麻省理工学院案例线性对撞机中超对称探测和精密测量_Particle Physics II（粒子物理学 II）.pdf_大学文库

I. Why Search for Supersymmetry? I.1 The Standard Model and its Failings For more than thirty years the study of physics at high energies has been dominated by what is known as the “Standard Model” of particle physics. This theory is based on the SU(3)C x SU(2)L x U(1)Y symmetry group [1]. The Standard Model separates all elementary particles into two groups: fermions and bosons. Fermions consist of quarks and leptons (and their anti-partners;) all of which carry half- integer spin. It is these particles (particularly the up and down quarks, and the electron) that come together to form mesons, baryons, and atoms that comprise “ordinary” matter. All other elementary particles (the ones with integer spin) are known as bosons. These include the photon, the W and Z bosons, and the gluons. These are the particles that mediate the electromagnetic, weak, and strong forces, respectively. Fermions interact with each other by emitting and absorbing bosons. Furthermore, the Standard Model assumes the symmetry is spontaneously broken to the SU(3)C x U(1)em symmetry by an SU(2)L doublet of spin-zero (scalar) fields. This field has associated boson, the Higgs boson, which also endows fermions and heavy bosons with their mass. While the Higgs has not yet been found, this should not be taken as a failing in the theory, but rather a failing in our experimental prowess. There is ample reason to believe that Higgs will indeed be observed once the Large Hadron Collider (LHC) is up and running [2]. For all intents and purposes, the Standard Model has been an unmitigated success. To date, no experiment has been performed that contradicts the theoretical predictions of the Standard Model. This leads to the obvious (and reasonable) question of why we are bothering to search for a “better” physical model (supersymmetry) when our old theory has not been proven wrong. Why try and fix our yet-unbroken theory? The reason we should search for extra-standard- model physics is that, at a theoretical level, the standard model is incomplete. It is not and indeed cannot be the fundamental description of nature. Perhaps most damaging in general (and probably least damaging with regards to this paper) is that the theory does not even attempt to explain the gravitational force. Also, the theory correctly predicts electroweak symmetry breaking (EWSB), but we really have no clue what the mechanism for this is. Furthermore, the standard model does not explain the seemingly arbitrary value of particle masses and mixing parameters. It seems content to describe these without any underlying motivation. It has been said that, “nature abhors a vacuum;” well, physicists abhor arbitrariness. Aesthetically, the Standard Model seems incomplete. However, there is one particular failing of the Standard Model that is of great importance to the topic at hand. 2

treatment, see ref. 3,4.) However, it is important to understand the basics of SUSY theory especially the physicality of the theory; that is, what will we be looking for when we search for evidence of SUSY. At the most basic level, SUSY theorizes that every fundamental particle-every quark, lepton, and boson-has an associated superpartner. With the exception of spin, a SUSY particle will carry the same quantum numbers (charge, weak-isospin, color, etc.) as its partner. The spin however, is where the two differ, and they invariably differ by exactly 1/2 unit. SUSY quark partners (squarks) and SUSY lepton partners (sleptons) will have spin 0, and they will be bosons. The SUSY W, B, and gluon (Wino, Bino, and gluino respectively) will all have spin 1/2 and thus they will all be fermions. The Higgs superpartner is special and deserves its own explanation. The Standard Model predicts the Higgs will be a SU(2)L doublet with spin 0. In SUSY, we require two doublets (Higgsinos) also with spin 1/2 [3]. It is important to note that, because of EWSB, the above particles are not necessarily mass eigenstates of SUSY theory. Taking our cues from the Standard Model, we would expect that the wino, bino, and Higgsino gauge eigenstates should mix to form the spin 1/2 mass eigenstates. This is crucial because it is the mass eigenstates that we look for in the detector. For the remainder of this paper, when we talk about detecting these gauginos, we will usually refer 0 to charginos, (χ ± i ) and neutralinos (χi ), the mass eigenstates of mixtures of winos, binos, Higgsinos. Most SUSY models predict that the gluino, squarks, and sleptons are indeed gauge and mass eigenstates of the theory. I.2.a R Parity Before we can discuss the decay chains of SUSY particles, we need to introduce the concept of R parity or matter parity. Currently, the most plausible supersymmetric models all postulate that R parity is conserved for all interactions (Standard Model and SUSY.) R parity is a multiplicative quantum number defined as: = (-1)3(B-L)+2s P R where B, L, and s are the baryon, lepton, and spin quantum numbers, respectively [5]. It is easy to see that all standard model particles and the standard model Higgs, carry even R parity (PR = +1.) All squarks, sleptons, gauginos, and Higgsinos (all sparticles) carry odd R parity (PR = -1.) The conservation of R parity carries a number of interesting consequences and three of them are of vital importance to our study. First, in our experimental collider environment, any reaction that produces sparticles must produce an even amount of them. In other words, all sparticles must be pair-produced. Second, the lightest supersymmetric particle 4

(LSP) must be absolutely stable.R parity conservation prevent.s the I.8P from decaying into any SM partiele,and,of course,the LSp cannot decay into a heavier sparticle. Finally,all eparticles (besides the LSP)muet eventually decay into an odd number of other sparticles. This meanB that all sparticles we manage to create will eventually decay into an LSP [3]. R parity conservation may seem like an arbitrary constraint on SUSY theories,simply to make our lives simpler:and as we will see,this does make the prospect of discovering SUSY much less daunting.Indeed it is possible to formulate SUSY without R parity conservatian. However, these outlying theories notwithstanding,the deeire to conserve R parity is well motivated by experiment.Recent experiments have placed a lower limit on the lifetime of the proton at 10"yeara (6].A consequence of R parity is that the proton,like the LSP,is absolutely stable over the lifetime of the universc,which scems to be the case. Moreover,one of the biggest problems with SUSY models without R parity conservation is that they prediet much shorter lifetimes for the proton.Also,the idea of a stable LSP provides an attractive candidate tor the non- baryonie dark matter that we know makea up around 25 of the energy density in the universe. Hence,for the majority of this paper,we will ignore models that do not conserve R parity. I.3 Supersymmetric Decays It is vitally important for us to underatand sparticle decays,since it is ultimately these decays that we will gearch for. Our knowledge will allow us to reconatruct specific interactions from the signals in our detector. In our treatment,we will assume that the lightest neutralino (x,'is the ISp and therefore all sparticles decays will ultimately contain the x in the final state. We will subsequently discuss sparticle decays in terms of how impartant the processes are in our experimental challenges. with this in mind we will start with neutralinos and charginos. then move an to sleptons and finally squarks gluinos. As we stated above,the charginog (y.)and neutralinos (are mass eigenstates that are mixtures of the charged and neutral winos,the bino,and the Higgsinos.As long as the decay products are not more massive than the original spartiele,a neutralino or chargino can decay into a lepton elepton,quark squark,or a lighter neutralino Ifiggs or Standard Model gauge boson.Neutralinos and chargino can

(LSP) must be absolutely stable. R parity conservation prevents the LSP from decaying into any SM particle, and, of course, the LSP cannot decay into a heavier sparticle. Finally, all sparticles (besides the LSP) must eventually decay into an odd number of other sparticles. This means that all sparticles we manage to create will eventually decay into an LSP [3]. R parity conservation may seem like an arbitrary constraint on SUSY theories, simply to make our lives simpler; and as we will see, this does make the prospect of discovering SUSY much less daunting. Indeed it is possible to formulate SUSY without R parity conservation. However, these outlying theories notwithstanding, the desire to conserve R parity is well motivated by experiment. Recent experiments have placed a lower limit on the lifetime of the proton at 1033 years [6]. A consequence of R parity is that the proton, like the LSP, is absolutely stable over the lifetime of the universe, which seems to be the case. Moreover, one of the biggest problems with SUSY models without R parity conservation is that they predict much shorter lifetimes for the proton. Also, the idea of a stable LSP provides an attractive candidate for the non- baryonic dark matter that we know makes up around 25% of the energy density in the universe. Hence, for the majority of this paper, we will ignore models that do not conserve R parity. I.3 Supersymmetric Decays It is vitally important for us to understand sparticle decays, since it is ultimately these decays that we will search for. Our knowledge will allow us to reconstruct specific interactions from the signals in our detector. In our treatment, we will assume that the lightest neutralino 0 (χ1 ) is the LSP and therefore all sparticles decays will 0 ultimately contain the χ1 in the final state. We will subsequently discuss sparticle decays in terms of how important the processes are in our experimental challenges. With this in mind we will start with neutralinos and charginos, then move on to sleptons and finally squarks gluinos. As we stated above, the charginos (χ ± i ) and neutralinos 0 (χi ) are mass eigenstates that are mixtures of the charged and neutral winos, the bino, and the Higgsinos. As long as the decay products are not more massive than the original sparticle, a neutralino or chargino can decay into a lepton + slepton, quark + squark, or a lighter neutralino + Higgs or Standard Model gauge boson. Neutralinos and chargino can 5

also participate in three-body decays,where one of the products is a sparticle and two are standard model particles.An example would be neutralino decaying into a lighter neutralino plus a fermion pair. As we will see later,the decays of charginos and neutralinos are the primary sector for our SuSY discavery searches. Sleptons and sneutrinos (I",U~)also participate in two- body decays.sleptons can decay into a charged lepton plus a neutralino or a neutrino plus a chargino. Sneutr生nog decay into a charged lepton and a chargino or a neutrino and a neutralino.These decays will play an important role in dotermining the mixing ratios for charginos and ncutralinos, especially when we employ polarized beams for our interactions. Squark and gluino decays will not.play a dominant role in SUSY discover at a linear collider.However, completeness purposes,we will not ionore them. gTua￥kg will decay into quark gluino with the highest probability, since this decay will have QCD-scale coupling. More rare decays include direct gquark to quark plus neutralino and squark to anti-quark plus chargino.similarly the dominant gluino decay will yield quark plus squark. These decay号 (especially these of the gluino)play a more prominent role in hadron colliders [4]. I.4 How SUSY "Fixes"the Standard Model We noted above that the main motivation for SUSY theories are the quadratic radiative corrections to the scalar Higgs mass in the Standard Model. The Standard Madel presents an unacceptab1 e sens1t1v1tyt0r七he11cg8mag8.SUS￥o上ow1deg a rather ingenious way around this problem.We illustrate this with an example. Imag1n8 a Higg8=ma8谷cor工6 ction of the type in figure la. The Higgs radiatee a quark-antiquark pair and this loop integral leads to the aforementioned quadratic divergence. when we introduce supersymmatry however,we must alsa introduce a squark-antisquark loop to the correctiong to the Higgs mass.When we integrate around this laop,we obtain exactly the same correction to the mass (because the quantum numbers and couplings are the samel except of courge for the difference in spin, which introduces a factor of (-1)to the loop integral.Therefore the two corrections exactly cancel cach other and thus we have eliminated the extreme sensitivity so damaging to the standard Mode1【31, To date,SUSY serves as the most prohable theory for extra-Standard Model physics. 6

also participate in three-body decays, where one of the products is a sparticle and two are standard model particles. An example would be neutralino decaying into a lighter neutralino plus a fermion pair. As we will see later, the decays of charginos and neutralinos are the primary sector for our SUSY discovery searches. Sleptons and sneutrinos (l˜,υ~) also participate in twobody decays. Sleptons can decay into a charged lepton plus a neutralino or a neutrino plus a chargino. Sneutrinos decay into a charged lepton and a chargino or a neutrino and a neutralino. These decays will play an important role in determining the mixing ratios for charginos and neutralinos, especially when we employ polarized beams for our interactions. Squark and gluino decays will not play a dominant role in SUSY discover at a linear collider. However, for completeness purposes, we will not ignore them. Squarks will decay into quark + gluino with the highest probability, since this decay will have QCD-scale coupling. More rare decays include direct squark to quark plus neutralino and squark to anti-quark plus chargino. Similarly the dominant gluino decay will yield quark plus squark. These decays (especially those of the gluino) play a more prominent role in hadron colliders [4]. I.4 How SUSY “Fixes” the Standard Model We noted above that the main motivation for SUSY theories are the quadratic radiative corrections to the scalar Higgs mass in the Standard Model. The Standard Model presents an unacceptable sensitivity for the Higgs mass. SUSY provides a rather ingenious way around this problem. We illustrate this with an example. Imagine a Higgs-mass correction of the type in figure 1a. The Higgs radiates a quark-antiquark pair and this loop integral leads to the aforementioned quadratic divergence. When we introduce supersymmetry however, we must also introduce a squark-antisquark loop to the corrections to the Higgs mass. When we integrate around this loop, we obtain exactly the same correction to the mass (because the quantum numbers and couplings are the same) except of course for the difference in spin, which introduces a factor of (-1) to the loop integral. Therefore the two corrections exactly cancel each other and thus we have eliminated the extreme sensitivity so damaging to the Standard Model [3]. To date, SUSY serves as the most probable theory for extra-Standard Model physics. 6

II. The Linear Collider II.1 Motivation Thus far, the scientific community has yet to observe any signals from SUSY particles. Currently, the highest energy collisions are obtained at the Tevatron at Fermi National Laboratory. The Tevatron collides protons and anti-protons at a center-of-mass energy (√s) of about 2 TeV. Within the next couple of years however, the Large Hadron Collider (LHC) at CERN is expected to turn on and will provide 14 TeV proton-proton collisions. With such a high-energy machine nearing completion it is not unreasonable to ask why we are discussing linear-collider (LC) SUSY searches. Certainly, the argument goes, if SUSY does indeed exist, it will be found at the LHC. We should be focusing our energy on hadronic, not leptonic, SUSY searches. Yes it is true that the completion of an LC such as the one we discuss is years, perhaps decades, away. Still, the LHC and an LC should not be viewed as in direct competition. Indeed it would be silly to place all of our eggs in the LHC’s basket. An LC and the LHC provide complementary approaches to discovering new physics. Neither could claim sole ownership of the extra-Standard Model landscape. The LHC may or may not discover SUSY. If it does not, an LC would provide our best shot at discovery, or in the absence of discover, our best shot at disproving SUSY. If the LHC is able to detect signals of SUSY, an LC may prove to be even more necessary to carry out precision measurements that would be far too complicated in the environment of a hadron collider. Indeed a linear collider has many features that make it an ideal tool for discovering and measuring new physics. While we will go into more detail in our analysis section, a couple of these properties are worth mentioning here. First, and perhaps most important, is the “clean” - environment produced in e+ e collisions. Hadronic collisions tend to be messy, with numerous spectator particles clouding the actual collision signal. The signal to background ratio - is much lower for hadronic collisions than for e+ e collisions. Furthermore, partons interact via QCD forces, which are not as well understood as electroweak forces. This makes precision measurements much more difficult at a place like the LHC. Finally, electron and positron beams are much more versatile than proton beams. Electron beams can be tuned to precise energies, and furthermore they can be polarized, allowing for asymmetry measurements unavailable at the LHC [7]. It is with these factors in mind that we propose a design for a linear collider facility. We will take our design cues from the proposed Next Linear Collider (NLC,) which 7

will deliver electron-positron collisions at a center of mass energy between .5 and 1.5 TeV. II.2 The Accelerator Figure removed for copyright reasons. Figure 1.5 in NLC Physics Working Group. Physics and Technology of the Next Linear Collider. FERMILAB-PUB-96/112 (1996). http://arxiv.org/PS_cache/hep-ex/pdf/9605/9605011.pdf Fig.2 Schematic of a high-energy LC [8] From a physics standpoint, and for the purposes of this paper, it is not vital to understand the workings of the accelerator complex. As long as electrons and positrons are delivered to our detectors at high energy and known polarization, and as long as these beams interact, we can make our measurements with no knowledge of how these beams arrived. As such we will not discuss in detail in inner workings of beam dynamics, positron production, klystrons etc. However, it is important to have a general idea how, and more importantly why, we use a linear accelerator to provide these beams. Figure 2 provides a schematic view of the NLC facility. The entire structure will be between 30 and 40 km long and will accelerate electrons and positrons to energies ranging from 250 – 750 GeV. The main accelerator contains many thousands of superconducting RF resonant cavities. These cavities are cooled by liquid helium and are driven in such a way as to create a high-frequency oscillating electric field inside the cavity. The main idea is that an electron (or positron) bunch enters each cavity and are accelerated a small amount by this electric field. After passing through the entire length of the accelerator (approximately 10,000 of these cavities,) the electron (or positron) bunch has been boosted to the desired energy. Dipole and quadrapole magnets are used to steer and focus the beam, creating tightly packed bunches to collide. Each bunch contains about 1010 particles and bunches are separated by approximately 1.5 nanoseconds. These bunches arrive at the interaction point where they collide with each other and hopefully, we are able to find the signals of interesting novel physics. 8 _________________________________________________________

II.3 The Detector For our purposes, the detector is the most vital part of our facility. Our experimental search for SUSY can only be as good as our detector. We must take great care in designing a detector that will optimize our chances of finding SUSY signals. Figure 3 [8] shows a cross-sectional view of our proposed detector. While the dimensions are not “set in stone,” this should give a good idea about what our detector will resemble. Of course, figure 3 only shows one quadrant of the detector. In reality the detector will cover the full 2π range in φ and up to .99 in Cosθ. In the next few subsections, we will describe the different detector systems starting at the beam pipe and moving radially outward. The capabilities of each system will also be described in the subsections. Our motivations will become clearer in the analysis section, where we will describe the physics goals for our detector. Figure removed for copyright reasons. Figure 2.49 in NLC Physics Working Group. Physics and  Technology of the Next Linear Collider. FERMILAB-PUB-96/112 (1996). Fig.3: cross-section of detector systems II.3.a The Inner Tracking System - One of the nice features of an e+ e detector is that the physical dimensions of the electron and positron bunches are relatively small, allowing the beam pipe at the interaction point also to be small (~1 cm.) This allows us to place our innermost tracking system very close to the primary interaction point [9]. This innermost tracking system (often referred to as the vertex detector) is used for precision secondary-vertex and flavor tagging. These tasks require very fine spatial resolution. Our design calls for 3-5 layers of 20-micron by 20-micron charged-coupled devices (CCDs.) This system is expected to achieve impact parameter resolution at high momentum of better than 3µm. 9 http://arxiv.org/PS_cache/hep-ex/pdf/9605/9605011.pdf _________________________________________________________

II.3.b Central and Forward Tracking It would be fiscally impractical (an unnecessary) to extend this CCD region too far. Outside of the inner vertex detector, we have a region of central tracking. This region is used to track charged particles as they fly from the central interactions. Designs for central tracking systems fall into two categories: gaseous and solid-state. Gaseous systems, such as the TPC at STAR, provide excellent momentum resolution, but such a system would be ill equipped to handle the extremely small bunch separation (1.2 ns) in our accelerator. So for our detector we suggest central tracking using 5 cylindrical layers of silicon strips, which would provide 5 micron spatial resolution and would be much better suited to handle the rapid collision rate of our machine. These layers would extend to cosθ = .9. This system should provide us with excellent momentum resolution, even at low angles. Taking into account the radius of our central tracking system (~50 cm) and the strength of our magnetic field (~4 T), we should expect δpT/PT = 2 x 10-4 at 100 GeV at cosθ = .9 [8]. As we will see later on, it is of vital importance that we are able to track charged particles in the far forward direction of our detector. Many of the processes we will look for involve missing energy and we must be careful to separate the events with true missing energy from those in which standard model particles escape detection in the forward direction. For this we suggest another series of silicon detectors (disks) in the far forward direction. This should provide us with momentum resolution on the order 2 of δpT/PT = 5 x 10-4 [8], all the way down to cosθ = .99. However, we believe that this can be improved upon and much of the R&D effort should be put into high-precision forward tracking. II.3.c The Electromagnetic Calorimeter Just outside of the tracking chamber would sit our electromagnetic calorimeter (Ecal.) The Ecal is important for measure the shape and energy of electromagnetic showers, which in turn allows us to reconstruct hadronic and leptonic final states. This is the principle way to identify the energy of a particle in our detector. As we shall see, our discovery searches as well as our precision measurements will require very good energy resolution. For our Ecal we recommend 25 radiation lengths (Xo), which should be able to fully contain the electromagnetic showers giving us a good energy measurement. We suggest SiW-Ecal, with 40 sampling layers and a full thickness of around 20 cm. The towers should have angular segmentation of 30 to 40 mrad2 . This option will cost more than a traditional sampling calorimeter but will provide much better energy resolution. With this type of Ecal we should expect energy resolution in 10

麻省理工学院 案例 线性对撞机中超对称探测和精密测量_Particle Physics II（粒子物理学 II）

麻省理工学院案例线性对撞机中超对称探测和精密测量_Particle Physics II（粒子物理学 II）