EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-305 LHCb-PAPER-2012-026 October 15, 2012

Measurement of the $D^{\pm}$ production asymmetry in
7$\mathrm{\,Te\kern-2.07413ptV}$ $pp$ collisions

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

The asymmetry in the production cross-section $\sigma$ of $D^{\pm}$ mesons,

$A_{\mathrm{P}}=\frac{\sigma(D^{+})-\sigma(D^{-})}{\sigma(D^{+})+\sigma(D^{-})},$

is measured in bins of pseudorapidity $\eta$ and transverse momentum $p_{\rm
T}$ within the acceptance of the LHCb detector. The result is obtained with a
sample of $D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ decays
corresponding to an integrated luminosity of 1.0$\mbox{\,fb}^{-1}$, collected
in $pp$ collisions at a centre of mass energy of
7$\mathrm{\,Te\kern-1.00006ptV}$ at the Large Hadron Collider. When integrated
over the kinematic range $2.0<\mbox{$p_{\rm
T}$}<18.0$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.20<\eta<4.75$, the
production asymmetry is $A_{\mathrm{P}}=(-0.96\pm 0.26\pm 0.18)\%$. The
uncertainties quoted are statistical and systematic, respectively. The result
assumes that any direct $C\\!P$ violation in the $D^{+}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ decay is negligible. No significant
dependence on $\eta$ or $p_{\rm T}$ is observed.

Submitted to Physics Letters B

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,
S. Amato2, Y. Amhis36, L. Anderlini17,f, J. Anderson37, R.B. Appleby51, O.
Aquines Gutierrez10, F. Archilli18,35, A. Artamonov 32, M. Artuso53, E.
Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, C. Baesso54, 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. Borghi48,51, A. Borgia53, T.J.V.
Bowcock49, 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. Contu52,15, 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 Capua21,k, M. De Cian37, J.M. De Miranda1, L. De
Paula2, 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, U. Egede50, V. Egorychev28, S. Eidelman31, D. van Eijk38,
S. Eisenhardt47, R. Ekelhof9, L. Eklund48, I. El Rifai5, Ch. Elsasser37, D.
Elsby42, A. Falabella14,e, C. Färber11, G. Fardell47, C. Farinelli38, S.
Farry12, V. Fave36, 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, A.
Gallas Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y. Gao3, J-C.
Garnier35, J. Garofoli53, P. Garosi51, J. Garra Tico44, L. Garrido33, C.
Gaspar35, R. Gauld52, E. Gersabeck11, M. Gersabeck35, T. Gershon45,35, Ph.
Ghez4, V. Gibson44, V.V. Gligorov35, C. Göbel54, D. Golubkov28, A.
Golutvin50,28,35, A. Gomes2, H. Gordon52, M. Grabalosa Gándara33, 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, P. Hopchev4, W. Hulsbergen38, P. Hunt52, T.
Huse49, N. Hussain52, D. Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12,
J. Imong43, R. Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E. Jans38, F.
Jansen38, P. Jaton36, B. Jean-Marie7, 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, Y.M. Kim47,
O. Kochebina7, V. 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, T.
Lesiak23, 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, J. Magnin1, M. Maino20, 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 Santos35, A. Massafferri1, R. Matev35,
Z. Mathe35, C. Matteuzzi20, M. Matveev27, E. Maurice6, A. Mazurov16,30,35,e,
J. McCarthy42, G. McGregor51, R. McNulty12, M. Meissner11, M. Merk38, J.
Merkel9, 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, J. Mylroie-Smith49, 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, N.
Nikitin29, T. Nikodem11, A. Nomerotski52,35, 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, 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. Qian3, 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. Rodrigues48,51,
P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35, V. Romanovsky32, A. Romero
Vidal34, J. Rouvinet36, T. Ruf35, H. Ruiz33, G. Sabatino21,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, R.
Santinelli35, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m,
A. Satta21, M. Savrie16,e, 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, 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. Storaci38, M. Straticiuc26, U.
Straumann37, V.K. Subbiah35, S. Swientek9, 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, 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, I.
Videau7, D. Vieira2, X. Vilasis-Cardona33,n, J. Visniakov34, A. Vollhardt37,
D. Volyanskyy10, D. Voong43, A. Vorobyev27, V. Vorobyev31, H. Voss10, C.
Voß55, 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. Witek23,35, W. Witzeling35, S.A. Wotton44, S.
Wright44, S. Wu3, K. Wyllie35, Y. Xie47, 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, 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

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 Large Hadron Collider (LHC) offers an excellent opportunity to study heavy
flavour physics. The rate of production of $c\overline{}c$ and $b\overline{}b$
pairs is substantial in the forward region close to the beam direction. The
associated cross-sections were measured at the LHCb experiment in the forward
region to be $\sigma_{c\overline{}c}=1230\pm 190$$\rm\,\upmu b$ and
$\sigma_{b\overline{}b}=74\pm 14$$\rm\,\upmu b$ at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ [1, 2].

Direct production of $c\overline{}c$ pairs at the LHC occurs almost entirely
via QCD and electroweak processes that do not discriminate between $c$ and
$\overline{}c$ quarks. However, in hadronization the symmetry is broken by the
presence of valence quarks, which introduce several processes that distinguish
between $c$ and $\overline{}c$ quarks [3, 4, 5]. For example, a $c$ quark
could couple to valence quarks to form a charmed baryon, leaving an excess of
$\overline{}c$ quarks. These would hadronize to create an excess of $D^{-}$
mesons over $D^{+}$ mesons. Furthermore, the kinematic distributions of
charmed hadrons and their antiparticles can differ, introducing production
asymmetries in local kinematic regions. Analogous production asymmetries in
the strange sector are well-established at the LHC, and are seen to be large
at high rapidity [6]. However, no evidence for a $D^{+}_{s}$ production
asymmetry was found in a recent study [7].

Searches for $C\\!P$ violation (CPV) in charmed hadron decays can be used to
probe for evidence of physics beyond the Standard Model [8]. Direct CPV is
measured using time-integrated observables, and is of particular interest
following evidence for CPV in two-body $D^{0}$ decays reported by LHCb [9] and
subsequently by CDF [10]. In order to understand the origin of this effect,
more precise measurements of $C\\!P$ asymmetries in a suite of decay modes are
required. Production asymmetries have the same experimental signature as
direct CPV effects and are potentially much larger than the $C\\!P$
asymmetries to be determined. This problem can sometimes be avoided by taking
the difference in asymmetry between two decay modes with a common production
asymmetry [9] or by studying the difference in kinematic distributions of
multi-body decays [11]. However, these methods result in a reduction in
statistical power and are not applicable to all final states. It is therefore
important to measure production asymmetries directly.

In this Letter, the $D^{\pm}$ production asymmetry, defined as

$A_{\mathrm{P}}=\frac{\sigma(D^{+})-\sigma(D^{-})}{\sigma(D^{+})+\sigma(D^{-})},$
(1)

for cross sections $\sigma(D^{\pm})$, is determined with a sample of
$D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$,
$K^{0}_{\rm\scriptscriptstyle S}\rightarrow\pi^{+}\pi^{-}$ decays.111Charge
conjugate decays are implied throughout this letter unless stated otherwise.
As there are no charged kaons in the final state, the detector biases in this
decay are simpler to understand than those in other $D^{+}$ decays with higher
branching fractions. The $K^{0}_{\rm\scriptscriptstyle S}$, a pseudoscalar
particle, has a charge-symmetric decay, and the charge asymmetry in the pion
efficiency at LHCb has been measured previously for the 2011 data sample [7].
However, there is the possibility of CPV in the decay. The expected CPV in the
$D^{+}$ decay, due to the interference of the Cabibbo-favoured and doubly
Cabibbo-suppressed amplitudes, is defined by the charge asymmetry in the
partial widths $\Gamma(D^{\pm})$,

$A_{CP}=\frac{\Gamma(D^{+})-\Gamma(D^{-})}{\Gamma(D^{+})+\Gamma(D^{-})}.$ (2)

$A_{CP}$ is negligible in the Standard Model: a simple consideration of the
CKM matrix leads to a value of at most $1\times 10^{-4}$ depending on the
strong phase difference between the two amplitudes [12]. Since both amplitudes
are at tree level, no enhancement of CPV due to new physics is expected. The
current world-best measurement of $A_{CP}$, by the Belle collaboration, is
consistent with zero: $(0.024\pm 0.094\pm 0.067)\%$ [13,
*PhysRevLett.109.119903]. On the other hand, CPV in the neutral kaon system
induces an asymmetry which must be considered. This will be discussed further
in Sect. 5.

##  2 Detector description

The LHCb detector [15] 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 of reversible polarity 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${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and an impact parameter (IP)
resolution of 20$\,\upmu\rm m$ for tracks with high transverse momentum
$p_{\rm T}$. 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 and pre-shower detectors,
an electromagnetic calorimeter and a hadronic calorimeter. Muons are
identified by a system composed of alternating layers of iron and multiwire
proportional chambers. The trigger consists of a hardware stage, based on
information from the calorimeter and muon systems, an inclusive software
stage, which uses the tracking system, and a second software stage that
exploits the full event information.

##  3 Dataset and selection

The data sample used in this analysis corresponds to 1.0$\mbox{\,fb}^{-1}$ of
$pp$ collisions taken at a centre of mass energy of
$7$$\mathrm{\,Te\kern-1.00006ptV}$ at the Large Hadron Collider in 2011. The
polarity of the LHCb magnetic field was changed several times during the run,
and approximately half of the data were taken with each polarity, referred to
as ‘magnet-up’ and ‘magnet-down’ data hereafter. To optimise the event
selection and estimate efficiencies, 12.5 million $pp$ collision events
containing $D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$,
$K^{0}_{\rm\scriptscriptstyle S}\rightarrow\pi^{-}\pi^{+}$ decays were
simulated with Pythia 6.4 [16] with a specific LHCb configuration [17]. Decays
of hadronic particles are described by EvtGen [18]. The interactions of the
generated particles with the detector and its response are implemented using
the Geant4 toolkit [19, *Agostinelli:2002hh] as described in Ref. [21].

Pairs of oppositely charged tracks with a pion mass hypothesis are combined to
form $K^{0}_{\rm\scriptscriptstyle S}$ candidates. Only those
$K^{0}_{\rm\scriptscriptstyle S}$ candidates with $\mbox{$p_{\rm
T}$}>700$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ and invariant mass within
35${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the nominal value [22] are
retained. Surviving candidates are then combined with a third charged track,
the bachelor pion, to form a $D^{+}$ candidate, with the mass of the
$K^{0}_{\rm\scriptscriptstyle S}$ candidate constrained to its nominal value
in a kinematic fit. Each of the three pion tracks must be detected in the
VELO, so only those $K^{0}_{\rm\scriptscriptstyle S}$ mesons that decay well
within the VELO are used. This creates a bias towards short
$K^{0}_{\rm\scriptscriptstyle S}$ decay times. Both the
$K^{0}_{\rm\scriptscriptstyle S}$ and $D^{+}$ candidates are required to have
acceptable vertex fit quality.

Further requirements are applied in order to reduce the background and to
align the selection of bachelor pions with the dataset used to determine the
charge asymmetry in the tracking efficiency (see Sect. 6). The daughters of
the $K^{0}_{\rm\scriptscriptstyle S}$ must have
$p>2$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $\mbox{$p_{\rm
T}$}>250$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. Impact parameter requirements
are used to ensure that both the $K^{0}_{\rm\scriptscriptstyle S}$ candidate
and its daughter tracks do not originate at any primary vertex (PV) in the
event, and the $K^{0}_{\rm\scriptscriptstyle S}$ decay vertex must be at least
10$\rm\,mm$ downstream of the PV with which it is associated. The bachelor
pion must have $p>5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $\mbox{$p_{\rm
T}$}>500$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, be positively identified as a
pion rather than as a kaon, electron or muon, and must not come from any PV.
In addition, fiducial requirements are applied as in Ref. [9] to exclude
regions with large tracking efficiency asymmetry. All three tracks must have
an acceptable track fit quality. The $D^{+}$ candidate is required to have
$\mbox{$p_{\rm T}$}>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, to point to a PV
(suppressing $D$ from $B$ decays), and to have a decay time significantly
greater than zero. After these criteria are applied, the remaining background
is mostly from random combinations of tracks. The invariant mass distribution
of selected candidates is shown in Fig. 1.

Figure 1:  Mass distribution of selected $K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}$ candidates. The data are represented by symbols with error bars.
The dashed curves indicate the signal and the $D^{+}_{s}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ decays, the lower solid line
represents the background shape, and the upper solid line shows the sum of all
fit components.

In selected events, a trigger decision may be based on part or all of the
$D^{+}$ signal candidate, on other particles in the event, or both. The second
stage of the software trigger is required to find a fully reconstructed
candidate which meets the criteria to be a signal $D^{+}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ decay. To control potential charge
asymmetries introduced by the hardware trigger, two possibilities, not
mutually exclusive, are allowed. The hardware trigger decision must be based
on one or both of the $K^{0}_{\rm\scriptscriptstyle S}$ daughter tracks, or on
a particle other than the decay products of the $D^{+}$ candidate. In both
cases, the inclusive software trigger must make a decision based on one of the
three tracks that form the $D^{+}$. For the first case, it is explicitly
required that the same track activated the hardware trigger, and therefore
this is independent of the $D^{+}$ charge. The second possibility does not
depend directly on the $D^{+}$ charge, but an indirect dependence could be
introduced if the probability for particles produced in association with the
signal candidate to activate the trigger differs between $D^{+}$ and $D^{-}$.
This will be discussed further in Sect. 7. After applying the selection and
trigger requirements, 1,031,068 $K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$
candidates remain.

##  4 Yield determination

Figure 2:  Background-subtracted distribution of transverse momenta $p_{\rm
T}$ versus pseudorapidity $\eta$ for selected $D^{+}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ candidates in a signal region of
$1845<m<1890$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The bin marked with
an asterisk is excluded from the weighted average over the production
asymmetries in the bins used to obtain the final result.

The signal yields are measured in 48 bins of $p_{\rm T}$ and $\eta$ using
binned likelihood fits to the distribution of the
$K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ mass $m$. The bins are shown in Fig.
2. The shapes of the $D^{+}_{(s)}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}$ mass peaks are described by ‘Cruijff’ functions [23],

$f(m)\propto\exp\left(\frac{-(m-\mu)^{2}}{2\sigma_{L,R}^{2}+(m-\mu)^{2}\alpha_{L,R}}\right)$
(3)

with the measured masses defined by the free parameter $\mu$, the widths by
$\sigma_{L}$ and $\sigma_{R}$, and the tails by $\alpha_{L}$ and $\alpha_{R}$.
The parameters $\alpha_{L}$ and $\sigma_{L}$ are used for $m<\mu$ and
$\alpha_{R}$ and $\sigma_{R}$ for $m>\mu$. The background is fitted with a
straight line plus an additional Gaussian component to account for background
from $D^{+}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}\pi^{0}$
decays. The yield of the latter is consistent with zero in most $p_{\rm T}$,
$\eta$ bins. The fit is performed simultaneously over four subsamples ($D^{+}$
magnet-up, $D^{+}$ magnet-down, $D^{-}$ magnet-up, and $D^{-}$ magnet-down
data) with the masses and yields of the $D^{\pm}_{(s)}$, and the yield of
background, allowed to vary independently in the four subsamples. All other
parameters are shared. The charge asymmetries are then determined from the
yields. The results are cross-checked with a sideband subtraction procedure
under the assumption of a linear background.

##  5 Effect of _CP_ violation in the neutral kaon system

$C\\!P$ violation in the neutral kaon system can affect the observed asymmetry
in the $D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ decay [24].
The bias on $A_{\mathrm{P}}$ due to the CPV depends on the decay time
acceptance $F(t)$ of the $K^{0}_{\rm\scriptscriptstyle S}$ meson, according to

$A_{\epsilon}\sim
2\Re(\epsilon)\left[1-\frac{\int_{0}^{\infty}F(t)e^{-\frac{1}{2}(\Gamma_{\mathrm{S}}+\Gamma_{\mathrm{L}})t}\left(\cos\Delta
mt-\frac{\Im(\epsilon)}{\Re(\epsilon)}\sin\Delta
mt\right)dt}{\int_{0}^{\infty}F(t)e^{-\Gamma_{\mathrm{S}}t}dt}\right],$ (4)

where $\epsilon$ parameterises the indirect CPV in neutral kaon mixing,
$\Gamma_{\mathrm{S}}$ and $\Gamma_{\mathrm{L}}$ are the decay widths of the
$K^{0}_{\rm\scriptscriptstyle S}$ and $K^{0}_{\rm\scriptscriptstyle L}$
respectively, and $\Delta m$ is their mass difference [25, 26]. Direct CPV and
terms of order $\epsilon^{2}$ are neglected. To determine the decay time
acceptance, the $K^{0}_{\rm\scriptscriptstyle S}$ decay time is fitted with an
empirical function shown in Fig. 3. All of the $K^{0}_{\rm\scriptscriptstyle
S}$ candidates used in this analysis decay inside the VELO with an average
measured lifetime of $6.97\pm 0.02$ ps, which is much shorter than the nominal
$K^{0}_{\rm\scriptscriptstyle S}$ lifetime of 89.5 ps. Using
$\Re(\epsilon)=1.65\times 10^{-3}$ [22] in Eq. 4, we obtain
$A_{\epsilon}=(2.831^{+0.003}_{-0.004})\times 10^{-4}$ for the CPV in the
neutral kaon system, where the uncertainty quoted is statistical only. This
value is subtracted from the measured production asymmetry and a systematic
uncertainty equal to its central value is assigned.

Figure 3:  Observed $K^{0}_{\rm\scriptscriptstyle S}$ decay time distribution
within the LHCb acceptance. The data points are fitted with an empirical
function (solid curve). This contains a component for the upper decay time
acceptance, due mainly to the requirement that the
$K^{0}_{\rm\scriptscriptstyle S}$ decays inside the VELO (dashed curve) and a
component for the lower decay time acceptance, due to the selection cuts
(dotted curve). These are shown scaled by arbitrary factors. The CPV is not
sensitive to the fine details of the distribution, so the fit quality is not
important.

##  6 Results

In order to convert the measured charge asymmetries in the 48 bins of $p_{\rm
T}$ and $\eta$ into production asymmetries, a correction for the asymmetry in
the pion reconstruction efficiency is made. This asymmetry was evaluated
previously in eight bins of pion azimuthal angle $\phi$ and two bins of pion
momentum with a control sample of $D^{*+}\rightarrow D^{0}\pi^{+}$,
$D^{0}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{+}$ decays in the same dataset [7].
The average efficiency asymmetry ratios
$\epsilon_{\pi^{+}}/\epsilon_{\pi^{-}}$ in that sample were found to be
$0.9914\pm 0.0040$ for magnet-up data and $1.0045\pm 0.0034$ for magnet-down
data.

After the correction is applied, the resulting asymmetries for magnet-up and
magnet-down data in each $D^{+}$ $p_{\rm T}$ and $\eta$ bin are averaged with
equal weights to obtain the production asymmetries in two-dimensional bins of
$p_{\rm T}$ and $\eta$, given in Table 6. Any left-right asymmetries that
differ between the signal $D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}$ decay and the $D^{0}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{+}$ control
channel will cancel in this average.

Figure 4: Production asymmetry as a function of (a) transverse momentum
$p_{\rm T}$ and (b) pseudorapidity $\eta$. The straight line fits have slopes
of $(0.09\pm 0.07)\times 10^{-2}$ (${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$)-1
and $(-0.36\pm 0.28)$%, and values of $\chi^{2}$ per degree of freedom of
$5.5/6$ and $2.2/4$, respectively. The error bars include only the statistical
uncertainty on the $D^{+}$ signal sample and are uncorrelated within a given
plot.

Reconstruction and selection efficiencies from the simulation are used to
calculate binned efficiency-corrected yields. These are used to weight the
production asymmetries in the average over the $p_{\rm T}$ and $\eta$ bins.
The result is an asymmetry for $D^{+}$ produced in the LHCb acceptance. The
same weighting technique is applied to obtain production asymmetries as one-
dimensional functions of $p_{\rm T}$ and $\eta$. The bin marked with an
asterisk in Fig. 2 has a high cross section but is mostly outside the
acceptance and so it is excluded from the average. After subtracting the
contribution from CPV in the kaon system, the production asymmetry is
$(-0.96\pm 0.19\pm 0.18)$%. The uncertainties are the statistical errors on
the $D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ yields and that
due to the tagged $D^{0}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{+}$ sample used to
calculate the pion efficiencies. Summing these in quadrature, we obtain

$A_{\mathrm{P}}=\left(-0.96\pm 0.26\,(\mathrm{stat.})\right)\%.$

The production asymmetry as a function of $p_{\rm T}$ and $\eta$ is given in
Fig. 4. No significant dependence of the asymmetry on these variables is
observed. As a cross-check, the average production asymmetry is calculated for
magnet-up and magnet-down data separately, and found to be fully consistent:
$(-1.07\pm 0.41)\%$ and $(-0.85\pm 0.34)\%$, respectively.

Table 1:  Production asymmetry for $D^{+}$ mesons, in percent, in
$(\mbox{$p_{\rm T}$},\eta)$ bins, for $2.0<\mbox{$p_{\rm
T}$}<18.0$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $2.20<\eta<4.75$. The
uncertainties shown are statistical only; the systematic uncertainty is
$0.17\%$ (see Table 2).

| $\eta$
---|---
$p_{\rm T}$ (${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$) | $(2.20,2.80)$ | $(2.80,3.00)$ | $(3.00,3.25)$ | $(3.25,3.50)$ | $(3.50,3.80)$ | $(3.80,4.75)$
$(2.00,3.20)$ | $-0.0\pm 2.5$ | $-2.2\pm 1.2$ | $-0.4\pm 0.8$ | $-0.4\pm 0.7$ | $-1.2\pm 0.6$ | $-1.2\pm 0.5$
$(3.20,4.00)$ | $-0.4\pm 0.9$ | $-0.4\pm 0.7$ | $-0.4\pm 0.5$ | $-1.1\pm 0.5$ | $+0.1\pm 0.5$ | $-1.2\pm 0.5$
$(4.00,4.55)$ | $+0.1\pm 0.8$ | $-1.0\pm 0.8$ | $-1.3\pm 0.6$ | $-2.0\pm 0.6$ | $-0.1\pm 0.6$ | $-2.1\pm 0.7$
$(4.55,5.20)$ | $-1.6\pm 0.7$ | $-0.6\pm 0.8$ | $-0.5\pm 0.6$ | $-0.7\pm 0.6$ | $-1.6\pm 0.6$ | $-2.0\pm 0.8$
$(5.20,6.00)$ | $-0.5\pm 0.7$ | $-0.8\pm 0.8$ | $+0.2\pm 0.7$ | $-0.3\pm 0.7$ | $-0.6\pm 0.7$ | $-1.2\pm 0.9$
$(6.00,7.00)$ | $-1.4\pm 0.8$ | $+0.5\pm 1.0$ | $-0.9\pm 0.9$ | $-0.6\pm 0.9$ | $-0.7\pm 0.9$ | $-1.6\pm 1.2$
$(7.00,9.50)$ | $-0.4\pm 0.8$ | $-0.4\pm 1.1$ | $-0.2\pm 1.1$ | $+1.7\pm 1.1$ | $-1.4\pm 1.1$ | $+1.2\pm 1.4$
$(9.50,18.00)$ | $-0.6\pm 1.3$ | $+1.8\pm 2.3$ | $-2.5\pm 2.2$ | $+1.8\pm 2.4$ | $+1.1\pm 2.5$ | $\phantom{0}\mathord{-}7\pm 11$

##  7 Systematic uncertainties

The sources of systematic uncertainty are summarised in Table 2. The dominant
uncertainty of $1.5\times 10^{-3}$ is due to asymmetries introduced by the
trigger. Events which are triggered independently of the signal decay, i.e. by
a track that does not form part of the signal candidate, could be triggered by
particles produced in association with the $D^{+}$ meson. If this occurs, the
asymmetry in this sample would be correlated with the production asymmetry,
and would bias the measurement of it. This was studied with a control sample
of the abundant $D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ decay. To mimic the
charge-unbiased sample of $D^{+}\rightarrow K^{0}_{\rm\scriptscriptstyle
S}\pi^{+}$ decays which are triggered by a $K^{0}_{\rm\scriptscriptstyle S}$
daughter, we choose the kaon and one pion at random and require that the
trigger decision is based on one of these tracks. This is close to being
charge-symmetric between $D^{+}$ and $D^{-}$ candidates, with some residual
effects due to differences in material interaction between $K^{+}$ and $K^{-}$
mesons. The raw asymmetry in this subsample of $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$ decays is then compared to that in the much larger sample
of candidates that are triggered independently of the signal decay. The
difference in raw charge asymmetry between these two samples, $(1.5\pm
0.4)\times 10^{-3}$, is a measure of the scale of the bias. Unlike the signal,
the $K^{-}\pi^{+}\pi^{+}$ decay also includes a component due to the
$K^{+}/K^{-}$ asymmetry, and therefore this is treated as a systematic
uncertainty rather than a correction. This is cross checked with other control
samples such as $D^{+}_{s}\rightarrow\phi\pi^{+}$ and the uncertainty is found
to be conservative.

Table 2: Summary of absolute values of systematic uncertainties on $A_{\mathrm{P}}$. For the binned production asymmetries given in Table 6, all uncertainties except that on the reconstruction efficiency apply, giving a combined systematic uncertainty of 0.17%.  Systematic effect | Uncertainty (%)
---|---
Trigger asymmetries | 0.15
$D$ from $B$ | 0.04
Selection criteria | 0.05
Running conditions | 0.04
Pion efficiency | 0.02
Fitting | 0.04
Kaon $C\\!P$ violation | 0.03
Weights (reconstruction efficiency) | 0.05
Total including uncertainty on weights | 0.18

Further systematic uncertainties arise from the contamination of the prompt
sample by $D$ candidates that originate from $B$ decays. The yield of these is
calculated using the measured cross-sections [1, 2], branching ratios, and
efficiencies determined from the simulation. The fraction of $D$ candidates
from $B$ decays is found to be $(1.2\pm 0.3)\%$. This quantity is combined
with the $B^{0}$ production asymmetry, which is estimated to be $(-1.0\pm
1.3)\%$ [27], to determine the systematic uncertainty.

Certain selection criteria differ between the $D^{+}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ signal sample and the
$D^{0}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{+}$ decays used to determine the
asymmetry in the pion efficiencies. The charge asymmetry is found to depend
weakly on the value of the requirement on the pion $p_{\rm T}$. Pions in the
signal sample must have $p_{\rm T}$
$>500$${\mathrm{\,Me\kern-0.90005ptV\\!/}c}$ while those in the control sample
must have $p_{\rm T}$ $>300$${\mathrm{\,Me\kern-0.90005ptV\\!/}c}$. A
systematic uncertainty is calculated by estimating the proportion of signal
candidates with $300<\mbox{$p_{\rm
T}$}<500$${\mathrm{\,Me\kern-0.90005ptV\\!/}c}$ and multiplying this fraction
by the difference between the charge asymmetries in the low $p_{\rm T}$ region
and the average.

The difference in signal yields per pb-1 of integrated luminosity between
magnet-up and magnet-down data is used to determine a systematic uncertainty
for changes in running conditions that could impair the cancellation of
detector asymmetries achieved by averaging over the magnet polarities. There
is also a systematic uncertainty on the pion efficiency asymmetry associated
with the determination of the yields of $D^{0}\rightarrow
K^{-}\pi^{+}\pi^{-}\pi^{+}$ decays. The error associated with the mass fit is
determined by comparing fitted and sideband-subtracted results. The CPV in the
neutral kaon decay, discussed in Sect. 5, is also included as a systematic
uncertainty.

Other systematic effects such as regeneration in the neutral kaon system [28],
second order effects due to the kinematic binning of the $D^{+}\rightarrow
K^{0}_{\rm\scriptscriptstyle S}\pi^{+}$ sample, and asymmetric backgrounds
such as that from $D^{+}_{s}\rightarrow K^{0}_{\rm\scriptscriptstyle S}K^{+}$
with the kaon misidentified as a pion, were considered but found to be
negligible. When taking the average asymmetry weighted by the efficiency-
corrected yield in each bin (Eq. 6), the limited number of simulated events
leads to an uncertainty on the reconstruction efficiency and hence on the per-
bin weights. This does not contribute to the uncertainty on the individual
asymmetries given in Table 6, which are calculated without using the
simulation. A quadratic sum yields an overall systematic uncertainty of
$1.8\times 10^{-3}$.

In principle, CPV in the charm decay could occur via the interference of
Cabibbo-favoured and doubly Cabibbo-suppressed amplitudes, but this is
strongly suppressed by the CKM matrix and no evidence for it has been observed
at the $B$-factories [29, 13]. If we allowed for the possibility of new
physics or large unexpected enhancements of the Standard Model CPV in these
tree-level $D^{+}$ decays, the uncertainty on the null result found at Belle
[13] would increase the total systematic uncertainty to $2.1\times 10^{-3}$.

##  8 Conclusions

Evidence for a charge asymmetry in the production of $D^{+}$ decays is
observed at LHCb. In the kinematic range $2.0<\mbox{$p_{\rm
T}$}<18.0$${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$ and $2.20<\eta<4.75$,
excluding the region with $2.0<\mbox{$p_{\rm
T}$}<3.2$${\mathrm{\,Ge\kern-0.90005ptV\\!/}c}$, $2.20<\eta<2.80$, the average
asymmetry is

$A_{\mathrm{P}}=(-0.96\pm 0.26\pm 0.18)\%,$

where the first uncertainty is statistical and the second is systematic. The
result is inconsistent with zero at approximately three standard deviations.
There is no evidence for a significant dependence on $p_{\rm T}$ or
pseudorapidity at the present level of precision. The bias on the measured
asymmetry due to $C\\!P$ violation in kaon decays has been calculated and
found to be almost negligible for this dataset. These results are consistent
with expectations [5] and lay the foundations for searches for $C\\!P$
violation in Cabibbo suppressed $D^{+}$ decays.

## 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), CIEMAT, IFAE and UAB (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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# Uncertainty-Aware Reward-based Deep Reinforcement Learning for Intent
Analysis of Social Media Information

Zhen Guo1, Qi Zhang1, Xinwei An2, Qisheng Zhang1, Audun Jøsang3,
Lance M. Kaplan4, Feng Chen5, Dong H. Jeong6, Jin-Hee Cho1

###### Abstract

Due to various and serious adverse impacts of spreading fake news, it is often
known that only people with malicious intent would propagate fake news.
However, it is not necessarily true based on social science studies.
Distinguishing the types of fake news spreaders based on their intent is
critical because it will effectively guide how to intervene to mitigate the
spread of fake news with different approaches. To this end, we propose an
intent classification framework that can best identify the correct intent of
fake news. We will leverage deep reinforcement learning (DRL) that can
optimize the structural representation of each tweet by removing noisy words
from the input sequence when appending an actor to the long short-term memory
(LSTM) intent classifier. Policy gradient DRL model (e.g., REINFORCE) can lead
the actor to a higher delayed reward. We also devise a new uncertainty-aware
immediate reward using a subjective opinion that can explicitly deal with
multidimensional uncertainty for effective decision-making. Via 600K training
episodes from a fake news tweets dataset with an annotated intent class, we
evaluate the performance of uncertainty-aware reward in DRL. Evaluation
results demonstrate that our proposed framework efficiently reduces the number
of selected words to maintain a high $95\%$ multi-class accuracy.

## Introduction

Several recent studies (Apuke and Omar 2021; Shen et al. 2021) reported that
fake news could be shared without bad intent, while it can contribute to a
huge adverse impact on its propagation. Therefore, this work is motivated to
provide a way of identifying the intent of fake news which can be used as the
basis for effective intervention in mitigating fake news. More specifically,
our intent classification method can contribute to identifying the right
population and dealing with them differently to mitigate the impact of fake
news propagation depending on their intent.

Text classification tasks have been studied by deep learning features of
embedding and structure representation (Yogatama et al. 2017). Deep
reinforcement learning (DRL) has been used to find an optimized structure
representation by removing the noises, such as non-related words and lexical
features (Zhang, Huang, and Zhao 2018). However, one of the main limitations
in existing DRL-based text classification approaches is the use of a delayed
reward to evaluate the prediction of the whole sequence of words. Because the
final processing state can only be determined when all words are processed,
this hinders the learning process as a DRL agent cannot receive an immediate
reward upon its local decision.

This work tackles this issue by introducing a multidimensional uncertainty-
aware reward in a DRL-based intent classifier. In addition, we propose an
intent classification framework that can analyze the intents of fake and true
news spreaders. In addition, we consider multidimensional uncertainty
estimates to identify optimal parameters.

Our work makes the following key contributions:

  1. 1.

We employ DRL algorithms to maximize the intent class prediction rate and
minimize the number of words used in the intent classification process.
Specifically, we introduce an immediate multidimensional uncertainty-aware
reward to formulate an accumulated certainty reward.

  2. 2.

We use the uncertainty estimates, such as vacuity and dissonance, in updating
the current policy. This approach is the first to leverage a belief model,
called Subjective Logic, that explicitly offers the capability of dealing with
multidimensional uncertainty.

  3. 3.

We resolve labor-intensive manual labeling tasks and annotate each news data
either fake news or true news, by three annotators. Finally, we assign the
dominant intent class to each news data piece to combine the labels collected
from three sources.

## Related Work

Intent Mining. A number of social science research (Apuke and Omar 2021;
Koohikamali and Sidorova 2017; Shen et al. 2021) has studied users’
motivations for sharing fake news and their intent. They found that the main
reason for spreading fake news or false information was because they thought
it was authentic and shared it unintentionally or even with good intent to
help others or make fun. Recent studies have proposed several natural language
processing (NLP) methods to do intent mining in different task domains, such
as user intent mining from reviews (Khattak et al. 2021) and email intent (Shu
et al. 2020).

DRL-based Text Mining. DRL has been explored in NLP classification tasks to
select meaningful word tokens and maintain the sequential relationship of
selected words (Zhang, Huang, and Zhao 2018). That is, a better structure
representation of whole text data can be learned by a DRL model to improve
classification performance. The sentiment classification research (Jian et al.
2021; Wang et al. 2019) has used DRL to reduce noisy tokens from whole
sentence to improve the accuracy of a prediction model. Unlike the works using
sentiment labels, our work identifies the intents of news articles user
intention identification from user reviews and emails. Hence, we manually
label the intent classes from an existing fake news dataset. To the best of
our knowledge, this work is the first that considers multidimensional
uncertainty in the immediate reward of actions and quantifies the
multidimensional uncertainty through a belief model called Subjective Logic
(SL) (Jøsang 2016).

## Intent Analysis Model

### Intent Classes from Social Studies

In social sciences research, the intents of news spreaders, regardless of real
or fake news, have been analyzed from the answers of questionnaires
(Koohikamali and Sidorova 2017; Shen et al. 2021). However, no data-driven
approaches have been used to study news spreaders’ intents. In our manual
annotations of news articles, we considers the following five intent classes
based on social sciences findings:

  * •

Information sharing: A common intent of online users’ spreading behavior is
purely sharing useful information to help other people. This intent includes
sense-making or expertise sharing to facilitate the truth of shared
information (Shen et al. 2021).

  * •

Political campaign: This intent uses fake news to falsely perceive an opponent
party’s political figure or group to mislead public opinions to win elections
(Purohit and Pandey 2019).

  * •

Socialization: Online users share information to attract more friends and stay
connected in online social networks (OSNs) (Apuke and Omar 2021). They can
expand his/her social cycle by sharing news, often leading to finding common
and interesting topics.

  * •

Rumor propagation: This intent misleads users by sharing a rumor or unverified
information (Purohit and Pandey 2019). Rumors can alter users’ emotions and
attitudes toward certain events and increase uncertainty.

  * •

Emotion venting: Online users can propagate fake news when they feel emotional
happiness or disturbances (e.g., anger, depression, sadness) from reading good
or bad events (Alsmadi, Alazzam, and AlRamahi 2021).

### Long Short-Term Memory (LSTM) Intent Classifier

Since the current dataset includes a collection of tweets, we call one piece
of news data “a news tweet” for consistency. First, we manually label each
fake or true news tweet with an intent class in the Experiment Setup section.
Accordingly, this label is a gold intent class $\mathbf{y}$ for a news tweet
$\mathbf{x}$. Then, a classifier is learned from the annotated dataset to
predict one’s intent.

#### Model Components.

This language model has a recurrent structure of $k$ embedding layers
($\theta_{em}$) and $k$ LSTM cells ($\theta_{lstm}$) to process a sequence of
$k$ input words in a news tweet $\mathbf{x}=\\{x_{1},\ldots,x_{k}\\}$. After
$k$ iterations with the final state $h_{k}$, a critic network
($\theta_{critic}$) with dense linear layers and ReLU and softmax activation
functions can predict a distribution of $P$ intent classes. We borrow the term
‘critic’ to highlight the role in the DRL model. As in a traditional LSTM cell
at iteration $t$, the inputs are a cell vector $c_{t-1}$, a hidden state
vector $h_{t-1}$, and the input word vector $w_{t}$ embedded from a word token
$x_{t}$. The outputs are new $c_{t}$ and $h_{t}$ sent to the next iteration
LSTM cell.

#### Loss Function.

A parameter set $\theta_{IC}$ of the three components in the intent classifier
is updated from the training step, which minimizes the cross-entropy loss with
the known gold intent labels. Considering the over-fitting prevention, the L2
regularization term $||\theta_{IC}||_{2}^{2}$ is added to this loss by:

$\mathcal{L}_{IC}=-\sum_{y=1}^{P}\hat{p}(y,\mathbf{x})\log
p(y|\mathbf{x},\theta_{IC})+\alpha||\theta_{IC}||_{2}^{2},$ (1)

where $\alpha$ is the regularization rate, $p(y|\mathbf{x},\theta_{IC})$ is
predicted from the final softmax layer, and $\hat{p}(y,\mathbf{x})$ is the
one-hot distribution of the gold label $\mathbf{y}$, which has $P$ values with
a single high as 1 and all others are 0.

### DRL-based Intent Classifier

This section discusses the sentence structure optimization steps by our policy
gradient-based DRL (see Figure 1 for detail). Keeping the temporal
relationship of the intent-related words can improve the intent prediction
from the LSTM intent classifier described in the previous section. Since the
previous LSTM classifier serves as a fixed environment to support the state
transitions, their parameters $\theta_{IC}$ are all frozen during the DRL
learning of $\theta$.

Figure 1: The overview of the DRL model with an uncertainty-based immediate
reward.

#### Model Steps.

The DRL model adds a word selection step to the LSTM classifier to form a time
series of actions $\tau=\\{a_{1},\ldots,a_{k}\\}$ from each ‘keeping’ or
‘masking’ decision of the actor network. Then, the selected or non-masked
words generate an optimized input sequence
$\mathbf{x^{\prime}}=\\{x_{1},x_{2},\dots,x_{k^{\prime}}\\}$ of $k^{\prime}$
words ($k^{\prime}\leq k$). Finally, this shorter $\mathbf{x^{\prime}}$ is
processed by the three components of the LSTM intent classifier to predict the
gold intent with higher accuracy. A training episode in DRL stands for one
trial of the Markov decision process (MDP) by masking non-intent words from
steps $1$ to $k$ of a news tweet. In addition, an episode is applied based on
only one news tweet data $\mathbf{x}$. It is obvious that the golden class
$\mathbf{y}$ for tweet $\mathbf{x}$ can be achieved during our annotation
step. The truth intent class $\mathbf{y}$ (e.g., socialization) can provide a
delayed reward to lead the DRL to a higher reward by repeating five episodes
in one training epoch.

#### Word Selection DRL.

By setting $\mathbf{x^{\prime}}=\mathbf{x}$, the DRL model extends an actor
network to each LSTM cell $\theta_{lstm}$ in the previous LSTM intent
classifier with the following details:

  * •

State: At each step $t$, an input feature vector $w_{t}$ from the embedding
layer $\theta_{em}$ represents the tokens of an input word $x_{t}$. The LSTM
cell $\theta_{lstm}$ processes $w_{t}$ with $c_{t-1}$ and $h_{t-1}$ and passes
$c_{t}$ and $h_{t}$. This hidden state vector $h_{t}$ serves as the state
$s_{t}$ for the actor network at the current step as
$s_{t}=\pi(w_{t},c_{t-1},h_{t-1};\theta_{lstm})$.

  * •

Actor: The actor network has one dense linear layer followed by a ReLU
activation and another dense linear layer followed by softmax activation of
two nodes. The parameters of all the neurons are in $\theta$ and can be
trained by the DRL. Given a state $s_{t}$, the actor generates a policy
$\pi(a_{t}|s_{t},\theta)$ for two actions.

  * •

Action: If an actor chooses $a_{t}=1$, the ‘keeping’ action maintains $x_{t}$
in the optimized input sequence $\mathbf{x^{\prime}}$. Otherwise, if the actor
chooses $a_{t}=0$, the ‘masking’ action removes $x_{t}$ from
$\mathbf{x^{\prime}}$.

  * •

State Transition: The state transition determines how each action $a_{t}$
controls the state $s_{t+1}$ for the next step. Since $s_{t+1}$ is generated
from the next LSTM cell, $a_{t}$ decides the inputs for the LSTM cell of step
$t+1$ by:

$\displaystyle
s_{t+1}=\begin{cases}\pi(w_{t+1},c_{t-1},h_{t-1};\theta_{lstm})\;\;\text{if
$a_{t}=0$ `masking'};\\\
\pi(w_{t+1},c_{t},h_{t};\theta_{lstm})\;\;\;\;\text{if $a_{t}=1$
`keeping'},\end{cases}$ (2)

#### Delayed Reward.

A delayed reward is from the intent class distribution of the whole optimized
input sequence $\mathbf{x^{\prime}}$ of one news tweet, which is calculated
from the LSTM classifier after the last word $w_{k^{\prime}}$. This delayed
reward is a unique feature in some NLP problems when common immediate reward
is unavailable. Considering the prediction of the true intent class label, as
$R_{pred}=p_{\theta_{critic}}(\mathbf{y}|\mathbf{x^{\prime}})$, and the masked
length reward of input words, the delayed reward is defined by:

$R=p_{\theta_{critic}}(\mathbf{y}|\mathbf{x^{\prime}})+\lambda(k-k^{\prime})/k,$
(3)

where $\theta_{critic}$ is a parameter for the critic network in the LSTM
intent classifier, y is the golden label for a news tweet x, $k^{\prime}$ is
the length of selected words in $\mathbf{x^{\prime}}$, and $\lambda$ is a
weight.

#### Policy Gradient.

The goal of our DRL model is to maximize the delayed reward in Eq. (3).
Similar to many other NLP problems where an immediate reward is unavailable
after deciding an individual step’s action, we will learn the actor’s policy
by policy gradient (PG)-based models. For example, the current stochastic
policy maximizes the expected delayed reward by calculating the gradients
$R\log\pi(a_{t}|s_{t},\theta)$ in REINFORCE algorithm (Williams 1992). Based
on the gradients for all $k$ transition steps in one episode following PG’s
on-policy property, REINFORCE calculates the negative log loss of the actor
$\theta$’s policy as:

$\mathcal{L}=-\sum_{t}R\log\pi(a_{t}|s_{t},\theta),$ (4)

### Uncertainty-based Immediate Reward

In each local step $t$ of the DRL model, when the hidden vector $h_{t}=s_{t}$
is passed directly to the critic network $\theta_{critic}$, the intent class
distribution $p(s_{t},\theta_{critic})$ from the critic network can be
represented by Subjective Logic (Jøsang 2016). Owing to the uncertainty
metrics in the SL-based opinion, we can access the accumulated uncertainties
or certainties from each $k$ decision steps in one training episode.

#### Formulating SL-based opinion from local intent classification
probabilities.

Remind that we adopt SL to consider multidimensional uncertainty where a
traditional Dirichlet probability density function (PDF) can be easily mapped
to a multinomial opinion which can provide a way to estimate different types
of uncertainties. These local intent probabilities $p(s_{t},\theta_{critic})$
can be regarded as a multinomial opinion in SL corresponding to five beliefs
towards the intent classes. The SL opinion considers uncertainty metrics, such
as vacuity caused by a lack of evidence and dissonance introduced by
conflicting evidence. Since the local intent probabilities cannot reflect the
level of vacuity, we apply the vacuity maximization technique (Jøsang 2016) on
the local probabilities of $P$ classes and generate a vacuity maximized
opinion $\omega_{t}=[\mathbf{b_{t}}$, $\mathbf{u_{t}}$, $\mathbf{g}]$. There
are $P$ belief masses in SL opinion as $\mathbf{b_{t}}$. The
$\mathbf{u_{t}}=[u^{vac}_{t},u^{dis}_{t}]$ refers to two considered
uncertainty metrics. The base rates in vector $\mathbf{g}$ are the
distribution of $P$ classes in annotated set $\mathcal{D}$.

#### Total Delayed Reward based on Accumulated Certainty Estimates.

Based on the previous discussion of the critic’s immediate certainty metrics
collected from local steps, the accumulated certainty metric serves as a new
component of the total delayed reward by extending Eq. (3) as:

$R_{delay}=p_{\theta_{critic}}(\mathbf{y}|\mathbf{x^{\prime}})+\lambda(k-k^{\prime})/k+\beta\sum_{t}(1-u_{t}).$
(5)

where $u_{t}$ is either vacuity $u^{vac}_{t}$ or dissonance $u^{dis}_{t}$, and
$\beta$ is the weight of accumulated certainty reward.

## Experiment Setup

#### Datasets.

We use the publicly available dataset LIAR 2015 (Wang 2017), which has 2,511
fake and 2,073 real news tweets verified by fact-checking agencies.

#### Intent annotation.

Each news tweet is manually annotated by three annotators to give one of the
five intent classes discussed. Then, $33\%$ of all news is annotated as a
dataset $\mathcal{D}$ of 1,500 tweets, with 835 fake and 665 true news.
Finally, we assign the dominant intent class from the three sources to each
news tweet. The base rate $\mathbf{g}$ for five classes are: ‘information
sharing’: 0.423, ‘political campaign’: 0.275, ‘socialization’: 0.135, ‘rumor
propagation’: 0.086, and ‘emotion venting:’ 0.081.

#### Data preparation.

The annotated dataset $\mathcal{D}$ is split into fake news only, true news
only, and both. By training LSTM and DRL models, we use $80\%$ as a training
set and $20\%$ as a testing set. We use prefix padding of length $k=20$.

#### Parameterization.

Our proposed DRL model aim to improve intent prediction by optimizing sentence
representation structures, which will cause a reduction of words from the
input data of the LSTM intent classifier. In addition, we discuss the role of
uncertainty-aware rewards by the SL in intent prediction. Table 1 summarizes
the model hyper-parameters and their default settings.

Table 1: Model Hyper-parameters Setting Model |  Parameter |  Value |  Parameter |  Value
---|---|---|---|---
LSTM |  Training epochs |  15 |  Padding words length $k$ |  20
Learning rate |  0.0003 |  Dimensions of $h_{t}$ and $c_{t}$ |  128, 128
Dropout rate |  0.25 |  Dense layers dimensions |  [257, 5]
Batch size |  32 |  Embedding dimensions |  128
DRL |  Training epochs |  100 |  Dense layers dimensions |  [257, 2]
Learning rate |  0.01 |  Mini-batch episodes |  5
|  Batch size |  32 |  Length reward weight $\lambda$ |  0.5

  * •

LSTM non-RL model (named ‘LSTM’) learns the parameters $\theta_{C}$ based on
the loss function in Eq. (1).

  * •

REINFORCE (named ‘DRL’, from section DRL-based Intent Classifier section) is a
basic PG method based on the delayed reward Eq. (3) and loss function Eq. (4).

  * •

REINFORCE with uncertainty-aware reward (named ‘DRL-CV’ and ‘DRL-CD’ for
vacuity and dissonance) uses the loss function in Eq. (4) by replacing $R$
with Eq. (5).

#### Metrics.

Our DRL framework is evaluated by measuring (1) the multi-class classification
accuracy counted by the ratio of correctly predicted data over the total of
the testing data; (2) the effectiveness of DRL by prediction of the gold
intent class from the critic network; and (3) the efficiency for DRL
represented by the length of the optimized sequence.

## Experiment Results & Analysis

During one DRL training epoch of each news tweet, we collect the states,
actions, and rewards by running five mini-batch episodes. Thus, each epoch
contains $6,000$ training episodes. Our models can converge within 100 epochs
and there are a maximum of 600K episodes. In the testing of DRL models, the
actors always follow the policy strictly.

### Multi-class Classification Accuracy

Although this accuracy is not directly optimized in the DRL algorithm and
rewards, it is crucial for our intent classification goal. We list the
accuracy scores for five classes and each intent class, along with the gold
class prediction $R_{pred}$ in Table Multi-class Classification Accuracy. The
highest accuracy scores for DRL models with different weights $\lambda$ are
within the same range, so we only show the case of $\lambda=0.5$ to compare to
the DRL with certainty reward models. The individual intent classes in the
last column follow the same order in $\mathbf{g}$. The basic DRL model
improved the gold class prediction by $5.3\%$ and increased the intent class
classification by $11\%$ for all news data. The LSTM model has similar
accuracy for fake and true news, but all DRL models classified fake news with
higher accuracies than true news. Although the overall accuracy under our DRL-
CV and DRL-CD is similar, the new certainty reward shows a slight improvement
for the annotated intent class prediction. Also, in general comparison, the
two uncertainty-based DRL models can increase the accuracy for classes 1
‘information sharing’ and 2 ‘political campaign’ but decrease the prediction
of classes 3 ‘socialization’ and 4 ‘rumor propagation’.

Table 2: Multi-class Accuracy from Testing

Model ($\lambda,\beta$) |  Test Data |  Gold Class Prediction |  Acc. |  Acc. by Intent Class
---|---|---|---|---
LSTM |  Fake |  0.806 |  0.866 |  [0.853, 0.852, 0.727, 0.941, 1.0]
|  True |  0.840 |  0.867 |  [0.898, 0.727, 0.889, 0.714, 1.0]
|  Total |  0.820 |  0.860 |  [0.871, 0.802, 0.792, 0.850, 1.0]
DRL  ($0.5$, N/A) |  Fake |  0.863 |  0.978 |  [0.941, 1.0, 1.0, 1.0, 1.0]
|  True |  0.887 |  0.958 |  [0.966, 0.909, 1.0, 0.857, 1.0]
|  Total |  0.873 |  0.970 |  [0.951, 0.963, 1.0, 0.943, 1.0]
DRL-CV ($0.5,0.01$) |  Fake |  0.871 |  0.983 |  [0.956, 1.0, 1.0, 1.0, 1.0]
|  True |  0.886 |  0.950 |  [0.966, 0.955, 0.944, 0.714, 1.0]
|  Total |  0.877 |  0.970 |  [0.960, 0.982, 0.978, 0.886, 1.0]
DRL-CD ($0.5,0.05$) |  Fake |  0.874 |  0.983 |  [0.956, 1.0, 1.0, 1.0, 1.0]
|  True |  0.890 |  0.958 |  [0.966, 0.955, 1.0, 0.714, 1.0]
|  Total |  0.880 |  0.973 |  [0.960, 0.982, 1.0, 0.886, 1.0]

Basically, DRL models show a high multi-class accuracy of $97\%$ across all
settings. Our DRL models aim to maximize the prediction accuracy while
reducing the length of the optimized sequences. Hence, in the next sections,
we use at least $95\%$ overall multi-class accuracy performance to check the
achieved minimum length for each DRL model.

### Effectiveness Reward by Prediction

Our reward function in Eq. (5) can maximize the effectiveness metric
$R_{pred}$ for the direct gold class prediction. We show this metric from the
training episodes and the testing data, and compare it with the total delayed
reward in Figure 2. For the basic DRL models, when the weight $\lambda$ of the
removed length is higher, both the training and testing effectivenesses
decrease while the total reward still increases. This means the loss of
effectiveness is compensated by the length reward. However, the uncertainty-
related reward can increase training and testing effectiveness, compared to
the DRL model with the same weight $\lambda=0.5$. In addition, the
effectiveness of true news data is improved with the help of the certainty
reward.

Figure 2: Effectiveness scores from DRL models.

### Efficiency by Optimized Length

The masked length reward in Eq. (5) is DRL’s main contribution to reducing the
number of noisy words in the news tweets. Figure 3 illustrates the minimum
number of words to maintain an overall classification accuracy of $95\%$. Both
training and testing lengths are reduced by adding a larger weight $\lambda$
for the masked length, meaning that the DRL models maintain $95\%$
classification accuracy while keeping less relevant words. Fake news in
testing removes more words than true news, leading to a higher reward. The two
uncertainty-related models reduce the length of both training and testing,
indicating that the additional small amount of certainty values, both vacuity
and dissonance, can help the DRL agent to explore more to the status of a
shorter length. The decrease of the kept length of DRL-CV and DRL-CD, compared
to DRL with $\lambda=0.5$, can increase the efficiency reward and finally
achieves a higher total delayed reward, as shown by the magenta line in Figure
2.

Figure 3: Efficiency metric from DRL models.

## Conclusions

We annotated the intent class for the fake and true news from the dataset
LIAR15. We used this annotated dataset to train the LSTM intent classifier,
and then created a DRL model to help reduce the noisy words. The DRL model
with optimized structure representation greatly improved the multi-class
classification accuracy from the pretrained LSTM intent classifier. We then
added an uncertainty-aware reward to help the DRL model reduce the length of
words further, while maintaining the high level of intent class classification
accuracy. Our findings prove that two uncertainty metrics, vacuity and
dissonance, can help the DRL agent’s training to reach shorter lengths and
higher the gold class predictions. The two uncertainty-aware reward models can
also decrease the length of testing data and increase the effectiveness of
true news testing data, resulting in attaining a higher total delayed reward
for the total test data. We will dig into more relevant metrics for the
rewards by effectiveness and efficiency in our future work.

## Acknowledgments

This work is partly supported by the Army Research Office under Grant Contract
Number W91NF-20-2-0140 and NSF under Grant Numbers 2107449, 2107450, and
2107451.

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