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Transverse Momentum Distribution of the Z Produced at the Large Hadron Collider and Related Phenomena

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Transverse momentum distribution of the Z produced at the Large Hadron Collider and related phenomena The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Gastmans, R., Sau Lan Wu, and Tai Tsun Wu. 2010. “Transverse Momentum Distribution of the Z Produced at the Large Hadron Collider and Related Phenomena.” Physics Letters B 693 (4) (October): 452–455. doi:10.1016/j.physletb.2010.08.075. Published Version doi:10.1016/j.physletb.2010.08.075 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:26516680 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Transverse Momentum Distribution of the Z Produced at the Large Hadron Collider and Related Phenomena R. Gastmans¤,1 Sau Lan Wuy,2 and Tai Tsun Wu3, 4 1Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium 2Department of Physics, University of Wisconsin, Madison WI 53706, USA 3Gordon McKay Laboratory, Harvard University, Cambridge MA 02138, USA 4Theory Division, CERN, CH-1211 Geneva 23, Switzerland From the recent theoretical result on the production of the Higgs boson at the large Hadron Collider, it follows that other particles will also be produced with small transverse momentum, of the order of 1 GeV=c. The leptonic decay mode of the Z is especially suited for a ¯rst observation of this phenomenon. Other related e®ects, such as paired jets, are also discussed. PACS numbers: 13.85.-t 1. Recently, it was found [1], in the production of an 3. It is therefore seen that the transverse momenta of isolated Higgs particle [2] at the energy of the Large the order of 1 GeV=c are consequences of the properties of Hadron Collider, that the transverse momentum of this the constituents of protons, and are in no way limited to Higgs particle is small, of the order of 1 GeV=c. The the production of the Higgs particle. In other words, at details of this theoretical work may be found in Ref. [3]. high energies, there are production processes besides that A typical transverse momentum distribution is shown in of the Higgs particle, where the transverse momentum Fig. 1. The e®ects of QCD radiative corrections have distributions have peaks at or near zero with widths of been discussed in [1, 3]. Such very narrow distributions the order of 1 GeV=c. have major implications in the hadronic interactions at The emphasis is on this width of the order of 1 GeV=c high energies, much beyond Higgs production. and its consequences. In contrast, even for the Higgs It is the purpose of this paper to study some of these production by gluon fusion, the existing Monte Carlo implications. predictions give a width of about 10 to 20 GeV=c. 4. Of course, particles are also produced with large 2. Gluon fusion is the most important production pro- transverse momenta. Here are, for example, two ways cess for the Higgs particle at the Large Hadron Collider. how this can happen. Indeed, this is the process studied in Refs. [1, 3], leading to this narrow distribution of the Higgs' transverse mo- (a) Particles may be produced in pairs. Gluon fusion mentum. Since the two gluons in gluon fusion come from can lead to the production of not only one Higgs the two incoming protons, one gluon from each proton, particle, but also a pair of Higgs particles. In this such narrow distribution for the produced Higgs particle case, the vector sum of the transverse momenta of must imply that the transverse momentum distribution the Higgs particles is small, but that of each of the of the gluons in the proton is also narrow. two Higgs particles can be large. On physical grounds, this result is understandable (b) Even in the gluon fusion to produce a single Higgs through the following considerations. Take a proton at particle, there is a signi¯cant tail in the distribution 2 rest: since the proton mass is about 1 GeV=c , all its of the transverse momentum, as shown in Fig. 1. constituents | quarks, anti-quarks, and gluons | may Such Higgs particles in the tail are of interest by be expected to have a typical momentum of the order themselves; furthermore, this part of the distribu- of 1 GeV=c. By a Lorentz transformation, the proton is tion is enhanced by QCD radiative corrections. boosted to a high energy. Since the momentum trans- verse to the direction of motion of the proton is invari- It will have to be determined by experiments at the ant under such a Lorentz transformation, the transverse Large Hadron Collider or the Tevatron Collider how momenta of the constituents must remain of the order large the fraction is for the various produced particles of 1 GeV=c. with transverse momenta of the order of 1 GeV=c. For each produced particle, the importance of the present considerations is determined by the size of this fraction. ¤Work supported in part by the FWO-Vlaanderen, project 5. The ¯rst step is to consider the production of Z: G.0235.05, and in part by the Federal O±ce for Scienti¯c, Tech- nical and Cultural A®airs through the `Interuniversity Attraction p + p ! Z + X; (1) Poles Programme { Belgian Science Policy' P6/11-P. yWork supported in part by the United States Department of En- where X is anything. The case of interest here is when ergy Grant No. DE-FG02-95ER40896. this Z is produced with a small transverse momentum 2 80 70 60 50 d2σ 2 dpH?d´ ´=0 40 [fb/GeV2] 30 20 10 0 0 0.3 0.6 0.9 1.2 pH? [GeV] FIG. 1: A typical distribution of the transverse momentum pH? of the produced Higgs particle with rapidity ´ = 0. This curve is for the Higgs mass of M = 115 GeV=c2 [4, 5]. of the order of 1 GeV=c. It is assumed that the frac- where ` is either e or ¹, and the hadronic decay mode tion of Z's with such a small transverse momentum is signi¯cant | see the preceding paragraph. Z ! q +q ¹ : (3) In general, let f denote this fraction. Let the experi- The branching ratios for these decay modes are 6.7 % mental data on the transverse momentum distribution be and 70 % respectively [6]. ¯tted with a narrow peak of the order of 1 GeV=c over a Consider ¯rst the leptonic decay mode (2). Since the broad background; the value of f is then the percentage decay product consists of only two charged leptons, the of events under this narrow peak. Thus, f = 0 means the events are clean and thus provide a prime candidate for absence of this narrow peak, while f = 1 means that all the ¯rst observation of the 1 GeV=c transverse momen- the events are under this narrow peak. In particular, fZ tum scale in high-energy hadron interactions. Several of denotes this fraction for the production process (1). It is the detectors at the Large Hadron Collider | includ- assumed here that the value of this fZ is not too small. ing ALICE, ATLAS, and CMS | have su±ciently good The advantage of studying the production of Z rather azimuth-angle resolutions to study such narrow trans- than that of the Higgs boson is that many Z's will be verse momentum distributions in detail, especially the produced at the Large Hadron Collider. The Z has the component perpendicular to the decay direction and the leptonic decay mode leptonic azimuth opening angle. Once the transverse momentum distribution of the pro- duced Z is found to have a component with a width of the Z ! `+ + `¡ ; (2) order of 1 GeV=c through the leptonic decay mode (2), 3 then this width must also hold for the hadronic mode (3). 7. It is sometimes argued that, because of the \fac- In this decay (3), both the quark q and the anti-quarkq ¹ torization theorem", the quark and the gluon distribu- are seen in the detector as jets, and the success of the jet tion functions must be the same for proton-proton and analysis is conveniently de¯ned as giving similar results electron-proton interactions. Here are the reasons why from both the leptonic and the hadronic modes. It may this argument should not be considered to be conclusive. be expected that the analysis is more di±cult for the c and b jets than for u and d jets. (a) The failure of the factorization theorem in terms of quark and gluon distributions has been thoroughly There is no reason for fZ to be more signi¯cant than the f for some other produced particles. It is therefore discussed by Collins, Rogers, and Sta¶sto[11]. What important to determine the value of the fraction f not they have found is that, in the factorization theo- only for Z but also for other particles. rem, the quark and the gluon distribution functions must be replaced by quark and gluon correlations 6. If the value of f is found experimentally to be suf- functions [12]. These correlation functions depend ¯ciently large for some produced particles, this will have on one more variable than the unintegrated distri- far-reaching consequences. bution functions; to our best knowledge, the corre- In a nutshell, at high energies there is an important lation functions have not been widely used by ex- new scale of 1 GeV=c for hadronic interactions, including perimentalists.
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