Article
Reference
Search for Kaluza-Klein Graviton Emission in pp Collisions at s√=1.8 TeV Using the Missing Energy Signature
CDF Collaboration
CLARK, Allan Geoffrey (Collab.), et al.
Abstract
We report on a search for direct Kaluza-Klein graviton production in a data sample of 84 pb−1 of pp¯ collisions at s√=1.8 TeV, recorded by the Collider Detector at Fermilab. We investigate the final state of large missing transverse energy and one or two high energy jets. We compare the data with the predictions from a (3+1+n)-dimensional Kaluza-Klein scenario in which gravity becomes strong at the TeV scale. At 95% confidence level (C.L.) for n=2, 4, and 6 we exclude an effective Planck scale below 1.0, 0.77, and 0.71 TeV, respectively.
CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Search for Kaluza-Klein Graviton Emission in pp Collisions at s√=1.8 TeV Using the Missing Energy Signature. Physical Review Letters , 2004, vol. 92, no. 12, p. 121802
DOI : 10.1103/PhysRevLett.92.121802
Available at:
http://archive-ouverte.unige.ch/unige:38064
Disclaimer: layout of this document may differ from the published version.
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Search for Kaluza-Klein Graviton Emission in pp Collisions at
p s
1:8 TeV Using the Missing Energy Signature
D. Acosta,14T. Affolder,7H. Akimoto,51M. G. Albrow,13D. Ambrose,37D. Amidei,28K. Anikeev,27J. Antos,1 G. Apollinari,13T. Arisawa,51A. Artikov,11T. Asakawa,49W. Ashmanskas,2F. Azfar,35P. Azzi-Bacchetta,36 N. Bacchetta,36H. Bachacou,25W. Badgett,13S. Bailey,18P. de Barbaro,41A. Barbaro-Galtieri,25V. E. Barnes,40
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A. Zanetti,48F. Zetti,25and S. Zucchelli3 (The CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
4Brandeis University, Waltham, Massachusetts 02254, USA
5University of California at Davis, Davis, California 95616, USA
6University of California at Los Angeles, Los Angeles, California 90024, USA
7University of California at Santa Barbara, Santa Barbara, California 93106, USA
8Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
9Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
10Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
11Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
12Duke University, Durham, North Carolina 27708, USA
13Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
14University of Florida, Gainesville, Florida 32611, USA
15Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
16University of Geneva, CH-1211 Geneva 4, Switzerland
17Glasgow University, Glasgow G12 8QQ, United Kingdom
18Harvard University, Cambridge, Massachusetts 02138, USA
19Hiroshima University, Higashi-Hiroshima 724, Japan
20University of Illinois, Urbana, Illinois 61801, USA
21The Johns Hopkins University, Baltimore, Maryland 21218, USA
22Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
23High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
24Center for High Energy Physics: Kyungpook National University, Taegu 702-701; Seoul National University, Seoul 151-742;
and SungKyunKwan University, Suwon 440-746; Korea
25Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
26University College London, London WC1E 6BT, United Kingdom
27Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
28University of Michigan, Ann Arbor, Michigan 48109, USA
29Michigan State University, East Lansing, Michigan 48824, USA
30Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
31University of New Mexico, Albuquerque, New Mexico 87131, USA
32Northwestern University, Evanston, Illinois 60208, USA
33The Ohio State University, Columbus, Ohio 43210, USA
121802-2 121802-2
34Osaka City University, Osaka 588, Japan
35University of Oxford, Oxford OX1 3RH, United Kingdom
36Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
37University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
38Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy
39University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
40Purdue University, West Lafayette, Indiana 47907, USA
41University of Rochester, Rochester, New York 14627, USA
42Rockefeller University, New York, New York 10021, USA
43Instituto Nazionale de Fisica Nucleare, Sezione di Roma, University di Roma I, ‘‘La Sapienza,’’ I-00185 Roma, Italy
44Rutgers University, Piscataway, New Jersey 08855, USA
45Texas A&M University, College Station, Texas 77843, USA
46Texas Tech University, Lubbock, Texas 79409, USA
47Institute of Particle Physics, University of Toronto, Toronto M5S 1A7, Canada
48Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
49University of Tsukuba, Tsukuba, Ibaraki 305, Japan
50Tufts University, Medford, Massachusetts 02155, USA
51Waseda University, Tokyo 169, Japan
52University of Wisconsin, Madison, Wisconsin 53706, USA
53Yale University, New Haven, Connecticut 06520, USA
(Received 15 September 2003; revised manuscript received 24 November 2003; published 26 March 2004) We report on a search for direct Kaluza-Klein graviton production in a data sample of84 pb1ofppp collisions at
ps
1:8 TeV, recorded by the Collider Detector at Fermilab. We investigate the final state of large missing transverse energy and one or two high energy jets. We compare the data with the predictions from a (31n)-dimensional Kaluza-Klein scenario in which gravity becomes strong at the TeV scale. At 95% confidence level (C.L.) forn2, 4, and 6 we exclude an effective Planck scale below 1.0, 0.77, and 0.71 TeV, respectively.
DOI: 10.1103/PhysRevLett.92.121802 PACS numbers: 11.25.Wx, 04.50.+h, 13.85.Rm, 14.80.–j
Early attempts to unify gravity and electromagnetism led to the idea of an extra circular spatial dimension [1].
Because of the periodicity of the extra dimension, the metric field of the five-dimensional spacetime is Fourier expandable in the extra dimension with four-dimensional fields [called Kaluza-Klein (KK) modes] as coefficients.
More recently, Kaluza-Klein theories appear in scenar- ios of large extra dimensions as introduced by Arkani- Hamed, Dimopoulos, and Dvali (ADD) [2]. In these theories the standard model gauge theory is confined to a three-dimensional domain wall (brane), embedded in a higher dimensional compactified bulk space. Only grav- ity propagates in the full bulk space. The n compacti- fied extra dimensions are assumed for simplicity to be
‘‘large’’ circles of common circumferenceR(anntorus).
As a result of compactification, the gravitational field that propagates in the bulk can be expanded in a series of states known collectively as the graviton KK tower.
Similar to a particle in a box, the momentum of the bulk field is quantized in the compactified dimensions.
For an observer trapped on the brane, each quantum of momentum in the compactified volume appears as a KK excited state with mass m2pp~n, where pp~n is the mo- mentum in the compactified dimensions, and with iden- tical spin and gauge numbers.
In such a model the Planck scaleMPl, the radiusR of the compactified space (here assumed to be a torus), and
the new effective Planck scaleMD are related by [3]
MPl2 8RnMD2n;
where nis the number of extra dimensions. IfMD takes values as low as a few TeV the Higgs naturalness problem [4] of the standard model can be solved by introducing a cutoff not too far above the electroweak scale with new physics entering at energies above this cutoff. The hier- archy problem of the standard model is also recast: the question of whyMPl is so large compared to theZboson mass (MZ) is replaced with the question of whyR is so large compared to 1=MZ, and an ultraviolet hierarchy problem is replaced with an infrared one. If we take the most optimistic case of MD 1 TeV and use MPl 1019GeV, we find that for n1, 2, 4, and 6, R 1011m, 1 mm, 10 nm, and 10 fm, respectively.
All the states in the KK graviton tower, including the massless state, couple in an identical manner with universal strength of M1Pl . However, there are ERn massive KK modes that are kinematically accessible in a collider process with energyE. The sum over the con- tribution from each KK state removes the Planck scale suppression and replaces it by powers of the fundamental scale MDTeV. The interactions of the massive KK graviton modes can then be observed in collider experi- ments either through their direct production and emission
or through their virtual exchange in standard model processes [5].
There are three processes in pp collisions that can result in the emission of a graviton and a hadronic jet: qq!gG, qg!qG, and gg!gG, where qand g are quarks and gluons andG is the graviton. The calcu- lation of graviton emission is based on the effective low- energy theory that is valid below the scale MD. The corresponding Feynman rules are cataloged in [3,6].
Since the graviton passes through the detector without decaying or interacting, the experimental signature is missing transverse energy (6ET) from the emitted graviton and a hadronic jet from the outgoing quark or gluon.
In this Letter we report the results of a search for the direct production of KK graviton modes using the rate of events with one or two energetic jets and large6ET at the Collider Detector at Fermilab (CDF). The search is based on 844 pb1 of integrated luminosity recorded with the CDF detector during the 1994 –1995 Tevatron run.
The CDF detector is described in detail in [7]. The momenta of charged particles are measured in the central tracking chamber (CTC), which is positioned inside a 1.4 T superconducting solenoidal magnet. Outside the magnet, electromagnetic and hadronic calorimeters ar- ranged in a projective tower geometry cover the pseudo- rapidity regionjj<4:2[8] and are used to identify jets.
Jets are defined as localized energy depositions in the calorimeters and are reconstructed using an iterative clustering algorithm with a fixed cone of radius R
22
p 0:7 in space [9]. The transverse energy of a jet isET Esin, whereEis the scalar sum of energy deposited in the calorimeter towers within the cone, and is the angle formed by the beamline and the cone axis [10]. For this analysis, jets are required to haveET 15 GeV.
The missing transverse energy is defined as the negative vector sum of the transverse energy in the electromagnetic and hadronic calorimeters, 6ET P
iEisininn^i, whereEiis the energy of theith tower,
^ n
ni is a transverse unit vector pointing to the center of each tower, and i is the polar angle of the tower. The sum extends tojj 3:6. The data sample was selected with an online trigger that requires6ET j6ETj>30 GeV.
This is a sample dominated by instrumental backgrounds and by multijet events, where the observed missing en- ergy is largely a result of jet mismeasurements and de- tector resolution.
The two-stage preselection we use to reject beam and detector-related backgrounds, beam halo, and cosmic ray events is described in [11]. Events that pass the preselec- tion are then required to have only one or two jets with ET 15 GeV, with at least one jet withinjj<1:1.
We remove events where the missing energy is due to energy flow from a jet to an uninstrumented region of the detector by requiring that the second highestET jet does not point into a detector gap if it is within 0.5 rad in
of the 6ET direction. We reduce the residual mismeasured multijet backgrounds by requiring that the minimum between the6ET vector and any jet in the event (min) is greater than 0.3 rad and thezposition of the event vertex is within 60 cm of the nominal interaction point.
To reduce the physics background contribution from electroweak processes with leptons in the final state [dominated byW!‘] we require that the two highest energy jets are not purely electromagnetic (by requiring the electromagnetic fraction fem Eem=ETot0:9) and the isolated track multiplicity, Nisotrk [12] is zero. For the final sample, we require6ET 80 GeV,ET 80 GeVfor the leading jet and ET 30 GeV for the second jet if there is more than one jet in the event. By accepting events with an energetic second jet we can reliably normalize the background predictions from QCD simulation using the jet data, control the systematic uncertainty on the signal due to initial/final state radiation (ISR/FSR), and inter- pret the results with a K factor [the ratio of the cross sections at leading-order (LO) and next-to-leading-order (NLO),K NLO= LO] included in the estimated signal cross section.
The selection requirements and the number of events passing at each stage are summarized in Table I.
Background events with missing energy and one or two jets arise from standard model sources, predominantly Z! jets,W!‘ jets‘!; "; e, and resid- ual QCD production. WhileZ! jetsproduces real 6ETjets, W!‘ jets mimics our signal when the lepton is lost or misidentified. To estimate theZjetsand Wjetsbackground levels and their uncertainties in the final sample we normalize PYTHIA [13] Monte Carlo (MC) predictions using the observed Z!ee jets data sample. QCD dijet events mimic our signal when one jet is badly mismeasured, resulting in large 6ET. For the QCD predictions we use the HERWIG MC program [14]
and normalize to the high statistics jet data samples using
TABLE I. The data selection path for the6ETplus one or two jets search.
Selection requirement Events passing
Pre-selection 300 945
1Njet2cone 0:7; ET15 GeV
jj1 or 2<1:1 157 035 2nd jet gap veto
min0:3
jzvertexj 60 cm 50 938
fem1,fem2 0:9 21 012
Ntrkiso0 16 459
ET1 80 GeV
If Njet2,ET2 30 GeV 897
6ET80 GeV 284
121802-4 121802-4
well-balanced dijet events. We estimate additional back- grounds fromttt, single top, and diboson production using MC predictions [13,14], which we normalize using the respective theoretical cross section calculations for these processes [15].
The predicted backgrounds from standard model pro- cesses are summarized in Table II. Of the 274 total events predicted to pass our selection requirements, 160 are predicted to come from Z! jets, 89 from the combined W!‘ jets electroweak processes, and 22 from QCD production. Because the MC predictions have been normalized to high statistics data samples, the dominant uncertainty on the Wjets and Zjets pre- dictions is the 4% luminosity uncertainty. The QCD prediction has an additional 14%uncertainty due to jet energy resolution [11]. We observe 284 events in the data.
In Fig. 1 the predicted standard model6ET distribution is compared with the distribution we observe in the data. In Fig. 2 the same comparison is shown for other kinematic distributions. In both figures the data are consistent with the expected background. An additional contribution from graviton production would result in a smooth excess over the background in nearly all the kinematic distribu- tions, as shown in Fig. 3 for6ET.
We use thePYTHIAMC program to generate datasets of graviton emission, using the leading-order production cross sections calculated in [3]. The signal processes are simulated forn2, 4, and 6 extra dimensions, and for a range of values ofMD. The signal efficiency ranges from 2.9% for two extra dimensions to 6:4% for six extra dimensions (due to different relative weights of the three production processes) and is largely independent ofMD. The total relative systematic uncertainty on the signal efficiency is 25%, mostly due to modeling of ISR/FSR (21%), jet energy scale (11%), renormalization scale (8%), and parton density functions (2%) [16].
Using a Monte Carlo technique to convolute the un- certainty on the background estimate with the relative systematic uncertainty on the signal efficiency, the 95%
C.L. [17] upper limit on the number of signal events is 62.
As shown in Fig. 4, forK1:0we exclude an effective Planck scale less than 1.00 TeV for n2, less than
0.77 TeV for n4, and less than 0.71 TeV for n6.
Recently the D0 Collaboration reported a limit on direct graviton emission using a K factor of 1.3 in the signal cross section [18]. They report limits of 0.99 TeV for n2, 0.73 TeV for n4 and 0.65 TeV for n6. For
1 10 102
80 100 120 140 160 180 200 220 240
FIG. 1 (color online). Comparison between data (points) and standard model predictions (boxes) of the 6ET distribution.
There are 284 data events, to be compared with 27416 events predicted from standard model sources. The distribu- tion is plotted with a variable bin size; the contents for bin sizes greater than 10 GeV are normalized accordingly. The height of the boxes shows the uncertainty on the standard model prediction.
1 10 102
100 150 200 1 10
40 60 80 100 120
1 10 102
0 1 2 3 0
50 100 150 200 250
0 1 2 3 4
FIG. 2 (color online). Comparison between data (points) and standard model predictions (histogram) of the first and second leading jet ET,min, andNjet distributions.
TABLE II. The predicted number of events in the final sample from standard model sources and the number observed in the data.
Background source Predicted events
Z! jets 160:211:5
W!! jets 46:65:5
W!" jets 23:85:0
W!e jets 18:14:3
QCD 21:76:7
ttt, single t, dibosons 3:90:3
Total predicted 274:115:9
Observed 284
direct comparison, using K1:3 our corresponding lower limits onMD are 1.06 TeV forn2, 0.80 TeV for n4, and 0.73 TeV forn6.
These are the best limits to date on direct graviton emission [18,19] from the Tevatron.
Assuming compactification on a torus, the limits on MD withK1:0correspond to limits on the compacti- fication radius of R <0:48 mm forn2,R <0:014 nm forn4, andR <42 fm forn6.
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, Science, Sports and Culture 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 fuer Bildung und Forschung, Germany; the Korea Science and Engineering Foundation (KoSEF); the Korea Research Foundation; the Comision Interministerial de Ciencia y Tecnologia, Spain; and the Pritzker Foundation. We thank Konstantin Matchev and Joe Lykken for providing the MC generation code for graviton production inppp colli- sions [20].
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