Article
Reference
Search for V + A Current in Top-Quark Decays in pp Collisions at s√=1.96 TeV
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We report an upper limit on the fraction of V+A current, fV+A, in top-quark decays, using approximately 700 pb−1 of pp collisions at s√=1.96 TeV acquired by the upgraded Collider Detector at Fermilab. For the decay t→Wb→ℓνb (where ℓ=e or μ), the invariant mass of the charged lepton and the bottom quark jet is sensitive to the polarization of the W boson. We determine fV+A=−0.06±0.25 given a top-quark mass of 175 GeV/c2. We set an upper limit on fV+A of 0.29 at the 95% confidence level, an improvement by a factor of 2 on the previous best direct limit.
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Search for V + A Current in
Top-Quark Decays in pp Collisions at s√=1.96 TeV. Physical Review Letters , 2007, vol. 98, no. 07, p. 072001
DOI : 10.1103/PhysRevLett.98.072001
Available at:
http://archive-ouverte.unige.ch/unige:38380
Disclaimer: layout of this document may differ from the published version.
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Search for V A Current in Top-Quark Decays in p p Collisions at p s
1:96 TeV
A. Abulencia,24J. Adelman,13T. Affolder,10T. Akimoto,56M. G. Albrow,17D. Ambrose,17S. Amerio,44D. Amidei,35 A. Anastassov,53K. Anikeev,17A. Annovi,19J. Antos,14M. Aoki,56G. Apollinari,17J.-F. Arguin,34T. Arisawa,58 A. Artikov,15W. Ashmanskas,17A. Attal,8F. Azfar,43P. Azzi-Bacchetta,44P. Azzurri,47N. Bacchetta,44W. Badgett,17 A. Barbaro-Galtieri,29V. E. Barnes,49B. A. Barnett,25S. Baroiant,7V. Bartsch,31G. Bauer,33F. Bedeschi,47S. Behari,25
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J. C. Yun,17L. Zanello,52A. Zanetti,55I. Zaw,22X. Zhang,24J. Zhou,53and S. Zucchelli5 (CDF Collaboration)a
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4Baylor University, Waco, Texas 76798, USA
5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6Brandeis University, Waltham, Massachusetts 02254, USA
7University of California, Davis, Davis, California 95616, USA
8University of California, Los Angeles, Los Angeles, California 90024, USA
9University of California, San Diego, La Jolla, California 92093, USA
10University of California, Santa Barbara, Santa Barbara, California 93106, USA
11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
16Duke University, Durham, North Carolina 27708, USA
17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
18University of Florida, Gainesville, Florida 32611, USA
19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
20University of Geneva, CH-1211 Geneva 4, Switzerland
21Glasgow University, Glasgow G12 8QQ, United Kingdom
22Harvard University, Cambridge, Massachusetts 02138, USA
23Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
072001-2
24University of Illinois, Urbana, Illinois 61801, USA
25The Johns Hopkins University, Baltimore, Maryland 21218, USA
26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
28Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;
Seoul National University, Seoul 151-742, Korea;
and SungKyunKwan University, Suwon 440-746, Korea
29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
30University of Liverpool, Liverpool L69 7ZE, United Kingdom
31University College London, London WC1E 6BT, United Kingdom
32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
34Institute of Particle Physics, McGill University, Montre´al, Canada H3A 2T8;
and University of Toronto, Toronto, Canada M5S 1A7
35University of Michigan, Ann Arbor, Michigan 48109, USA
36Michigan State University, East Lansing, Michigan 48824, USA
37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
38University of New Mexico, Albuquerque, New Mexico 87131, USA
39Northwestern University, Evanston, Illinois 60208, USA
40The Ohio State University, Columbus, Ohio 43210, USA
41Okayama University, Okayama 700-8530, Japan
42Osaka City University, Osaka 588, Japan
43University of Oxford, Oxford OX1 3RH, United Kingdom
44University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
47Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
49Purdue University, West Lafayette, Indiana 47907, USA
50University of Rochester, Rochester, New York 14627, USA
51The Rockefeller University, New York, New York 10021, USA
52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy
53Rutgers University, Piscataway, New Jersey 08855, USA
54Texas A & M University, College Station, Texas 77843, USA
55Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
56University of Tsukuba, Tsukuba, Ibaraki 305, Japan
57Tufts University, Medford, Massachusetts 02155, USA
58Waseda University, Tokyo 169, Japan
59Wayne State University, Detroit, Michigan 48201, USA
60University of Wisconsin, Madison, Wisconsin 53706, USA
61Yale University, New Haven, Connecticut 06520, USA (Received 29 August 2006; published 15 February 2007)
We report an upper limit on the fraction of VA current, fVA, in top-quark decays, using approximately 700 pb1 of pp collisions at
ps
1:96 TeV acquired by the upgraded Collider Detector at Fermilab. For the decay t!Wb!‘b (where ‘e or ), the invariant mass of the charged lepton and the bottom quark jet is sensitive to the polarization of theW boson. We determine fVA 0:060:25given a top-quark mass of175 GeV=c2. We set an upper limit onfVAof 0.29 at the 95% confidence level, an improvement by a factor of 2 on the previous best direct limit.
DOI:10.1103/PhysRevLett.98.072001 PACS numbers: 13.85.t, 12.15.Ji, 12.38.Qk, 13.88.+e
The decay of the top-quark, the most massive funda- mental particle observed by experiment [1,2], is particu- larly interesting as a direct probe of the charged current weak interaction at the highest energy scale presently available. In the standard model, the spin-12 top-quark decays via the charged current weak interaction to a spin-1Wboson and a spin-12bquark [3], with a branch- ing fraction above 99% and widtht1:4 GeV[4] for a
top-quark mass of 175 GeV=c2. The lifetime of the top- quark, @=t51025 s, is an order of magnitude shorter than the typical strong interaction time scale for binding of quarks into hadrons, @=QCD31024 s.
Therefore, the top-quark decays before hadronization, and the spin information is directly transferred to the decay products. In the limitmb!0, the pureVAtheory of the weak interaction predicts that thebquark has left-handed
(1=2) polarization (helicity), and theWboson can only have either longitudinal (zero) or left-handed (1) polar- ization. The right-handed (1) polarization is forbidden.
The fractionf0 ofW bosons with longitudinal polariza- tion is predicted at leading order in perturbation theory to bef0m2t=2m2Wm2t 0:70[5]. The nonzerobquark mass and the higher-order QCD and electroweak radiative corrections modify these predictions below the 1% level [6,7]. However, the presence of non-standard-model cou- plings in the tWb vertex could significantly modify the polarization of the top-quark decay products [5,8–10].
Previous results have either been limited by the small statistics of the top-quark samples [11–14] or have only set indirect limits [15].
In this Letter, we search for aVAcurrent in top-quark decay, while assuming that thettproduction mechanism is in agreement with the standard model prediction. We further assume the absence of couplings from magnetic moment interactions in thetWb interaction, so thatf0 is unchanged from 0.70 [5]. Then, theVAfractionfVAis related to the fractionf of right-handedW bosons by fVAf=1f0, and theVAfractionfVA 1 fVA is related to the fraction f of left-handed W bosons byfVAf=1f0. TheWboson polariza- tion can be inferred from the angular distribution of the charged lepton [16] in the decayW!‘,
1
d dcos3
41cos2f03
81cos2f 3
81cos2f;
where the angleis the polar angle of the charged lepton in the rest frame of theWboson. Thez-axis is defined to be the direction of motion of theWboson in the rest frame of the top-quark. We use the observableM2‘b, the square of the invariant mass of the charged lepton and the jet from thebquark, which is related tocosby
M‘b2 ’1
2m2t m2W1cos:
The relation is exact in the limitmb!0.
This search is based on a data set with an integrated luminosity of approximately 700 pb1 acquired by the Collider Detector at Fermilab (CDF II) [17] from pp collisions atps
1:96 TeV. We study three independent data samples enriched inttevents. Two of the data samples are in the leptonjets channel, with tt!WbWb events where one of the W bosons decays hadronically and the other leptonically. The leptonjets event selec- tion requires one isolated lepton withET>20 GeV,6ET >
20 GeV[18], at least three jets withET>15 GeV, and one or two b-tagged jets. More details on the selection, the b-tagging procedure, and the sample composition can be found in Ref. [19]. We model the hardttprocess with the Monte Carlo (MC) event generator ALPGEN [20] with
CTEQ5L[21] parton densities andPYTHIA[22] for hadroni- zation, under the assumption that the top-quark mass is 175 GeV=c2. We simulate the detector response using
GEANT [23,24]. For ttproduction with VA top-quark decay, we estimate a selection efficiency, including the branching fraction, of AVA3:4%1:2% for events with one (two)b-tagged jets. Because of the lower average pT of the charged lepton forVA, this is a factor 0.92 below the efficiency forVA.
For the leptonjets sample with a singleb-tagged jet, the b-tagged jet is from the same top-quark decay as the charged lepton in approximately half of thettevents. The background M2‘b distribution is a combination of 85%
Wjets, modeled by ALPGEN Wbb, and 15% multijet events, modeled by nonisolated leptonjets data events.
Background-dominated data samples with only one jet or only two jets are consistent, in terms of both the rate and the shape of the M2‘b distribution, with our model of the background. In695 pb1, we observe 304 candidates with a total expected background of8811events.
For the leptonjets sample with two b-tagged jets, the two possible M2‘b values of the charged lepton with either the highest or the second highestET b-tagged jet are used to construct a 2-D distribution. In this way, we keep both the correct and incorrect combinations, and account for their correlation. The background is modeled by
ALPGENWbb; here the multijet background is negligible.
Nonuniform binning was applied in the 2-DM‘b2 distribu- tions in order to ensure sufficient MC events in each bin. In 695 pb1, we find 75 candidates with a total expected background of92events.
The third sample is in the dilepton channel, with tt! WbWbevents where bothWbosons decay leptonically.
The dilepton event selection requires two identified leptons with opposite electric charge and ET>20 GeV, 6ET>
25 GeV, and at least two jets with ET>15 GeV. More details on the selection and the sample composition can be found in Ref. [25]. Forttproduction withVAtop-quark decay, modeled by ALPGEN as described above, we esti- mate a selection efficiency, including the branching frac- tion, ofAVA0:72%, a factor 0.88 below the efficiency for VA. The two possible M2‘b values for a charged lepton with either the highest or the second highest ET jet, assumed to be produced by the fragmentation of theb quarks, are used to construct a 2-D distribution. As we can reconstruct M2‘b from the top-quark decay and from the anti-top-quark decay, we make one entry for each charged lepton. The effect of the correlation between the spins of the top-quark and the anti-top-quark is negligible here.
Again, nonuniform binning in the 2-D M‘b2 distributions is applied. The backgroundM‘b2 distribution is the combi- nation of three background types: approximately 50% from Z= !‘‘ with associated jets, 30% from W !‘ with associated jets where a jet is misidentified as a lepton, and 20% from massive diboson pairs,WW=WZ. TheZ=
072001-4
and diboson backgroundM2‘bdistributions are modeled by
ALPGEN. The misidentified lepton background is based on inclusive lepton trigger data where the second lepton is instead a jet (charged particle track) weighted by a proba- bility for misidentification as an electron (muon). A background-dominated data sample with only one jet is consistent, in terms of both the rate and the shape of the M2‘b distribution, with our model of the background. In 750 pb1, we observe 64 candidates (12ee,24, and 28e) with a total estimated background of204events.
The fraction fVA is estimated by comparing the M‘b2 distribution in data with parent M‘b2 distributions for tt production withVA top-quark decay (fVA0:0),tt production withVAtop-quark decay (fVA1:0), and backgrounds. A binned log likelihood fit procedure is used to extract the parameter of interest,fVA. We represent the imperfectly known accepted background cross section for each sample,bg, and thettcross section [26,27],tt, by nuisance parameters. The analytic expression for the like- lihood for each sample,
L YN
i0
Pni; i
Gbg; bgGtt; tt; (1) is the product over all N bins in M2‘b of the Poisson probabilities of observingnientries in a given bini, where the average expected bin content isi, and the Gaussian constraints on the estimated background and the predicted ttproduction cross sections, as shown in Table I. The i are given by
iNdataxVAT^iVAxVAT^iVAxbgT^ibg; (2) xVA fVAAVAtt
bgttAVAfVAAVA1fVA; (3) xVA 1fVAAVAtt
bgttAVAfVAAVA1fVA; (4)
xbg bg
bgttAVAfVAAVA1fVA: (5) Here,Ndata is the total number of observed events for the
sample. The xVA, xVA, and xbg are the fractions of tt production withVAtop-quark decay,ttproduction with VAtop-quark decay, and background, respectively. The T^iVA,T^iVA, andT^ibg are the probabilities for an event to occupy bini of the correspondingM2‘bdistribution. Note thatP
iT^i1:0. The combined likelihood is the product of the likelihoods of the three samples, but with one common Gaussian constraint on thettcross section.
The robustness of the fitting procedure has been tested with MC simulated experiments. For a given experiment and a particular sample, the number of observed data events is distributed in three categories (tt production with VA top-quark decay, tt production with VA top-quark decay, and background) according to their ex- pected fractions from Eqs. (3) –(5). For each category, the events are generated from the relevant M2‘b parent distri- bution. The hypotheses that fVA0:0;0:1;. . .;1:0 are studied for 2000 experiments for all samples combined, as well for the three samples separately. In all cases, the fit is unbiased and stable. We find an expected statistical uncer- tainty of 0.22 on fVAfor the combined case, 0.27 for all leptonjets events, with 0.35 for one b-tagged jet and 0.41 for twob-tagged jets, and 0.46 for dilepton events. In all cases, this includes a small component (0:02) due to the uncertainties on the background andttcross sections.
The maximum likelihood fit to the leptonjets sample yields a value of fVA0:210:28, with fVA 0:160:36 for the subset of events with one b-tagged jet and fVA0:280:44for the subset of events with two b-tagged jets. For the dilepton sample, we obtain fVA 0:640:37. The probability to obtain a value smaller than the dilepton result is 10% for the hypothesis fVA0. The leptonjets and dilepton results are com- patible at about 1.8 standard deviations.
The estimates of the systematic uncertainties on the measured value for fVA are shown in Table II for all samples combined. The leading sources of systematic un- certainty arise from uncertainties on the measured jet energy [28], the background shape and normalization, and limited MC statistics. All systematic uncertainties
TABLE I. The input values for the nuisance parameters and the values from the best fit to the combined samples.
Nuisance parameter Input (pb) Fit (pb)
tt 6:71:0 7:30:9
bgleptonjets 1b-tag 0:1560:017 0:1540:016 bgleptonjets 2b-tag 0:0130:002 0:0130:002
bgdilepton 0:0260:006 0:0220:006
TABLE II. The systematic uncertainties on the measurement offVAfor all samples combined.
Source Uncertainty
Jet energy 0.10
Background modeling 0.04
MC statistics 0.04
Initial/Final state QCD radiation 0.02
Multipleppinteractions 0.02
b-tag efficiency (ET) 0.02
MC generator 0.01
Parton densities 0.01
Total 0.12
are evaluated at fVA0; we find the dominant uncer- tainty is insensitive to the value of fVA. We quote our result at a top-quark mass value of175 GeV=c2, where the dependence of the measurement (upper limit) forfVA is 0:070:06 for a2 GeV=c2 shift in top-quark mass.
Note that many of the above sources of systematic uncer- tainty also contribute significantly to the systematic uncer- tainty on the measurement of the top-quark mass [29].
Combining all samples, the result for the fraction ofV Acurrent in top-quark decay is
fVA 0:060:22stat 0:12syst:
This value is in agreement with the standard model. TableI summarizes the fitted values for the nuisance parameters.
The likelihood distribution is shown in Fig. 1 for the combined sample as well as for each individual sample.
The good agreement in theM2‘bdistribution between data and the best fit result forfVAfrom the combined sample is shown in Figs. 2–4, where the highest bins also contain
overflow entries. For comparison, fVA1:00 is also shown.
In the absence of a signal, we evaluate an upper limit on fVA using a Bayesian approach. The profile likelihood function is first determined as a function of fVA, multi- plied by a prior flat between 0.0 and 1.0, and normalized to yield the posterior distribution forfVA. The upper limit at 95% confidence level (C.L.) is formed by integrating the posterior from zero to the value offVAthat yields 0.95 for the integral. We verified that this approach yields proper frequentist coverage for fVA0:3; a small correction, derived by the Neyman construction, would be applied to any upper limit greater than 0.3 to restore coverage in the
Events per bin 2 4 6 8
Events per bin 2 4 6 8
-1) Data (695 pb
=-0.06 t fV+A t
= 1.00 t fV+A t Background
/c4 < 1500 GeV2 lb2 M2
≤ 0
Events per bin 2 4 6 8
Events per bin 2 4 6
8 1500≤ Mlb22 < 3000 GeV2/c4
Events per bin 2 4 6 8
Events per bin 2 4 6
8 3000≤ Mlb22 < 4500 GeV2/c4
Events per bin 2 4 6 8
Events per bin 2 4 6
8 4500≤ Mlb22 < 7500 GeV2/c4
4)
2/c (GeV
lb1
M2
0 10000 20000
Events per bin
0 2 4 6 8 10 12 14
4)
2/c (GeV
lb1
M2
0 10000 20000
Events per bin
0 2 4 6 8 10 12
14 4
2/c 7500 GeV lb2≥
M2 Mlb12 (GeV2/c4)
0 10000 20000
0
FIG. 3 (color online). The M‘b12 distribution for the charged lepton and the highestETb-tagged jet, in five regions ofM2‘b2for the charged lepton and the second highest ET b-tagged jet, for the leptonjets sample with two b-tagged jets. For fVA 0:06, the2probabilities are 92%, 3%, 10%, 18%, and 47% in order of increasingM2‘b2.
4)
2/c (GeV
lb
M2
0 10000 20000 30000
4 /c2 Events per 1200 GeV
0 10 20 30 40
4)
2/c (GeV
lb
M2
0 10000 20000 30000
4 /c2 Events per 1200 GeV
0 10 20 30
40 Data (695 pb-1)
=-0.06 t fV+A
t
= 1.00 t fV+A
t
Background
FIG. 2 (color online). The M2‘b distribution for the lepton jets sample with one b-tagged jet. For fVA 0:06, the 2 probability is 69%.
Entries per bin 2 4 6 8 10 12
Entries per bin 2 4 6 8 10 12
-1) Data (750 pb
=-0.06 t fV+A t
= 1.00 t fV+A t Background
/c4 < 2000 GeV2 lb2 M2
≤ 0
Entries per bin 2 4 6 8 10 12
Entries per bin 2 4 6 8 10
12 < 4000 GeV2/c4 lb2
M2
≤ 2000
4) 2/c (GeV lb1 M2
0 10000 20000 30000
Entries per bin
0 2 4 6 8 10 12
4) 2/c (GeV lb1 M2
0 10000 20000 30000
Entries per bin
0 2 4 6 8 10
12 4000≤ Mlb22 < 6000 GeV2/c4
4) 2/c (GeV lb1 M2
0 10000 20000 30000
Entries per bin
0 5 10 15 20
4) 2/c (GeV lb1 M2
0 10000 20000 30000
Entries per bin
0 5 10 15 20
/c4 6000 GeV2 lb2≥ M2
FIG. 4 (color online). The M‘b12 distribution for a charged lepton and the highest ET jet, in four regions of M2‘b2 for a charged lepton and the second highest ET jet, for the dilepton sample. There are two entries per event, one for each lepton. For fVA 0:06, the2 probabilities are 58%, 14%, 54%, and 51% in order of increasing M2‘b2.
fV+A
-1.5 -1 -0.5 0 0.5 1 1.5
Likelihood
0 5 10 15
fV+A
-1.5 -1 -0.5 0 0.5 1 1.5
Likelihood
0 5 10
15 Lepton+jets 1 b-tag -tag b Lepton+jets 2 Dilepton Combined 95% CL
FIG. 1 (color online). Likelihood distribution [see Eq. (1)] for the leptonjets and dilepton data samples separately and combined.
072001-6
region fVA>0:3. From MC simulated experiments for the standard model case where fVA0, the median upper limit is 0.38 and 68% of experiments set an upper limit between 0.2 and 0.6.
Combining all samples, we set an upper limit on the fraction ofVAcurrent in top-quark decay of
fVA<0:29 at 95%C:L:
This is an improvement by a factor of 2 on the previous best direct limit [11]. In terms of the fraction of right- handed W bosons, our results are f 0:02 0:07stat 0:04systandf<0:09at 95% C.L.
We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.
This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundes- ministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, UK;
the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; the European Community’s Human Potential Programme under contract No. HPRN-CT- 2002-00292; and the Academy of Finland.
aVisiting scientist from the University of Athens.
bVisiting scientist from the University of Bristol.
cVisiting scientist from the University Libre de Bruxelles.
dVisiting scientist from Cornell University.
eVisiting scientist from the University of Cyprus.
fVisiting scientist from the University of Dublin.
gVisiting scientist from the University of Edinburgh.
hVisiting scientist from the University of Heidelberg.
iVisiting scientist from the Universidad Iberoamericana.
jVisiting scientist from the University of Manchester.
kVisiting scientist from the Nagasaki Institute of Applied Science.
lVisiting scientist from the University de Oviedo.
mVisiting scientist from the University of London, Queen Mary and Westfield College.
nVisiting scientist from the Texas Tech University.
oVisiting scientist from the IFIC (CSIC-Universitat de Valencia).
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