Measurement of Resonance Parameters of Orbitally Excited Narrow <em>B⁰</em> Mesons

Article

Reference

Measurement of Resonance Parameters of Orbitally Excited Narrow B

Mesons

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al.

Abstract

We report a measurement of resonance parameters of the orbitally excited (L=1) narrow B0 mesons in decays to B(*)+π− using 1.7  fb−1 of data collected by the CDF II detector at the Fermilab Tevatron. The mass and width of the B*02 state are measured to be

m(B*02)=5740.2+1.7−1.8(stat)+0.9−0.8(syst)  MeV/c2 and

Γ(B*02)=22.7+3.8−3.2(stat)+3.2−10.2(syst)  MeV/c2. The mass difference between the B*02 and B01 states is measured to be 14.9+2.2−2.5(stat)+1.2−1.4(syst)  MeV/c2, resulting in a B01 mass of 5725.3+1.6−2.2(stat)+1.4−1.5(syst)  MeV/c2. This is currently the most precise measurement of the masses of these states and the first measurement of the B*02 width.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of Resonance

Parameters of Orbitally Excited Narrow B

Mesons. Physical Review Letters , 2009, vol. 102, no. 10, p. 102003

DOI : 10.1103/PhysRevLett.102.102003

Available at:

http://archive-ouverte.unige.ch/unige:38538

Disclaimer: layout of this document may differ from the published version.

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Measurement of Resonance Parameters of Orbitally Excited Narrow B

Mesons

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(CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

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

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, Pennylsvania A 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

102003-2

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

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, M5S 1A7, Canada

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, I-35131 Padova, Italy

44bSezione di Padova-Trento, University 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, I-00185 Roma, Italy

52bSezione di Roma 1, Sapienza 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, Italy

55bUniversity 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 September 2008; published 12 March 2009)

We report a measurement of resonance parameters of the orbitally excited (L¼1) narrowB⁰mesons in decays toB^ðÞþusing1:7 fb¹of data collected by the CDF II detector at the Fermilab Tevatron. The mass and width of the B⁰₂ state are measured to be mðB⁰₂Þ ¼5740:2^þ1:7_1:8ðstatÞ^þ0:9_0:8ðsystÞMeV=c² and ðB⁰₂ Þ ¼22:7^þ3:8_3:2ðstatÞ^þ3:2_10:2ðsystÞMeV=c². The mass difference between the B⁰2 and B⁰1 states is measured to be 14:9^þ2:2_2:5ðstatÞ^þ1:2_1:4ðsystÞMeV=c², resulting in a B⁰1 mass of 5725:3^þ1:6_2:2ðstatÞ^þ1:4_1:5 ðsystÞMeV=c². This is currently the most precise measurement of the masses of these states and the first measurement of theB⁰₂ width.

DOI:10.1103/PhysRevLett.102.102003 PACS numbers: 14.40.Nd, 12.40.Yx

Mesons consisting of a light and a heavy quark are an interesting laboratory for the study of quantum chromody- namics, the theory of strong interactions. The role of the heavy-light quark mesons is similar to that played by the hydrogen atom in understanding quantum electrodynam- ics. The bound states of abquark with either a lightuord quark are referred to as B mesons. The states with zero internal orbital angular momentum (L¼0) and spin parity J^P¼0(B) and1(B) are well established [1], but the spectroscopy of the orbitally excitedBstates has not been well studied. ForL¼1, the total angular momentum of the light quark isj¼¹₂ orj¼³₂. With the addition of the spin of the heavy quark, two doublets of states are ex- pected: states withj¼¹₂, namedB₀ (J¼0) andB⁰₁ (J¼ 1), and states withj¼³₂, namedB1 (J¼1) andB₂ (J¼ 2). These four states are collectively referred to asB.

Heavy quark effective theory [2] predicts that the mass splitting within each doublet of a heavy-light quark meson is inversely proportional to the heavy quark mass [2–8].

The j¼¹₂ states are expected to decay to B^ðÞ via an S-wave transition and to exhibit resonance widths in the range100–200 MeV=c²[9]. Thej¼³₂states are expected to decay to B^ðÞ via a D-wave transition and to have widths of 10–20 MeV=c² [7,8]. This Letter focuses on theB1andB₂observed inBfinal states. The decayB1 ! B is forbidden by conservation of angular momentum and parity, while bothB₂ !BandB₂!Bdecays are allowed. Decays to aBare followed byB!B, where the photon is not reconstructed in the CDF II detector due to its low energy. Because of the missing photon, the measured B mass in B1 !B!B and B₂ ! B!B events is lower than the B mass by 45:780:35 MeV=c² [1], resulting in an expected signal structure of three narrowBpeaks for theB1 andB₂.

Previous measurements of properties of thej¼³₂B⁰₁and B⁰₂ mesons using inclusive or partially reconstructed de- cays did not separate the narrow states [10,11] or were limited by low sample statistics [12]. Recently, the D0 Collaboration resolved the B⁰₁ andB⁰₂ masses [13]. The superb mass resolution of the CDF II detector allows better precision and enables us to measure theB⁰₂ width. Here, we present measurements of the masses of theB⁰₁andB⁰₂ states and the width of theB⁰₂ state. We reconstructB⁰in B^þandB^þdecays, where theB^þcandidates decay into J=cK^þ, D^0þ, and D^0þþ final states with J=c !^þ and D⁰!K^þ. Throughout this Letter, any reference to a specific charge state implies the charge conjugate state as well.

We use a data sample of events produced inpp colli- sions at ffiffiffi

ps

¼1:96 TeVrecorded by the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 1:7 fb¹. The components and performance parameters of CDF II [14] most relevant for this analysis are the tracking, the muon detectors, and the trigger on displaced vertices.

The tracking system lies in a uniform axial magnetic field

of 1.4 T. The inner tracking volume is instrumented with a layer of single-sided silicon microstrip detectors mounted directly on the beam pipe at a radius of 1.5 cm, and 7 layers of double-sided silicon that extend out to a radius of 28 cm [15]. This system provides excellent resolution of the impact parameter, d0, defined as the distance of closest approach of the track to the interaction point in the trans- verse plane. The outer tracking volume contains an open- cell drift chamber (COT) up to a radius of 137 cm [16].

Muons are detected in planes of drift tubes and scintillators [17] located outside the hadronic and electromagnetic calorimeters. The muon detectors used in this study cover the pseudorapidity range jj 1:0, where ¼ lntanð=2Þ andis the polar angle measured from the proton beam.

A three-level trigger system selects events in real time.

A dimuon trigger [14] requires two tracks of opposite charge that match track segments in the muon chambers and have a combined dimuon mass consistent with theJ=c mass. An extremely fast tracker at level 1 (XFT) [18]

groups COT hits into tracks in the transverse plane. A silicon vertex trigger at level 2 (SVT) [19] adds silicon hits to tracks found by the XFT, thus providing better- defined tracks and allowing candidate selection based on the impact parameter. A displaced vertex trigger [20]

requires two tracks each with a scalar transverse momen- tum, pT, greater than 2 GeV=c and with 0:12< d0<

1 mm. Additionally, the intersection point of the track pair must be transversely displaced from theppinteraction point by at least 0.2 mm, and the pair must have a scalar sumpTð1Þ þpTð2Þ>5:5 GeV=c.

Decays B^þ !J=cK^þ are reconstructed from the di- muon trigger data while decays B^þ!D^0þð^þÞ are reconstructed from the displaced vertex trigger data. In each decay, the tracks are constrained in a three- dimensional kinematic fit to the appropriate B^þ vertex topology with the J=c ^andD⁰ masses constrained to the world average values [1]. Each track compatible with originating from the same interaction point as the B^þand not used to reconstruct the B^þ is considered as a pion candidate, and its four-momentum is combined with that of theB^þcandidate to form aB⁰candidate. We search for narrow resonances in the mass difference distribution of Q¼mðB^þÞ mðB^þÞ m, where mðB^þÞ and mðB^þÞ are the reconstructed invariant masses of the B^þ pair and the B^þ candidate, and m is the pion mass.

TheB^þcandidates are selected using independent arti- ficial neural networks for each of the three B^þ decay modes. The neural networks are based on the

NEUROBAYES package [21]. For the decays B^þ! J=cK^þ andB^þ!D^0þ, we use the training and selec- tion methods developed in Ref. [22]. For the decayB^þ! D^0þþ, we closely follow the construction of the neural networks for the other two decays. To train this

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last neural network, we use data from the region 5325<

mðB^þÞ<5395 MeV=c² as the background sample and simulatedB^þ events as the signal sample [23]. The most discriminating inputs to the neural networks arep_TðB^þÞ, d₀ðB^þÞ,d₀of the kaon or pion with respect to theB^þdecay vertex, and the projected distance of theB^þ decay vertex from the primary vertex along theB^þ transverse momen- tum. We select approximately 51 500 B events in the J=cK^þdecay channel, 40 100 in the D^0þ channel, and 11 000 in theD^0þþchannel.

To selectB⁰mesons, three additional neural networks are trained on a combination of a simulated signal sample and real data for a background sample. The data for the background sample are taken from the entireQrange of 0 to1000 MeV=c², which includes only a small contribution from the signal in the data. To avoid biasing the network training, the simulated events are generated with the same Qdistribution as the data. TheB⁰neural networks use the same inputs as theB^þ neural networks, together with the kinematic and particle identification quantities for the pion from theB⁰decay. The most important discriminants are thep_T andd₀ of the pion from theB⁰ decay vertex and the output of theB^þ neural network.

For eachB^þ decay channel, we require fewer than six B⁰ candidates in an event in order to enhance the signal- to-background ratio. The observedB⁰signals are consis- tent for all threeB^þ decay channels. Therefore, we com- bine the B⁰ events for all decay channels and use this combined Q distribution to measure the B⁰ properties.

We count the number of Monte Carlo signal events,NMC, and the number of signal and background events in the data,Ndata, in theQsignal region of 200 to400 MeV=c² for a given cut on each of the three network outputs. We then optimize theB⁰selection for eachB^þdecay channel to maximize the combined significance,N_MC= ffiffiffiffiffiffiffiffiffiffi

N_data

p . The

resulting combinedQdistribution is shown in Fig.1.

TheB⁰signal structure is interpreted as resulting from the three signal processes B⁰₁!B^þ, B⁰₂ !B^þ, andB⁰₂ !B^þ, withB^þ!B^þ. TheQdistribution for each signal process is modeled by a nonrelativistic fixed-width Breit-Wigner function convoluted with the detector resolution model. The resolution on Q is deter- mined from simulation and modeled as a sum of two Gaussian distributions, a dominant narrow core and a broad tail with Q-dependent standard deviations of about 2 MeV=c² and 4 MeV=c², respectively. The fraction of events in the broad tail is fixed to be 0.2.

We perform an unbinned maximum-likelihood fit to the combined Q distribution, from which we extract the Q value of the B⁰₂ !B^þ decay, the mass difference between the B⁰₁ andB⁰₂ states, the width of theB⁰₂ , and the number of events in each signal process. The following parameters in the fit are constrained to their values from either previous measurements or theoretical predictions:

the energy of the B^þ decay photon, EðÞ ¼45:78

0:35 MeV=c² [1]; the ratio of the B⁰₁ and B⁰₂ widths,

ðB⁰₁Þ

ðB⁰₂Þ¼0:90:2 [7]; and the ratio of theB⁰₂ branching fractions, _BRðB^BRðB₀^02!BþÞ

2!B^þÞ¼1:10:3 [11], consistent with the value measured in Ref. [13].

The background is modeled by a sum of two compo- nents, each being the product of a power law and an exponential function. We also expect reflections from B⁰s !B^þK decays when the kaon is mistakenly as- signed the pion mass. The shape of the reflection in the Q distribution is determined in simulations ofB⁰s states [22] and fixed in the fit. The normalization of the B⁰s is obtained by correcting the observed yield from Ref. [22] by a ratio of efficiencies to reconstruct aB⁰s decay as aB⁰ andB⁰s . In theB⁰ data sample, we expect2412B⁰_s1 events and6231B⁰_s2 events. These normalizations enter the fit as Gaussian constraints.

Sources of systematic uncertainty on the mass difference and width measurements include mass scale, mass- dependent signal efficiency, fit model bias, assumptions entered as Gaussian constraints in the fit, choice of back- ground and resolution models, and location and amount of B⁰ broad states. The systematic uncertainties are sum- marized in TableI.

To determine the mass scale uncertainty, we reconstruct cð2SÞ !J=c^þ with J=c !^þ, which has a similar Q value as the B⁰ decays. We compare the measured Qto the world average [1] and take the differ- ence as the mass scale uncertainty. To evaluate the effect of signal efficiency with changing Q, we generate a large number of samples of the same size as the data, called

2) (MeV/c ) - m(B) - mπ

π Q = m(B

0 200 400 600

2 Candidates per 5 MeV/c

0 20 40 60 80 100 120 140 160 180

200 Data

Total Fit π B*

→

0

B1

π B* 2→ B*0

π

→ B

2

B*0 (*)K

→ B

**0

Bs

Background

FIG. 1 (color online). Distribution of the mass differenceQ¼ mðB^þÞ mðB^þÞ m for exclusiveB^þ decays. Curves are shown separately for the background, the B⁰s !B^ðÞK reflec- tions, and the threeB⁰decays.

pseudoexperiments, with the Q-dependent efficiency ob- tained from simulation. We then apply the default fit to the pseudoexperiments.

Tests of the fit and signal model on pseudoexperiments show a small fit bias on theB⁰ signal parameters, which is included as a systematic uncertainty. Signal parameters entered as Gaussian constraints in the fit contribute to the fit uncertainty. To determine their systematic contribution, we refit the data with these constrained parameters fixed.

This fit returns the statistical fit uncertainties, which are subtracted in quadrature from the total fit uncertainties to obtain the systematic contribution.

To estimate the uncertainties due to the choice of back- ground and resolution models, we generate pseudoexperi- ments with varied background parameterizations or worse mass resolution. The background is also well modeled by the sum of a broad Breit-Wigner function with the product of a power law and an exponential function. From com- parisons of the detector resolution in data and Monte Carlo for thecð2SÞsample, we expect the Monte Carlo to under- estimate the resolution by no more than 20%. These pseu- doexperiments are fit with the default fit and the generating model. The distribution of the differences between these fit results is modeled by a Gaussian, whose mean is assigned as the systematic uncertainty.

Possible effects of the decays of the broad B₀ and B⁰₁ states on our background model are studied by adding two Breit-Wigner functions of identical width varied over the range 100–200 MeV=c². The Q values of the states are independently varied in the range 240 to360 MeV=c², the region around the narrowB⁰peaks. We refit the data for various masses and widths of the broad states, with the normalizations of the broad Breit-Wigner functions as additional free parameters in the fit model. We then take the largest variation in the narrowB⁰ parameters from any configuration of broad states as the systematic uncer- tainty due to theB⁰broad states.

The result of the likelihood fit to the data is shown in Fig.1, and we measure the following:

mðB⁰₂ ÞmðB^þÞm¼321:5^þ1:7_1:8ðstatÞ^þ0:9_0:7ðsystÞMeV=c²; mðB⁰₂ ÞmðB⁰₁Þ ¼14:9^þ2:2_2:5ðstatÞ^þ1:2_1:4ðsystÞMeV=c²;

and ðB⁰₂ Þ ¼22:7^þ3:8_3:2ðstatÞ^þ3:2_10:2ðsystÞMeV=c²: The signal is consistent with theoretical predictions [5,6], and Gaussian-constrained parameters remain close to their input values, the largest departure being 0.4 standard de- viations. The numbers of events are NðB⁰₁Þ ¼503^þ75₆₈, NðB⁰₂ !B^þÞ ¼385^þ48₄₅, and NðB⁰₂ !B^þÞ ¼ 351^þ48₄₅, where uncertainties are statistical only. Using the mass of the B^þ [1] and the correlations between the fit parameters, the masses of the B⁰₁ and B⁰₂ are mðB⁰₂ Þ ¼5740:2^þ1:7_1:8ðstatÞ^þ0:9_0:8ðsystÞMeV=c²andmðB⁰₁Þ ¼ 5725:3^þ1:6_2:2ðstatÞ^þ1:4_1:5ðsystÞMeV=c². With the current statis- tics, the data are also consistent with containing only theB⁰₁ andB⁰₂ !B^þpeaks.

In summary, using the three fully reconstructed decays B^þ!J=cK^þ, B^þ!D^0þ, and B^þ!D^0þþ, we observe two narrow B⁰ states in the decays B⁰₁! B^þandB⁰₂ !B^ðÞþ. This is the most precise mea- surement of the narrowB⁰ masses to date. We have also measured the B⁰₂ width for the first time. There is some discrepancy between these measurements and those re- ported by the D0 collaboration [13], the largest being close to a 3 difference in the mass splitting of the two B⁰ states.

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 Founda- tion; the A. P. Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS;

the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacio´n, Spain; the Slovak R&D Agency;

and the Academy of Finland.

aDeceased

bWith visitors from University of Massachusetts Amherst, Amherst, MA 01003., USA

cWith visitors from Universiteit Antwerpen, B-2610 Antwerp, Belgium.

TABLE I. Systematic uncertainties on the B⁰ parameter measurements. Each row corresponds to one source of system- atic uncertainty. The columns show the uncertainties for each of the three B⁰ signal parameters. Uncertainties are in units of MeV=c².

Source QðB⁰₂ Þ ðB⁰₂ Þ mðB⁰₂Þ mðB⁰₁Þ

Mass scale 0:2 <0:01

Efficiency _0:03^{þ0 þ0:4}_{0 0:3}^þ0

Fit bias and signal model _0:3^{þ0 þ0:4}_{0 0:2}^þ0 Fit constraints ^þ0:4_0:3 ^þ2:1_1:5 ^þ0:7_0:9

Background ^þ0:2_{0 1:6}^{þ0 þ0:2}₀

Resolution <0:01 _0:4^þ0 <0:01

Broad states ^þ0:7_0:5 ^þ2:3_9:9 ^þ0:9_1:0

Total ^þ0:9_{0:7 10:2}^{þ3:2 þ1:2}_1:4

102003-6

dWith visitors from University of Bristol, Bristol BS8 1TL, United Kingdom.

eWith visitors from Chinese Academy of Sciences, Beijing 100864, China.

fWith visitors from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy.

gWith visitors from University of California Irvine, Irvine, CA 92697., USA

hWith visitors from University of California Santa Cruz, Santa Cruz, CA 95064., USA

iWith visitors from Cornell University, Ithaca, NY 14853., USA

jWith visitors from University of Cyprus, Nicosia CY-1678, Cyprus.

kWith visitors from University College Dublin, Dublin 4, Ireland.

lWith visitors from Royal Society of Edinburgh/Scottish Executive Support Research Fellow.

mWith visitors from University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.

nWith visitors from Universidad Iberoamericana, Mexico D.F., Mexico.

oWith visitors from Queen Mary, University of London, London, E1 4NS, England.

pWith visitors from University of Manchester, Manchester M13 9PL, England.

qWith visitors from Nagasaki Institute of Applied Science, Nagasaki, Japan.

rWith visitors from University of Notre Dame, Notre Dame, IN 46556., USA

sWith visitors from University de Oviedo, E-33007 Oviedo, Spain.

tWith visitors from Simon Fraser University, Vancouver, British Columbia, Canada V6B 5K3.

uWith visitors from Texas Tech University, Lubbock, TX 79409., USA

vWith visitors from IFIC (CSIC-Universitat de Valencia), 46071 Valencia, Spain.

wWith visitors from University of Virginia, Charlottesville, VA 22904., USA

xWith visitors on leave from J. Stefan Institute, Ljubljana, Slovenia.

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