DOCSLIB.ORG

Charged Leptons Conveners: B

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Charged Leptons Conveners: B 14 Charged Leptons Conveners: B. C. K. Casey, Y. Grossman, D. G. Hitlin J. Albrecht, M. Artuso, K. Babu, R.H. Bernstein, T. Blum, D. N. Brown, B. C. K. Casey, C.-h. Cheng, V. Cirigliano, A. Cohen, A. Deshpande, E. C. Dukes, B. Echenard, A. Gaponenko, D. Glenzinski, M. Gonzalez-Alonso, F. Grancagnolo, Y. Grossman, R.C. Group, R. Harnik, D.G. Hitlin, B. Kiburg, K. Knoepfel, K. Kumar, G. Lim, Z.-T. Lu, D. McKeen, J.P. Miller, M. Ramsey-Musolf, R. Ray, B.L. Roberts, M. Rominsky, Y. Semertzidis, D. Stoeckinger, R. Talman, R. Van De Water, P. Winter 14.1 Executive Summary The enormous physics potential of the charged lepton experimental program was very much in evidence at the Workshop. There are discovery opportunities in experiments that will be conducted over the coming decade using existing facilities and in more sensitive experiments possible with future facilities such as Project X. Exquisitly sensitive searches for rare decays of muons and tau leptons, together with precision measurements of their properties will either elucidate the scale and dynamics of flavor generation, or limit the scale of flavor generation to well above 104 TeV. The crown jewel of the program is the discovery potential of muon and tau decay experiments searching for charged lepton flavor violation (CLFV) with several orders-of-magnitude improvement in sensitivity in multiple processes. There is an international program of CLFV searches, with experiments recently completed, currently running, and soon to be constructed in the United States, Japan, and Europe. These include the completion of the MEG experiment at PSI, an upgrade of MEG, the proposed mu3e search at PSI, new searches from muon to electron conversion (Mu2e at Fermilab, COMET at J-PARC), SuperKEKB, and over the longer term, experiments exploiting megawatt proton sources such as Project X. Over the next decade gains of up to five orders-of-magnitude are feasible in muon-to-electron conversion and in the µ 3e searches, while gains of at least two orders-of-magnitude are possible in µ eγ and τ 3` decay! and more than one order of magnitude in τ `γ CLFV searches. The question of! which of these! processes is the more sensitive was addressed in some! detail at the Workshop; the answer is that the relative sensitivity depends on the type of new physics amplitude responsible for lepton flavor violation. The four-fermion operators that mediate these decays or conversions can be characterized by two parameters, Λ which determines the mass scale of the four fermion amplitude κ, which governs the ratio of the four fermion amplitude and the dipole amplitude. For κ << 1 the dipole-type operator dominates CLFV phenomena, while for κ >> 1 the four-fermion operators are dominant. Figures 14-1 and 14-2, from A. de Gouvea and P. Vogel, Progress in Particle and Nuclear Physics 71, 75 (2013), show these relationships and the capability of new experimental searches, which can extend our knowledge quite dramatically in the next decade. Thus the pattern of violation that emerges thus yields quite specific information about new physics in the lepton sector. Existing searches already place strong constraints on many models of physics beyond the standard model; the contemplated improvements increase these constraints significantly, covering substantial regions of the parameter space of many new physics models. These improvements are important regardless of the outcome of new particle searches of the LHC; the next generation of CLFV searches are an essential 2 Charged Leptons component of the particle physics road map going forward. If the LHC finds new physics, then CLFV searches will confront the lepton sector in ways that are not possible at the LHC, while if the LHC uncovers no sign of new physics, CLFV may provide the path to discovery. 7000 6000 (TeV) (TeV) " " 5000 4000 B(µ # eee)=10-16 3000 B(µ # e conv in 27Al)=10-18 4 -14 10 2000 B(µ # e$)=10 B(µ # e$)=10-13 -14 B(µ # e conv in 27Al)=10-16 B(µ # eee)=10 1000 900 800 700 -14 B(µ # e$)=10 600 B(µ # e$)=10-13 500 400 10 3 300 EXCLUDED (90% CL) EXCLUDED (90% CL) -2 -1 2 -2 -1 2 10 10 1 10 10 10 10 1 10 10 ! ! Figure 14-1. Sensitivity of a µ ! e con- Figure 14-2. Sensitivity of a µ ! eee ex- 27 version in Al experiment27 that can probe a periment that is sensitive to branching ratios 14 Figure 2: Sensitivity of a µ e conversion in Al16 experiment18 that canFigure probe a 3: normalized Sensitivity14 of a µ 16eee experiment that is sensitive to branching ratios 10− normalized16 →18 capture rate of 10 and 10 , and of 16 10 and 10→ , and of a µ ! eγ search that 13 14 capture rate of 10− and 10− , and of a µ eγ search that is sensitiveand to a 10 branching− , and ratio of a µ eγ search that is sensitive to a branching ratio of 10− and 10− , 13 14 → → 13 of 10− and 10−a ,µ to! theeγ newsearch physics that scale is Λ sensitive as a function to a of branchingκ, as definedto the in Eq. new (2). physics Alsois sensitive scale Λ as toa function a branching of κ, as ratiodefined of in10 Eq. (3).and Also depicted is the depicted is the currentlyratio of excluded1013 and region1014 of, to this the parameter new physics space. scalecurrently excluded1014 region, to of the this new parameter physics space. scale Λ as a function Λ as a function of κ, as defined in the text. Also of κ, as defined in the text. Also depicted is depicted is the currently excluded region of this the currently excluded region of this parameter parameter space. κ and Λ if Eq. (3) describesspace. CLFV), studies of electromagnetic properties of charged leptons (g 2, A model independent comparison between the reach of µ eee andelectricµ e dipoleconversion moments), in nuclei precision is studies of neutrino processes (including oscillations), and, of course,− a lot less straight forward. If the new physics is such that the→ dipole-type operator→ is dominant (κ 1 “direct” searches for new, heavy degrees of freedom (Tevatron, LHC). Valuable information, including in Figures 2 andIn 3), general, it is easy muon to see that measurements near-future prospects have the for µthe best naturee sensitivityconversion and chirality searches over of the theare effective largest operators range of that the mediate parameter CLFV, can space be obtained of by observing 16 → comparable to those for µ eee, assuming both can reach the 10− level.µ µe conversione conversion in different searches nuclei [14, 29, 30] or by studying the kinematical distribution of the many new→ physics models. There are,17 however, models→ in which rare tau decays could provide the discovery will ultimately dominate, assuming these can reach beyond 10− , andfinal-state→ assuming electronsµ eee in searchesµ eee (see [14] and references therein). “saturate” at thechannel. 10 16 level.τ Underflavor all violation other theoretical searches circumstances, will have keeping their in sensitivity mind→ that κ →and extended Λ by around an order of magnitude at − + − Before moving on to specific new physics scenarios, it is illustrative to compare, as model-independently in Eqs. (2,3) arenewnot thee same,e flavor it is impossible factories. to unambiguously Polarized electron compareas possible,beams the two CLFV cannew physicsprovide probes. that an mediates additional CLFV gain and the in sensitivity. new physics that It wasmay haveclear manifested itself in The discussionsfrom above the also discussion serve to illustrate that as another many “feature” different ofprecision searches CLFV measurements for searches CLFV violation. as of feasible the muon should anomalous be magnetic conducted, moment. since In athe nutshell, best the world’s most In the case of adiscovery positive signal, channel the amount is model-dependent of information regarding and theprecise the new model measurement physics is is not limited. of yet the Forg known.2 of the Should muon disagrees a signal with be the observed world’s best in Standard any Model estimate − example, a positivechannel, signal in searches a µ e conversion and measurements experiment does in not as allow manyfor this one CLFV observableto measure channels at either theΛ 3 as.6 orσ possiblelevel (for willan updated be crucial overview to determiningsee [1], and references the therein). New, κ but only a function of the two.→ In order to learn more about the newheavy physics, physics one needs contributions to combine to the muon g 2 are captured by the following effective Lagrangian: − information involvingnature the rateof the of aunderlying particular CLFV physics, process with since other correlations observables. Thesebetween include the other rates expected in different channels provide mµ µν CLFV observablesa powerful (e.g., a positive discriminator signal in µ betweeneγ and µ physicseee would model. allow one to measure both g 2 µ¯RσµνµLF + h.c. (4) → → L − ⊃ Λ2 The new muon g 2 experiment7 will measure the anomaly to close to 100 parts8 per billion precision with different experimental− techniques. This will be an important measurement whether or not the LHC sees new physics. If the LHC sees SUSY-like new physics, g 2 will be used as a constraint in determining which model we see. The LHC will be particularly sensitive to− color super-partners, while g 2 can pin down the flavor sector. The sensitivity of g 2 to tan β will provide a test the universality of that− parameter. If the LHC does not see new physics, then− g 2 can be used to constrain other models, such as theories involving − Community Summer Study: Snowmass 2013 14.2 Overview 3 dark photons and extra dimensions.
Load more

Recommended publications
  • The Five Common Particles
    The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2.
    [Show full text]
  • Lepton Flavor and Number Conservation, and Physics Beyond the Standard Model
    Lepton Flavor and Number Conservation, and Physics Beyond the Standard Model Andr´ede Gouv^ea1 and Petr Vogel2 1 Department of Physics and Astronomy, Northwestern University, Evanston, Illinois, 60208, USA 2 Kellogg Radiation Laboratory, Caltech, Pasadena, California, 91125, USA April 1, 2013 Abstract The physics responsible for neutrino masses and lepton mixing remains unknown. More ex- perimental data are needed to constrain and guide possible generalizations of the standard model of particle physics, and reveal the mechanism behind nonzero neutrino masses. Here, the physics associated with searches for the violation of lepton-flavor conservation in charged-lepton processes and the violation of lepton-number conservation in nuclear physics processes is summarized. In the first part, several aspects of charged-lepton flavor violation are discussed, especially its sensitivity to new particles and interactions beyond the standard model of particle physics. The discussion concentrates mostly on rare processes involving muons and electrons. In the second part, the sta- tus of the conservation of total lepton number is discussed. The discussion here concentrates on current and future probes of this apparent law of Nature via searches for neutrinoless double beta decay, which is also the most sensitive probe of the potential Majorana nature of neutrinos. arXiv:1303.4097v2 [hep-ph] 29 Mar 2013 1 1 Introduction In the absence of interactions that lead to nonzero neutrino masses, the Standard Model Lagrangian is invariant under global U(1)e × U(1)µ × U(1)τ rotations of the lepton fields. In other words, if neutrinos are massless, individual lepton-flavor numbers { electron-number, muon-number, and tau-number { are expected to be conserved.
    [Show full text]
  • Accessible Lepton-Number-Violating Models and Negligible Neutrino Masses
    PHYSICAL REVIEW D 100, 075033 (2019) Accessible lepton-number-violating models and negligible neutrino masses † ‡ Andr´e de Gouvêa ,1,* Wei-Chih Huang,2, Johannes König,2, and Manibrata Sen 1,3,§ 1Northwestern University, Department of Physics and Astronomy, 2145 Sheridan Road, Evanston, Illinois 60208, USA 2CP3-Origins, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark 3Department of Physics, University of California Berkeley, Berkeley, California 94720, USA (Received 18 July 2019; published 25 October 2019) Lepton-number violation (LNV), in general, implies nonzero Majorana masses for the Standard Model neutrinos. Since neutrino masses are very small, for generic candidate models of the physics responsible for LNV, the rates for almost all experimentally accessible LNV observables—except for neutrinoless double- beta decay—are expected to be exceedingly small. Guided by effective-operator considerations of LNV phenomena, we identify a complete family of models where lepton number is violated but the generated Majorana neutrino masses are tiny, even if the new-physics scale is below 1 TeV. We explore the phenomenology of these models, including charged-lepton flavor-violating phenomena and baryon- number-violating phenomena, identifying scenarios where the allowed rates for μ− → eþ-conversion in nuclei are potentially accessible to next-generation experiments. DOI: 10.1103/PhysRevD.100.075033 I. INTRODUCTION Experimentally, in spite of ambitious ongoing experi- Lepton number and baryon number are, at the classical mental efforts, there is no evidence for the violation of level, accidental global symmetries of the renormalizable lepton-number or baryon-number conservation [5]. There Standard Model (SM) Lagrangian.1 If one allows for are a few different potential explanations for these (neg- generic nonrenormalizable operators consistent with the ative) experimental results, assuming degrees-of-freedom SM gauge symmetries and particle content, lepton number beyond those of the SM exist.
    [Show full text]
  • 1 Drawing Feynman Diagrams
    1 Drawing Feynman Diagrams 1. A fermion (quark, lepton, neutrino) is drawn by a straight line with an arrow pointing to the left: f f 2. An antifermion is drawn by a straight line with an arrow pointing to the right: f f 3. A photon or W ±, Z0 boson is drawn by a wavy line: γ W ±;Z0 4. A gluon is drawn by a curled line: g 5. The emission of a photon from a lepton or a quark doesn’t change the fermion: γ l; q l; q But a photon cannot be emitted from a neutrino: γ ν ν 6. The emission of a W ± from a fermion changes the flavour of the fermion in the following way: − − − 2 Q = −1 e µ τ u c t Q = + 3 1 Q = 0 νe νµ ντ d s b Q = − 3 But for quarks, we have an additional mixing between families: u c t d s b This means that when emitting a W ±, an u quark for example will mostly change into a d quark, but it has a small chance to change into a s quark instead, and an even smaller chance to change into a b quark. Similarly, a c will mostly change into a s quark, but has small chances of changing into an u or b. Note that there is no horizontal mixing, i.e. an u never changes into a c quark! In practice, we will limit ourselves to the light quarks (u; d; s): 1 DRAWING FEYNMAN DIAGRAMS 2 u d s Some examples for diagrams emitting a W ±: W − W + e− νe u d And using quark mixing: W + u s To know the sign of the W -boson, we use charge conservation: the sum of the charges at the left hand side must equal the sum of the charges at the right hand side.
    [Show full text]
  • Neutrino Vs Antineutrino Lepton Number Splitting
    Introduction to Elementary Particle Physics. Note 18 Page 1 of 5 Neutrino vs antineutrino Neutrino is a neutral particle—a legitimate question: are neutrino and anti-neutrino the same particle? Compare: photon is its own antiparticle, π0 is its own antiparticle, neutron and antineutron are different particles. Dirac neutrino : If the answer is different , neutrino is to be called Dirac neutrino Majorana neutrino : If the answer is the same , neutrino is to be called Majorana neutrino 1959 Davis and Harmer conducted an experiment to see whether there is a reaction ν + n → p + e - could occur. The reaction and technique they used, ν + 37 Cl e- + 37 Ar, was proposed by B. Pontecorvo in 1946. The result was negative 1… Lepton number However, this was not unexpected: 1953 Konopinski and Mahmoud introduced a notion of lepton number L that must be conserved in reactions : • electron, muon, neutrino have L = +1 • anti-electron, anti-muon, anti-neutrino have L = –1 This new ad hoc law would explain many facts: • decay of neutron with anti-neutrino is OK: n → p e -ν L=0 → L = 1 + (–1) = 0 • pion decays with single neutrino or anti-neutrino is OK π → µ-ν L=0 → L = 1 + (–1) = 0 • but no pion decays into a muon and photon π- → µ- γ, which would require: L= 0 → L = 1 + 0 = 1 • no decays of muon with one neutrino µ- → e - ν, which would require: L= 1 → L = 1 ± 1 = 0 or 2 • no processes searched for by Davis and Harmer, which would require: L= (–1)+0 → L = 0 + 1 = 1 But why there are no decays µµµ →→→ e γγγ ? 2 Splitting lepton numbers 1959 Bruno Pontecorvo
    [Show full text]
  • Introduction to Flavour Physics
    Introduction to flavour physics Y. Grossman Cornell University, Ithaca, NY 14853, USA Abstract In this set of lectures we cover the very basics of flavour physics. The lec- tures are aimed to be an entry point to the subject of flavour physics. A lot of problems are provided in the hope of making the manuscript a self-study guide. 1 Welcome statement My plan for these lectures is to introduce you to the very basics of flavour physics. After the lectures I hope you will have enough knowledge and, more importantly, enough curiosity, and you will go on and learn more about the subject. These are lecture notes and are not meant to be a review. In the lectures, I try to talk about the basic ideas, hoping to give a clear picture of the physics. Thus many details are omitted, implicit assumptions are made, and no references are given. Yet details are important: after you go over the current lecture notes once or twice, I hope you will feel the need for more. Then it will be the time to turn to the many reviews [1–10] and books [11, 12] on the subject. I try to include many homework problems for the reader to solve, much more than what I gave in the actual lectures. If you would like to learn the material, I think that the problems provided are the way to start. They force you to fully understand the issues and apply your knowledge to new situations. The problems are given at the end of each section.
    [Show full text]
  • Lecture 5: Quarks & Leptons, Mesons & Baryons
    Physics 3: Particle Physics Lecture 5: Quarks & Leptons, Mesons & Baryons February 25th 2008 Leptons • Quantum Numbers Quarks • Quantum Numbers • Isospin • Quark Model and a little History • Baryons, Mesons and colour charge 1 Leptons − − − • Six leptons: e µ τ νe νµ ντ + + + • Six anti-leptons: e µ τ νe̅ νµ̅ ντ̅ • Four quantum numbers used to characterise leptons: • Electron number, Le, muon number, Lµ, tau number Lτ • Total Lepton number: L= Le + Lµ + Lτ • Le, Lµ, Lτ & L are conserved in all interactions Lepton Le Lµ Lτ Q(e) electron e− +1 0 0 1 Think of Le, Lµ and Lτ like − muon µ− 0 +1 0 1 electric charge: − tau τ − 0 0 +1 1 They have to be conserved − • electron neutrino νe +1 0 0 0 at every vertex. muon neutrino νµ 0 +1 0 0 • They are conserved in every tau neutrino ντ 0 0 +1 0 decay and scattering anti-electron e+ 1 0 0 +1 anti-muon µ+ −0 1 0 +1 anti-tau τ + 0 −0 1 +1 Parity: intrinsic quantum number. − electron anti-neutrino ν¯e 1 0 0 0 π=+1 for lepton − muon anti-neutrino ν¯µ 0 1 0 0 π=−1 for anti-leptons tau anti-neutrino ν¯ 0 −0 1 0 τ − 2 Introduction to Quarks • Six quarks: d u s c t b Parity: intrinsic quantum number • Six anti-quarks: d ̅ u ̅ s ̅ c ̅ t ̅ b̅ π=+1 for quarks π=−1 for anti-quarks • Lots of quantum numbers used to describe quarks: • Baryon Number, B - (total number of quarks)/3 • B=+1/3 for quarks, B=−1/3 for anti-quarks • Strangness: S, Charm: C, Bottomness: B, Topness: T - number of s, c, b, t • S=N(s)̅ −N(s) C=N(c)−N(c)̅ B=N(b)̅ −N(b) T=N( t )−N( t )̅ • Isospin: I, IZ - describe up and down quarks B conserved in all Quark I I S C B T Q(e) • Z interactions down d 1/2 1/2 0 0 0 0 1/3 up u 1/2 −1/2 0 0 0 0 +2− /3 • S, C, B, T conserved in strange s 0 0 1 0 0 0 1/3 strong and charm c 0 0 −0 +1 0 0 +2− /3 electromagnetic bottom b 0 0 0 0 1 0 1/3 • I, IZ conserved in strong top t 0 0 0 0 −0 +1 +2− /3 interactions only 3 Much Ado about Isospin • Isospin was introduced as a quantum number before it was known that hadrons are composed of quarks.
    [Show full text]
  • Neutrino Masses-How to Add Them to the Standard Model
    he Oscillating Neutrino The Oscillating Neutrino of spatial coordinates) has the property of interchanging the two states eR and eL. Neutrino Masses What about the neutrino? The right-handed neutrino has never been observed, How to add them to the Standard Model and it is not known whether that particle state and the left-handed antineutrino c exist. In the Standard Model, the field ne , which would create those states, is not Stuart Raby and Richard Slansky included. Instead, the neutrino is associated with only two types of ripples (particle states) and is defined by a single field ne: n annihilates a left-handed electron neutrino n or creates a right-handed he Standard Model includes a set of particles—the quarks and leptons e eL electron antineutrino n . —and their interactions. The quarks and leptons are spin-1/2 particles, or weR fermions. They fall into three families that differ only in the masses of the T The left-handed electron neutrino has fermion number N = +1, and the right- member particles. The origin of those masses is one of the greatest unsolved handed electron antineutrino has fermion number N = 21. This description of the mysteries of particle physics. The greatest success of the Standard Model is the neutrino is not invariant under the parity operation. Parity interchanges left-handed description of the forces of nature in terms of local symmetries. The three families and right-handed particles, but we just said that, in the Standard Model, the right- of quarks and leptons transform identically under these local symmetries, and thus handed neutrino does not exist.
    [Show full text]
  • GRAND UNIFIED THEORIES Paul Langacker Department of Physics
    GRAND UNIFIED THEORIES Paul Langacker Department of Physics, University of Pennsylvania Philadelphia, Pennsylvania, 19104-3859, U.S.A. I. Introduction One of the most exciting advances in particle physics in recent years has been the develcpment of grand unified theories l of the strong, weak, and electro­ magnetic interactions. In this talk I discuss the present status of these theo­ 2 ries and of thei.r observational and experimenta1 implications. In section 11,1 briefly review the standard Su c x SU x U model of the 3 2 l strong and electroweak interactions. Although phenomenologically successful, the standard model leaves many questions unanswered. Some of these questions are ad­ dressed by grand unified theories, which are defined and discussed in Section III. 2 The Georgi-Glashow SU mode1 is described, as are theories based on larger groups 5 such as SOlO' E , or S016. It is emphasized that there are many possible grand 6 unified theories and that it is an experimental problem not onlv to test the basic ideas but to discriminate between models. Therefore, the experimental implications are described in Section IV. The topics discussed include: (a) the predictions for coupling constants, such as 2 sin sw, and for the neutral current strength parameter p. A large class of models involving an Su c x SU x U invariant desert are extremely successful in these 3 2 l predictions, while grand unified theories incorporating a low energy left-right symmetric weak interaction subgroup are most likely ruled out. (b) Predictions for baryon number violating processes, such as proton decay or neutron-antineutnon 3 oscillations.
    [Show full text]
  • Lepton Number Violation at the LHC with Leptoquarks and Diquarks\*
    EPJ Web of Conferences 49, 18002 (2013) DOI: 10.1051/epjconf/ 20134918002 C Owned by the authors, published by EDP Sciences, 2013 Lepton number violation at the LHC with leptoquarks and diquarks? Hiroaki Sugiyama1 1Department of Physics, University of Toyama, Toyama 930-8555, Japan Abstract. We investigate a model in which tiny neutrino masses are generated at the two-loop level by using scalar leptoquark and diquark multiplets. The diquark can be singly produced at the LHC, and it can decay into a pair of leptoquarks through the lepton number violating interaction. Subsequent decays of the two leptoquarks can provide a clear signature of the lepton number violation, namely two QCD jets and a pair of same-signed charged leptons without missing energy. We show that the signal process is not suppressed while neutrino masses are appropriately suppressed. 1 Introduction Table 1. List of scalar particles added to the SM. Although the lepton number is conserved in the standard SU(3)C SU(2)L U(1)Y L# B# model (SM) of particle physics, the addition of the Ma- S α 3 1 −1=3 1 1=3 jorana mass term of neutrinos (ννc where c denotes the LQ αβ − = = charge conjugation) breaks the lepton number conserva- S DQ 6 1 2 3 0 2 3 tion by two units. The measurement of the lepton number violating (L#V) processes such as the neutrinoless dou- ble beta decay is extremely important because it gives ev- SU(2)L, and hypercharge Y = −1=3. We also introduce a idence that neutrinos are Majorana particles.
    [Show full text]
  • Lecture 18 - Beyond the Standard Model
    Lecture 18 - Beyond the Standard Model Why is the Standard Model incomplete? • Grand Unification • Baryon and Lepton Number Violation • More Higgs Bosons? • Supersymmetry (SUSY) • Experimental signatures for SUSY • 1 Why is the Standard Model incomplete? The Standard Model does not explain the following: The relationship between different interactions • (strong, electroweak and gravity) The nature of dark matter and dark energy • The matter-antimatter asymmetry of the universe • The existence of three generations of quarks and leptons • Conservation of lepton and baryon number • Neutrino masses and mixing • The pattern of weak quark couplings (CKM matrix) • 2 Grand Unification The strong, electromagnetic and weak couplings αs, e and g are 15 running constants. Can they be unified at MX 10 GeV? ≈ We would also like to include gravity at the Planck scale 19 MX 10 GeV. Is string theory a candidate for this? ≈ 3 SU(5) Grand Unified Theory (GUT) Simplest theory that unifies strong and electroweak interactions (Georgi & Glashow) 15 Introduces 12 gauge bosons X and Y at MX 10 GeV ≈ These are known as leptoquarks. They make charged and neutral couplings between leptons and quarks Explains why Qν Qe = Qu Qd − − Existence of three colors is related to fractional quark charges Predicts proton decay p π0e+ → 4 2 Prediction of sin θW Loop diagram with ff¯ pair couples a Z0 boson to a photon In electroweak theory the Z0 and γ are orthogonal states The sum of loop diagrams over all fermion pairs must be zero: 2 2 P QI3 X Q(I3 Q sin θW )=0 sin θW = 2 − P Q
    [Show full text]
  • Lecture 7: Symmetries II
    Lecture 7: Symmetries II • Charge Conjugation • Time Reversal • CPT Theorem • Baryon & Lepton Number • Strangeness • Applying Conservation Laws Useful Sections in Martin & Shaw: Sections 3.1-3.4, 5.3, 5.4, 5.6 C-Parity (charge conjugation) Changes particle to anti-particle (without affecting linear or angular momentum) Electromagnetism is obviously symmetric with respect to C-parity (flip the signs of all charges and who would know?). It turns out that the strong force is as well. But, again, not the weak force (otherwise there would be left-handed anti-neutrinos... there aren’t !) For particles with distinct anti-particles (x = e-, p, π-, n, ...) a state characterized C ∣x, ψ> = ∣ x, ψ > ! where∣x, ψ > ≡ by a particle x and a wave function ψ For particles which no not have distinct anti-particles (y = γ, π0, ...) where C is a ''phase factor" of ±1 ∣ ∣ y C y, ψ > = Cy y, ψ > ! (like for parity) used to determine C-conservation in interactions For multi-particle systems ∣ ∣ | C x, ψ1; x, ψ2 > = x, ψ1; x, ψ2 > = ± x, ψ1; x, ψ2 > depending on whether the system is symmetric or antisymmetric under the operation Example: consider a π+π- pair in a state of definite orbital angular momentum L C ∣ π+π-, L > = (-1)L ∣ π+π-, L > since interchanging π+ and π- reverses their relative position vector in the spatial wave function Example: Experimentally, π0 → γ + γ but never π0 → γ + γ + γ How is this reconciled with the concept of C-parity ?? using a similar argument 0 0 C ∣ π > = C ∣ π > as for parity, π° Cγ = -1 C = +1 π° ∣ ∣ C ∣ γγγ = C C C ∣ γγγ
    [Show full text]