Minimal süpersimetrik model ve hadron çarpıştırıcılarının fenomenolojisi
Minimal supersymmetric model and its phenomenology at hadron colliders
- Tez No: 66868
- Danışmanlar: PROF. DR. JAN KALAYCI
- Tez Türü: Yüksek Lisans
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Süpersimetri, Çarpıştırıcılar, Supersymmetry, Colliders
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Fizik Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Günümüzde, Standart Model, kuvvetli, zayıf ve elektromanyetik etkileşmeleri betimleyen başarılı bir model olarak durmaktadır; şimdiye kadar, yapılan bütün deneyler, modelin öndeyişlerini doğrulamışlardır. Bununla birlikte, bu model, bazı yetersizlikleri içermektedir. Yetersizliklere çözüm olarak, en ümit verici model, Süpersimetrik ModePdir. Bu çalışmanın giriş bölümünde, Standart Model'in betimlemesi verildikten sonra başarısı ve yetersizlikleri ortaya konmaya çalışılmıştır, ikinci bölümde ise, Süpersimetrik Model'in en basit yorumu olan Minimal Süpersimetrik Model ele alınmıştır. Burada, bu modelin parçacık kapsamından, teorisinden, simetri kırılmasından ve bunun sonucu olarak ortaya çıkan yeni serbest parametreler ile öndenen yeni süpersimetrik parçacıklardan bahsedilmiştir. Böyle bir model üzerindeki incelemeler, Standart Model ötesini araştıran ve betimlemeye çalışan diğer modeller gibi, birkaç TeV enerji seviyesinde ortaya çıkacağına inanılan yeni bir fiziğe götürmektedir. Bu yeni fiziği araştırmak için, hadron çarpıştıncılarım kullanmak, söz konusu enerji seviyesine ulaşmak açısından uygun gözükmektedir. Bazı süpersimetrik parçacıkların hadronik çarpıştıncılarda oluşumları ile bu parçacıkların bozunumlarına yine ikinci bölümde yer verilmiştir. Üçüncü bölüm, hadronik çarpıştıncılarda, Minimal Süperçekim Modeli çerçevesinde yapılan araştırmalara ayrılmıştır. İçerdiği az sayıda serbest parametre, bu modeli çekici kılmaktadır. Bu parametrelerin tanımı yapıldıktan sonra, aynı çerçevede yapılan araştırmalara fenomenolojik bir bakış geliştirilmiş ve özel olarak, söz konusu parametreler uzayında 3 no'lu nokta olarak tanımlanan, parametre değerleri ile üç-dört lepton kanalı araştırması üzerinde durulmuştur. vm
Özet (Çeviri)
SUMMARY The Standard Model is actually a very successful model which describes the weak, strong and electromagnetic interactions among the fundamental particles; however, it is incomplete. There are three kinds of reasons why the Standard Model is incomplete. First, it contains many arbitrary assumptions and parameters. Second, the Standard Model is not asymptotically free, therefore, at some energy scale, its interactions must become strong. Finally, if one calculates radiative corrections to the mass of the Higgs boson of the Standart Model, the diagrams contributing to the renormalization, (fig. 1) diverge quadratically with energy and this does not allow a naturel fine tuning. To deal with these problems, several approaches have emerged. The most important approach is to use a symmetry which transforms the fermions into bosons and vice-versa. This symmetry is called Supersymmetry. W.Z.T W.Z.T n g g h - fi(3i“:~H a*& Figure 1: The diagrams contributing to the renormalisation of the mass of the Higgs boson. IXThe algebra that defines supersymmetry is given by [Qa>P,] = 0 0) {&4} = 2<rJ/»”(2) where the Q's are the generators of the supersymmetric transformations and PM and a denote the energy momentum operator and the Pauli matrices respectively. The simplest version of the supersymmetry, which contains only one generator, is called Minimal Supersymmetric Model. In this model, each particle has only one supersymmetric partner. The supermultiplets are chiral supermultiplet, which contains a complex scalar ^ and a Weyl spinor y/, and vector or gauge supermultiplet which contains a gauge boson VM and its supersymmetric partner gaugino X. The interactions between these multiplets allow a few new couplings apart from the usual one. However, no new coupling constants are introduced. It is only after the breaking of the supersymmetry that new parameters appear. Due to the presence of the supersymmetric partners, new one-loop graphs contributing to the Higgs mass renormalization appear. (Fig. 2) These diagrams cancel the quadratic divergence mentioned above. This solves the naturality problem. On the other hand, the Minimal Supersymmetric Model allows to observe an intersection of the coupling constants of three forces (weak, strong and electromagnetic) at an energy scale of 1016 GeV. W.Z.Î,'-*\ H / \ \ J H- ? H ^- H. H- - / -H ? ? H--?*H / n atX.aB.sf v ; H-T-H Figure 2 : The diagrams of the contributions of the supersimetric partenaires to the renormalization of the mass of the Higgs boson.The particles constituting the same supermultiplet must have identical masses. However, no supersymmetric particle has been detected up to now. It is then obvious that supersymmety has to be a broken symmetry. The most elegant mecanism to achieve this symmetry breaking is Supergravity which considers the coupling of the Minimal Supersymmetric Model to gravitation. After breaking of supersymmetry, some new parameters occur:. a common mass m^ for the scalars,. a trilinear universal parameter Aq,. a common mass w,/2 for the gauginos,. the coupling ju, among two Higgs fields. Taking account the mass of the top-quark m, and the ratio of the vacuum expectation values of two Higgs fields, tan/?, which are important in the process of electro weak symmetry breaking, one can give the free parameters of the model, nto, my,, 4,, tan/?, sgn(//) (3) After the breaking of the electroweak symmetry, the five new parameters appear as five Higgs bosons: Two scalars h and H, a pseudo-scalar A and two charged bosons i/*. One can remark that with its breaking mecanism, the Minimal Supersymmetric Model introduce the gravitation which is absent in the Standard Model. The Minimal Supersymmetric Model has a symmetry called i?-parity which is defined by a quantum number R, R = (-lf2s+3B (4) where L, S and B are the lepton number, spin and baryon number respectively. The R multiplicatively conserved, is +1 for the standard particles and -1 for the supersymmetric partners. This has two important consequences. First, the sparticles have to be produced in pairs. Second, the lightest supersymmetric particle (LSP) is necessarily stable. To explore the particles predicted by the Minimal Supersymmetric Model at an energy scale of few TeV, the proton-proton collisions seem a necessary outil. A proton-proton collider LHC, is therefore in construction at CERN with its energy of 14 TeV in the mass center and its high luminosity of \0Mcm~2s~l. The most copious production at hadron colliders is the production of strongly interacting sparticles. Therefore, the studies of the detection of gluinos and squarks XIare important works for these colliders. The subprocesses for the gluino production are gg->gg an(i <l<f->8g- This production is governed by the vertex ğğg. The production of skuarks introduces the subprocesses gg ->. qq, qq -» qq and qg^qg and one remarks the vertex gqq and gqq. Then, gluinos decay into a.q-q pair and into a neutralino or a chargino via a virtuel skuark. A skuark can decay into a quark and a neutralino. Since the Minimal Supergravity Model does not have many free parameters, the early studies of supersymmetry at hadron colliders, in particular at LHC, focussed on the framework of this model with its parameters given in (3). The several researches in this framework gave ideas about the energy scales at which the supersymmetric particles could be detected at LHC experiments. In particular, a study of the point 3 has been given in this work. In the SUGRA parameter space, the point 3 is defined by the following values: mo = 200 GeV, m^ = 100 GeV, tan/? = 2, \ = 0, sgn/i = - The study of the lepton pair invariant mass distribution of the opposite sign same flavour dileptons from directly produced squarks and gluinos, allows to extract an unmistakable signal %°2 -> %\tC For this neutralino decay, one can determine the mass difference of the neutralinos from the end-point of the curve. (Fig. 3) On the other hand, the fact that the mass of the gluino and the squarks are relatively small, around 300 GeV, and therefore, the direct production of the SUSY particles is dominated by gluino and squark production, would allow to confirm the predictions of the supersymmetry at this point near the proton-antiproton collider Tevatron or linear collider in the near future. Xll> tu ?S. 9000 m m a ?o z ?a 8000 7000 6000 - saoa 4000 3000 2000 1000 How-IumLHCyear: 104 pb"1 1/ Of in h u I Sig: gluinos, squarks + Bg t 0^ ^nJ 1 ? -1 ' ' 10 SUGRA Point 11*3 mo = 200GeV ml/2 = 100 GeV mu = -l tanB = 2 A0 = 0 Bgonly: tt, (W/Z)+<W/Z) 20 30 40 SO 60 70 80 90 1C0 (I+I-) Invariant mass (GeV) (e+e- )/(mu+mu- ) + bb events Figure 3: Invariant mass distribution of the opposite sign same flavour dileptons from directly produced squarks and gluinos as well as from the Standart Model background. xni
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