12.2 Problem Set 2 Solutions
|
|
- Winfred Golden
- 6 years ago
- Views:
Transcription
1 78 CHAPTER. PROBLEM SET SOLUTIONS. Problem Set Solutions. I will use a basis m, which ψ C = iγ ψ = Cγ ψ (.47) We can define left (light) handed Majorana fields as, so that ω = ψ L + (ψ L ) C (.48) χ = ψ R + (ψ R ) C (.49) Note that ω = ω C (.50) χ = χ C (.5) Then (ψ L ) C = (ψ C ) R (.5) (ψ R ) C = (ψ C ) L (.53) µ R ψψ = µ R (ψ R (ψ R ) C + ψr C ψ R ) (.54) µ L ωω = µ L (ψ L (ψ L ) C + ψl C ψ L ) (.55) are the right (left) handed mass terms for Majorana fields. Generalizing to N flavor, i,j =,,N, we have µ ij ψ Ci ψ j + h.c Using above definition for C and anti-symmetry of Grassmann variables are sees that µ ij can be taken as symmetric. For one flavor case general Dirac and Majorana mass is Since ( ) ( ) ( ) m µ ω ω χ L m (.56) µ χ R
2 .. PROBLEM SET SOLUTIONS 79 m (ωχ + ψω) = m(ψ L ψ R + ψ R ψ L ) = Dirac Mass (.57) One can diagnolize this by a unitary transformation to get the eigenvalues (in case µ L = 0 for instance) µ = µ R, m µ R This is an example of the see saw mechanism. Although one can not right down relevant (dimension 4) Majorana mess term in standard model, one can in some GUT s, e.g. SO(0). Therefore, the natural Majorana mass O(0 5 Gev), which is the GUT scale in typical theories.then above mechanism would give a LH fermion with a tiny mass m (00 Gev) 0 ev (.58) µ 0 5 Gev which is consistent with observation of scalar neutrinos. Note that for the typical Dirac mass µ, I take 00 Gev since they are obtained by Higgs much at weak scale. Same mechanism works for N > flavors in which case one diagonalizes the general mass make it with a unitary transformation.. (a) Let s begin with listing the matter content of Sµ indicating the hypercharges: Quarks: u R 3 d R 3 ρ L = q = q = ( ) ( ) ( ) u L c L t,, L (.59) d L s L b L 6 6 u R,c R,t R (.60) d R,s R,b R (.6) 6 Leptons: ( ) ( ) ( ) ν el ν µl ν l τl L =,, (.6) e L µ τ L L l R = l R,µ R,τ R (.63) Higgs:
3 80 CHAPTER. PROBLEM SET SOLUTIONS Φ = ( + ) (.64) We want to find a term with B = 0. Clearly this term should involve quarks. The restrictions are: SU(3) color, SU() weak, U() Y and Lorentz invariance. (l, ρ, τ separately are not fundamental). SU(3) requires three combinations: = (.65) = (.66) 3 3 = + 8 (.67) Last one can not violate B hence discarded. First two are ρρρ (or ρ c ρ c ρ c ) and ρρρ (or ρ c ρ c ρ c ) which are not Lorentz invariant unless we include another fermion which should be a lepton in order not to spoil SU(3) color. Hence the lowest dimensional operators which has B = 0 are ρρρl with dimension 6. (b) There are four types: ρρρl, ρ ρ ρ l, ρρρl, ρ ρ ρ l. First two does not violate B L, last two does. This problem amounts to see that last two are in violation of at last one of the after mentioned symmetries of Sµ. Consideration of ρρρl is sufficient: To have SU() invariance we need even number of left handed: ρ L ρ L ρ L ll, ρ R R L, ρ L ρ u ρ d L, ρ L ρ d ρ d L, ρ u ρ u ρ u R, ρ u ρ u ρ d R, ρ u ρ d ρ d R, ρ d ρ d ρ d l L ρ u ρ u l R Rl R Rl R R Rl R R Rl R R Rl R R R R. Note that ρ is either ρ or ρ c. l can only be a l. None of the above can be Lorentz invariant hence it is impossible to violate B L with a dimension 6 operator. Actually a generalization of above reasoning glons that B L can not be involved in Sµ neither perturbatively nor non-perturbatively. However B L violation would after a nice explanation for observed baryon asymmetry in the universe. One nice feature of GUT s is that there are consistent GUT s with relevant B L violating terms (e.g. SO(0)). (c) To violate L we need at least are lepton. If we insist to have only one lepton than we need to contract it with at least one quark. This would violate SU(3) hence we need three quarks, but this term (lρρρ) is dimension 6, no way. Consider two leptons, in order to violate L these should have same lepton number, hence Majorana type contraction: ll c l L or lr c l R. But these
4 .. PROBLEM SET SOLUTIONS 8 have total hypercharge and each. To cancel this we are only left with φ s to add. Therefore, we get ll c l L φ with dimension 5 or lr c l R φ 4 with dimension 7. As φ gets a VEV by Higgs l c l L φ l c l L v (.68) L L becomes a Majorana mess term. 3. (a) SU() in adjoint can be represented by τ 3 = 0 (.69) i τ = i i (.70) i τ = (.7) To have a cross product representation under SU() U() Y all elements in the triplet should carry same hypercharge Y. Then the covariant derivative takes the form Y where, Y = Y Y We want to give a VEV to triplet Higgs Δ µ = I µ + iga a µ τ a + ig B µ Y (.7) φ 3 = 3 (.73) such that only one of the linear combinations of generators τ, τ, τ 3, Y is unbroken. This will be the electric charge Q. This will be a diagonal U(), hence overall constant can be observed into charge Q = aτ 3 + by (.74)
5 8 CHAPTER. PROBLEM SET SOLUTIONS b is arbitrary but for convenience we take as Q = τ 3 + by (.75) Y Q = τ 3 + Y = 0 Y Y (.76) This should have a zero eigenvalue, hence Y {+,, 0}. However 0 in case Y = 0 only τ and τ are broken by Y, hence we get SU() 0 U() U() U(). We should choose Y {+, }. (b) Consider both a doublet φ with the covariant derivative and a triplet with σ a D µ φ = (I µ + ig A µ + ig B µ )φ (.77) D µ φ 3 = (I µ + iga τ a + ig Y B µ )φ 3 (.78) µ Expanding out D µφ + D µ φ 3 for φ = v, φ 3 = v3 we get for Y = ±: m w± = g (v + v 3 ) (.79) 4 m = (g + ρ z )(v + 4v 3 ) (.80) 4 m γ = 0 (.8) If we keep φ we have the option Y = 0 in contrast to above since φ already breaks to U(). For this case, Y = 0: w± 4 m = (v + 4v 3 ) (.8) m = 4 (g z + ρ )v (.83) m γ = 0 (.84) Note that m is entirely coming from usual doublet Higgs. z
6 .. PROBLEM SET SOLUTIONS 83 v 3 can be constrained as follows: See H. E. Haber, Minimal and Nonv minimal Higgs Bosons, in Phenomenology of Sµ and Beyond, D.P. Rey and P. Rey world scientific, 989 (this is in library: QC793.W66 989). An experimental fact that is very close to : ρ µ µ w z cos θw (.85) ρ = ɛ, 0 < ɛ (.86) On the other hand for a general Higgs content one can express ρ in term so f the casming of SU() and U() as: T,Y (T(T + ) Y ) < φ T,Y > ρ = (.87) T,Y Y < φ T,Y > where T,Y denote the representation, < φ T,Y > is the VEV of particular Higgs in the sum. Note that for T =, Y = ± one naturally gets ρ = (for any number of Higgs fields with T =, Y = ± ). For our problem we get + ( v 3 v ) + v 3 v ρ = = = ɛ (.88) 3 + 4( v 3 + v ) v v Therefore, 3 should be very small. v v 3 v 3 ρ ( ) ɛ = ɛ = (.89) v v This shows that adding a new type of Higgs field to the usual doublet is highly constrained by experiments. However, one can clearly add any number of doublets without violating ρ = ɛ constraint. This possibly is explored in the next problem. (c) Initially we have = 0 real D.O.F. 3 is eaten and we have left with 7 real scalar D.O.F. One of them is usual Higgs with Q = 0, isospin. The rest for Y = ± are two neutral scalars, two scalars of charge ±, two scalars of charge ± as clear from above Q matrix. (d) We now have the possibility of a Higgs field with Y = ±. Recall from Problem that the biggest constraint for a L violating term was imposed c by preserving hypercharge. Now we can write down l L l L φ 3 +, which is dimension 4 hence marginal. Note however, that lepton number violating v
7 84 CHAPTER. PROBLEM SET SOLUTIONS processes are quick constrained by experiments hence v 3 should again be v very small in accord with our discussion in previous part. 4. (a) We have two Higgs doublets φ and φ with condensation Then the masses of the gauge fields are ( ) 0 < φ >= (.90) v ( ) 0 < φ >= (.9) v w± m = m z = m γ = g (v + v ) (.9) 4 (ρ + ρ )(v + v 3 ) (.93) 4 0 (.94) Therefore, m w m z g = g + g (.95) is same as in the case of single doublet. Furthermore, using the general formula for ρ (from previous problem) we saw that m ρ = = w (.96) m z cos θ w Therefore, θ w is also the same as before. Started with 8 real scalar D.O.F. 3 absorbed into congitiduval modes of gauge mesons w± and z. ( Therefore, ) 5 left out of which ( one is the ) 0 α + iβ usual neutral Higgs: φ =, 4 others are φ v + h =, γ + iδ α and β are charge +(α + iβ), (α iβ), γ and δ are both charge zero. (b) See H. E. Haber in QC793.W (c) General Yukawa coupling to quarks reads α α d Lφ qr + λ ɛ αβ qlφ α β u q d + λ 3 qlφ α α d qr + λ 4 ɛ αβ qlφ α β u λ q qr+ (.97)
8 .. PROBLEM SET SOLUTIONS 85 d However, under new U(), φ has charge, φ has +, q R, qr u has + then nd and 3 rd terms not allowed. u d This means φ cannot couple to q d, φ cannot couple to q R as in part above. Extra restriction on the potential in the previous part is that (φ + φ )(φ φ + ) term is not allowed. From continuous U() breaking we get an additional Goldstone boson, the axion. It is proportional to Tv, where T is the U() generator that generates φ φ e iλ φ e iλ, φ. Therefore, its coupling to quarks are α u ɛ αβ q L q R φ β (u L u R λ u + c L c R λ c + t L t R λ t ) }{{} ax (.98) axion
Lecture III: Higgs Mechanism
ecture III: Higgs Mechanism Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for eptons Quark Masses & Mixing III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest
More informationIntroduction to the SM (5)
Y. Grossman The SM (5) TES-HEP, July 12, 2015 p. 1 Introduction to the SM (5) Yuval Grossman Cornell Y. Grossman The SM (5) TES-HEP, July 12, 2015 p. 2 Yesterday... Yesterday: Symmetries Today SSB the
More informationMirror fermions, electroweak scale right-handed neutrinos and experimental implications
Mirror fermions, electroweak scale right-handed neutrinos and experimental implications P. Q. Hung University of Virginia Ljubljana 2008 Plan of Talk The question of parity restoration at high energies:
More informationTwo-Higgs-Doublet Model
Two-Higgs-Doublet Model Logan A. Morrison University of California, Santa Cruz loanmorr@ucsc.edu March 18, 016 Logan A. Morrison (UCSC) HDM March 18, 016 1 / 7 Overview 1 Review of SM HDM Formalism HDM
More informationNeutrino Mass Models
Neutrino Mass Models S Uma Sankar Department of Physics Indian Institute of Technology Bombay Mumbai, India S. Uma Sankar (IITB) IWAAP-17, BARC (Mumbai) 01 December 2017 1 / 15 Neutrino Masses LEP experiments
More informationModels of Neutrino Masses
Models of Neutrino Masses Fernando Romero López 13.05.2016 1 Introduction and Motivation 3 2 Dirac and Majorana Spinors 4 3 SU(2) L U(1) Y Extensions 11 4 Neutrino masses in R-Parity Violating Supersymmetry
More informationNon-Abelian SU(2) H and Two-Higgs Doublets
Non-Abelian SU(2) H and Two-Higgs Doublets Technische Universität Dortmund Wei- Chih Huang 25 Sept 2015 Kavli IPMU arxiv:1510.xxxx(?) with Yue-Lin Sming Tsai, Tzu-Chiang Yuan Plea Please do not take any
More informationElectroweak-scale Right-handed Neutrino Model And 126 GeV Higgs-like Particle
Electroweak-scale Right-handed Neutrino Model And 126 GeV Higgs-like Particle Ajinkya S. Kamat ask4db@virginia.edu http://people.virginia.edu/ ask4db With Prof. P. Q. Hung and Vinh Van Hoang (paper in
More informationLeaving Plato s Cave: Beyond The Simplest Models of Dark Matter
Leaving Plato s Cave: Beyond The Simplest Models of Dark Matter Alexander Natale Korea Institute for Advanced Study Nucl. Phys. B914 201-219 (2017), arxiv:1608.06999. High1 2017 February 9th, 2017 1/30
More informationProblems for SM/Higgs (I)
Problems for SM/Higgs (I) 1 Draw all possible Feynman diagrams (at the lowest level in perturbation theory) for the processes e + e µ + µ, ν e ν e, γγ, ZZ, W + W. Likewise, draw all possible Feynman diagrams
More informationLecture 6 The Super-Higgs Mechanism
Lecture 6 The Super-Higgs Mechanism Introduction: moduli space. Outline Explicit computation of moduli space for SUSY QCD with F < N and F N. The Higgs mechanism. The super-higgs mechanism. Reading: Terning
More informationThe Standard Model and beyond
The Standard Model and beyond In this chapter we overview the structure of the Standard Model (SM) of particle physics, its shortcomings, and different ideas for physics beyond the Standard Model (BSM)
More informationMay 7, Physics Beyond the Standard Model. Francesco Fucito. Introduction. Standard. Model- Boson Sector. Standard. Model- Fermion Sector
- Boson - May 7, 2017 - Boson - The standard model of particle physics is the state of the art in quantum field theory All the knowledge we have developed so far in this field enters in its definition:
More informationNeutrino masses respecting string constraints
Neutrino masses respecting string constraints Introduction Neutrino preliminaries The GUT seesaw Neutrinos in string constructions The triplet model (Work in progress, in collaboration with J. Giedt, G.
More informationNeutrino Oscillation, Leptogenesis and Spontaneous CP Violation
Neutrino Oscillation, Leptogenesis and Spontaneous CP Violation Mu-Chun Chen Fermilab (Jan 1, 27: UC Irvine) M.-C. C & K.T. Mahanthappa, hep-ph/69288, to appear in Phys. Rev. D; Phys. Rev. D71, 351 (25)
More informationFermions of the ElectroWeak Theory
Fermions of the ElectroWeak Theory The Quarks, The eptons, and their Masses. This is my second set of notes on the Glashow Weinberg Salam theory of weak and electromagnetic interactions. The first set
More informationPati-Salam GUT-Flavour Models with Three Higgs Generations
Pati-Salam GUT-Flavour Models with Three Higgs Generations Florian Hartmann in collaboration with Wolfgang Kilian and Karsten Schnitter based on: JHEP 1405 (2014) 064 and arxiv:1405.1901 Universität Siegen
More informationThe Yang and Yin of Neutrinos
The Yang and Yin of Neutrinos Ernest Ma Physics and Astronomy Department University of California Riverside, CA 92521, USA The Yang and Yin of Neutrinos (2018) back to start 1 Contents Introduction The
More informationFermions of the ElectroWeak Theory
Fermions of the ElectroWeak Theory The Quarks, The eptons, and their Masses. This is my second set of notes on the Glashow Weinberg Salam theory of weak and electromagnetic interactions. The first set
More informationIntroduction to Supersymmetry
Introduction to Supersymmetry 1: Formalism of SUSY M. E. Peskin Maria Laach Herbstschule September, 2004 Among models of electroweak symmetry breaking and physics beyond the Standard Model Supersymmetry
More informationLecture 4 - Relativistic wave equations. Relativistic wave equations must satisfy several general postulates. These are;
Lecture 4 - Relativistic wave equations Postulates Relativistic wave equations must satisfy several general postulates. These are;. The equation is developed for a field amplitude function, ψ 2. The normal
More informationFermion Mixing Angles and the Connection to Non-Trivially Broken Flavor Symmetries
Fermion Mixing ngles and the Connection to Non-Trivially Broken Flavor Symmetries C. Hagedorn hagedorn@mpi-hd.mpg.de Max-Planck-Institut für Kernphysik, Heidelberg, Germany. Blum, CH, M. Lindner numerics:.
More informationWeek 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books
Week 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books Burgess-Moore, Chapter Weiberg, Chapter 5 Donoghue, Golowich, Holstein Chapter 1, 1 Free field Lagrangians
More informationGrand Unification. Strong, weak, electromagnetic unified at Q M X M Z Simple group SU(3) SU(2) U(1) Gravity not included
Pati-Salam, 73; Georgi-Glashow, 74 Grand Unification Strong, weak, electromagnetic unified at Q M X M Z Simple group G M X SU(3) SU() U(1) Gravity not included (perhaps not ambitious enough) α(q ) α 3
More information+ µ 2 ) H (m 2 H 2
I. THE HIGGS POTENTIAL AND THE LIGHT HIGGS BOSON In the previous chapter, it was demonstrated that a negative mass squared in the Higgs potential is generated radiatively for a large range of boundary
More informationGauge Symmetry in QED
Gauge Symmetry in QED The Lagrangian density for the free e.m. field is L em = 1 4 F µνf µν where F µν is the field strength tensor F µν = µ A ν ν A µ = Thus L em = 1 (E B ) 0 E x E y E z E x 0 B z B y
More informationA model of the basic interactions between elementary particles is defined by the following three ingredients:
I. THE STANDARD MODEL A model of the basic interactions between elementary particles is defined by the following three ingredients:. The symmetries of the Lagrangian; 2. The representations of fermions
More informationSU(3)-Flavons and Pati-Salam-GUTs
SU(3)-Flavons and Pati-Salam-GUTs Florian Hartmann in collaboration with Wolfgang Kilian and Karsten Schnitter Universität Siegen Theoretische Physik I Dortmund, 03.07.2012 Outline 1 Running couplings
More informationNeutrino Mixing and Cosmological Constant above GUT Scale
EJTP 6, No. 22 (2009) 197 202 Electronic Journal of Theoretical Physics Neutrino Mixing and Cosmological Constant above GUT Scale Bipin Singh Koranga Department of Physics, Kirori Mal college (University
More informationSuccessful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism
Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism Pierre Hosteins Patras University 13th November 2007 Brussels P.H., S. Lavignac and C. Savoy, Nucl. Phys. B755, arxiv:hep-ph/0606078
More informationE 6 Spectra at the TeV Scale
E 6 Spectra at the TeV Scale Instituts-Seminar Kerne und Teilchen, TU Dresden Alexander Knochel Uni Freiburg 24.06.2010 Based on: F. Braam, AK, J. Reuter, arxiv:1001.4074 [hep-ph], JHEP06(2010)013 Outline
More informationNeutrino Masses in the MSSM
Neutrino Masses in the MSSM Steven Rimmer Supervisor: Dr. Athanasios Dedes Institute of Particle Physics Phenomenology, University of Durham A supersymmetric standard model Find the most general Lagrangian
More informationSymmetry Groups conservation law quantum numbers Gauge symmetries local bosons mediate the interaction Group Abelian Product of Groups simple
Symmetry Groups Symmetry plays an essential role in particle theory. If a theory is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. For example,
More informationLeptons and SU(2) U(1)
Leptons and SU() U(1) Contents I. Defining the Leptonic Standard Model 1 II. L kin and the gauge symmetry 3 III. L mψ = 0 4 IV. L φ and spontaneous symmetry breaking 4 V. Back to L kin (φ): The vector
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 99890701 Allowed tools: mathematical tables Some formulas can be found on p.2. 1. Concepts.
More informationTriplet Higgs Scenarios
Triplet Higgs Scenarios Jack Gunion U.C. Davis Grenoble Higgs Workshop, March 2, 203 Higgs-like LHC Signal Fits with MVA CMS suggest we are heading towards the SM, but it could simply be a decoupling limit
More informationStandard Model & Beyond
XI SERC School on Experimental High-Energy Physics National Institute of Science Education and Research 13 th November 2017 Standard Model & Beyond Lecture III Sreerup Raychaudhuri TIFR, Mumbai 2 Fermions
More informationThe Higgs Mechanism and the Higgs Particle
The Higgs Mechanism and the Higgs Particle Heavy-Ion Seminar... or the Anderson-Higgs-Brout-Englert-Guralnik-Hagen-Kibble Mechanism Philip W. Anderson Peter W. Higgs Tom W. B. Gerald Carl R. François Robert
More informationSM predicts massless neutrinos
MASSIVE NEUTRINOS SM predicts massless neutrinos What is the motivation for considering neutrino masses? Is the question of the existence of neutrino masses an isolated one, or is connected to other outstanding
More informationHidden two-higgs doublet model
Hidden two-higgs doublet model C, Uppsala and Lund University SUSY10, Bonn, 2010-08-26 1 Two Higgs doublet models () 2 3 4 Phenomenological consequences 5 Two Higgs doublet models () Work together with
More informationThe Strong Interaction and LHC phenomenology
The Strong Interaction and LHC phenomenology Juan Rojo STFC Rutherford Fellow University of Oxford Theoretical Physics Graduate School course Lecture 2: The QCD Lagrangian, Symmetries and Feynman Rules
More informationLittle Higgs Models Theory & Phenomenology
Little Higgs Models Theory Phenomenology Wolfgang Kilian (Karlsruhe) Karlsruhe January 2003 How to make a light Higgs (without SUSY) Minimal models The Littlest Higgs and the Minimal Moose Phenomenology
More informationFlavour and Higgs in Pati-Salam Models
Flavour and Higgs in Pati-Salam Models Florian Hartmann Universität Siegen Theoretische Physik I Siegen, 16.11.2011 Florian Hartmann (Uni Siegen) Flavour and Higgs in Pati-Salam Models Siegen 16.11.2011
More informationSpace-Time Symmetries
Space-Time Symmetries Outline Translation and rotation Parity Charge Conjugation Positronium T violation J. Brau Physics 661, Space-Time Symmetries 1 Conservation Rules Interaction Conserved quantity strong
More informationThe SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry Breaking Gell-Mann Okubo Mass Formulae Quark-Mo
Lecture 2 Quark Model The Eight Fold Way Adnan Bashir, IFM, UMSNH, Mexico August 2014 Culiacán Sinaloa The SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry
More informationScaling in the Neutrino Mass Matrix and the See-Saw Mechanism. Werner Rodejohann (MPIK, Heidelberg) Erice, 20/09/09
Scaling in the Neutrino Mass Matrix and the See-Saw Mechanism Werner Rodejohann (MPIK, Heidelberg) Erice, 20/09/09 1 A. S. Joshipura, W.R., Phys. Lett. B 678, 276 (2009) [arxiv:0905.2126 [hep-ph]] A. Blum,
More informationTheory toolbox. Chapter Chiral effective field theories
Chapter 3 Theory toolbox 3.1 Chiral effective field theories The near chiral symmetry of the QCD Lagrangian and its spontaneous breaking can be exploited to construct low-energy effective theories of QCD
More informationDetection Prospects of Doubly Charged Higgs Bosons from the Higgs Triplet Model at the LHC
UPTEC F11 44 Examensarbete 3 hp Juni 11 Detection Prospects of Doubly Charged Higgs Bosons from the Higgs Triplet Model at the LHC Viveca Lindahl Abstract Detection Prospects of Doubly Charged Higgs Bosons
More informationF. Börkeroth, F. J. de Anda, I. de Medeiros Varzielas, S. F. King. arxiv:
F. Börkeroth, F. J. de Anda, I. de Medeiros Varzielas, S. F. King S FLASY 2015 arxiv:1503.03306 Standard Model Gauge theory SU(3)C X SU(2)L X U(1)Y Standard Model Gauge theory SU(3)C X SU(2)L X U(1)Y SM:
More informationNeutrinos: status, models, string theory expectations
Neutrinos: status, models, string theory expectations Introduction Neutrino preliminaries and status Models String embeddings Intersecting brane The Z 3 heterotic orbifold Embedding the Higgs triplet Outlook
More informationThe Higgs Boson and Electroweak Symmetry Breaking
The Higgs Boson and Electroweak Symmetry Breaking 1. Minimal Standard Model M. E. Peskin Chiemsee School September 2014 The Higgs boson has an odd position in the Standard Model of particle physics. On
More informationNeutrino Mass in Strings
Neutrino Mass in Strings Introduction Neutrino preliminaries Models String embeddings Intersecting brane The Z 3 heterotic orbifold Embedding the Higgs triplet Outlook Neutrino mass Nonzero mass may be
More informationSupersymmetry, Dark Matter, and Neutrinos
Supersymmetry, Dark Matter, and Neutrinos The Standard Model and Supersymmetry Dark Matter Neutrino Physics and Astrophysics The Physics of Supersymmetry Gauge Theories Gauge symmetry requires existence
More informationTeV-scale type-i+ii seesaw mechanism and its collider signatures at the LHC
TeV-scale type-i+ii seesaw mechanism and its collider signatures at the LHC Wei Chao (IHEP) Outline Brief overview of neutrino mass models. Introduction to a TeV-scale type-i+ii seesaw model. EW precision
More informationTHE STANDARD MODEL AND THE GENERALIZED COVARIANT DERIVATIVE
THE STANDAD MODEL AND THE GENEALIZED COVAIANT DEIVATIVE arxiv:hep-ph/9907480v Jul 999 M. Chaves and H. Morales Escuela de Física, Universidad de Costa ica San José, Costa ica E-mails: mchaves@cariari.ucr.ac.cr,
More informationFundamental Symmetries - 2
HUGS 2018 Jefferson Lab, Newport News, VA May 29- June 15 2018 Fundamental Symmetries - 2 Vincenzo Cirigliano Los Alamos National Laboratory Plan of the lectures Review symmetry and symmetry breaking Introduce
More informationAn Introduction to the Standard Model of Particle Physics
An Introduction to the Standard Model of Particle Physics W. N. COTTINGHAM and D. A. GREENWOOD Ж CAMBRIDGE UNIVERSITY PRESS Contents Preface. page xiii Notation xv 1 The particle physicist's view of Nature
More informationLectures on Chiral Perturbation Theory
Lectures on Chiral Perturbation Theory I. Foundations II. Lattice Applications III. Baryons IV. Convergence Brian Tiburzi RIKEN BNL Research Center Chiral Perturbation Theory I. Foundations Low-energy
More informationPAPER 45 THE STANDARD MODEL
MATHEMATICAL TRIPOS Part III Friday, 6 June, 014 1:0 pm to 4:0 pm PAPER 45 THE STANDARD MODEL Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight.
More informationBINARY TETRAHEDRAL GROUP (T )
Thank you for the invitation. BINARY TETRAHEDRAL GROUP (T ) AND THE CABIBBO ANGLE Paul H Frampton UNC-CHAPEL HILL OUTLINE 1. Introduction on renormalizability. 2. A 4 symmetry. 3. Minimal A 4 model. 4.
More informationNeutrinos. Riazuddin National Centre for Physics Quaid-i-Azam University Campus. Islamabad.
Neutrinos Riazuddin National Centre for Physics Quaid-i-Azam University Campus Islamabad. Neutrino was the first particle postulated by a theoretician: W. Pauli in 1930 to save conservation of energy and
More informationPARTICLE PHYSICS Major Option
PATICE PHYSICS Major Option Michaelmas Term 00 ichard Batley Handout No 8 QED Maxwell s equations are invariant under the gauge transformation A A A χ where A ( φ, A) and χ χ ( t, x) is the 4-vector potential
More informationParticle Physics. Dr Victoria Martin, Spring Semester 2013 Lecture 17: Electroweak and Higgs
Particle Physics Dr Victoria Martin, Spring Semester 013 Lecture 17: Electroweak and Higgs Weak Isospin and Weak Hypercharge Weak Isospin and Weak Hypercharge currents γ W ± Z 0 bosons Spontaneous Symmetry
More informationElectroweak physics and the LHC an introduction to the Standard Model
Electroweak physics and the LHC an introduction to the Standard Model Paolo Gambino INFN Torino LHC School Martignano 12-18 June 2006 Outline Prologue on weak interactions Express review of gauge theories
More informationFlavor, Minimality and Naturalness in Composite Higgs Models
eth zurich Flavor, Minimality and Naturalness in Composite Higgs Models Adrián Carmona Bermúdez Institute for Theoretical Physics, ETH Zurich In collaboration with F. Goertz A naturally light Higgs without
More informationQED and the Standard Model Autumn 2014
QED and the Standard Model Autumn 2014 Joel Goldstein University of Bristol Joel.Goldstein@bristol.ac.uk These lectures are designed to give an introduction to the gauge theories of the standard model
More informationTPP entrance examination (2012)
Entrance Examination Theoretical Particle Physics Trieste, 18 July 2012 Ì hree problems and a set of questions are given. You are required to solve either two problems or one problem and the set of questions.
More informationNovember 24, Scalar Dark Matter from Grand Unified Theories. T. Daniel Brennan. Standard Model. Dark Matter. GUTs. Babu- Mohapatra Model
Scalar from November 24, 2014 1 2 3 4 5 What is the? Gauge theory that explains strong weak, and electromagnetic forces SU(3) C SU(2) W U(1) Y Each generation (3) has 2 quark flavors (each comes in one
More informationThe Standard Model. Zack Sullivan
The Standard Model Zack Sullivan Illinois Institute of Technology CTEQ Collaboration July 11, 2011 Zack Sullivan ( IIT) The Standard Model CTEQ Summer School 2011 1 / 24 What is the Standard Model? Definition
More informationFor Review Only. General Structure of Democratic Mass Matrix of Lepton Sector in E 6 Model. Canadian Journal of Physics
General Structure of Democratic Mass Matrix of Lepton Sector in E 6 Model Journal: Canadian Journal of Physics Manuscript ID cjp-2017-0783.r1 Manuscript Type: Article Date Submitted by the Author: 08-Jan-2018
More informationNeutrino Masses SU(3) C U(1) EM, (1.2) φ(1, 2) +1/2. (1.3)
Neutrino Masses Contents I. The renormalizable Standard Model 1 II. The non-renormalizable Standard Model III. The See-Saw Mechanism 4 IV. Vacuum Oscillations 5 V. The MSW effect 7 VI. Experimental results
More informationNon Abelian Higgs Mechanism
Non Abelian Higgs Mechanism When a local rather than global symmetry is spontaneously broken, we do not get a massless Goldstone boson. Instead, the gauge field of the broken symmetry becomes massive,
More informationSteve King, DCPIHEP, Colima
!!! 1/6/11 Lecture I. The Flavour Problem in the Standard Model with Neutrino Mass Lecture II. Family Symmetry and SUSY Lecture III. SUSY GUTs of Flavour with Discrete Family Symmetry Steve King, DCPIHEP,
More informationBeta and double beta decay
Fakultät Mathematik und Naturwissenschaften, Institut für Kern- und Teilchenphysik Beta and double beta decay Kai Zuber Institut für Kern- und Teilchenphysik 10-12. 6. 2014, SNOLAB Contents Lecture 1 History,
More informationBack to Gauge Symmetry. The Standard Model of Par0cle Physics
Back to Gauge Symmetry The Standard Model of Par0cle Physics Laws of physics are phase invariant. Probability: P = ψ ( r,t) 2 = ψ * ( r,t)ψ ( r,t) Unitary scalar transformation: U( r,t) = e iaf ( r,t)
More informationDIRAC vs MAJORANA? Neutrinos are the only electrically neutral fermions. ff (quarks, charged leptons) If a fermion is charged, ff
DIRAC vs MAJORANA? Neutrinos are the only electrically neutral fermions If a fermion is charged, ff ff (quarks, charged leptons) Majorana Neutrino: ff = ff, cccccccccccc cccccccccc llllllllllll nnnnnnnnnnnn.
More informationGauge-Higgs Unification on Flat Space Revised
Outline Gauge-Higgs Unification on Flat Space Revised Giuliano Panico ISAS-SISSA Trieste, Italy The 14th International Conference on Supersymmetry and the Unification of Fundamental Interactions Irvine,
More informationarxiv: v1 [hep-ph] 16 Mar 2017
Flavon-induced lepton flavour violation arxiv:1703.05579v1 hep-ph] 16 Mar 017 Venus Keus Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu, FIN-00014 University of Helsinki,
More informationNeutrinos and Fundamental Symmetries: L, CP, and CP T
Neutrinos and Fundamental Symmetries: L, CP, and CP T Outstanding issues Lepton number (L) CP violation CP T violation Outstanding issues in neutrino intrinsic properties Scale of underlying physics? (string,
More informationIntroduction to Neutrino Physics. TRAN Minh Tâm
Introduction to Neutrino Physics TRAN Minh Tâm LPHE/IPEP/SB/EPFL This first lecture is a phenomenological introduction to the following lessons which will go into details of the most recent experimental
More informationNeutrino Masses and Dark Matter in Gauge Theories for Baryon and Lepton Numbers
Neutrino Masses and Dark Matter in Gauge Theories for Baryon and Lepton Numbers DPG Frühjahrstagung 014 in Mainz Based on Phys. Rev. Lett. 110, 31801 (013), Phys. Rev. D 88, 051701(R) (013), arxiv:1309.3970
More informationDuality in left-right symmetric seesaw
Duality in left-right symmetric seesaw Evgeny Akhmedov KTH, Stockholm & Kurchatov Institute, Moscow In collaboration with Michele Frigerio Evgeny Akhmedov SNOW 2006 Stockholm May 4, 2006 p. 1 Why are neutrinos
More informationAs usual, these notes are intended for use by class participants only, and are not for circulation. Week 8: Lectures 15, 16
As usual, these notes are intended for use by class participants only, and are not for circulation. Week 8: Lectures 15, 16 Masses for Vectors: the Higgs mechanism April 6, 2012 The momentum-space propagator
More informationPAPER 305 THE STANDARD MODEL
MATHEMATICAL TRIPOS Part III Tuesday, 6 June, 017 9:00 am to 1:00 pm PAPER 305 THE STANDARD MODEL Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight.
More informationShow, for infinitesimal variations of nonabelian Yang Mills gauge fields:
Problem. Palatini Identity Show, for infinitesimal variations of nonabelian Yang Mills gauge fields: δf i µν = D µ δa i ν D ν δa i µ..) Begin by considering the following form of the field strength tensor
More informationThis means that n or p form a doublet under isospin transformation. Isospin invariance simply means that. [T i, H s ] = 0
1 QCD 1.1 Quark Model 1. Isospin symmetry In early studies of nuclear reactions, it was found that, to a good approximation, nuclear force is independent of the electromagnetic charge carried by the nucleons
More informationCP violation in charged Higgs production and decays in the Complex 2HDM
CP violation in charged Higgs production and decays in the Complex 2HDM Abdesslam Arhrib National Cheung Keung University (NCKU), Faculté des Sciences et Techniques Tangier, Morocco Based on: A.A, H. Eberl,
More informationRethinking Flavor Physics
Rethinking Flavor Physics René Sondenheimer FSU Jena & L. Egger, A. Maas arxiv:1701.02881 Cold Quantum Coffee, Heidelberg 30th of May 2017 LHC works remarkably well Higgs discovery completed SM 2 LHC works
More informationMaria Dimou In collaboration with: C. Hagedorn, S.F. King, C. Luhn. Tuesday group seminar 17/03/15 University of Liverpool
Maria Dimou In collaboration with: C. Hagedorn, S.F. King, C. Luhn Tuesday group seminar 17/03/15 University of Liverpool 1 Introduction Outline The SM & SUSY Flavour Problem. Solving it by imposing a
More informationTheories with Compact Extra Dimensions
Instituto de Física USP PASI 2012 UBA Theories with Compact Extra dimensions Part II Generating Large Hierarchies with ED Theories Warped Extra Dimensions Warped Extra Dimensions One compact extra dimension.
More informationHiggs Boson Phenomenology Lecture I
iggs Boson Phenomenology Lecture I Laura Reina TASI 2011, CU-Boulder, June 2011 Outline of Lecture I Understanding the Electroweak Symmetry Breaking as a first step towards a more fundamental theory of
More informationMasses and the Higgs Mechanism
Chapter 8 Masses and the Higgs Mechanism The Z, like the W ± must be very heavy. This much can be inferred immediately because a massless Z boson would give rise to a peculiar parity-violating long-range
More informationUniversal Extra Dimensions
Universal Extra Dimensions Add compact dimension(s) of radius R ~ ant crawling on tube Kaluza-Klein tower of partners to SM particles due to curled-up extra dimensions of radius R n = quantum number for
More informationYou may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.
MATHEMATICAL TRIPOS Part III Monday 7 June, 004 1.30 to 4.30 PAPER 48 THE STANDARD MODEL Attempt THREE questions. There are four questions in total. The questions carry equal weight. You may not start
More informationQuark Model. Ling-Fong Li. (Institute) Note 8 1 / 26
Quark Model Ling-Fong Li (Institute) Note 8 1 / 6 QCD Quark Model Isospin symmetry To a good approximation, nuclear force is independent of the electric charge carried by the nucleons charge independence.
More informationUnification without Doublet-Triplet Splitting SUSY Exotics at the LHC
Unification without Doublet-Triplet Splitting SUSY Exotics at the LHC Jürgen Reuter Albert-Ludwigs-Universität Freiburg W. Kilian, JR, PLB B642 (2006), 81; and work in progress (with F. Deppisch, W. Kilian)
More informationElements of Grand Unification
Elements of Grand Unification Problems with the Standard Model The Two Paths Grand Unification The Georgi-Glashow SU(5) Model Beyond SU(5) arger Groups Supersymmetry Extra Dimensions Additional Implications
More informationSUSY models of neutrino masses and mixings: the left-right connection
SUSY models of neutrino masses and mixings: the left-right connection GK Workshop Bad Liebenzell Wolfgang Gregor Hollik October 10, 2012 INSTITUT FÜR THEORETISCHE TEILCHENPHYSIK KIT CAMPUS SÜD KIT University
More informationCombining Pati-Salam and Flavour Symmetries
QFET-015-01 SI-HEP-015-01 Combining Pati-Salam and Flavour Symmetries Thorsten Feldmann, Florian Hartmann, Wolfgang Kilian, Christoph Luhn arxiv:1506.0078v1 [hep-ph] Jun 015 Theoretische Physik 1, Naturwissenschaftlich-Technische
More informationU(1) Gauge Extensions of the Standard Model
U(1) Gauge Extensions of the Standard Model Ernest Ma Physics and Astronomy Department University of California Riverside, CA 92521, USA U(1) Gauge Extensions of the Standard Model (int08) back to start
More information