The Strong Interactions

Transcription

1 1 The Strong Interactions Paul Hoyer Helsingin yliopisto Hiukkasfysiikan kesäkoulu Tvärminne

2 The Standard Model 2 SU(3) x SU(2)L x U(1) QCD Electroweak As simple as 1-2-3? Not exactly: The strong, electromagnetic and weak interactions manifest themselves very differently in Nature This suggests that guessing what (if anything) lies Beyond the Standard Model is a challenging task: LHC is needed!

3 Neutrino vs. Electron in EW 3 The (unbroken) electroweak theory is fully symmetric under ν e ( ) νe The neutrinos and electrons form a doublet of SU(2)EW: e This means that the theory is unchanged if these particles are redefined by an SU(2) matrix (2 x 2 unitary matrix with determinent = 1) ( ν e e ) ( a b c d )( νe e We may even choose a = a(t,x), etc: The rotation can be local in space-time. ( ) ( ) a b 0 1 For = i we have ν = i e and e = i ν c d 1 0 You might think that the neutrino and electron should have similar properties? Well, think again! )

4 Neutrino cross section 4 The neutrino interacts extremely weakly with matter. Its total cross section on nucleons (= protons and neutrons) is measured to be σ tot (ν µ N) = (0.667 ± 0.014) E ν GeV cm 2 Where the neutrino energy E ν is expressed in GeV = 10 9 ev = J speed ofll light in vacuum Planck constant Planck constant, reduced electron charge magnitude e conversion constant c conversion constant ( c) 2 electron mass proton mass c h = m e m p Constants of Nature h/ 2π m s (33) J s (53) J s = (16) MeV s (40) C = (12) esu ( 49) MeV fm (19) GeV 2 mbarn (13) MeV /c 2 = (45) kg (23) MeV /c 2 = (83) kg = (10) u = (80) m e fine-structure constant α = e 2 /4 0 c = 1 / (94)

5 Neutrino interaction length 5 The cross section σ measures the scattering probability: Typically, there is one neutrino interaction in a length L of matter when there is one nucleon in the volume Lσ. L In what length L of water does a neutrino with energy ν σ E ν = 1 MeV typically N interact one time? # nucleons cm 3 = 1 g cm g = cm 3 L = cm cm 2 = m = 0.25 light-years Compare: 1 MeV electrons in water have L = 5 mm

6 Range of weak force 6 The neutrino interacts via the exchange of W- and Z-bosons W, Z W, Z W, Z ν R < 1/M W,Z A neutrino can emit W and Z bosons which live for a time allowed by the Heisenberg uncertainty relation E t Now ΔE MW,Z c 2 so the range R of the weak interaction is R c t c M W,Z c MeV fm MeV fm = m The electron similarly emits photons, now the range REM 1/m γ =

7 Comparison of EM and Weak cross sections 7 The idea behind the unification of the weak and electromagnetic forces is that their difference is caused by the Higgs mechanism gives large masses to the weak bosons, while leaving the photon massless. Mγ = 0 (< ev) MW = 80.4 GeV/c 2 MZ = 91.2 GeV/c 2 e e γ Q µ + µ + dσ dq 2 (e µ + e µ + )= 8πα2 Q 4 α W α α e W νe Q µ + ν µ dσ dq 2 (e µ + ν e ν µ )= 8πα 2 W (Q 2 + M 2 W )2 8πα2 W M 4 W (Q M W ) 8πα2 W Q 4 (Q M W )

8 Rough estimate of α W 8 Combining the weak elastic scattering dσ dq 2 8πα2 W M 4 W with the measured total cross section We can determine the effective coupling σ tot (ν µ N) = (0.667 ± 0.014) E ν GeV cm 2 M 4 W αw 2 = σ tot (νn) 16πM N E ν which gives αw 1/256, not so different from α 1/137! This supports the idea that the neutrino cross section is small because MW is large, not because the coupling αw is tiny.

9 Comparison of EM and Weak cross sections 9 Today we have also verified experimentally that the electron and neutrino cross sections are similar when MW is small compared to Q: dσ dq 2 (e µ + ν e ν µ )= 8πα 2 W (Q 2 + M 2 W )2 8πα2 W Q 4 (Q M W ) dσ dq 2 (e µ + e µ + )= 8πα2 Q 4 HERA e(28 GeV) + p(820 GeV) collider at DESY near Hamburg, Germany. The center-of-mass energy is ca. ECM 300 GeV >> MW,Z Hence one can have collisions where Q > M W,Z

10 Comparison of EM and Weak cross sections Robert Ciesielski, (DESY) J.Phys.Conf.Ser.110:042007, ) 2 HERA II Neutral Current (NC) (pb/gev 2 d!/dq e + e + e e e νe e + νe + H1 e p CC (prel.) - H1 e p CC 2005 (prel.) + ZEUS e p CC ZEUS e p CC (prel.) + SM e p CC (CTEQ6M) - SM e p CC (CTEQ6M) y < 0.9 P e = H1 e p NC (prel.) - H1 e p NC 2005 (prel.) + ZEUS e p NC ZEUS e p NC (prel.) + SM e p NC (CTEQ6M) - SM e p NC (CTEQ6M) M 2 Z M 2 W Q 2 (GeV ) e ± q e ± q γ,z 0 e ± q Charged Current (CC) W ± νe q At Q = 1 MeV the ratio is ( ) GeV = MeV

11 Spin dependence of Weak cross sections 11 (pb)! CC rent e ± Charged Current e p Scattering - e p # "X ± p Scattering - e p # "X H (prel.) H1 CTEQ6D ZEUS MRST (prel.) ZEUS e + p # "X H ZEUS (prel.) ZEUS e p # "X H (prel.) H ZEUS (prel.) ZEUS e + p # "X H ZEUS (prel.) ZEUS Q > 400 GeV y < 0.9 ) 2 (pb/gev 2 d!/dq d!/dx (pb) break parity invariance - ZEUS ZEUS CC (prel.) e p (78.8 pb - ZEUS CC (prel.) e p (42.7 pb 2 Charged and neutral current cros 10 1 Deutsches Elektronen-Synchrotron, DESY, Notk Charged and neutral current crossrobert.ciesielski@desy.de sections from HERA e ± polarization Only left-handed electrons and right-handed positrons interact via W exchange! The weak interactions Charged and neutral current cross Robert Ciesielski 1, on behalf of Abstract. the H1 andthe ZEUS cross Collaborations sections for inclusive neut P e robert.ciesielski@desy.de Deutsches Journal Elektronen-Synchrotron, of Physics: DESY, scattering Conference Notkestr. at 85, high Series QHamburg, 2 with 110 polarised Germany (2008) lepton beams robert.ciesielski@desy.de effects in spacelike scattering are highlighted and c 10 3 Robert Ciesielski 1, on behalf of the H Robert Ciesielski 1, on behalf of the 1 Deutsches Elektronen-Synchrotron, DESY, Not Journal of Physics: Conference Seri SM Abstract. (ZEUS-JETS) P e = The cross sections for inclusive neu

12 The Discovery of the Strong Interaction 12 Rutherford s experiment 1911: The positive charges in matter are located in a tiny nucleus, whose radius is ~ 10 5 of the atomic size. There must be a strong, short-ranged force to counteract the Coulomb repulsion Thomson s atom: Rutherford s atom: F = α r 2

13 Structure of matter after Rutherford 13 M. Attisha

14 The Pion as a carrier of the strong force 14 In 1935 Hideki Yukawa suggested the existence of a new, strongly interacting particle U (later named the pion). The strength and range of the strong interaction could be understood as arising from pion exchange. π π π N R < 1/M π Postulating a new particle was considered very bold in those days, when only a handful of elementary particles were known: photon, proton, neutron, electron, (neutrino). It has been suggested that social pressure may have kept physicists in the West from a similar proposal.

15 Yukawa s 1935 paper H. Yukawa, PTP, 17, On the Interaction of Elementary Particles H. Yukawa (Received 1935) The interactions of elementary particles are described by considering a hypothetical quantum which has the elementary charge and the proper mass and which obeys Bose s statistics. The interaction of such a quantum with the heavy particle should be far greater than that with the light particle in order to account for the large interaction of the neutron and the proton as well as the small probability of β-disintegration. Estimated M π = MeV based on proton-neutron scattering data Considered that the pion may also cause β-decay, i.e., have the role of the present W boson. Heavy particle = proton, neutron Light particle = electron, neutrino Yukawa received the Nobel Prize for his proposal in 1949.

16 Pauli s Neutrino Hypothesis (1930) To explain the continuous energy spectrum in n p + e (+ ν) 16

17 Birth of Yang-Mills Theory 17 Quantum ElectroDynamics (QED) is invariant under local (space and time - dependent) gauge transformations: Electron field: Photon field: ψ(x) e ieλ(x) ψ(x) A µ (x) A µ (x) µ Λ(x) Λ(x) may be any regular function In 1954, Yang and Mills generalized this local U(1) gauge symmetry to the SU(2) group of isospin, with the proton and neutron forming an SU(2) ( ) p doublet just as in Yukawa s theory: n This established the structure of non-abelian gauge symmetry. Nature has, however, completely different uses of YM theories.

18 Physical Review 96 (1954) For a local gauge transformation defined by an SU(2) matrix U(x), Yang and Mills found that the theory is symmetric provided the fields transform as: Matter field: Gauge field: ψ(x) U(x)ψ(x) A µ (x) U(x)A µ (x)u (x) i g U(x) µu (x) The same rule holds for any group, such as SU(3). In QED, U(x) =e ieλ(x) Then U1U2 = U2U1, i.e., all group elements commute, hence the U(1) gauge symmetry is said to be abelian.

19 Particles found in Experiments 19 Einstein γ Pauli ν Dirac e + Yukawa π ± using cosmic rays using particle accelerators

20 Cosmic rays 20

21 Discovery of quarks 21 GIM charm Particles of the Standard Model All strongly interacting particles found in experiments (hadrons) have quantum numbers consistent with the Quark Model

22 Quark Model classification of Hadrons 22 Mesons q q Hadrons may be formed with any combination of q = u,d,s,c,b,t Baryons qqq π p Free quarks have never been seen: Are quarks mere mathematical rules, or true particles? (Gell-Mann)

23 Quarks are for real: Pointlike scattering of electrons 23 High energy electrons scatter from pointlike quarks inside the proton: e +q e +q (in analogy to Rutherford s experiment) The struck quark flies out of the proton and hadronizes into a spray (jet) of hadrons (mostly pions). At relativistic energies quark-antiquark pairs are created to ensure that all quarks end up as constituents of mesons or baryons. Deep Inelastic Scattering (DIS): e + p e + anything SLAC 1969: Ee = 20 GeV

24 Quantum Chromodynamics (1972) 24 QCD, the quantum field theory describing quark and gluon interactions, is similar to QED, the theory of electrons and photons α s (M Z )= g2 4π = ± Quark-Gluon coupling Cf. α = e 2 /4π 1/ (94) Electron-Photon coupling All quarks u,d,s,c,b,t have the same strong coupling g The SU(3) gauge symmetry is unbroken and transforms the three colors of the quarks: ψ Uψ U SU(3) ψ = q q q

25 Color Confinement 25 Three quark colors were introduced by O.W. Greenberg in 1964, to make the quark model of the proton compatible with the Pauli exclusion principle: Baryon wave functions must be antisymmetric under the interchange of quarks. In the Quark Model, the space spin wf is symmetric. The color wf is antisymmetric, rescuing the Pauli principle. The antisymmetric color wave function (A,B,C = red, blue, yellow) means that the proton is a color singlet (does not change under gauge transformations). p = A,B,C ε ABC q A q B q C U p = p QCD apparently has Color Confinement: Only color singlet mesons and baryons can propagate over long distances. Quarks are color triplets and gluons are color octets: Due to color confinement they cannot exist as free particles. Color confinement is verified numerically in numerical lattice simulations, but the mechanism is still poorly understood.

26 Scale dependence of the QCD coupling α s 26 S. Bethke, hep-ex/ The effective coupling α s (Q 2 ) = 12π (33 2n f ) log(q 2 /Λ 2 QCD ) is valid up to corrections of order 1/log(Q / ΛQCD). ΛQCD 200 MeV The large coupling at low Q may be related to color confinement.

27 Perspective: The divisibility of matter 27 Since ancient times we have wondered whether matter can be divided into smaller parts ad infinitum, or whether there is a smallest constituent. Democritus, ~ 400 BC Vaisheshika school Common sense suggest that these are the two possible alternatives. However, physics requires us to refine our intuition. Quantum mechanics shows that atoms (or molecules) are the identical smallest constituents of a given substance yet they can be taken apart into electrons, protons and neutrons. Hadron physics gives a new twist to this age-old puzzle: Quarks can be removed from the proton, but cannot be isolated. Relativity the creation of matter from energy is the new feature which makes this possible. We are fortunate to be here to address and hopefully develop an understanding of this essentially novel phenomenon!

28 Hadron mass spectrum is relativistic 28 Unlike atoms, hadrons have no ionization threshold, where the quark constituents would be liberated. Hadron masses are generated by the potential and kinetic energies of the constituents R e! (m 2 ) P.Desgrolard, M.Giffon, E.Martynov, E.Predazzi, hep-ph/ Spin " (770) # (782) Regge trajectory f 2(1270) a 2 (1318) " 3(1670) (1700) #3 f 4 (2050) a (2020) 4 " 5 (2350) f (2510) 6 a (2 450) 6 For unknown reasons, hadron spins are proportional to their mass m 2 2 (G ev )

29 The parton picture of the proton 29 Since the constituents are relativistic quark pairs and gluons may be created: p uud! The proton state is expressed as as a superposition of Fock states, containing any number of quarks and gluons (partons) p uud gluon q q Partonic picture of the proton The wave function of each Fock state specifies the momentum distributions of all partons i in a proton: xi is the fractional longitudinal momentum carried by the parton k i is the relative transverse momentum carried by the parton The DIS (e + p e + anything) cross section measures the probability distribution for a quark or gluon to carry momentum fraction x

30 e p γ * e Quarks move relativistically inside hadrons Non-relativistic uud state q 30 DIS measures the fraction x of the proton energy which is carried by the quarks, anti-quarks and gluons. For non-relativistic internal motion the x-distribution would be sharply peaked

31 Quark masses 31 In QCD, mass terms can be directly introduced in the lagrangian, but they are not allowed due to EW symmetry. Hence in the SM all masses result from Yukawa interactions involving the Higgs field. The quark masses inferred from experiment are: mu = MeV The huge mass ratios remain unexplained: md = MeV ms = 104 ± 30 MeV mc = 1.27 ±.10 GeV m u m t 2.5 MeV 171 GeV ??? mb = 4.20 ±.15 GeV mt = ± 2.1 GeV

32 Origin of the proton mass 32 The u, d quarks in the proton have small masses 2m u + m d m p 10 MeV 938 MeV 1% 99% of the proton mass is due to interactions! 1% is due to Higgs. Ultra-relativistic state Compare this with positronium (e + e ), the lightest QED atom: 2m e % Binding energy is tiny wrt mc 2 m pos Nonrelativistic state The compatibility of the non-relativistic p = uud quark model description of the proton with its ultra-relativistic parton model picture remains a mystery but a mystery that we can address within QCD. Both are supported by data: =?? p uud gluon q q

33 Creating quark pairs using photons 33 In QED, an electron and a positron can annihilate via a virtual photon into any charged particle pair allowed by the available energy. e + e γ* µ + µ Since quarks have electric charge, they can be similarly created, at a rate given by their charges. In the total hadronic cross section we sum over the poorly understood processes by which quarks turn into hadrons, which occur with probability = 1

34 34 s s c c b b R = σ(e+ e hadrons) σ(e + e µ + µ ) =3 q e 2 q ( 1+ α s π )

35 35 Charmonium the Positronium of QCD Binding energy [mev] Mass [MeV] 4100 (4040) Ionisationsenergie 3 1 S S D D2 3 3 D1 2 1 S 2 3 S 2 1 P 2 3 P P D2 2 3 P ev ~ 600 mev c(3590) (3770) (3686) 3 D 1 h c (3525) 3 P 2 (~ 3940) 3 P 1 (~ 3880) 3 P 0 (~ 3800) 2(3556) 1(3510) 0(3415) 1 D 2 DD 3 D 3 (~ 3800) 3 D S S ev e nm e c(2980) (3097) C 1 fm C 2900

36 LEP determination of neutrino number 36 e + e hadrons at Z peak

37 Quark and Gluon jets at LEP 37 e + e e + e 2 jets Z q _ q h s e + e e + e 3 jets Z q _ q g h s h s :02 PM h s h s

38 S. Bethke, hep-ex/ Measurement of quark and gluon color charges in e + e annihilations quark color charge gluon charge

39 Jet production in hadron collisions arxiv: (Inclusive sum) (or: h + X) (log. scaling violations) (Nonperturbative) (Nonperturbative) (Perturbative) (log. scaling violations) (Higher order in αs)

40 Fermilab: pp jet + X ECM = 1.96 TeV Quarks and gluons are pointlike down to the best resolution that has been reached ECM = 1960 GeV 40 Ex: Estimate the maximum radius of quarks and gluons, given the agreement of QCD with the Fermilab jet data. Rapidity: CDF Collab., hep-ex/ y = log E + p m2 + p 2 log tan(θ/2)

41 Determinations of the strong coupling 41 &'()*+(,*-)./0123(45 ( H ( F 2)*4(5 6B.4.F<).-G140./ (<2('(/425B*<(5 6.7*)08(-29:; 9((<2:/(7*54012;1*44()0/+2=9:;> τ2-(1*?5 ;<(14).51.<?2=E*4401(> Υ2-(1*?!"#!"#$!"#% α 5 >