Black Hole Production in Large Extra Dimensions at the Tevatron: a Chance to Observe a ﬁrst Glimpse of Tev Scale Gravity

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Physics Letters B 548 (2002) 73–76 www.elsevier.com/locate/npe

Black hole production in large extra dimensions at the Tevatron: a chance to observe a ﬁrst glimpse of TeV scale gravity

Marcus Bleicher a, Stefan Hofmann b, Sabine Hossenfelder b, Horst Stöcker b

a SUBATECH, Laboratoire de Physique Subatomique et des Technologies Associées, University of Nantes, IN2P3/CNRS, Ecole des Mines de Nantes, 4 rue Alfred Kastler, F-44072 Nantes cedex 03, France b Institut für Theoretische Physik, J.W. Goethe Universität, 60054 Frankfurt am Main, Germany Received 13 August 2002; accepted 23 September 2002 Editor: P.V. Landshoff

Abstract

The production of black holes in large extra dimensions is studied√ for Tevatron energies. We ﬁnd that black√ holes may have already been created in small abundance in pp¯ collisions at s = 1.8 TeV. For the next Tevatron run ( s = 2.0 TeV) large production rates for black holes are predicted.  2002 Published by Elsevier Science B.V.

Recently the possibility of black hole production 4-dimensional Planck scale MPl via [12] in large extra dimension (LXD) at LHC and from 2 = 2+d cosmic rays has received great attention [1–11]. In MPl Mf Vd . (1) these LXD scenarios [12] the Standard Model of particle physics is localized on a three-dimensional This raises the exciting possibility that the fundamen- brane in a higher-dimensional space. One scenario tal Planck scale Mf can be as low as mW . As a conse- for realizing TeV scale gravity is a brane world in quence, future high energy colliders like LHC, CLIC which the Standard Model particles including gauge or TESLA could probe the scale of quantum gravity degrees of freedom reside on a 3-brane within a with its exciting new phenomena, namely, the production of black holes in high energetic interactions ﬂat compact space of volume Vd ,whered is the number of compactiﬁed spatial extra dimensions with (for LHC energies see [3]). However, the experimental radius L. Gravity propagates in both the compact bounds on the Planck mass in the presently discussed and non-compact dimensions. The fundamental (D = scenarios from absence of missing energy signatures is much lower: M 0.8TeVfortwotosixextradi- 4 + d)-dimensional scale Mf is then connected to the f mensions [13–15]. Astrophysical bounds seem to be more stringent and require fundamental scales of order 10–100 TeV for two extra dimensions, larger limits might also be advocated by direct measurements E-mail address: [email protected] of Newtons law in the sub-millimeter region or pro- (M. Bleicher). ton stability. However, those limits can be overcome

0370-2693/02/$ – see front matter  2002 Published by Elsevier Science B.V. PII:S0370-2693(02)02732-6 74 M. Bleicher et al. / Physics Letters B 548 (2002) 73–76 by increasing the number of extra dimension or invok- ing additional theoretical assumptions (for a discus- sion see, e.g., [16]). Thus, we will consider only the well-known collider bounds on Mf as limits for our present investigation. In this Letter we investigate whether a first glimpse of a (sub-)TeV scale gravity associated with black hole production might already be observed at the Tevatron. As discussed elsewhere (see, e.g., [3,4,17]) the horizon radius of a black hole is given by + + 8Γ(3 d ) 1 d M 1+d = 2 1 RH 1+d (2) (2 + d)π 2 Mf Mf with M denoting the black hole mass. The production rate black holes is classically given by [1,18,19]1 2 σ(M)≈ πR . H Fig. 1. Feynman x distribution of black holes with√M Mf TeV The reader should be aware, that the behavior of the produced in pp interactions at the Tevatron ( s = 1.8TeV) black hole formation cross section at energies around with four compactified spatial extra dimensions and different = Planck mass might strongly deviate from the classical fundamental scales Mf 0.8, 1.0, 1.2 and 1.5 TeV (from top to estimate above. However, without any deeper knowl- bottom). edge of the underlying theory, we have to proceed in good faith and assume it is applicable, keeping in mind that the prediction are order of magnitude esti- partons from projectile p1 and target p2 are summed mates. We will also neglect complications due to the over. finite angular momentum of the black hole and as- Fig. 1 depicts the momentum distribution√ of pro- = sume non-spinning black holes (roughly a factor two duced black holes in pp interactions at s 1.8TeV. ≈ uncertainty). The influence of finite angular momen- Most black holes are of lowest mass (MBH Mf )and tum on the formation and evaporation process of black are formed in scattering processes of valence quarks. = holes is studied in [22]. With these assumptions we Here we show the result for d 4 extra spatial extra ask whether black holes might already have been cre- dimensions. A strong dependence on the fundamental ated at the Tevatron and predict their cross section for gravity scale Mf is observed. For the lowest possible ≈ Run II. Mf √800 GeV, significant black hole production in pp¯ at s = 1.8 TeV is predicted. Higher fundamen- Thus, the Feynman xF distribution√ of black holes tal scales suppress the production of black holes at the for masses from M ∈[Mf , s = 1.8TeV] given by √ Tevatron strongly. s Fig. 2 shows the production cross section for black dσ 2y 2 2 = dy f1 x1,Q f2 x2,Q σ(y,d), holes as a function of the fundamental scale Mf (full dx x s −1 F p ,p 2 line). Using an integrated luminosity of 100 pb per 1 2 M f (3) year, the dashed line gives the expected abundance of 2 with xF = x2 − x1 and the restriction x1x2s = M . black holes produced at Tevatron per year. For most We used the CTEQ4 [23] parton distribution functions optimistic values of Mf ≈ 0.8–1.2 TeV signals of 2 2 f1, f2 with Q = M . All kinematic combinations of black hole creation might have be observable in past or present day experimental data. With the update of the Tevatron for Run II higher 1 Note that the given classical estimate of the black hole luminosities√ at an increased center of mass energy (pp¯ production cross section is still under debate [19,20]. However, for = the present calculations the maximal suppression in the cross section at s 2.0 TeV) are available. Prediction of black − is by a factor 10 1 [21], which does not invalidate the present hole creation cross sections for these runs are shown arguments. in Fig. 3 as a function of the fundamental scale Mf M. Bleicher et al. / Physics Letters B 548 (2002) 73–76 75

2 is Mf is below ≈ 1.5TeV, ﬁrst signals of black hole creation might be observed at Tevatron before the start of LHC. Note that it has been argued whether it is possible to observe the emission spectrum of a black hole directly, since most of the energy may be radiated in Kaluza–Klein modes. However, from the higher- dimensional perspective this seems to be incorrect and most of the energy goes into modes on the brane [24]. The life time of the black holes is predicted to be ≈ 10 fm/c [4]. It can be observed by the emission of multiple jets with energies of ≈ 100–150 GeV or might even produce new kinds of elementary particles [11]. In conclusion, we have predicted the production cross section and the momentum distribution of black Fig. 2. Black hole production cross section (full line) and black holes in space–times with large and compact extra hole yield per year (dashed line) at Tevatron as a function of the √ dimensions. We have shown that most optimistic fundamental scale Mf for d = 4 extra dimensions, s = 1.8TeV, − L = 100 pb 1. values for the mass scale of quantum gravity, a ﬁrst glimpse of black hole√ production might be present in todays√ Tevatron ( s = 1.8 TeV) data. For the Run II ( s = 2.0 TeV) the calculation predicts the production of several thousand black holes per year, if the fundamental scale Mf is not too high. This might make the study of TeV scale gravity experimentally accessible long before the start of LHC.

Acknowledgements

This work was supported in parts by BMBF, DFG, and GSI.

References

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