University of Liverpool Department of Physics Faculty of Science and Engineering Review of Literature Relating to LHCb 2 sin (✓W ) Measurement Author: Abbie Jane Chadwick Supervisors: Prof. Tara Shears Dr. Stephen Farry Areportconcludingthefirstyearof PhD June 2020 Contents 1 The Standard Model 1 1.1 TheBasics .................................................. 1 1.2 TheUnderlyingPhysics ........................................... 2 1.3 TheDownfalls ................................................ 2 2 Collider Physics 4 2.1 ProbingtheStandardModel ........................................ 4 2.2 WorldColliderOverview........................................... 4 + 2.2.1 e e− .................................................. 4 2.2.2 pp and pp ............................................... 4 2.2.3 e±p .................................................. 5 2.2.4 Heavyions .............................................. 5 2 3 Sin (✓w) Measurement Survey 6 3.1 CMS...................................................... 6 3.2 LEPandSLD................................................. 8 3.3 CDFandD0 ................................................. 9 3.4 ATLAS .................................................... 9 3.5 LHCb ..................................................... 10 1 1 The Standard Model 1.1 The Basics The Standard Model (SM) is the most complete description of known elementary particles and their interactions currently within physics. It combines electromagnetic, weak and strong interactions into a quantum field theory, with the notable exclusion of gravity. Other concepts not outlined within, or explained by, the SM include dark matter and dark energy, both of which need to be accounted for somehow. The matter and antimatter asymmetry of the universe is not understood or explained within the SM and so continues to be probed. The SM does very much deliver however when scrutinised experimentally relating to elementary particles, but on the smallest of scales. Figure 1.1: Standard Model of elementary particles including the 12 fundamental fermions (purple and green) and 5 fundamental bosons (orange and yellow).[1] Fundamentally, matter consists of particles which intrinsically have half-integer spin values, called fermions. Fermions can be split further into two groups: quarks (6 flavours) and leptons (6 flavours), and again within each 2 of those categories into three generations. A quark generation has one quark of fractional electric charge + 3 e(i.e. 1 up (u), charm (c) or top (t)) and a quark of electric charge - 3 e (i.e. down (d), strange (s) or bottom/beauty (b)) [2]. The specifics of the generation orientations can be found in figure 1.1. Each leptonic generation is outlined by an electron e, muon µ or tau ⌧ each with their corresponding neutrino flavour, ⌫e, ⌫µ or ⌫⌧ respectively. All of these leptonic particles have integer electric charge. Fermions of half integer spin are the building blocks of matter, coming together in various combinations to create what is around us. For each fermion there is a corresponding antiparticle which has the same mass but opposite additive quantum numbers, such as electric charge and parity. In the case of quarks, each type of quark can be one of three colours: red, blue or green. Fermion interaction is mediated by gauge bosons, which are force carriers with integer spin. The four types 0 of gauge boson are gluons, photons, Z and W±, and each is coupled to a specific force. Each gauge boson has characteristics which fit with one of electromagnetic force, weak force and strong force. Photons, γ, are coupled with electric charge, therefore mediating electromagnetic force. The electromagnetic force is fundamentally shaped by the characteristics of the photon, such that electromagnetic interactions have an infinite range linked with the fact that photons are massless. This is contrary to the weak force which is mediated 0 17 by a massive gauge boson, either Z or W±. As a result the weak force only has a very short range, 10− m [3]. The weak force is a way in which quark flavour can be altered within an interaction, for example when⇡ a neutron (ddu) transmutes into a proton (uud). The strong force is mediated by gluons. At the larger range protons and neutrons are bound together to form the nucleus but at lower ranges gluons couple to colour charge, red, blue and green. Gluons are massless like photons but the two forces di↵er in that the strong force is ranged. It is limited because gluons interact with 1 each other (gluon-gluon coupling) as well as with quarks (quark confinement) due to their colour charge. Quark confinement is, in essence, that a single quark cannot be not seen outside of a nucleus, resulting in the range being approximately the radius of one nucleon. Quarks are confined to being with at least one other quark due to their colour needing to be being balanced in colour neutral states, i.e. hadrons. A balanced state would be a colour-anti-colour pair, mesons (e.g. red anti-red), all three colours or anti-colours, bosons (e.g. rbg). Quantum chromodynamics (QCD) is the study of strong interactions at hadronic energy scale, aiming to predict properties of hadrons. Only at high energies can quarks be free. For many years a hypothetical quantum field, the Higgs field, was theorised to exist to compliment the SM. The Higgs boson is a physical manifestation of the Higgs field, a field which when interacted with gives a particle mass. This physical manifestation is the result of wave-particle duality: all quantum fields have an associated fundamental particle. 12 During the big bang, the Higgs field had an average value of zero, which began to change 10− s later as the universe was cooling. The field was unstable and underwent spontaneous symmetry breaking to adopt a lover energy configuration. As a result, the more a particle interacts with the field the heavier it is. Photons do not 0 interact with the field and so have no mass but particles such as Z or W± become massive. The Higgs boson was observed in 2012 by LHC experiments ATLAS [4] and CMS [5] as a scalar with spin 0 and 125 GeV mass. 1.2 The Underlying Physics The mathematical framework of the SM is based within quantum field theory, QFT. Within QFT particles are thought of as field quanta, representing excited states of an underlying field. Lagrangians are used to describe these particles and their interactions, which is broken down only into their kinetic and potential energies. A lagrangian density, L , determines the dynamics of the system, and is invariant under global transformations. Local transformations, transformations dependant on space-time, also leave the lagrangian invariant. A field theory where this is the case is classified as a gauge theory and there is one for all fundamental interactions apart from gravity. The SM is a local gauge theory described by the product of symmetry groups [6]. SU(3) [SU(2) U(1) ] (1.1) C ⇥ L ⇥ Y SU(3)C group describes the strong force while SU(2)L U(1)Y describes the electroweak interaction relating to 0 ⇥ Z ,W± and γ (the massive gauge bosons). The subscripts C, L and Y relate to the quantum numbers colour, weak isospin and hypercharge respectively. Within the SM, the electroweak symmetry (SU(2) U(1) ) is spontaneously L ⇥ Y broken by the Higgs mechanism to give U(1)EM. Each generation within the SM consists of five representations of SU(3) [SU(2) U(1) ] [7]: C ⇥ L ⇥ Y I I I I I QLi(3, 2)+1/6,uRi(3, 1)+2/3,dRi(3, 1) 1/3,LLi(1, 2) 1/2,lRi(1, 1) 1 (1.2) − − − Plus a single scalar representation composed of two complex scalar fields: φ+ φ(1, 2) = (1.3) +1/2 φ0 ✓ ◆ I I I T An example of left handed quarks, QL =(uL,dL) would be triplets of SU(3)C , doublets of SU(2)2 and have hypercharge Y equal to +1/6. In the above equations I is interaction eigenstates and i is generation index, equal I I to 1, 2 or 3. Singlets uR and LL are generic right handed up and down quarks. 1.3 The Downfalls While the SM is the most complete description of particle interaction, there are still crucial elements missing from it revolving around those that are included. To quickly outline those below: 12 fermion masses • All coupling constants • 3 electroweak parameters (↵,sin2 ✓ and G ) • W F Higgs mass • 3 quark mixing angles and 1 CP violation parameter • 2 3 lepton mixing angles and 1 CP violation parameter • 2 Where by GF is the Fermi constant, ↵ is the fine structure constant and sin ✓W is the electroweak mixing angle. Within the SM forces between elementary fermions are due to SU(3) SU(2) U(1) gauge symmetry[8]. SU(2) U(1) symmetry generates electroweak forces involving the photon⇥ and W and⇥ Z gauge bosons. SU(3) symmetry⇥ related to the strong force. The electroweak symmetry is spontaneously broken by the Higgs mechanism while conserving the electric charge symmetry[8], giving rise to W and Z boson masses. The weak mediator masses (W and Z bosons) are related by the Weinberg angle, ✓W , otherwise known as the weak mixing angle. mW = mZ cos✓W This parameter also determines the relative strengths of electromagnetic coupling, ge, and the weak W and Z couplings. ge gW = sin✓W ge gZ = sin✓W cos✓W 2 Also true is that sin ✓W can be viewed as a fundamental parameter within the SM due to it probing the mixing of fields. 2 2 mW sin ✓W =1 2 (1.4) − mZ In order to test the SM, electroweak parameters need to be very well characterised with high precision and they 2 currently are not. Electroweak parameters include sin ✓W , mW , mZ , ↵ and GF . 2 eff What is regularly used within HEP (High Energy Physics) is the e↵ective weak mixing angle, sin ✓W ,which di↵ers from the weak mixing angle in that the former has been renormalised to a di↵erent order.