DOCSLIB.ORG

Probing Supersymmetry with Neutral Current Scattering Experiments

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Probing Supersymmetry with Neutral Current Scattering Experiments Probing Supersymmetry with Neutral Current Scattering Experiments † A. Kurylov∗, M.J. Ramsey-Musolf∗ and S.Su∗ ∗California Institute of Technology, Pasadena, CA 91125 USA †Department of Physics, University of Connecticut, Storrs, CT 06269 USA Abstract. We compute the supersymmetric contributions to the weak charges of the electron e p (QW ) and proton (QW ) in the framework of Minimal Supersymmetric Standard Model. We also consider the ratio of neutral current to charged current cross sections, Rν and Rν¯ at ν (ν¯ )-nucleus deep inelastic scattering, and compare the supersymmetric corrections with the deviations of these quantities from the Standard Model predictions implied by the recent NuTeV measurement. INTRODUCTION 2 In the Standard Model (SM) of particle physics, the predicted running of sin θW from 2 2 Z-pole to low energy: sin θW (0) sin θW (MZ) = 0.007, has never been established − 2 experimentally to a high precision. sin θW (MZ) can be obtained through the Z-pole 2 precision measurements with very small error. However, no determination of sin θW at low energy with similar precision is available. More recently, the results of cesium atomic parity-violation (APV) [1] and ν- (ν¯ -) nucleus deep inelastic scattering (DIS)[2] 2 have been interpreted as determinations of the scale-dependence of sin θW . The cesium APV result appears to be consistent with the SM prediction for q2 0, whereas the neutrino DIS measurement implies a +3σ deviation at q2 100 GeV≈2. If conventional hadron structure effects are ultimately unable to account| f|or ≈ the NuTeV “anomaly", the results of this precision measurement would point to new physics. arXiv:hep-ph/0309027v1 2 Sep 2003 In light of this situation, two new measurements involving polarized electron scat- tering have taken on added interest: parity-violating (PV) Möller (ee) scattering at SLAC[3] and elastic, PV ep scattering at the Jefferson Lab (JLab)[4]. In the absence of 2 new physics, both measurements could be used to determine sin θW at the same scale: 2 2 2 q 0.03 GeV , with comparable precision in each case: δ sin θW = 0.0007. Further- more,| | ≈ the precision needed to probe new physics effects, e.g. supersymmetry (SUSY), is roughly an order of magnitude less stringent, owing to a fortuitous suppression of the p e 2 θ SM electron and proton weak charge: QW = QW = 1 4sin W 0.1 at tree-level. Consequently, experimental precision of order− a few percen− t, rather than≈ a few tenths of a percent, is needed to probe new physics corrections. The goal of our study is to developconsistency check for theories of new physics using the low energy neutral current scattering measurements. In particular, we will consider the Minimal Supersymmetric Extension of SM (MSSM)[5], which is the most promis- ing candidate for new physics beyond SM. For R-parity conserved MSSM, low-energy precision observables experience SUSY only via loop effects involving virtual super- symmetric particles. Tree level corrections appear once R-parity is broken explicitly. We studies both the PV electron scattering (PVES) and ν (ν¯ )-nucleus DIS processes. Details of the calculations presented here can be found in Ref. [6] and [7]. RADIATIVE CONTRIBUTION TO WEAK CHARGE The weak charge of a particle f is defined as the strength of the effective A(e) V( f ) ef Gµ f × interaction: L = Q e¯γµ γ5e f¯γµ f . With higher-order corrections included, the EFF − 2√2 W f ρ f κ 2 θ λ weak charge can be written as QW = PV 2T3 4Q f PV sin W + f . The quantities h − i ρPV and κPV are universal, while the correction λ f , on the other hand, does depend on the fermion species. At tree-level, one has ρPV = 1 = κPV and λ f = 0, while at one-loop ρ δρSM δρSUSY κ λ order PV = 1 + PV + PV , and similar formulae apply to PV and f . The counterterm δGˆ µ determined by muon life time and the Z0 boson self-energy are combined into ρPV (expressed in terms of the oblique parameters S, T [8]): δGˆ µ Πˆ (0) Πˆ (0) Πˆ (0) µ µ ρ ZZ WW ZZ δˆ αˆ δˆ PV = 1 + + 2 = 1 2 + 2 VB = 1 + T VB. (1) Gµ MZ − MW MZ − − δˆ µ The quantity VB denotes the the electroweak vertex, external leg, and box graph correc- tions to the muon decay amplitude. e Z γ mixing and parity-violating electron-photon coupling F (0) contribute to κPV : − A Πˆ 2 δ 2 2 α cˆ γZ(q ) 2 e sˆnew cˆ ˆ ˆ µ κPV = 1 + + 4c ˆ F (0) + = 1 + S αˆ T + δ sˆ q2 A sˆ2 cˆ2 sˆ2 4s ˆ2cˆ2 − VB 2 2 2 2 − cˆ Πˆ Zγ(q ) Πˆ Zγ(M ) cˆ Πˆ γγ (M ) ∆αˆ + Z + Z + + 4c ˆ2Fe(q2) (2) sˆ q2 − M2 cˆ2 sˆ2 − M2 α A h Z i − h Z i δ 2 2 2 α The shift sˆnew ins ˆ follows from the definition ofs ˆ in terms of , Gµ , and MZ[6]. The non-universal contribution λ f to the weak charge is determined by the sum of the the renormalized vertex corrections and the box graphs. SUSY CORRECTION TO WEAK CHARGES In order to evaluate the potential size of SUSY loop corrections, a set of about 3000 different combinations of SUSY-breaking parameters was generated. Fig. 1(a) shows the δ p δ u δ d shift in the weak charge of the proton, QW = 2 QW + QW , versus the corresponding shift in the electron’s weak charge, δQe , normalized to the respective SM values. The W p corrections in the MSSM (with R-parity conserved) can be as large as 4% (QW ) and e ∼ 8% (QW ) – roughly the size of the proposed experimental errors for the two PVES ∼ δ e,p δκSUSY measurements. The shifts QW are dominated by PV , which is nearly always −4 x 10 20 0.1 15 SM ) p W 10 | ν /(Q R 0 δ SUSY ) 5 p W (Q δ 0 −0.1 (b) −0.2 −0.15 −0.1 e−0.05 e0 0.05 0.1 −1 0 1 2 δ (Q ) /(Q ) δ R −3 W SUSY W SM ν x 10 FIGURE 1. Plot(a) shows the relative shifts in electron and proton weak charges due to SUSY effects. Plot(b) shows the MSSM contribution to Rν and Rν¯ . Dots indicate MSSM loop corrections for 3000 randomly-generatedSUSY-breaking parameters. Interior of truncated elliptical region gives possible∼ shifts due to RPV SUSY interactions (95% confidence). 2 θ eff 2 κ 2 2 θ negative,corresponding to a reduction in the value of sin W (q ) = PV (q )sin W for e p the PVES experiments. Since this effect is identical for both QW and QW , the dominant effect of δκPV produces a linear correlation between the two weak charges. p As evident from Fig. 1 (a), the relative sign of the loop corrections to both QW and e QW is nearly always the same and positive. This correlation is significant, since the effects of other new physics scenarios can display different signatures. For example, for the general class of theories based on E6 gauge group, with neutral gauge bosons Z′ p e δ e,p e,p having mass < 1000 GeV, the effects on QW and QW also correlate, but QW /QW can have either sign in this case[9, 10]. In contrast, leptoquark interactions would not lead to e p discernible effects in QW but could induce sizable shifts in QW [9, 10]. As a corollary, we also find that SUSY loop corrections to the weak charge of cesium δ Cs Cs is suppressed: QW /QW < 0.2% and is equally likely to have either sign, which is smaller than the presently quoted uncertainty for the cesium nuclear weak charge of about 0.6% [11]. Therefore, the present agreement of QCs with the SM prediction e,p W does not preclude significant shifts in QW arising from SUSY. The situation is rather e,p different, for example, in the E6 Z′ scenario, where sizable shifts in QW would also Cs imply observable deviations of QW from the SM prediction. New tree-level SUSY contributions to the weak charges can be generated when the R parity in MSSM is not conserved. The effects of R-parity violating (RPV) contribution can be parametrized by positive, semi-definite, dimensionless quantities ∆i jk( f˜) and ∆ ˜ i′ jk( f )[12], which are constrained from the existing precision data [12]. The 95% CL δ p p δ e e region allowed in the QW /QW vs. QW /QW plane is shown by the closed curve in Fig. 1 (a). We observe that the prospective effects of RPV are quite distinct from SUSY δ e e loops. The value of QW /QW is never positive in contrast to the situation for SUSY loop δ p p effects, whereas QW /QW can have either sign. Thus, a comparison of the two PVES measurements could help determine which extension of the MSSM is to be favored over other new physics scenarios [10]. NUTEV MEASUREMENT Recently, the NuTeV collaboration has performed a precise determination of the ratio Rν (Rν¯ ) of neutral and charged current deep-inelastic νµ (ν¯µ )-nucleus cross sections[2], which can be expressed in terms of the effective ν q hadronic couplings (geff )2: − L,R σ ν ν ν ν ( ( ¯ )N ( ¯ )X) eff 2 ( 1) eff 2 Rν ν¯ = → =(g ) + r − (g ) , (3) ( ) σ(ν(ν¯)N l (+)X) L R → − σCC σCC eff 2 where r = ν¯ N / νN .
Load more

Recommended publications
  • The Weak Charge of the Proton Via Parity Violating Electron Scattering
    The Weak Charge of the Proton via Parity Violating Electron Scattering Dave “Dawei” Mack (TJNAF) SPIN2014 Beijing, China Oct 20, 2014 DOE, NSF, NSERC SPIN2014 All Spin Measurements Single Spin Asymmetries PV You are here … … where experiments are unusually difficult, but we don’t annoy everyone by publishing frequently. 2 Motivation 3 The Standard Model (a great achievement, but not a theory of everything) Too many free parameters (masses, mixing angles, etc.). No explanation for the 3 generations of leptons, etc. Not enough CP violation to get from the Big Bang to today’s world No gravity. (dominates dynamics at planetary scales) No dark matter. (essential for understanding galactic-scale dynamics) No dark energy. (essential for understanding expansion of the universe) What we call the SM is only +gravity part of a larger model. +dark matter +dark energy The astrophysical observations are compelling, but only hint at the nature of dark matter and energy. We can look but not touch! To extend the SM, we need more BSM evidence (or tight constraints) from controlled experiments4 . The Quark Weak Vector Charges p Qw is the neutral-weak analog of the proton’s electric charge Note the traditional roles of the proton and neutron are almost reversed: ie, neutron weak charge is dominant, proton weak charge is almost zero. This suppression of the proton weak charge in the SM makes it a sensitive way to: 2 •measure sin θW at low energies, and •search for evidence of new PV interactions between electrons and light quarks. 5 2 Running of sin θW 2 But sin θW is determined much better at the Z pole.
    [Show full text]
  • TRIUMF & Canadian Scientists Help Measure Proton's Weak Charge
    Canada’s national laboratory for particle and nuclear physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules News Release | For Immediate Release | 17 Sep 2013, 5:00 p.m. PDT TRIUMF & Canadian Scientists Help Measure Proton’s Weak Charge (Newport News, VA, USA) --- An international team including Canadian researchers at TRIUMF has reported first results for the proton’s weak charge in Physical Review Letters (to appear in the October 18, 2013 issue) based on precise new data from Jefferson Laboratory, the premier U.S. electron-beam facility for nuclear and particle physics in Newport News, Virginia. The Q-weak experiment used a high-energy electron beam to measure the weak charge of the proton—a fundamental property that sets the scale of its interactions via the weak nuclear force. This is distinct from but analogous to its more familiar electric charge (Q), hence, the experiment’s name: ‘Q-weak.’ Following a decade of design and construction, Q-weak had a successful experimental run in 2010–12 in Hall C at Jefferson Laboratory. Data analysis has been underway ever since. “Nobody has ever attempted a measurement of the proton’s weak charge before,” says Roger Carlini, Q- weak’s spokesperson at Jefferson Laboratory, “due to the extreme technical challenges to reach the required sensitivity. The first 4% of the data have now been fully analyzed and already have an important scientific impact, although the ultimate sensitivity awaits analysis of the complete experiment.” The first result, based on Q-weak’s commissioning data set, is Q_W^p= 0.064 ± 0.012.
    [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]
  • The Search for Supersymmetry
    The Search for Supersymmetry • Introduction the Standard Model of Particle Physics • Introduction to Collider Physics • Successes of the Standard Model • What the Standard Model Does Not Do • Physics Beyond the Standard Model • Introduction to Supersymmetry • Searching for Supersymmetry • Dark Matter Searches • Future Prospects • Other Scenarios • Summary Peter Krieger, Carleton University, August 2000 Force Unifications Standard Model does NOT account magnetism for gravitational interactions Maxwell electromagnetism electricity electroweak S T A Planck Scale (or Planck Mass) weak interactions N D A is defined as the energy scale at R GUT D which gravitational interactions M O become of the same strength as D E SM interactions strong interactions L TOE celestial movement gravitation Newton terrestrial movement - - - MEW MGUT Mplanck The Standard Model Describes the FUNDAMENTAL PARTICLES and their INTERACTIONS All known FORCES are mediated by PARTICLE EXCHANGE a a Effective strength of an interaction depends on X • the coupling strength at the vertex αα • the mass of the exchanged particle MX a a Force Effective Strength Process Strong 100 Nuclear binding Electromagnetic 10-2 Electron-nucleus binding Weak 10-5 Radioactive β decay The Standard Model SPIN-½ MATTER PARTICLES interact via the exchange of SPIN-1 BOSONS MATTER PARTICLES – three generations of quarks and leptons |Q| m < m < m ⎛ e ⎞ ⎛ µ ⎞ ⎛ τ ⎞ 1 e µ τ Mass increases with generation: ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ m = 0 ⎜ ⎟ ⎜ν ⎟ ⎜ ⎟ ν ⎝ν e ⎠ ⎝ µ ⎠ ⎝ν τ ⎠ 0 Mu,d ~ 0.3 GeV ⎛u⎞ ⎛c⎞ ⎛ t ⎞ 2 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 3 Each quark comes in 1 three ‘colour’ changes Mt ~ 170 GeV ⎝d⎠ ⎝s⎠ ⎝b⎠ 3 GAUGE BOSONS – mediate the interaction of the fundamental fermions γ 1 Gauge particle of electromagnetism (carries no electric charge) W ± ,Z 0 3 Gauge particles of the weak interaction (each carries weak charge) g 8 Gauge particles of the strong interaction (each gluon carries a colour and an anti-colour charge charge) All Standard Model fermions and gauge bosons have been experimentally observed There is one more particle in the SM – the Higgs Boson.
    [Show full text]
  • Weak Interactioninteraction
    WeakWeak InteractionInteraction OutlineOutline Introduction to weak interactions Charged current (CC) interactions Neutral current (NC) Weak vector bosons W± and Z0 Weak charged interactions Beta decay Flavour changing charged current W± boson propagator Fermi coupling constant Parity violation Muon decay Decay rate /lifetime Lepton Universality W± boson couplings for leptons Tau decays Weak quark decays W± boson couplings for quarks Cabibbo angle, CKM mechanism Spectator model Nuclear and Particle Physics Franz Muheim 1 IntroductionIntroduction Weak Interactions Account for large variety of physical processes Muon and Tau decays, Neutrino interactions Decays of lightest mesons and baryons Z0 and W± boson production at √s ~ O(100 GeV) Natural radioactivity, fission, fusion (sun) Major Characteristics Long lifetimes Small cross sections (not always) “Quantum Flavour Dynamics” Charged Current (CC) Neutral Current (NC) mediated by exchange of W± boson Z0 boson Intermediate vector bosons MW = 80.4 GeV ± 0 W and Z have mass MZ = 91.2 GeV Self Interactions of W± and Z0 also W± and γ Nuclear and Particle Physics Franz Muheim 2 BetaBeta DecayDecay Weak Nuclear Decays See also Nuclear Physics Recall β+ = e+ β- = e- Continuous energy spectrum of e- or e+ Î 3-body decay, Pauli postulates neutrino, 1930 Interpretation Fermi, 1932 Bound n or p decay − n → pe ν e ⎛ − t ⎞ N(t) = N(0)exp⎜ ⎟ ⎝ τ n ⎠ p → ne +ν (bound p) τ n = 885.7 ± 0.8 s e 32 τ 1 = τ n ln 2 = 613.9 ± 0.6 s τ p > 10 y (p stable) 2 Modern quark level picture Weak charged current mediated
    [Show full text]
  • Supersymmetry Lecture Notes for FYS5190/FYS9190
    Supersymmetry Lecture notes for FYS5190/FYS9190 Paul Batzing and Are Raklev December 4, 2015 2 Contents 1 Introduction 7 2 Groups and algebras 9 2.1 Whatisagroup?.................................. 9 2.2 Representations................................. 12 2.3 Liegroups...................................... 13 2.4 Liealgebras..................................... 15 2.5 Exercises ...................................... 16 3 The Poincar´ealgebra and its extensions 19 3.1 TheLorentzGroup................................. 19 3.2 ThePoincar´egroup ............................... 20 3.3 The Casimir operators of the Poincar´egroup . ........ 20 3.4 The no-go theorem and graded Lie algebras . ...... 22 3.5 Weylspinors .................................... 23 3.6 The Casimir operators of the super-Poincar´ealgebra . ............ 25 3.7 Representations of the superalgebra . ....... 26 3.8 Exercises ...................................... 28 4 Superspace 31 4.1 Superspacecalculus .............................. 31 4.2 Superspacedefinition.. .. .. .. .. .. .. .. 33 4.3 Covariantderivatives. 35 4.4 Superfields ..................................... 35 4.4.1 Scalarsuperfields.............................. 36 4.4.2 Vectorsuperfields. .. .. .. .. .. .. .. .. 37 4.5 Supergauge ..................................... 38 4.6 Exercises ...................................... 39 5 Construction of a low-energy SUSY Lagrangian 41 5.1 Supersymmetry invariant Lagrangians . ....... 41 5.2 Albaniangaugetheories . 42 5.3 Non-Abelian gauge theories . 43 5.4 Supersymmetricfieldstrength.
    [Show full text]
  • Bounds on Supersymmetry from Electroweak Precision Analysis
    SLAC{PUB{7634 UPR{788{T January, 1998 Bounds on Sup ersymmetry from Electroweak Precision Analysis Jens Erler DepartmentofPhysics and Astronomy UniversityofPennsylvania Philadelphia, PA 19104 Damien M. Pierce Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 Abstract The Standard Mo del global t to precision data is excellent. The Minimal Sup ersym- metric Standard Mo del can also t the data well, though not as well as the Standard Mo del. At b est, sup ersymmetric contributions either decouple or only slightly decrease 2 the total , at the exp ense of decreasing the numb er of degrees of freedom. In general, regions of parameter space with large sup ersymmetric corrections from light sup erpart- ners are asso ciated with p o or ts to the data. We contrast results of a simple (oblique) approximation with full one-lo op results, and show that for the most imp ortant observ- ables the non-oblique corrections can be larger than the oblique corrections, and must b e taken into account. We elucidate the regions of parameter space in b oth gravity- and gauge-mediated mo dels which are excluded. Signi cant regions of parameter space are excluded, esp ecially with p ositive sup ersymmetric mass parameter . We give a com- plete listing of the b ounds on all the sup erpartner and Higgs b oson masses. For either sign of , and for all sup ersymmetric mo dels considered, we set a lower limit on the mass of the lightest CP{even Higgs scalar, m 78 GeV. Also, the rst and second h generation squark masses are constrained to b e ab ove 280 (325) GeV in the sup ergravity (gauge-mediated) mo del.
    [Show full text]
  • 1 Charge, Neutron, and Weak Size of the Atomic Nucleus G. Hagen1,2 , A
    Charge, neutron, and weak size of the atomic nucleus G. Hagen1,2 , A. Ekström1,2, C. Forssén1,2,3 , G. R. Jansen1,2, W. Nazarewicz1,4,5, T. Papenbrock1,2, K. A. Wendt1,2, S. Bacca6,7, N. Barnea8, B. Carlsson3, C. Drischler9,10, K. Hebeler9,10, M. Hjorth-Jensen4,11, M. Miorelli6,12, G. Orlandini13,14, A. Schwenk9,10 & J. Simonis9,10 Summary What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus 48Ca. We show that the neutron skin (difference between radii of neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities are currently targeted by precision measurements. Based on ab initio results for 48Ca, we provide a constraint on the size of a neutron star. 1Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 2Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA. 3Department of Fundamental Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden. 4Department of Physics and Astronomy and NSCL/FRIB, Michigan State University, East Lansing, Michigan 48824, USA.
    [Show full text]
  • 9. the Weak Force Particle and Nuclear Physics
    9. The Weak Force Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 9. The Weak Force 1 In this section... The charged current weak interaction Four-fermion interactions Massive propagators and the strength of the weak interaction C-symmetry and Parity violation Lepton universality Quark interactions and the CKM Dr. Tina Potter 9. The Weak Force 2 The Weak Interaction The weak interaction accounts for many decays in particle physics, e.g. − − − − µ ! e ν¯eνµ τ ! e ν¯eντ + − − π ! µ ν¯µ n ! pe ν¯e Characterised by long lifetimes and small interaction cross-sections Dr. Tina Potter 9. The Weak Force 3 The Weak Interaction Two types of weak interaction Charged current (CC): W ± bosons Neutral current (NC): Z bosons See Chapter 10 The weak force is mediated by massive vector bosons: mW = 80 GeV mZ = 91 GeV Examples: (The list below is not complete, will see more vertices later!) Weak interactions of electrons and neutrinos: − νe − e e νe Z W − W + Z + ν¯e e+ e ν¯e Dr. Tina Potter 9. The Weak Force 4 Boson Self-Interactions In QCD the gluons carrycolour charge. In the weak interaction the W ± and Z bosons carry the weak charge W ± also carry the electric charge ) boson self-interactions W − W − Z γ W + W + Z W + Z W + γ W + W + W + W − W − Z W − γ W − γ W − (The list above is complete as far as weak self-interactions are concerned, but we have still not seen all the weak vertices. Will see the rest later) Dr.
    [Show full text]
  • A Geometric Theory of Everything Deep Down, the Particles and Forces of the Universe Are a Manifestation of Exquisite Geometry
    Nature’s zoo of elementary particles is not a random mish- mash; it has striking patterns and interrelationships that can be depicted on a diagram correspond- ing to one of the most intricate geometric objects known to mathematicians, called E8. 54 Scientific American, December 2010 Photograph/Illustration by Artist Name © 2010 Scientific American A. GarrettAuthor Lisi balances Bio Tex this until time an between ‘end nested research style incharacter’ theoretical (Command+3) physics andxxxx surfing. xxxx xx xxxxxAs an itinerantxxxxx xxxx scientist, xxxxxx hexxxxxx is in thexxx xxprocess xxxxxxxxxx of xxxx realizingxxxxxxxxxx a lifelong dream: xxxxxx founding xxxxxxxx the xxxxxxxx. Pacific Science Institute, located on the Hawaiian island of Maui. James Owen Weatherall, having recently completed his doctorate in physics and mathematics at the Stevens Institute of Technology, is now finishing a second Ph.D. in philosophy at the University of California, Irvine. He also manages to find time to work on a book on the history of ideas moving from physics into financial modeling. PHYSICS A Geometric Theory of Everything Deep down, the particles and forces of the universe are a manifestation of exquisite geometry By A. Garrett Lisi and James Owen Weatherall odern physics began with a sweeping unification: in 1687 isaac Newton showed that the existing jumble of disparate theories describing everything from planetary motion to tides to pen- dulums were all aspects of a universal law of gravitation. Unifi- cation has played a central role in physics ever since. In the middle of the 19th century James Clerk Maxwell found that electricity and magnetism were two facets of electromagnetism.
    [Show full text]
  • QUANTUM FIELD THEORY from QED to the Standard Model Silvan S
    P1: GSM 0521571995C19 0521571995-NYE March 6, 2002 13:59 19 QUANTUM FIELD THEORY From QED to the Standard Model Silvan S. Schweber Until the 1980s, it was usual to tell the story of the developments in physics during the twentieth century as “inward bound” – from atoms, to nuclei and electrons, to nucleons and mesons, and then to quarks – and to focus on conceptual advances. The typical exposition was a narrative beginning with Max Planck (1858–1947) and the quantum hypothesis and Albert Einstein (1879–1955) and the special theory of relativity, and culminating with the formulation of the standard model of the electroweak and strong interac- tions during the 1970s. Theoretical understanding took pride of place, and commitment to reductionism and unification was seen as the most impor- tant factor in explaining the success of the program. The Kuhnian model of the growth of scientific knowledge, with its revolutionary paradigm shifts, buttressed the primacy of theory and the view that experimentation and instrumentation were subordinate to and entrained by theory.1 The situation changed after Ian Hacking, Peter Galison, Bruno Latour, Simon Schaffer, and other historians, philosophers, and sociologists of science reanalyzed and reassessed the practices and roles of experimentation. It has become clear that accounting for the growth of knowledge in the physical sciences during the twentieth century is a complex story. Advances in physics were driven and secured by a host of factors, including contingent ones. Furthermore, it is often difficult to separate the social, sociological, and political factors from the technical and intellectual ones. In an important and influential book, Image and Logic, published in 1997, Peter Galison offered a framework for understanding what physics was about in the twentieth century.
    [Show full text]
  • Phy489 Lecture 3
    Phy489 Lecture 3 1 So far…… • Fundamental interactions in the Standard Model (SM) – Mediated by particle exchange – Three fundamental forces • have different effective strengths These two statements are correlated • act over different timescales } • Particle content of the Standard Model – Matter particles (fundamental spin-1/2 fermions) – Force carriers (spin-1 gauge bosons) – Higgs boson – Particle masses – Hadrons (made up of quarks, which do not exist freely) • Feynman diagrams for fundamental processes • Particle Decays • Today continue this discussion and introduce first simple conservation laws…… Note that not all conservation laws apply to all three fundamental interactions (the ones we will discuss today do). 2 Kinematic effects in Particle Decays • If multiple final states are available (for the same interaction) the dominant one (kinematically) will often be the one with the largest mass difference between the initial and final states. We will see that for two-body decays 1 2 + 3: statistical factor ⎧ is the magnitude of the momentum 1 p 2 of the final state products (2,3). This ⎪ ≡ Γ = 2 S M p ⎨ is a measure of the energy release τ 8πm1 c in the decay. We will derive this ⎪ expression later on. kinematics ⎩ decay rate (width) dynamics However, this rule of thumb is seldom of much practical use: + + charged pion decay occurs dominantly (99.988%) via π → µ ν µ + + although π → e ν e is kinematically favoured. The difference is from the dynamics (as we will see explicitly, later in the course). 3 Or look at it the other way around • This principle is perhaps better illustrated in reverse: so consider the decay of a free neutron (why do I say “free”?): − this occurs via n → p e ν e with a very long lifetime of about 15 minutes.
    [Show full text]