Article
Reference
Precision Measurement of the X (3872) Mass in J/ψπ
+π
−Decays
CDF Collaboration
CLARK, Allan Geoffrey (Collab.), et al.
Abstract
We present an analysis of the mass of the X(3872) reconstructed via its decay to J/ψπ+π−
using 2.4 fb−1 of integrated luminosity from pp collisions at s√=1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. The possible existence of two nearby mass states is investigated. Within the limits of our experimental resolution the data are consistent with a single state, and having no evidence for two states we set upper limits on the mass difference between two hypothetical states for different assumed ratios of contributions to the observed peak. For equal contributions, the 95% confidence level upper limit on the mass difference is 3.6 MeV/c2. Under the single-state model the X(3872) mass is measured to be 3871.61±0.16(stat)±0.19(syst) MeV/c2, which is the most precise determination to date.
CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Precision Measurement of the X (3872) Mass in J/ψπ
+π
−Decays. Physical Review Letters , 2009, vol. 103, no. 15, p. 152001
DOI : 10.1103/PhysRevLett.103.152001
Available at:
http://archive-ouverte.unige.ch/unige:38622
Disclaimer: layout of this document may differ from the published version.
1 / 1
Precision Measurement of the Xð3872Þ Mass in J= c
þDecays
T. Aaltonen,24J. Adelman,14T. Akimoto,56B. A´ lvarez Gonza´lez,12,uS. Amerio,44b,44aD. Amidei,35A. Anastassov,39 A. Annovi,20J. Antos,15G. Apollinari,18A. Apresyan,49T. Arisawa,58A. Artikov,16W. Ashmanskas,18A. Attal,4 A. Aurisano,54F. Azfar,43W. Badgett,18A. Barbaro-Galtieri,29V. E. Barnes,49B. A. Barnett,26P. Barria,47c,47aP. Bartos,15 V. Bartsch,31G. Bauer,33P.-H. Beauchemin,34F. Bedeschi,47aD. Beecher,31S. Behari,26G. Bellettini,47b,47aJ. Bellinger,60
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X. Zhang,25Y. Zheng,9,eand S. Zucchelli6b,6a (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439
3University of Athens, 157 71 Athens, Greece
4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
5Baylor University, Waco, Texas 76798, USA
6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy
6bUniversity of Bologna, I-40127 Bologna, Italy
7Brandeis University, Waltham, Massachusetts 02254, USA
8University of California, Davis, Davis, California 95616, USA
9University of California, Los Angeles, Los Angeles, California 90024, USA
10University of California, San Diego, La Jolla, California 92093, USA
11University of California, Santa Barbara, Santa Barbara, California 93106, USA
12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
13Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
15Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
17Duke University, Durham, North Carolina 27708, USA
18Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
19University of Florida, Gainesville, Florida 32611, USA
20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
21University of Geneva, CH-1211 Geneva 4, Switzerland
22Glasgow University, Glasgow G12 8QQ, United Kingdom
23Harvard University, Cambridge, Massachusetts 02138, USA
152001-2
24Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
25University of Illinois, Urbana, Illinois 61801, USA
26The Johns Hopkins University, Baltimore, Maryland 21218, USA
27Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
28Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;
Seoul National University, Seoul 151-742, Korea;
Sungkyunkwan University, Suwon 440-746, Korea;
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea;
Chonnam National University, Gwangju 500-757, Korea;
Chonbuk National University, Jeonju 561-756, 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, Que´bec, Canada H3A 2T8;
Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6;
University of Toronto, Toronto, Ontario, Canada M5S 1A7;
and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3
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
44aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
44bUniversity of Padova, I-35131 Padova, Italy
45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
47aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy
47bUniversity of Pisa, I-56127 Pisa, Italy
47cUniversity of Siena, I-56127 Pisa, Italy
47dScuola 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
52aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy
52bSapienza Universita` di Roma, I-00185 Roma, Italy
53Rutgers University, Piscataway, New Jersey 08855, USA
54Texas A&M University, College Station, Texas 77843, USA
55aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, Italy
55bUniversity of Trieste/Udine, I-33100 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 5370, USA6
61Yale University, New Haven, Connecticut 06520, USA (Received 29 June 2009; published 5 October 2009)
We present an analysis of the mass of theXð3872Þreconstructed via its decay to J=cþ using 2:4 fb1 of integrated luminosity from pp collisions at ffiffiffi
ps
¼1:96 TeV, collected with the CDF II detector at the Fermilab Tevatron. The possible existence of two nearby mass states is investigated. Within the limits of our experimental resolution the data are consistent with a single state, and having no evidence for two states we set upper limits on the mass difference between two hypothetical states for different assumed ratios of contributions to the observed peak. For equal contributions, the 95% confidence level
PRL103,152001 (2009) P H Y S I C A L R E V I E W L E T T E R S 9 OCTOBER 2009
upper limit on the mass difference is3:6 MeV=c2. Under the single-state model the Xð3872Þmass is measured to be3871:610:16ðstatÞ 0:19ðsystÞMeV=c2, which is the most precise determination to date.
DOI:10.1103/PhysRevLett.103.152001 PACS numbers: 14.40.Gx, 12.39.Mk, 13.25.Gv
The discovery of theXð3872Þ[1,2] and many additional unexpected states [3] has revived general interest in spec- troscopy in the charmonium mass region. Initial attempts to explain theXð3872Þas a conventional bound state of a cquark and an anti–cquark have shortcomings [4] which triggered the development of unconventional explanations.
Two popular models are a molecular state composed ofD0 andD0 mesons [5,6], and a four-quark state [7].
In an effort to resolve the nature ofXð3872Þ, several of its properties have been measured. The first determinations of its mass [1,2,8,9] resulted in values very close to the D0D0 mass threshold. The observed width in these mea- surements was compatible with zero. Studies of the Xð3872Þproduction properties inpp collisions [8,10] sug- gest that the production mechanisms are similar to those for the cð2SÞ charmonium state. Several measurements constrained the quantum numbers spin (J), parity (P), and charge-conjugation parity (C) of the Xð3872Þ. These in- clude evidence for the decay modes Xð3872Þ !J=c, J=c!, and cð2SÞ[11], and a measurement of the mass distribution of the dipions from theXð3872Þ !J=cþ decay [12]. These measurements indicate an evenCparity.
A subsequent angular analysis constrained the quantum numbers to only two possibilities, JPC¼1þþ or 2þ [13]. A possible further decay mode of theXð3872Þwas identified as a peak near threshold in theD0D00invariant mass spectrum [14] with a mean mass more than 3 MeV=c2 above measurements in theJ=cþ mode.
Despite efforts on both the experimental and theoretical sides, the nature of theXð3872Þstill remains an unresolved puzzle.
A measurement of the Xð3872Þ mass with increased precision can provide crucial information for understand- ing its nature. Under the hypothesis of a molecular state the mass of theXð3872Þhas to be lower than the sum of theD0 andD0 masses. The four-quark state hypothesis predicts the existence of two distinct particles that differ by the light-quark content bound to the cc quarks. These two particles should have slightly different masses, and the model of Maiani et al. [7] predicts a mass difference at the level of 83 MeV=c2. Recent measurements of the difference between the Xð3872Þ mass in Bþ ! Xð3872ÞKþandB0 !Xð3872ÞK0 decays [15,16] disfavor this model under the hypothesis that one state is domi- nantly produced in Bþ decays and the other one in B0 decays.
In this Letter we report a study of the mass of the Xð3872Þresonance produced inpp collisions. We consider
the conjecture that the structure observed in our data is composed of two different states with distinct masses; but failing to discern any evidence for this possibility we set an upper limit on the mass difference between two hypotheti- cal states. In light of this result we perform a precision measurement of theXð3872Þmass, the main result of this Letter.
The data were collected by the CDF II detector at the Fermilab Tevatronpp collider between February 2002 and August 2007, and correspond to an integrated luminosity of 2:4 fb1. The CDF II detector [17] consists of a mag- netic spectrometer surrounded by electromagnetic and hadronic calorimeters and muon detectors. The tracking system is immersed in a 1.4 T axial magnetic field and is composed of a silicon microstrip detector [18] surrounded by an open-cell drift chamber (COT) [19]. It extends out to a radius of 138 cm with up to 96 position measurements in the COT, and achieves a transverse momentum resolution of ðpTÞ=pT 0:15%pT=ðGeV=cÞ. We detect muons in planes of multiwire drift chambers and scintillators [20] in the pseudorapidity range jj 1:0. Events with J=c ! þ decays are recorded using a dimuon trigger, which requires two oppositely charged COT tracks matched to muon chamber track segments. The reconstructed invariant mass of a dimuon pair is required to be between 2.7 and 4:0 GeV=c2.
To reconstruct Xð3872Þ candidates we first build J=c candidates by combining pairs of oppositely charged muon candidates with a transverse momentum, pT, larger than 1:5 GeV=c. TheXð3872Þcandidates are formed by com- bining J=c candidates in the invariant mass range from 2.95 to 3:25 GeV=c2 with pairs of oppositely charged tracks, each with pT>0:4 GeV=cand assigned the pion mass. We require that all four tracks have at least 10 COT and 2 silicon hits. For the resulting Xð3872Þ candidates withpT >3:5 GeV=c, we perform a kinematic fit in which the tracks are constrained to originate from a common vertex and the dimuon invariant mass is constrained to the world average J=c mass [21]. Candidates having a kinematic fit of good quality are selected in a broad invari- ant mass range containing, in addition to Xð3872Þ candi- dates, also cð2SÞ candidates that decay to the same final state. The cð2SÞserves as a valuable control sample.
Several discriminating quantities are combined by a neural network into a single selection variable. The indi- vidual quantities are transformed such that linear depen- dences on the invariant mass are removed. The most important inputs to the neural network are the Qvalue of 152001-4
the decay, defined as Q¼mJ=cþmþmJ=c, the transverse momenta of the two pions, the quality of the kinematic fit of the Xð3872Þ candidate, and muon identification quantities. The offline muon identification is based on the matching of tracks found in the tracking system to track segments in the muon system and on the energy deposited in the calorimeter by the muon- candidates. For the training of the neural network, a back- ground sample is extracted from data, selecting events in regions of theJ=cþmass away from theXð3872Þand cð2SÞ signals, mainly consisting of J=c particles com- bined with two random tracks. For the signal sample we use simulatedXð3872Þevents. In the simulation we gen- erate a single Xð3872Þ per event using the momentum distribution of the cð2SÞ, which is then decayed using the EVTGEN package [22]. Each event is then passed through a detector simulation based on theGEANT3pack- age [23] and a trigger simulation, and is reconstructed with the same code as for real data. The simulation is in good agreement with the data as verified with several kinematic quantities. The final selection places a requirement on the neural network output and the number of candidates per event. Using wrong-sign candidates, where the two pion candidates have the same charge, we verify that the selec- tion does not create an artificial excess in the mass spec- trum. The invariant mass distribution of the selected candidates in theXð3872Þmass region is shown in Fig.1.
The sample contains about 6000Xð3872Þsignal events.
Before we perform a mass measurement, we test whether the signal is consistent with a single state or we have evidence for more than one state. In the test we perform a binned maximum-likelihood fit to the mass distribution in data, where we describe the combinatorial background by a second-order polynomial, and the signal by a nonrelativistic Breit-Wigner function convolved with a resolution function determined from simulated events and parametrized by the sum of two Gaussians. The core Gaussian, with a width of3:2 MeV=c2, accounts for two thirds of the resolution function; the second Gaussian has about twice the width. In the fit we fix the width of the Breit-Wigner function to ¼1:34 MeV=c2, our average of the widths measured inJ=cþ decays [1,15]. The uncertainty onof0:64 MeV=c2 is taken into account in the hypothesis test described below. As a test statistic we introduce a factortthat scales the intrinsic and resolution widths of the signal shape. The value oftdetermined by the fit to the data is then compared to the distribution oftfrom an ensemble of simulated experiments that assume a single state. Based on this comparison the consistency of the data with the single-state hypothesis is evaluated. The pseu- doexperiments are generated using the same fit model as in data. As several quantities are known only with limited precision, we vary those in the sample generation accord- ing to their uncertainties. The varied parameters include background shape parameters, the number of signal and
background events, the width of the Breit-Wigner function, and the overall width of the resolution function. From a comparison of the cð2SÞ signal in the data to that of simulated events we observe that the simulation under- estimates the resolution by about 5%. The samples were generated with a resolution corrected for this discrepancy.
From data we obtain a width scale parameter value of t¼1:052. In Fig.2 we show a comparison of the fitted scale parameter to the distribution obtained from simulated experiments assuming a single state. We conclude that the data are fully consistent with a single state. In the absence of evidence for two distinct states we set an upper limit on the possible mass difference between two hypothetical states. As a test statistic we use the width scale t, which is compared to expectations from samples simulated with different mass splittings. We assume that both states have the same mass shape and do not interfere. We derive upper limits as a function of the fraction f1 of the lower lying state to the total observed signal. The resulting 90% and 95% C.L. upper limits are shown in Fig. 3. For an equal mixture of the two contributing states, the limits arem <
3:2 MeV=c2 and m <3:6 MeV=c2 at 90% and 95%
confidence levels, respectively. This result is complemen- tary to other measurements [15,16] in that it does not rely on assumptions about the production of the two hypotheti- cal states inBþversusB0decays, but depends onf1.
2 Candidates per 2.5 MeV/c
500 1000 1500 2000 2500 3000 3500 4000 4500
3.85 3.86 3.87 3.88 3.89
2Candidates per 1.25 MeV/c
1400 1600 1800 2000 2200
2
) Mass (GeV/c π
-π
+ψ J/
3.75 3.80 3.85 3.90 3.95 4.00
data-fit -200
0 200
FIG. 1 (color online). Invariant mass distribution of the Xð3872Þcandidates. The points show the data distribution, the full line is the projection of the unbinned maximum-likelihood fit, and the dashed line corresponds to the background part of the fit. The inset shows an enlargement of the region around the Xð3872Þpeak. Residuals of the data with respect to the fit are displayed below the mass plot.
PRL103,152001 (2009) P H Y S I C A L R E V I E W L E T T E R S 9 OCTOBER 2009
Lacking any indication of dual states we proceed to extract the mass of theXð3872Þby performing an unbinned maximum-likelihood fit using the same fit model as used in the previous two-state test. In this fit we fix the intrinsic width to¼1:34 MeV=c2 and the resolution parameters to their expected values. Free parameters in the fit are the mass of the Xð3872Þ, the fraction of signal events in the sample, a resolution scale factor, and two parameters de- termining the background shape.
To check the absolute mass scale we use the nearby cð2SÞsignal in the sameJ=cþinvariant mass spec- trum. We use the identical fit model as for the Xð3872Þ, with the exception that the signal shape parameters are adjusted to the world average value of¼0:337 MeV=c2 [21] for the intrinsic width, and that resolution parameters are determined from simulatedcð2SÞevents. The fit yields mcð2SÞ¼3686:030:02ðstatÞMeV=c2. While this value is consistent with the world average cð2SÞ mass of 3686:090:03 MeV=c2 [21], we use the60 keV=c2 dif-
ference between our measurement and the world average value as an estimate of a possible uncertainty due to un- certainties both on our measurement and on the world average value.
Since a possible miscalibration of the momentum scale would show up as a dependence of the measured mass on momentum, we measure the cð2SÞmass as a function of several kinematic variables. We find that any tested depen- dence has an effect below0:1 MeV=c2, which is taken as an additional measure of the systematic uncertainty. This uncertainty is summed in quadrature with the systematic uncertainty on the absolute mass scale derived above. To translate the estimation of the mass-scale uncertainty from the cð2SÞto theXð3872Þwe scale the sum by a factor of 1.6 that is modeled by a linear dependence on the mass with respect to theJ=cþthreshold. This yields a total systematic uncertainty of 0:19 MeV=c2 attributed to the momentum scale.
To estimate the effect due to the uncertainties in the fit model, we refit the data using alternative models. These include the use of a linear function instead of a second- order polynomial for the background description, a single Gaussian function instead of a nonrelativistic Breit-Wigner function convolved with double Gaussian resolution func- tion for the signal description, and fixing the natural width to zero or to twice the nominal value. We also perform a fit in a mass window reduced by 40%. All of these mod- ifications have a negligible effect on the fitted mass, below 20 keV=c2, and therefore we do not assign any systematic uncertainty to the measurement due to the fit model.
Because the observed decays to D0D0 may stem from a different particle we assume that the mass line shape is not distorted by them. If this were the case, as discussed in Ref. [24], it would be expected to increase the measured mass by about150 keV=c2.
The final mass measurement for the Xð3872Þ is 3871:610:16ðstatÞ 0:19ðsystÞ MeV=c2. The measured value is in good agreement with the world average [21] and the more precise average of measurements in the J=cþ channel including the preliminary Belle mea- surement [16]. It is the most precise single measurement to date and improves the precision of the latter average by about a factor of 1.5.
Our measurement is below theD0D0mass threshold of 3871:800:35 MeV=c2 [21] by 0:190:43 MeV=c2. This implies that the interpretation of the Xð3872Þ as D0D0 molecule is still possible, although the current precision does not preclude an Xð3872Þ mass above the D0D0 mass threshold. A future increase in precision of this comparison will therefore require improvements in the precision of theD0 andD0masses. Concerning the four- quark hypothesis, our mass splitting upper limits for two hypothetical states with relative fractions between 0.2 and 0.8 exclude the range of 83 MeV=c2 predicted in Ref. [7].
Low-Mass Signal Fraction f1
0.2 0.4 0.6 0.8
)2 m (MeV/c∆
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
95% C.L. Upper Limit 90% C.L. Upper Limit
FIG. 3 (color online). The upper limit on the mass difference m between two states as a function of the fractionf1 of the yield of the lower mass state.
Width Scale t
0.8 1.0 1.2 1.4
Experiments per 0.012
0200400 600 800 1000 1200 1400 1600 1800
Measured Value
FIG. 2 (color online). Distribution of the width scale t for generated experiments using the single-state hypothesis (histo- gram). Also shown is the measured value from data (vertical line).
152001-6
In summary, we present a new measurement of the Xð3872Þmass using its decay toJ=cþ. Our measured value of3871:610:16ðstatÞ 0:19ðsystÞMeV=c2super- sedes that of Ref. [2], and is more than 2 times more precise than the best single measurement so far. In addi- tion, we derive upper limits on the mass difference for the hypothesis of twoXð3872Þstates, which are predicted by some four-quark scenarios, as a function of their relative contribution to the observed signal. For an equal mixture of the two possible states, the limit is m <3:6 MeV=c2 at 95% confidence level.
We thank E. Braaten for useful discussions. We thank the Fermilab staff and the technical staffs of the participat- ing 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 Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Founda- tion and the Korean Research Foundation; the Science and Technology Facilities Council and the Royal Society, U.K.;
the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacio´n, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and the Academy of Finland.
aDeceased.
bVisitor from University of Massachusetts Amherst, Amherst, MA 01003, USA.
cVisitor from Universiteit Antwerpen, B-2610 Antwerp, Belgium.
dVisitor from University of Bristol, Bristol BS8 1TL, United Kingdom.
eVisitor from Chinese Academy of Sciences, Beijing 100864, China.
fVisitor from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy.
gVisitor from University of California Irvine, Irvine, CA 92697, USA.
hVisitor from University of California Santa Cruz, Santa Cruz, CA 95064, USA.
iVisitor from Cornell University, Ithaca, NY 14853, USA.
jVisitor from University of Cyprus, Nicosia CY-1678, Cyprus.
kVisitor from University College Dublin, Dublin 4, Ireland.
lVisitor from University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.
mVisitor from University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017.
nVisitor from Kinki University, Higashi-Osaka City, Japan 577-8502.
oVisitor from Universidad Iberoamericana, Mexico D.F., Mexico.
pVisitor from University of Iowa, Iowa City, IA 52242, USA.
qVisitor from Queen Mary, University of London, London, E1 4NS, United Kingdom.
rVisitor from University of Manchester, Manchester M13 9PL, United Kingdom.
sVisitor from Nagasaki Institute of Applied Science, Nagasaki, Japan.
tVisitor from University of Notre Dame, Notre Dame, IN 46556, USA.
uVisitor from University de Oviedo, E-33007 Oviedo, Spain.
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wVisitor from IFIC(CSIC-Universitat de Valencia), 46071 Valencia, Spain.
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yVisitor from Bergische Universita¨t Wuppertal, 42097 Wuppertal, Germany.
zOn leave from J. Stefan Institute, Ljubljana, Slovenia.
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