Charm production in charged current deep inelastic scattering at HERA

Charm production in charged current deep inelastic scattering has been measured for the first time in $e^{\pm}p$ collisions, using data collected with the ZEUS detector at HERA, corresponding to an integrated luminosity of $358 pb^{-1}$. Results are presented separately for $e^{+}p$ and $e^{-}p$ scattering at a centre-of-mass energy of $\sqrt{s} = 318 GeV$ within a kinematic phase-space region of $200 GeV^{2}<Q^{2}<60000 GeV^{2}$ and $y<0.9$, where $Q^{2}$ is the squared four-momentum transfer and $y$ is the inelasticity. The measured cross sections of electroweak charm production are consistent with expectations from the Standard Model within the large statistical uncertainties.


In tro d u ctio n
M easurem ents of heavy-flavour production serve as a good testing ground to investigate th e predictive power of p ertu rb ativ e quantum chrom odynam ics (pQCD ) as th e large mass provides a n a tu ra l hard scale. W hile charm production in n eutral current deep inelastic scattering (NC DIS) and in photoproduction has been extensively studied at H ERA , it has not been m easured in charged current deep inelastic scattering (CC DIS) owing to its small cross section.
In CC DIS, single charm quarks in the final sta te already occur a t th e level of the Q uark P a rto n M odel (Q PM ) when either an incom ing s or d quark is converted to a charm quark, or an incoming charm quark is converted to an s or d quark, as illustrated in figure 1 (i, ii). In th e la tte r case, th e single charm in th e event arises from th e associated charm quark in th e proton rem nant. In addition, single charm can arise from boson-gluon fusion (BG F) producing a cs (cd) quark pair. In this case, th e incom ing v irtual W boson fuses w ith a gluon from th e proton. T he gluon splits into a s s (dd) or cc pair in the initial state, as shown in figure 1 (iii, iv). All these e+p processes lead to th e same final state, e+p ^ Ve c s (d) X ; this is also tru e for e-p, e-p ^ ve cs(d) X . T he characteristics of In the QPM process (ii) c ^ s(d), the charm in the final state arises from the associated charm quark in the proton remnant X . In the BGF processes, the incoming W boson couples to (iii) an ss(dd) or (iv) a cc pair from the gluon in the proton, producing a cs pair in the final state.
the events associated with these subprocesses and their association to particular kinematic configurations in the final state depend on the QCD scheme chosen, as detailed in the next section. The subprocess depicted in figure 1 (i) is directly sensitive to the strange-quark content of the proton and can be used to constrain it. However, the extraction of the relevant part of the cross section is model dependent.
In the SU(3) flavour model, a perfect symmetry is assumed between the three light flavours, which results in equal quark densities for the sea quark components in nucleons. This symmetry is broken if the strange-quark density is suppressed by the mass of the strange quark, as happens in the well established strange-quark suppression in fragmen tation [1]. This symmetry breaking can also occur in the initial state, depending on x,

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th e fraction of the proton m om entum carried by th e interacting parton. For larger values of x, some support for this has been found experim entally, such as in dim uon produc tion in charged current by th e C C FR [2] and NuTeV [3], as well as th e NOM AD [4] and CHORUS [5] neutrino scattering experim ents. However, th e in terp retatio n of these m ea surem ents depends on nuclear corrections and charm fragm entation and no consensus has emerged on the exact level of suppression as a function of x . Additionally, th e recent highprecision m easurem ents of inclusive W and Z production by th e ATLAS collaboration [6] report an unsuppressed strange sea in th e low-x regime. A sim ilar result was obtained in a combined global QCD analysis of inclusive W and Z d a ta from b o th th e ATLAS and CMS experim ents [7]. This observation was also supported by th e analysis of th e ATLAS W + c d a ta [8]. However, th e CMS W + c d a ta [9,10] favour strangeness suppression also a t low x . A re-evaluation of th e LHC inclusive and W + c m easurem ents and th e neutrino scat tering m easurem ents by NOM AD [4] and CHORUS [5] has been perform ed [11,12], p artly in an a tte m p t to reconcile th e factor-of-two discrepancy in th e m easured strange-quark densities. T he resulting strange-quark p arto n distrib u tio n function (PD F) was reported to be inconsistent w ith th e ATLAS fit [6]. This paper presents m easurem ents of charm production in CC DIS in e±p collisions using d a ta from th e H ER A II data-tak in g period. T he electroweak contribution to charmproduction cross sections is com pared w ith several QCD schemes th a t are detailed in the following section.

C harm p r o d u ctio n in C C D IS at H E R A
T he kinem atics of lepton-proton scattering can be described in term s of th e Lorentzinvariant variables x Bj, y and Q 2. T he variable Q 2 is th e negative squared four-m om entum of th e exchange boson -q 2 = -(k -k ' )2, where k and k' are th e four-m om enta of the incom ing and outgoing lepton, respectively. T he B jorken-x scaling variable, x Bj , is defined as xBj = Q 2/(2 p ■ q), where p is th e four-m om entum of th e incom ing proton. T he variable y is th e inelasticity defined as y = Q 2/ ( s x Bj), where s is th e squared centre-of-m ass energy of th e collision. T he differential cross section of charm production in CC DIS a t H ERA , m ediated by a W boson, can be expressed in term s of th e proton stru ctu re functions F 2, x F 3 and F L as follows [13] where G F is th e Ferm i coupling constant, M W is th e m ass of th e W boson and Y± = 1 ± (1 -y )2. T he contribution from th e longitudinal stru ctu re function, F l , vanishes except a t values of y w 1. T he basic electroweak single-charm production mechanism s (MC) sim ulation, th e core electroweak m atrix elem ents are based on th e Q PM graphs in figure 1 (i, ii) and BG F-like configurations in figure 1 (iii, iv) th rough initial-state p arton have been outlined in section 1. In th e leading-order plus parton-show er M onte Carlo -3 -

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F ig u re 2. Example Feynman diagram of QCD charm process. The cc pairs from the final-state gluons, illustrated in the figure, are referred to as QCD charm in the text.
showering. In addition, other tree-level higher-order processes are also added through leading-log (LL) p arto n showering. T he electroweak m atrix elem ents involving only light quarks are com plem ented by occasional final-state gluon splitting into cc pairs in th e p arton shower, as depicted in figure 2, w ith a cutoff m imicking charm -m ass effects. At th e single event level, if only one of th e two charm quarks (or its resulting hadron) is detected and its charge is not m easured (such as in th e m easurem ent technique used in this paper), th en th e contribution of this final-state Q C D radiation is experim entally indistinguishable from electroweak production. T he experim ental m easurem ent thus refers to a sum of all these processes, which m ake differing contributions to different regions of phase space, but cannot be disentangled w ith th e presently available statistics.
In fixed-order Q C D calculations, th e final-state gluon-splitting contribution in figure 2 is form ally of next-to-next-to-leading order (NNLO, O (a^)) and thus not included in the next-to-leading-order (NLO, O (as)) QCD predictions considered in this work, even though its contribution can be substantial. C ontributions from QPM -like (figure 1 (i, ii)) and BG F-like (figure 1 (iii, iv)) processes are separated by th e virtu ality of th e quark entering th e electroweak process in relation to th e chosen factorisation scale. T he NLO corrections to figure 1 (i, ii) arise in th e form of initial-or final-state gluon radiation, or a vertex correction.
In th e NLO fixed-flavour-num ber (FFN ) scheme [16,17], charm -m ass effects are treated explicitly up to O ( a S) in th e m atrix elem ents. In this scheme, there is no charm -quark content in th e proton, thus th e charm Q PM graph in figure 1 (ii) and its associated higherorder corrections do not occur. This is com pensated by a correspondingly larger gluon content in th e proton, such th a t all initial-state charm contributions irrespective of scale are tre a te d explicitly in th e B G F m atrix elem ent (figure 1 (iv)). No resum m ation is perform ed.
In th e FONLL-B scheme [18,19], a general-m ass variable-flavour-num ber scheme, charm -m ass effects are accounted for by interpolating betw een th e ZM -VFNS and F F N predictions, such th a t all m ass effects are correctly included up to O ( a S).
T he x F itte r fram ew ork [20] was used to interface th e theoretical predictions. P re dictions in th e F F N scheme were obtained from O PEN Q C D R A D [21] using th e ABM P 16.3 NLO P D F sets [22,23]. Predictions in th e FONLL-B scheme were obtained from A P F E L [24] w ith N N PD F3.1 [25]. T he to ta l uncertainties of th e F F N and FONLL-B schemes were obtained by adding in q u ad ratu re th e P D F , scale and charm -m ass uncertainties.
In order to study th e effects of strangeness suppression, th e ZM -VFNS predictions were obtained from QCDNUM [26] w ith H E R A P D F2.0 [27]. T he strange-quark fraction, f s = s /( d + s ) , was chosen to vary in th e range betw een a suppressed strange sea [28,29] and an unsuppressed strange sea [6,30]. In addition, two more variations of th e assum ptions about th e strange sea were m ade. Instead of assum ing th a t th e strange contribution is a fixed fraction of th e d-type sea, an x-dependent shape, x s = 0.5fS ta n h ( -20(x -0.07)) x D , where x D = x d + x s , was used in which high-x strangeness is highly suppressed. This shape was suggested by H ERM ES m easurem ents [31,32]. T he value of fS was also varied betw een fS = 0.3 and fS = 0.5. T he ZM -VFNS prediction was also evaluated w ith the A T L A S-epW Z 16 P D F sets [6].

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A detailed description of th e ZEUS detector can be found elsewhere [33]. A brief outline of th e com ponents th a t are m ost relevant for this analysis is given below.
Charged particles were tracked in th e central tracking detector (CTD ) [34][35][36], the m icrovertex detector (MVD) [37] and th e straw -tube tracker (STT) [38]. T he CTD and the MVD operated in a m agnetic field of 1.43 T provided by a th in superconducting solenoid. T he CTD drift cham ber covered th e polar-angle 1 region 15° < 0 < 164°. T he MVD silicon tracker consisted of a barrel (BM VD) and a forw ard (FM VD) section. T he BM VD provided polar angle coverage for tracks w ith three m easurem ents from 30° to 150°. The FM V D extended th e polar-angle coverage in th e forw ard region to 7°. T he ST T covered th e polar-angle region 5° < 0 < 25°.
T he high-resolution uranium -scintillator calorim eter (CAL) [39][40][41][42]  T he iron yoke surrounding th e CAL was instrum ented w ith proportional drift cham bers to form the backing calorim eter (BAC) [43]. T he BAC consisted of 5142 alum inium cham bers inserted into th e gaps betw een 7.3 cm thick iron plates (10, 9 and 7 layers in forecap, barrel and rearcap, respectively) serving as calorim eter absorber. T he cham bers were typically 5 m long and had a wire spacing of 1.5 cm. T he anode wires were covered by 50 cm long cathode pads. T he BAC was equipped w ith energy readout and position sensi tive readout for m uon tracking. T he form er was based on 1692 pad towers (50 x 50cm 2), providing an energy resolution of ~ 100% /V E , w ith E in GeV. T he position inform ation from th e wires allowed the reconstruction of muon trajectories in two dim ensions (X Y in barrel and Y Z in endcaps) w ith spatial accuracy of a few mm.
T he lum inosity was m easured using the B ethe-H eitler reaction ep ^ eup by a lu m inosity detector which consisted of independent lead-scintillator calorim eter [44][45][46] and m agnetic spectrom eter [47] system s. T he fractional system atic uncertainty on th e m easured lum inosity was 2%.

M o n te C arlo sim u la tio n
Inclusive CC DIS MC samples were generated to sim ulate the charm signal and lightflavour (LF) background. N eutral current DIS and photoproduction samples were used to sim ulate non-CC DIS backgrounds, which were found to be negligible after th e CC selec tion defined below. T he charged current events were generated w ith D JA N G O H 1.6 [48], using th e C TEQ 5D P D F sets [49] including QED and QCD radiative effects a t th e par-1T he ZEUS coordinate system is a right-handed C artesian system , w ith th e Z axis pointing in the nom inal proton beam direction, referred to as th e "forward direction" , and th e X axis pointing tow ards th e centre of HERA. T he coordinate origin is at th e centre of th e CTD . T he pseudorapidity is defined as n = -ln ( ta n | ) , where th e polar angle, 0, is m easured w ith respect to th e Z axis. to n level. T he A R IA D N E 4.12 colour-dipole m odel [50] was used for p arto n showering.
T he Lund string m odel was used for hadronisation, as im plem ented in JE T S E T 7.4.1 [51]. T he N C DIS events and photoproduction events were sim ulated by using D JA N G O H and H ERW IG 5.9 [52], respectively. betw een th e tru e and reconstructed kinem atic variables was found to be w ithin w 1% in th e M C sim ulation study.

C C D IS s e le c tio n
T he ZEUS online three-level trigger system loosely selected CC DIS candidates based on calorim eter and tracking inform ation [53,54]. T he triggered events were th en required to pass th e following offline selection criteria to reject non-CC DIS events: • a kinem atic selection cut was im plem ented at 200 G eV 2 < Q2b < 60000 GeV2 and yJB < 0.9 to confine th e sam ple into a region w ith good resolution of the kinem atic quantities and small background; • a characteristic of CC DIS events is th e large missing transverse m om entum , pT,miss, in the calorim eter due to th e undetected final-state neutrino. Events were required to have pT,miss > 12 GeV and pT miss > 10 GeV, where pT miss is th e missing tra n s verse m om entum , excluding m easurem ents taken from th e CAL cells adjacent to the forward beam hole;

C h a rm s e le c tio n an d sig n a l e x tr a c tio n
C harm quarks in CC DIS events were tagged by using an inclusive lifetime m ethod [56,57].
In CC DIS a t H ER A , LF production has th e highest production rate and is th e m ajor source of background. T he lifetime m ethod uses th e m easurem ent of th e decay length of the heavyflavour (HF) particle to discrim inate betw een signal and background contributions. The underlying principle of this m ethod [56] is th a t ground-state H F particles travel on average a m easurable distance before they decay a t a secondary vertex.
Jets were reconstructed from energy-flow objects [58,59], which combine the infor m ation from calorim etry and tracking, corrected for energy loss in th e detector m aterial. T he kT clustering algorithm [60] was used w ith a radius param eter R = 1 in th e longi tudinally invariant m ode [61,62]. T he E -recom bination scheme, which produces massive jets whose four-m om enta are th e sum of th e four-m om enta of th e clustered objects, was used. Events were selected if they contained a t least one je t w ith transverse energy, ET*, greater th a n 5 GeV and w ithin th e je t pseudorapidity range -2 .5 < n*et < 2.0 (1.5).2 These selection criteria constrained th e kinem atic phase-space region of this analysis, along w ith th e kinem atic selection criteria at th e event-level selection stage.
Tracks from th e selected jets were required to have a transverse m om entum , p T k > 0.5 GeV, and th e to ta l num ber of hits in th e MVD, N^v d E 4 to reduce th e effect of m ultiple scattering and ensure a good spatial resolution. If m ore th a n two such tracks were associated w ith th e jet, a secondary-vertex candidate was fitted from th e selected tracks using a determ inistic annealing filter [63][64][65]. This fit provided th e vertex position and its error m atrix as well as th e hadronic invariant mass, M secvtx, of th e charged tracks associated w ith th e reconstructed vertex. T he charged-pion m ass was assum ed for all tracks when 2T he tracking efficiency and resolution in th e forward region njet > 1.5 suffered in th e 2005 (e-p) datataking period as th e S T T was tu rn ed off during this tim e. Thus, th e jets from th is period were required to satisfy a tighter nJet upper lim it nJet = 1.5. calculating the vertex mass. The secondary-vertex candidates were required to satisfy the following criteria: • y /A x 2 + A y2 < 1cm, where NticVta is the number of tracks used to reconstruct the vertex, x 2/N dof is the good ness of the vertex fitting, zsecvtx is the Z-coordinate of the secondary vertex and Ax, Ay are the X -and Y -displacement of the secondary vertex from the prim ary interaction ver tex. These selection criteria ensure a good fit quality and high acceptance of the CTD and MVD for tracks used to reconstruct the vertices. The requirement on the track multiplicity was implemented in order to reduce the number of background vertices. Figures 5 and 6 show the distributions of the chosen jets and secondary-vertex candidates for the e+p and e-p periods, respectively. The transverse decay length of the selected secondary vertices was projected onto the jet axis. Due to the finite resolution of the MVD and the prompt production of LF particles, the distributions of the 2D decay length (Lxy) and the significance of the decay length (S = Lxy/óLxy) for LF jets were symmetric. In contrast, the distributions for HF jets, in this case containing charmed particles, were asymmetric, as illustrated in figures 7 and 8  (a, b). A very small contribution from beauty is also shown; this is treated as background. This enabled the LF background to be suppressed by subtracting the negative decay-length distribution from the positive decay-length distribution. The region around |Lxy | = 0 or |S| = 0 is dominated by LF production, resulting in a large statistical uncertainty of the distribution due to subtraction of two large numbers. To optimise the precision of the extracted signal, vertex candidates were required to satisfy a significance threshold, |S| > 2. Figures 7 and 8 (c, d) illustrate the shape of the variable distributions after the background subtraction. The surviving events after the decay-length subtraction were used to extract charm cross sections in two bins of Q2.

C harm cross sec tio n
The lifetime method used in this analysis tags charm quarks regardless of their origin. Thus, the selected reactions include charm production from final-state gluon splitting, such as shown in figure 2, which is here denoted by QCD charm, in addition to the electroweak (EW) charm production discussed in section 2. In the present analysis, charm production was measured inclusively for 200 GeV2 < Q 2 < 60000 GeV2 and y < 0.9. Additionally, to reflect the detector acceptance, a visible phase-space region was defined as: 200 GeV2 < Q 2 < 60000 GeV2, y < 0.9, E^ > 5 GeV and -2.5 < n>et < 2.0. The limited statistics T able 1. MC contributions (%) of charm subprocesses to and as predicted by ARI ADNE. The first two columns (d ^ c and s ^ c for e+p collisions, for example) reflect the contri butions from the QPM processes described in figure 1 (i) and a higher-order correction described in figure 1 (iii). The contribution of the final-state gluon splitting described in figure 2 enters the fourth column (g ^ cc).
are generated in th e MC w ithin th e visible kinem atic region and associated to a generated charm or anti-charm quark when A^2 + A p 2 < 1, where A 0 and A n are, respectively, the azim uthal angle and pseudorapidity difference betw een th e je t and th e charm quark. Each charm quark was associated to th e je t w ith th e highest satisfying the above criteria and each such je t entered th e visible cross section. T he different processes contributing to C T cvis as predicted by MC are given in table 1.
T he E W contribution in the charm -quark signal, u^^S, should be evaluated by sub tra c tin g th e QCD contribution from gluon splitting (figure 2) . However, the prediction from A R IA D N E 4.12, like any prediction from gluon splitting in th e massless m ode w ith cutoff, cannot be considered to be reliable. Since th e contribution predicted by A R IA DN E (see table 1) is b o th small and imprecise, it was not subtracted b u t ra th e r included in the system atic uncertainties. T he visible je t cross section was ex trapolated and converted to th e to ta l E W cross section via a factor Cext, calculated from th e ratio of th e num ber of charm events generated in th e full kinem atic range, , to th e num ber of charm jets of E W origin w ithin th e visible kinem atic region, N^W : (6.2) N vis T he resulting to ta l E W charm cross section, a cew , is th en given by C T cEW = Cext ffc,vis NEW Ndata _ N MC = N gen N______ ffMC (6 3) N EW N MC CTc,vis.
T his is predicted by th e A R IA D N E MC to be approxim ately 9 pb.

S y ste m a tic u n certa in ties
A lthough the statistical power of th e current d a ta is lim ited, it is im p o rtan t for future studies to understand the lim itations of th e current m ethod by careful evaluation of the system atic uncertainties. T he sources of uncertainty and th eir estim ated effects on the to ta l E W charm cross sections provided in parentheses (5 a e p , 5 a e p) are: • Secondary vertex rescaling T he MC samples used in this analysis produced a higher fraction of events w ith secondary vertices th a n th e d ata. For th e nom inal result, N , 40 and NbgC in eq. (6.1) were reduced proportionally. For th e system atic uncertainty, only NbgC was rescaled (-1.2 pb, + 0.9 pb).
• E W charm fraction T he MC predictions of th e QCD contribution (figure 2) shown in table 1 of +6% for e+p collisions and +12% for e -p collisions were taken as system atic uncertainty (-0.6pb, -1.1 pb).
• CC DIS selection T he uncertainty due to th e CC selection cuts was estim ated by varying these cuts as in th e previous ZEUS analysis [66] (± 0.2 pb, ±0.1 pb).
• Je t energy scale T he p a rt of th e transverse je t energy m easured in th e calorim eter in th e MC was varied by its estim ated uncertainty of ±3% (± 0.0 pb, ±0.1 pb).
These uncertainties were added in q u adrature. T he uncertainty in th e ZEUS lum inosity m easurem ent is ±2% and was not included in th e results.
In addition, th e effect of th e significance cut, |S| > 2, was studied. Small changes in th e value of th e significance cut resulted in large changes of th e extracted signal. This was found to be due to statistical fluctuations in th e num ber of events in th e region close to the |S| lower cut value. From a dedicated study, the effects on th e cross sections were found to be as large as ± 5 pb. As this result was still strongly affected by statistical fluctuations, which have been included in the quoted statistical uncertainty, it was not included in the system atic uncertainty.
Additionally, th e uncertainty in th e secondary-vertex selection m ethod was estim ated by reducing th e requirem ent on th e num ber of tracks, N te J^, from three to two. The effects on th e cross sections were found to be as large as + 3 pb. This was again strongly affected by statistical fluctuations and not included in the system atic uncertainty.
The QCD contribution to charm production was introduced as an additional systematic un certainty. Theory predictions obtained at NLO QCD with the F F N and FONLL-B schemes are compared to the d ata in bins of Q2 in figure 10. Table 2   strange-quark fraction are given in table 5. A further reduction of the theory uncertainty can be achieved in the future by including NNLO corrections [67].
The theory predictions in table 3 suggest th a t the most interesting subprocess, namely the QPM process depicted in figure 1 (i), contributes about 30 -50% to the final EW cross section, depending on the kinematic range and QCD scheme used. In general, the d ata are well described by the theory predictions, however the large experimental uncertainties prevent a discrimination between the different models.   figure 1 (ii) enters in the third column (c ^ s(d)) with a higher-order correction from the BGF process in figure 1 (iv). For the FFN scheme, the process described in figure 1 (ii) does not participate. Thus the content of the third column is provided by the BGF process of figure 1 (iv) only.

S u m m ary and o u tlo o k
M easurem ents of charm production in charged current deep inelastic scattering in e±p collisions have been perform ed based on H ER A II d a ta w ith an integrated lum inosity of 358 p b -1 , which corresponds to e+p collisions w ith an integrated lum inosity of 173 p b -1 and e -p collisions w ith an integrated lum inosity of 185 p b -1 . Visible charm -jet cross sections for each lepton beam type were m easured w ithin a kinem atic region 200 G eV 2 < Q 2 < 60000 GeV2, y < 0.9, E j t > 5 GeV and -2 .5 < r fet < 2.0. They were extrapolated to the E W cross sections given in th e kinem atic range 200 G eV 2 < Q 2 < 60000 GeV2 and y < 0.9. T heoretical predictions w ith several assum ptions about th e strange-quark content of the proton and using different heavy-flavour schemes were found to be consistent w ith the d a ta w ithin th e large experim ental uncertainties. T he analysis presented here shows the potential of D IS m easurem ents to increase th e knowledge ab o u t th e strange-quark content of th e proton. F uture lepton-ion collider projects such as th e electron-ion collider [68] or LHeC [69] will have m uch higher lum inosity th a n H ERA , accom panied by improved vertex detection capabilities. These projects should th en be able to m ake an im portant contribution to th e knowledge of th e strange-quark content of th e proton.

A ck n o w led g m en ts
We appreciate th e contributions to th e construction, m aintenance and operation of the ZEUS detector of m any people who are not listed as authors. T he H ER A m achine group and th e D ESY com puting staff are especially acknowledged for th eir success in providing excellent operation of th e collider and th e data-analysis environm ent. We th an k th e DESY d irectorate for their strong support and encouragem ent.