated experimental systematic uncertainties
respectively, and the fourth is the uncertainty in the FSR correction. The
common luminosity uncertainty of 3.5% is not explicitly included here. The
results are given for the combined data sample. The right-hand column gives
the values used for the FSR correction factor.

$y_{\rm Z}$ | $N(\mathrm{e}^{+}\mathrm{e}^{-})$ | $N(\mathrm{e}^{\pm}\mathrm{e}^{\pm})$ | d$\sigma$/d$y_{\rm Z}$ [pb] | $f_{\mathrm{FSR}}$
---|---|---|---|---
2.00– | 2.25 | 988 | 40 | $13.6\pm 0.7\pm 0.4\pm 0.3\pm 0.1$ | $1.049\pm 0.004$
2.25– | 2.50 | 3064 | 121 | $39.4\pm 1.0\pm 0.6\pm 0.8\pm 0.2$ | $1.046\pm 0.002$
2.50– | 2.75 | 4582 | 202 | $56.7\pm 1.2\pm 0.7\pm 1.3\pm 0.3$ | $1.050\pm 0.002$
2.75– | 3.00 | 5076 | 214 | $63.2\pm 1.3\pm 0.8\pm 1.5\pm 0.3$ | $1.049\pm 0.002$
3.00– | 3.25 | 4223 | 181 | $59.9\pm 1.4\pm 0.8\pm 1.6\pm 0.3$ | $1.056\pm 0.002$
3.25– | 3.50 | 2429 | 135 | $43.8\pm 1.3\pm 0.8\pm 1.1\pm 0.2$ | $1.054\pm 0.003$
3.50– | 3.75 | 906 | 61 | $20.5\pm 1.0\pm 0.7\pm 0.6\pm 0.1$ | $1.030\pm 0.006$
3.75– | 4.00 | 143 | 18 | $5.9\pm 0.8\pm 0.5\pm 0.3\pm 0.1$ | $1.074\pm 0.029$
4.00– | 4.25 | 9 | 2 | $0.66\pm 0.44\pm 0.30\pm 0.04\pm 0.02$ | $1.074\pm 0.029$
4.25– | 4.50 | 0 | 0 | — |

$\phi^{*}$ | $N(\mathrm{e}^{+}\mathrm{e}^{-})$ | $N(\mathrm{e}^{\pm}\mathrm{e}^{\pm})$ | d$\sigma$/d$\phi^{*}$ [pb] | $f_{\mathrm{FSR}}$
---|---|---|---|---
0.00– | 0.05 | 9696 | 363 | $693\pm 10\pm 6\pm 17\pm 3$ | $1.059\pm 0.001$
0.05– | 0.10 | 4787 | 219 | $326\pm 7\pm 4\pm 8\pm 2$ | $1.047\pm 0.002$
0.10– | 0.15 | 2382 | 115 | $164\pm 5\pm 3\pm 4\pm 1$ | $1.039\pm 0.002$
0.15– | 0.20 | 1384 | 80 | $99.1\pm 4.0\pm 2.0\pm 2.2\pm 0.5$ | $1.043\pm 0.003$
0.20– | 0.30 | 1434 | 82 | $49.6\pm 2.0\pm 1.1\pm 1.0\pm 0.3$ | $1.042\pm 0.003$
0.30– | 0.40 | 707 | 39 | $25.5\pm 1.4\pm 0.8\pm 0.6\pm 0.1$ | $1.049\pm 0.004$
0.40– | 0.60 | 583 | 41 | $10.8\pm 0.7\pm 0.4\pm 0.3\pm 0.1$ | $1.052\pm 0.005$
0.60– | 0.80 | 217 | 13 | $4.05\pm 0.38\pm 0.20\pm 0.09\pm 0.03$ | $1.054\pm 0.005$
0.80– | 1.00 | 91 | 9 | $1.41\pm 0.23\pm 0.11\pm 0.03\pm 0.02$ | $1.051\pm 0.009$
1.00– | 2.00 | 119 | 9 | $0.41\pm 0.06\pm 0.03\pm 0.01\pm 0.02$ | $1.035\pm 0.011$

The results may be compared with theoretical calculations similar to those
used in the interpretation of the $\rm Z\rightarrow\upmu^{+}\upmu^{-}$
analysis [2]. These calculations are performed at NNLO (${\cal
O}(\alpha_{\scriptscriptstyle S}^{2})$) with the program FEWZ [18] version
2.1.1 and using the NNLO PDF sets of MSTW08 [19], NNPDF21 [20] or CTEQ (CT10
NNLO) [21, *Nadolsky:2012ia]. In Fig. 3 we present the measured cross-section
and in Fig. 4(a) the measurements of the Z rapidity distribution, compared in
each case with the three calculations. The uncertainties in the predictions
include the effect of varying the renormalisation and factorisation scales by
factors of two around the nominal value, which is set to the Z mass, combined
in quadrature with the PDF uncertainties at 68% confidence level. The data
agree with expectations within the uncertainties.

Figure 3: Cross-section for $\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ measured in LHCb, shown as the
yellow band. The inner (darker) band represents the statistical uncertainty
and the outer the total uncertainty. The measurement corresponds to the
kinematic acceptance, $\mbox{$p_{\rm
T}$}>20$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2<\eta<4.5$ for the
leptons and $60<M<120$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ for the
dilepton. The points show the various theoretical predictions with their
uncertainties as described in the text.

The differential cross-section as a function of $\phi^{*}$ is shown in Fig.
4(b), compared with the predictions of QCD to NNLO. Figure 5(a) displays the
ratios of these predictions to the measurements. The NNLO calculations tend to
overestimate the data at low $\phi^{*}$ and to underestimate the data at high
$\phi^{*}$. It is expected that the $\phi^{*}$ distribution, like that of
$p_{\rm T}$, is significantly affected by multiple soft gluon emissions, which
are not sufficiently accounted for in fixed order calculations. A QCD
calculation which takes this into account through resummation is provided by
Resbos [23, *Balazs:1997xd, *Landry:2002ix].222The P branch of Resbos is used
with grids for LHC at $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ based on
CTEQ6.6. Another resummed calculation [26] has been compared with ATLAS data
[27] in the central region of rapidity, but is not yet available for the LHCb
acceptance. Alternatively, Powheg [28, *Alioli:2010qp] provides a framework
whereby a NLO QCD (${\cal O}(\alpha_{\scriptscriptstyle S})$) calculation can
be interfaced to a parton shower model such as Pythia which can approximate
higher order effects. Comparisons with these models, and with the LHCb version
[9] of Pythia [8] are shown in Fig. 5(b). The Resbos and Powheg distributions
are normalised to their own cross-section predictions, while the Pythia
distribution is normalised to the cross-section measured in data. It is seen
that Resbos gives a reasonable description of the $\phi^{*}$ distribution.
Powheg shows that the combination of a parton shower with the ${\cal
O}(\alpha_{\scriptscriptstyle S})$ QCD prediction significantly improves the
description of data in the low $\phi^{*}$ region, while in the high $\phi^{*}$
region the data are still underestimated. Pythia models the data reasonably
well. Overall, Resbos and Pythia seem to be the more successful of the
calculation schemes considered here.

Figure 4:  Differential cross-section for $\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ as a function of (a) Z rapidity and
(b) $\phi^{*}$. The measurements based on the
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ LHCb data are shown as the yellow
bands where the inner (darker) band represents the statistical uncertainty and
the outer the total uncertainty. NNLO QCD predictions are shown as points with
error bars reflecting their uncertainties as described in the text.

Figure 5:  Ratios of various QCD calculations to data for the differential
cross-section for $\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ as a function of $\phi^{*}$. The
measurements based on the $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ LHCb data
are shown as the yellow band centred at unity where the inner (darker) band
represents the statistical uncertainty and the outer the total uncertainty.
(a) NNLO QCD predictions shown as points with error bars reflecting their
uncertainties as described in the text. Small lateral displacements of the
theory points are made to improve clarity. (b) Ratios of the predictions of
Pythia, Resbos and Powheg to the data shown as points, with error bars that
reflect the statistical uncertainties in the predictions. For most points,
these errors are so small that they are not visible.

##  6 Summary

A measurement of the $\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ cross-section in pp collisions at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ using 0.94$\mbox{\,fb}^{-1}$ of
data recorded by LHCb is presented. Although the characteristics of the LHCb
detector prevent a sharp mass peak from being seen, a clean sample of events
is identified with less than 5% background. Within the kinematic acceptance,
$\mbox{$p_{\rm T}$}>20$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2<\eta<4.5$
for the leptons and $60<M<120$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ for
the dielectron, the cross-section is measured to be

$\sigma(\mathrm{p}\mathrm{p}\rightarrow\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-})=76.0\pm 0.8\,(\mathrm{stat.})\pm
2.0\,(\mathrm{syst.})\pm 2.6\,(\mathrm{lumi.})\pm 0.4\,(\mathrm{FSR})\rm\,pb.$

The cross-section is also measured in bins of the rapidity of the Z and of the
angular variable $\phi^{*}$. The measurements of the rapidity distribution and
of the integrated cross-sections are consistent with previous measurements
using Z decays to $\upmu^{+}\upmu^{-}$ and $\uptau^{+}\uptau^{-}$ and show
good agreement with the expectations from NNLO QCD calculations. The
$\phi^{*}$ distribution, related to the Z $p_{\rm T}$ distribution, is better
modelled by calculations which approximately include the effects of higher
orders.

## 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); ANCS/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.

## Appendix

Table A.1: Correlation coefficients for the differential cross-section of $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ at 7 TeV between bins of Z rapidity,
$y_{\rm Z}$. Both statistical and systematic contributions are included.

$y_{\rm Z}$ bin | 2.–2.25 | 2.25–2.5 | 2.5–2.75 | 2.75–3. | 3.–3.25 | 3.25–3.5 | 3.5–3.75 | 3.75–4. | 4.–4.25
---|---|---|---|---|---|---|---|---|---
2.00– | 2.25 | 1 |  |  |  |  |  |  |  |
2.25– | 2.50 | 0.47 | 1 |  |  |  |  |  |  |
2.50– | 2.75 | 0.50 | 0.70 | 1 |  |  |  |  |  |
2.75– | 3.00 | 0.51 | 0.70 | 0.75 | 1 |  |  |  |  |
3.00– | 3.25 | 0.50 | 0.69 | 0.74 | 0.75 | 1 |  |  |  |
3.25– | 3.50 | 0.45 | 0.62 | 0.66 | 0.67 | 0.66 | 1 |  |  |
3.50– | 3.75 | 0.35 | 0.49 | 0.52 | 0.52 | 0.51 | 0.46 | 1 |  |
3.75– | 4.00 | 0.20 | 0.27 | 0.29 | 0.29 | 0.29 | 0.26 | 0.20 | 1 |
4.00– | 4.25 | 0.05 | 0.07 | 0.08 | 0.08 | 0.08 | 0.07 | 0.06 | 0.03 | 1

Table A.2: Correlation coefficients for the differential cross-section of $\rm
Z\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ at 7 TeV between bins of $\phi^{*}$.
Both statistical and systematic contributions are included.

$\phi^{*}$ bin | 0.–0.05 | 0.05–0.1 | 0.1–0.15 | 0.15–0.2 | 0.2–0.3 | 0.3–0.4 | 0.4–0.6 | 0.6–0.8 | 0.8–1. | 1.–2.
---|---|---|---|---|---|---|---|---|---|---
0.00– | 0.05 | 1 |  |  |  |  |  |  |  |  |
0.05– | 0.10 | 0.80 | 1 |  |  |  |  |  |  |  |
0.10– | 0.15 | 0.73 | 0.67 | 1 |  |  |  |  |  |  |
0.15– | 0.20 | 0.63 | 0.58 | 0.53 | 1 |  |  |  |  |  |
0.20– | 0.30 | 0.62 | 0.58 | 0.53 | 0.45 | 1 |  |  |  |  |
0.30– | 0.40 | 0.51 | 0.48 | 0.43 | 0.38 | 0.38 | 1 |  |  |  |
0.40– | 0.60 | 0.46 | 0.43 | 0.39 | 0.34 | 0.34 | 0.28 | 1 |  |  |
0.60– | 0.80 | 0.34 | 0.31 | 0.29 | 0.25 | 0.25 | 0.20 | 0.18 | 1 |  |
0.80– | 1.00 | 0.21 | 0.20 | 0.18 | 0.16 | 0.15 | 0.13 | 0.11 | 0.08 | 1 |
1.00– | 2.00 | 0.23 | 0.21 | 0.19 | 0.17 | 0.17 | 0.14 | 0.12 | 0.09 | 0.06 | 1

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