Measurement of the Mass Difference between <em>t</em> and <em>t</em> Quarks

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Reference

Measurement of the Mass Difference between t and t Quarks

CDF Collaboration

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

Abstract

We present a direct measurement of the mass difference between t and t quarks using tt candidate events in the lepton+jets channel, collected with the CDF II detector at Fermilab's 1.96 TeV Tevatron pp Collider. We make an event by event estimate of the mass difference to construct templates for top quark pair signal events and background events. The resulting mass difference distribution of data is compared to templates of signals and background using a maximum likelihood fit. From a sample corresponding to an integrated luminosity of 5.6   fb−1, we measure a mass difference, ΔMtop=Mt−Mt=−3.3±1.4(stat)±1.0(syst)  GeV/c2, approximately 2 standard deviations away from the CPT hypothesis of zero mass difference.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of the Mass Difference between t and t Quarks. Physical Review Letters , 2011, vol. 106, no. 15, p.

152001

DOI : 10.1103/PhysRevLett.106.152001

Available at:

http://archive-ouverte.unige.ch/unige:38679

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

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Measurement of the Mass Difference between t and t Quarks

T. Aaltonen,^a21B. A´ lvarez Gonza´lez,^a9,wS. Amerio,^a41aD. Amidei,^a32A. Anastassov,^a36A. Annovi,^a17J. Antos,^a12 G. Apollinari,^a15J. A. Appel,^a15A. Apresyan,^a46T. Arisawa,^a56A. Artikov,^a13J. Asaadi,^a51W. Ashmanskas,^a15 B. Auerbach,^a59A. Aurisano,^a51F. Azfar,^a40W. Badgett,^a15A. Barbaro-Galtieri,^a26V. E. Barnes,^a46B. A. Barnett,^a23

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

a2Argonne National Laboratory, Argonne, Illinois 60439, USA

a3University of Athens, 157 71 Athens, Greece

a4Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

a5Baylor University, Waco, Texas 76798, USA

a6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

a6bUniversity of Bologna, I-40127 Bologna, Italy

a7University of California, Davis, Davis, California 95616, USA

a8University of California, Los Angeles, Los Angeles, California 90024, USA

a9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

a10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

a11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

a12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

a13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

a14Duke University, Durham, North Carolina 27708, USA

a15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

a16University of Florida, Gainesville, Florida 32611, USA

a17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

a18University of Geneva, CH-1211 Geneva 4, Switzerland

a19Glasgow University, Glasgow G12 8QQ, United Kingdom

a20Harvard University, Cambridge, Massachusetts 02138, USA

a21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

a22University of Illinois, Urbana, Illinois 61801, USA

a23The Johns Hopkins University, Baltimore, Maryland 21218, USA

a24Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

a25Center 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

a26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

a27University of Liverpool, Liverpool L69 7ZE, United Kingdom

152001-2

a28University College London, London WC1E 6BT, United Kingdom

a29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

a30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

a31Institute 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

a32University of Michigan, Ann Arbor, Michigan 48109, USA

a33Michigan State University, East Lansing, Michigan 48824, USA

a34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

a35University of New Mexico, Albuquerque, New Mexico 87131, USA

a36Northwestern University, Evanston, Illinois 60208, USA

a37The Ohio State University, Columbus, Ohio 43210, USA

a38Okayama University, Okayama 700-8530, Japan

a39Osaka City University, Osaka 588, Japan

a40University of Oxford, Oxford OX1 3RH, United Kingdom

a41aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

a41bUniversity of Padova, I-35131 Padova, Italy

a42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

a43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

a44aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

a44bUniversity of Pisa, I-56127 Pisa, Italy

a44cUniversity of Siena, I-56127 Pisa, Italy

a44dScuola Normale Superiore, I-56127 Pisa, Italy

a45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

a46Purdue University, West Lafayette, Indiana 47907, USA

a47University of Rochester, Rochester, New York 14627, USA

a48The Rockefeller University, New York, New York 10065, USA

a49aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

a49bSapienza Universita` di Roma, I-00185 Roma, Italy

a50Rutgers University, Piscataway, New Jersey 08855, USA

a51Texas A&M University, College Station, Texas 77843, USA

a52aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, Italy

a52bUniversity of Trieste/Udine, I-33100 Udine, Italy

a53University of Tsukuba, Tsukuba, Ibaraki 305, Japan

a54Tufts University, Medford, Massachusetts 02155, USA

a55University of Virginia, Charlottesville, Virginia 22906, USA

a56Waseda University, Tokyo 169, Japan

a57Wayne State University, Detroit, Michigan 48201, USA

a58University of Wisconsin, Madison, Wisconsin 53706, USA

a59Yale University, New Haven, Connecticut 06520, USA

a60Instituto de Fisica de Cantabria, CSIS-University of Cantabria, 39005 Santander, Spain (Received 14 March 2011; published 14 April 2011)

We present a direct measurement of the mass difference between tandtquarks usingttcandidate events in the leptonþjets channel, collected with the CDF II detector at Fermilab’s 1.96 TeV Tevatronpp Collider. We make an event by event estimate of the mass difference to construct templates for top quark pair signal events and background events. The resulting mass difference distribution of data is compared to templates of signals and background using a maximum likelihood fit. From a sample corresponding to an integrated luminosity of 5:6 fb¹, we measure a mass difference, M_top¼MtMt¼ 3:3 1:4ðstatÞ 1:0ðsystÞGeV=c², approximately 2 standard deviations away from the CPT hypothesis of zero mass difference.

DOI:10.1103/PhysRevLett.106.152001 PACS numbers: 14.65.Ha, 12.15.Ff, 13.85.Ni, 13.85.Qk

Discrete symmetries reflecting the invariance under dis- crete transformations, such as charge conjugation (C), space reflection or parity (P), and time reversal (T), are not always exact. Examples include theCandPsymme- tries and theirCPcombination, which are violated by the

weak interactions [1]. CPT symmetry, which reflects the invariance under the combined operation of C, P, and T transformations, has not been found to be violated in any experiment so far [2,3]. However, it is important to exam- ine the possibility of CPT violation in all sectors of the

standard model, as there are well-motivated extensions of the standard model allowing forCPT symmetry breaking [4]. In theCPT theorem, particle and antiparticle masses must be identical; thus, a mass difference between a par- ticle and its antiparticle would indicate a violation ofCPT. The mass equality has been verified to high precision for leptons and hadrons, but not for quarks. With the exception of the top quark, it is impossible to measure quark masses directly, because a newly created quark dresses itself with other quarks and gluons to form a hadron, and hadron masses yield, at best, only rough estimates of the quark mass. The top quark is by far the most massive quark and, with lifetime of the order of10²⁴s, decays before it can hadronize. This allows a precise measurement of the mass difference betweentandtquarks and provides a probe of CPT violation in the quark sector [5].

This Letter reports a measurement of the mass difference (M_top¼MtMt) betweentandtquarks using a sample of tt candidates in the leptonþjets final state. The data correspond to an integrated luminosity of 5:6 fb¹ in proton-antiproton collisions at the Tevatron withffiffiffi ps

¼1:96 TeV, collected with the CDF II detector [6].

Assuming unitarity of the three-generation Cabibbo- Kobayashi-Maskawa matrix,t andtquarks decay almost exclusively into aWboson and a bottom quark (t!bW^þ andt!bW ) [1]. The case where one W decays into a charged lepton and a neutrino (W^þ!‘ or W!‘) and the other into a pair of jets defines the leptonþjets decay channel. The electric charge of the lepton (1for‘ and þ1 for ‘) determines the flavor of top quarks with event reconstruction. To select tt candidate events in this channel, we require one electron (muon) with E_T>20 GeV (p_T>20 GeV=c) and pseudorapidity jj<1:1 [7]. We also require high missing transverse energy [8], E_T>20 GeV, and at least four jets. Jets are reconstructed with a cone algorithm [9] with radius R¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðÞ²þ ðÞ²

p ¼0:4. Jets originating from b

quarks are identified using a secondary vertex tagging algorithm [10]. In order to optimize the background re- duction process and improve the statistical power of the events, we divide the sample of tt candidate events into subsamples with zero, one, and two or moreb-tagged jets.

When an event has zero or oneb-tagged jet, we require exactly four jets with transverse energyET >20 GeVand jj<2:0. If an event has two or morebjets, three jets are required to haveET>20 GeVandjj<2:0, and a fourth jet is required to haveET>12 GeVandjj<2:4, with no restriction on the total number of jets. To reject back- grounds, we require the scalar sum of transverse energies in the event, HT ¼E^lepton_T þETþP

four jetsE^jet_T , to be greater than 250 GeV.

The primary sources of background events areWþjets and QCD multijet production. Contributions fromZþjets, diboson, and single top production are expected to be small. To estimate the contribution of each process, we

use a combination of data and Monte Carlo (MC) based techniques described in Ref. [11]. For the Zþjets, diboson, and single top quark events, we normalized MC simulation events using their respective theoretical cross sections. The QCD multijet background is estimated with a data-driven approach. We model Wþjets background events using MC simulation, but the overall rate is deter- mined using data after subtracting the rate of all the other backgrounds and tt. Table I shows the expected back- ground composition and the expected number ofttevents.

We assume selected events to be tt events in the leptonþjets channel and reconstruct them to form esti- mators ofM_top, using a special purpose kinematic fitter, in which we modify the standard fitter [12] to allow a mass difference between tandt. Measured four-vectors of jets and lepton are corrected for known effects [13], and reso- lutions are assigned. The unclustered transverse energy (UT), which is the sum of all transverse energy in the calorimeter that is not associated with the primary lepton or one of the leading four jets, is used to calculate the neutrino transverse momentum. The longitudinal momen- tum of the neutrino is a free (unconstrained) parameter which is effectively determined by the constraint on the invariant mass of the leptonic W. We then define a kine- matic fit² having a free parameterdm_reco,

²¼_i¼‘;4 jetsðp^i;fit_T p^i;meas_T Þ²=²_i

þk¼x;yðU^fit_TkU^meas_Tk Þ²=²_kþðMjjMWÞ²=²_W þðM_‘M_WÞ²=²_WþfM_bjjðM_topþdm_reco=2Þg²=²_t þfMb‘ðMtopdmreco=2Þg²=²t; (1) wheredm^min_reco, thedm_recovalue at the lowest², represents the reconstructed mass difference between the hadronic and leptonic top decay (MbjjMb‘). In this² formulation, the first term constrains the p_T of the lepton and four leading jets to their measured values within their unce- rtainties (_i); the second term does the same for both transverse componentsxandyof the unclustered transverse energy. In the remaining four terms, the quantities Mjj, TABLE I. Expected and observed numbers of signal and back- ground events assumingttproduction cross sectiontt¼7:4 pb andMtop¼172:5 GeV=c².

0b-tag 1b-tag 2b-tag Wþjets 59698 88:323:0 11:13:6 QCD multijet 95:874:4 14:712:1 2:43:2 Zþjets 48:89:4 5:71:3 0:80:2

Diboson 50:14:7 6:60:8 1:00:2

Single top 4:00:4 5:50:5 2:20:2

Background 795124 12124 17:34:8

ttsignal 42657 57872 28244

Expected 1220137 69976 29944

Observed 1278 720 296

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M_‘,M_bjj, andM_b‘refer to the invariant masses of the four vector sum of the particles denoted in the subscripts.MW

andM_topare the masses of theWboson (80:4 GeV=c²) [1]

and the average oftandtquark masses (172:5 GeV=c²), close to the current best experimental determination [14], respectively._W(2:1 GeV=c²) and_t(1:5 GeV=c²) are the total widths of theWboson and thetquark [1]. We assume that the total widths of the t and t quarks are equal.

Determining the reconstructed mass difference oftandt, m_reco, requires the identification of the flavor (tversust), and this is done using the electric charge of the lepton (Qlepton), definingmreco¼ Qleptondm^minreco.

The use of different detector components and the differ- ent resolutions of the measured values for jet, lepton, and unclustered energy make the reconstructed mass distribu- tion of hadronic top quarks differ from that of leptonic top quarks. Because the sign ofmreco depends on the lepton charge,m_reco distributions for the positive and negative lepton events are different. We divide the sample into six subsamples, two samples with positively and negatively charged leptons for each of 0b-tag, 1b-tag, and 2b-tag samples.

With the assumption that the leading four jets in the event come from the four final quarks at the hard scattering level, there are 12, 6, and 2 possible assignments of jets to quarks for 0b-tag, 1b-tag, and 2b-tag, respectively. The minimization of ² is performed for each jet-to-parton assignment, andm_reco is taken from the assignment that yields the lowest ² (²_min). Events with ²_min>9:0 (²_min>3:0) are removed from the sample to reject poorly reconstructed events for b-tagged (zero b-tagged) events.

To increase the statistical power of the measurement, we employ an additional observablem^ðreco^2Þ from the assign- ment that yields the 2nd lowest². Although it has a poorer sensitivity, m^ðreco^2Þ provides additional information on Mtopand improves the statistical uncertainty by approxi- mately 10%.

Using MADGRAPH [15], we generate tt signal samples with Mtop between 20 and 20 GeV=c² using almost 2 GeV=c²step size, where we take the average mass value oftandtto beMtop¼172:5 GeV=c². Parton showering of the signal events is simulated with PYTHIA [16], and the CDF detector is simulated using aGEANT-based software package [17].

We estimate the probability density functions (PDFs) of signal and background templates using the kernel density estimation (KDE) [18,19]. For the M_top measurement with two observables (mreco and m^ðreco^2Þ ), we use the two-dimensional KDE that accounts for the correlation between them. First, at discrete values of M_top from 20to20 GeV=c², we estimate the PDFs for the observ- ables from the above-mentionedttMC samples. We inter- polate the MC distributions to find PDFs for arbitrary values of M_top using the local polynomial smoothing

method [20]. We fit the signal and background PDFs to the measured distributions of the observables in the data using an unbinned maximum likelihood fit [21], where we minimize the negative logarithm of the likelihood with

MINUIT[22]. Likelihoods are built for each of six subsam- ples separately, and an overall likelihood is then obtained by multiplying them together. We evaluate the statistical uncertainty onM_topby searching for the points where the negative logarithm of the likelihood exceeds the minimum by 0.5. References [18,23] provide detailed information about this technique.

We test the fitting procedure using 3000 MC pseudoex- periments (PEs) for each of 11 equally spaced Mtop

values ranging from10to10 GeV=c². The distributions of the average residual of measuredM_top(deviation from the input Mtop) for simulated experiments is consistent with zero. However, the width of the pull (the ratio of the residual to the uncertainty reported by MINUIT) is 4%

greater than unity. We therefore increase the measured uncertainty by 4%.

We examine a variety of systematic effects that could change the measurement by comparing results from PEs in which we vary relevant systematic parameters within their uncertainties. All systematic uncertainties are summarized in TableII. The dominant source of systematic uncertainty is the signal modeling, which we estimate using PEs with events generated with MADGRAPH and PYTHIA. We also estimate a parton showering uncertainty by applying differ- ent showering models (PYTHIA and HERWIG [24]) to a sample generated withALPGEN[25]. We address a possible difference in the detector response betweenbandbjets by comparing data and MC simulation events [26]. We add a systematic uncertainty due to multiple hadron interactions to account for the fact that the average number of inter- actions in our MC samples is not exactly equal to the number observed in the data. The jet energy scale, the dominant uncertainty in most of the top quark mass mea- surements, is partially canceled in the measurement of

TABLE II. Summary of systematic uncertainties onM_top.

Source Uncertainty (GeV=c²)

Signal modeling 0.7

bandbjets asymmetry 0.4

Jet energy scale 0.2

Parton distribution functions 0.1

b-jet energy scale 0.1

Background shape 0.2

Gluon fusion fraction 0.1

Initial and final state radiation 0.1

Monte Carlo statistics 0.1

Lepton energy scale 0.1

Multiple hadron interaction 0.4

Color reconnection 0.2

Total systematic uncertainty 1.0

the mass difference. Therefore, the jet energy scale con- tributes only a small uncertainty to this measurement.

Other sources of systematic effects, including uncertainties in parton distribution functions, gluon radiation, back- ground shape and normalization, lepton energy scale, and color reconnection [23,27], give small contributions. The total systematic uncertainty of1:0 GeV=c²is derived from a quadrature sum of the listed uncertainties.

The likelihood fit to the data returns a mass difference M_top ¼ 3:31:4ðstatÞ 1:0ðsystÞGeV=c²

¼ 3:31:7 GeV=c²: (2) Figure1 shows the measured distributions of the observ- ables used for theM_topmeasurement overlaid with den- sity estimates usingttsignal events withMtop ¼ 4and 0 GeV=c² and the full background model. The choice of M_top ¼ 4 GeV=c² (solid line) gives better agreement with the data than that of0 GeV=c²(dashed line).

In conclusion, we examine the mass difference between t and t quarks in the leptonþjets channel using data corresponding to an integrated luminosity of 5:6 fb¹ from pp collisions at ffiffiffi

ps

¼1:96 TeV. We measure the mass difference to be M_top ¼ M_t Mt ¼ 3:3 1:4ðstatÞ 1:0ðsystÞ GeV=c² ¼ 3:3 1:7 GeV=c². This result is consistent withCPT-symmetry expectation, M_top ¼0 GeV=c², with approximately 2 level devia- tions. It is consistent with the recent result from the D0 Collaboration [28], but is 2.2 times more precise. This is the most precise measurement of the mass difference be- tweentandtquarks.

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 Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean World Class University Program, the National Research Foundation of Korea; 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, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland; and the Australian Research Council (ARC).

aDeceased.

bVisitor from University of Massachusetts Amherst, Amherst, MA 01003, USA.

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

dVisitor from University of California Irvine, Irvine, CA 92697, USA.

eVisitor from University of California Santa Barbara, Santa Barbara, CA 93106, USA.

fVisitor from University of California Santa Cruz, Santa Cruz, CA 95064, USA.

gVisitor from CERN, CH-1211 Geneva, Switzerland.

hVisitor from Cornell University, Ithaca, NY 14853, USA.

2) (GeV/c mreco

∆

-100 0 100

)2 Events/(15 GeV/c

0 50 100

150 CDF Data (5.6 fb^-1) Background

2 ) ( 0 GeV/c t t

2 ) (-4 GeV/c t t

nontagged mreco

∆

2) (GeV/c

(2)

mreco

∆

-100 0 100

)2Events/(15 GeV/c

0 50 100

nontagged

(2)

mreco

∆

2) (GeV/c mreco

∆

-100 0 100

)2 Events/(15 GeV/c

0 20 40 60 80 100 120 140 160

tagged mreco

∆

2) (GeV/c

(2)

mreco

∆

-100 0 100

)2Events/(15 GeV/c

0 20 40 60 80 100 120

tagged

(2)

mreco

∆

FIG. 1 (color online). Distributions ofm_reco andm^ðreco^2Þ used to extract M_top for zero b-tagged (nontagged) events and one or more b-tagged (tagged) events. The data are overlaid with the predictions from the KDE probability distributions assuming M_top¼ 4 GeV=c²(solid red line) andM_top¼0 GeV=c²(dashed blue line).

152001-6

iVisitor from University of Cyprus, Nicosia CY-1678, Cyprus.

jVisitor from University College Dublin, Dublin 4, Ireland.

kVisitor from University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017.

lVisitor from Universidad Iberoamericana, Mexico D.F., Mexico.

mVisitor from Iowa State University, Ames, IA 50011, USA.

nVisitor from University of Iowa, Iowa City, IA 52242, USA.

oVisitor from Kinki University, Higashi-Osaka City, Japan 577-8502.

pVisitor from Kansas State University, Manhattan, KS 66506, USA.

qVisitor from University of Manchester, Manchester M13 9PL, United Kingdom.

rVisitor from Queen Mary, University of London, London, E1 4NS, United Kingdom.

sVisitor from Muons, Inc., Batavia, IL 60510, USA.

tVisitor from Nagasaki Institute of Applied Science, Nagasaki, Japan.

uVisitor from National Research Nuclear University, Moscow, Russia.

vVisitor from University of Notre Dame, Notre Dame, IN 46556, USA.

wVisitor from Universidad de Oviedo, E-33007 Oviedo, Spain.

xVisitor from Texas Tech University, Lubbock, TX 79609, USA.

yVisitor from Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile.

zVisitor from Yarmouk University, Irbid 211-63, Jordan.

aaOn leave from J. Stefan Institute, Ljubljana, Slovenia.

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