Lectures 1 & 2
The Violation of Symmetry between Matter and Antimatter
Andreas Höcker CERN
CERN Summer Student Lectures, August 5 – 7, 2008
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) M.C. Escher1 Lectures 1 & 2
CP Violation
Andreas Höcker CERN
CERN Summer Student Lectures, August 5 – 7, 2008
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) M.C. Escher2 A definition, which we will understand later in this lecture:
The matter-antimatter symmetry violation in physics reactions corresponds to the breaking of the so-called CP symmetry Î C·P Violation
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 3 Matter-Antimatter Asymmetry
q q
1 CtiCElEurrenarly unt un iverseiverse ?
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 4 Sakharov Conditions
(*) Bigi-Sanda, CP Violation, 2000
• The Universe is not empty* ! nn− n baryon baryon ≈ baryon ~ ()O −10 10 • The Universe is almost empty* nn ! γγ
Sakharov conditions (1967) for Baryogenesis 1. Baryon number violation 2. C and CP violation 3. Departure from thermodynamic equilibrium (non-stationary system)
So, if we believe to have understood CPV in the quark sector, and if it cannot account for the observed baryon asymmetry … what does it signify ? A sheer accident of nature ? What would be the consequence of a different value for the CKM phase ?
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 5 Much is Strange Out There … !! to dark matter to dark ecessarily due ecessarily nn Hubble space telescope picture of Cluster ZwCl0024+1652
: ring is not Image: NASA, ESA, M.J. JEE AND H. FORD (Johns ote
N Hopkins University)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 6 Much is DarkStrange Matter Out There …
Dark matter does not emit or reflect Bullet cluster: Collision of galaxy clusters: baryonic matter, sufficient electromagnetic radiation to stars – weakly affected by collisions – andDark strongly energy bdttdbe detected affected gas (pink in picture) Image, and collisionlessDark matter dark matter (blue) Free H and He Evidence for dark matter stems from: Stars 65% Neutrinos Gravitational lensing Heavy elements strongest gravitational lensing Kinetics of galaxies Anisotropy of cosmic microwave Foreground background (blackbody) radiation cluster 30% 0.03% 0.03% 0.5% 4%
gravitational lensing Mass density contours superimposed over photograph taken with Hubble Space Telescope
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 7 And: There is Much More Strangeness …
E m p i r i c a l a n d T h e o r e t i c a l L i m i t a t i o n s o f t h e StS t a n d a r d M o d e l
Dark matter (and, perhaps, dark energy) Baryogenesis (CKM CPV too small) Grand Unification of the gauge couplings The gauge hierarchy Problem (Higgs sector, NP scale ~ 1 TeV) The strong CP Problem (why is θ ~ 0 ?) NtiNeutrino masses Gravitation
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 8 Most of these problems are related to the earliest moments of our Universe
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 9 The understanding of matter-antimatter symmetry violation is crucial if we want to move closer into the heart of the Big Bang
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 10 Lecture Themes
I. Introduction Antimatter Discrete Symmetries II. The Phenomena of CP Violation Electric and weak dipole moments The strong CP problem The discovery of CP violation in the kaon system III. CP Violation in the Standard Model The CKM matrix and the Unitarity Triangle B FtiFactories CP violation in the B-meson system and a global CKM fit Penguins IV. CP Violation and the Genesis of a Matter World Baryogenesis and CP violation Models for Baryogenesis
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 11 digression: CP Violation, a Family History of Flavour
Discovery of strange particles (Rochester, Butler) (1946-47)
NtlkNeutral kaons can m ix (Gell-Mann, Pais) (1952)
KL discovery (Lederman et al.) (1956)
Parity (P) violation: possible explanation (Lee, Yang ) (1956)
P Violation found in β decay (Wu et al.) (1957) later: maximum P and C violation, but CP invariance
Cabibbo-Theory (1963)
CP violation (CPV) discovered (Cronin, Fitch et al.) (1964)
GIM-Mechanism (Glashow, Illiopolous, Maiani) (1970)
J/ψ Resonance: c quarks (Ting, Richter) (1974)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 12 digression: CP Violation, a Family History of Flavour
CPV Phase requires 3 families (Kobayashi-Maskawa) (1973)
Discovery o f τ ltlepton: 3rd filfamily (Perl et al.) (1975)
ϒ resonance: b quarks (Lederman et al.) (1977)
Neutral Bd mesons mix (ARGUS) (1987) t-Quark discovery (CDF) (1995)
ν-Oscillation discovery (Super-K) (1998)
Direct CP violation in K system (NA31, NA48, KTeV) (1999)
Start of Bd Factories: BABAR (PEP II) , Belle (KEKB) (1999) β ≠ CPV in Bd system : sin(2 ) 0 (BABAR, Belle) (2001)
Direct CPV in Bd system (BABAR, Belle) (2004)
Bs mesons oscillate (CDF) (2006) D0 mesons oscillate (()BABAR & Belle) (()2007)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 13 Evolution of working conditions (example BABAR, discovery of CP violation in B system, 2001) :
Discovery of CP violation (in K system, 1964): V.L. Fitch R. Turlay J.W. Cronin J.H. Christenson
PRL 13, 138 (1964)
… 623 physicists (in 2005). BABAR: PRL 87, 091801 (2001) Belle: PRL 87 , 091802 (2001)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 14 Through the Looking Glass Wha t’s the Matter with Antimatter ?
David Kirkby, APS, 2003
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 15 Paul Dirac (1902 – 1984)
Combining quantum mechanics with special relativity, and the wish to linearize ∂/∂t, leads Dirac to the equation
μ ixtmxtγψ∂−() ψ,,0 () =(1928) μ
for which solutions with negative energy appear Dirac, imagining holes and seas in 1928 Vt“”fhtiVacuum represents a “sea” of such negative-energy Energy particles (fully filled according to Pauli’s principle) + ′ E Dirac identified holes in this sea as “antiparticles” with +m e opposite charge to particles … (however, he conjectured 0 that these holes were protons, despite their large difference in mass, because he thought “positrons” would have been discovered already) −m e −E An electron with energy E can fill this hole, emitting an s =−1/ 2 s =+1/ 2 energy 2E and leaving the vacuum (hence, the hole This picture fails for bosons ! hfftilthhhas effectively the charge +e anditid positive energy ).
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 16 AntiprotonAntineutronPositron – Antiparticleincoming of the Electron incomingantiproton discovery 1955 antiproton 61956 GeV Fixed target threshold Discoveredenergy required in tocosmic produce rays by Carl Anderson in 1932 (Caltech) p + p Æ p + p + anti-p + p ReproductionAntiproton charge- of an Has the same mass as the electron but positive charge antiprotonexchange annihilation reaction into star asneutron-antineutron seen in nuclear emulsion pair in 63 MeV (source: O. Chamberlain, Nobel Lecture) Anderson saw a track in a cloudpropane bubble chamberpositron chamber left by “something((gsource: E.G. Segrè, Nobel Lecturetrack ) positively charged, and with the same mass as an electron” 6mm Pb plate π p + anti-p → n + anti-n History of antiparticle discoveries: 23 MeV “annihilation star”positron (large energy release track 1955: antiproton (Cham ber la in-SSèBkl)egrè, Berkeley) ftitdtti)from antiproton destruction) outgoing charged1956: antineutron (Cork et al., LBNL) “annihilation star” particles (large energy release 1965: antideuteron (Zichichi, CERN and Lederman,from BNL) antineutron destruction)
1995: antihydrogen atom (CERN, by now millions produced !) Every particle has an antiparticle
Some particles (e.gπ., the photon) are their own antiparticles !
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 17 Particles and Antiparticles Annihilate
What happens if we bring particles and antiparticles together ?
A modern A particleexample: can annihilate with its Fermilab antiparticle to form gamma rays
An examppyle whereby matter is converted into pure energy by Einstein’s formula E = mc2
Conversely, gamma rays with sufficiently high energy can turn ALEPHinto a particle-antiparticle pair Higgs candidate Particle-antiparticle tracks in a ee+−→→ ZHZ() qqbb bubble chamber
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 18 Symmetries
A s ymmetr y is a change of something that leav es the physical description of the system unchanged.
1. Physical symmetries: People are approximately bilaterally symmetric Spheres have rotational symmetries 2. Laws of nature are symmetric with respect to mathematical operations, that is: an observer cannot tell whether or not this operation has occurred
Pollen of the hollyhock exhibits spherical symmetry (magnification x 100,000)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 19 Continuous Symmetries and Conservation Laws
In classical mechanics we have learned that to each continuous symmetry transformation, which leaves the scalar Lagrange density invariant, can be attributed a conservation law and a constant of movement (E. Noether, 1915)
Continuous symmetry transformations lead to additive conservation laws
Invariance under Homogeneity of Symmetry Isotropy of space movement in time space
Translation in Transformation Translation in time Rotation in space space
Conserved Angular Energy Linear momentum quantity momentum
No evidence for violation of these symmetries seen so far
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 20 digression: Symmetry of Reference Systems
Another type of symmetry has to do with reference frames moving with respect to one in which the laws of physics are valid (inertial reference frames):
Physical laws are unchanged when viewed in any reference frame moving at constant velocity with respect to one in which the laws are valid
Note that while laws are unchanged between reference frames, quantities are not
The fact that the laws of motion are unchanged between frames, plus the fact that the spgpeed of light is alwa ys the same lead to the theor y of spypecial relativity with two consequences
Two events that are simultaneous in one reference frame are not necessarily simultaneous in a reference frame moving with respect to it There are some quantities (called Lorentz scalars) that have values independent of the reference frame in which their value is calculated
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 21 Continuous Symmetries and Conservation Laws
In general, if U is a symmetry of the Hamiltonian H, one has: [HU,0]= ⇒ H= U† HU
fHi′′== UfHUi fUHUi† = fHi
Accordingly, the Standard Model Lagrangian satisfies local gauge symmetries (the physics must not depend on local (and global) phases that cannot be observed):
U(1) gauge transformation Î Electromagnetic interaction
SU(2) gauge transformation Î Weak interaction
SU(3)C gauge transformation Î Strong interaction (QCD)
Conserved additive quantum numbers:
Electric charge (processes can move charge between quantum fields, but the sum of all charges is constant) Similar: color charge of quarks and gluons, and the weak charge
Quark (baryon) and lepton numbers (however, no theory for these, therefore believed to be only approximate symmetries) Æ evidence for lepton flavor violation in “neutrino oscillation”
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 22 Discrete Symmetries
Discrete symmetry transformations lead to multiplicative conservation laws
The followinggppy discrete transformations are fundamental in particle physics:
Parity P (“handedness”):Quantity PC T In particle physics: Reflection of space aroundSpace an vector arbitrary center;–x x x −−= P invariance Æ cannot know whether we live in this world, or in its mirror world PeLR e These are interestingTime becausett–t it is not obvious whether P ππ00=− the laws of natureMomentum should look – thepp same for–p any of these Particle-antiparticle transformation C : Pn= + n tftransformati ons,Spin and theanswessr was surpr–s iiising when Change of all additive quantum numbers (for example the Ce−+= e electricalthese symmetriescharge) in itElectricals opposite were field (“charge first conjugation”) tested –E !– EE LL MMtifildagnetic field B –B –B Cu= u Time reversal T : Cd= d The time arrow is reversed in the equations; C ππ00= + T invariance Æ if a movement is allowed by a the physics law, the movement in the opposite direction is also allowed
Time reversal symmetry (invariance under change of time direction) does certainly not correspond to our daily experience. The macroscopic violation of T symmetry follows from maximising thermodynamic entropy (leaving a parking spot has a larger solution space than entering it). In the microscopic world of single particle reactions thermodynamic effects can be neglected, and T invariance is realised.
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 23 The CPT Theorem
The CPT theorem (()1954): “Any Lorentz-invariant local quantum field theory is invariant under the successive application of C, P and T ”
Proofs: G. Lüders, W. Pauli (1954); J. Schwinger (1951) Derived from Lorentz invariance and the “principle of locality”
FdFundament tlal consequences: Relation between spin and statistics: fields with integer spin (“bosons”) commute and fields with half-numbered spin (“fermions”) anticommute Æ Pauli exclusion principle Particles and antiparticles have equal mass and lifetime, equal magnetic moments with opposite sign, and opposite quantum numbers
()mmm−
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 24 If CPT is Conserved, how about P, C and T ?
Parity is often violated in the macroscopic world:
Strongly Left -sided Strongly Right-sided Mixed Sided
Handedness 5% 72% 22% Footedness 4% 46% 50% (?) Eyedness 5% 55%4% 41% Earedness 15% 35% 60%
Porac C & Coren S. Lateral preferences and human behavior. New York: Springer-Verlag, 1981
About 25% of the population drives on the left side: why ? In ancient societies people walked (rode) on the left to have their sword closer to the middle of the street (for a right-handed man) !?
The DNA is an oriented double helix
Two right-handed polynucleotide chains that are coiled about the same axis:
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 25 Not so in the microscopic World ?
Electromagnetic and strong interactions are (so far) C, P and T invariant
Example: neutral pion decays via electromagnetic (EM) interaction : π0 → γγ but not π0 → γγγ
1 πππ000=−⎡⎤uu dd ⇒, C =+ 2 ⎣⎦LS==0, 0 r rrr CBE⋅=−−,, B E ⇒, Cγγ=−
the initial (π0) and final states (γγ) are C even: hence, C is conserved !
LLSLSI++1 ++ Generalization: P qq′′=−()1 qq , C qq =−() 1 qq , G uu()1() d =−() uu d
Experimental tests of P and C invariance of the EM interaction: C invariance: BR()πγ08→<× 3 3.1 10− P invariance: BR(η →<× 4π 07) 6.9 10−
Experimental tests of C invariance of strong interaction: compare rates of positive and negative par tic les in reac tions like: pp → ππ+−XKKX, + −
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 26 And … the Surprise in Weak Interaction !
T.D.Lee &Lee Yang: and C.N. Yang pointed out in 1956 (to explain the observation of the decays K → 2π and 3π - the cosmic-ray θ/τ puzzle) that P invariance had not“Past been exppyg testederiments in weakon the interaction weak interactions Æ C. S. Wuhad performed actually no in bearin g on 1957the the question experiment of parity they suggestedconservation.” and observed parity violation “In strong interactions, ... there were indeed many experiments that Angularestabli distribution s he d par itof y electron conserva intensity: tion to a hig h degree o f accuracy... ” θαr α θ σr ⋅P v I()“To=+ 1decide unequivocallye =+ 1 cos whether parity is conserved in weak interactions, Ec one must performe an experiment to determine whether weak interactions helicity where:differentiateσr - spin vector the rightof electron from the left.” Yang, C. N., The law of parity conservation and other symmetry r laws of physics, Nobel Lectures Physics: 1942-1962, 1964. Lee, T. D., and C. N. Yang, Question of Parity Conservation in Pe - electron momentum Weak Interactions, The Physical Review, 104, Oct 1, 1956. Ee - electron energy ⎧−1 for electron α = ⎨ ⎩+1 for positron
TCO ~ 0.01 K Parity is maximally violated in weak polarized in interactions ! magnetic field
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 27 P and C Violation in Weak Interaction
Goldhaber et al. demonstrated in 1958 that in the β decay of the nucleus, the neutrino (e–) is left-handed, while the antineutrino (e+) is right-handed:
Particle : ee−+ ν ν Helicity : −−vc/ + vc/11/ 1 + 1 ( Æ C violation ! )
In the Dirac theory, fermions are described as 4-component spinor wave × Γ functions upon which 4 4 Operators i apply, which are classified according to their space reflection properties :
ψψ ψ γ ψ≡ †0 , scalar (S ) P -even ψγ ψ 5 , pseudoscalar (P ) P -odd ψγμ ψ , vector (V ) P -even ψψ(44× ) crrentcurrent ψγ γ ψμ 14243 μν ν μ 5 , axial vector (A ) P -odd Lorentz-covariant bilinear ψγγ() γγ− ψ , tensor ()T antisymmetric tensor 1442443 −2iσ μν
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 28 P and C Violation in Weak Interaction
Let’s consider the β reaction: nep+→ν − +
General ansatz for the current-current some constants matrix element : GF ′ M =ΓΓ+⎡⎤ψψ ψ⎡ γ− ψ()C C ⎤ ∑ ⎣⎦p in⎣ e ii 5 i v⎦ 2 iS= ,... 1 OneUse the transparency helicity projection withoperators a bitfor Dirac of math spinors: uu= ()1 γ LR/52 m μμ μμ γγ=+()()… += sorry γγ … + Æ at high energies, the EM interaction uuuuLR uu LR uuuu LLRR conserves the he lic ity o f the sca ttere d ferm ions won’t happen again (almost) … μμ1 so that one has for a V interaction: uuγγγ=−= u(12 ) u 0 and similar for A LR4 5 {=1 1 while for a scalar interaction: uu=+≠ u(1γ ) u 0 and similar for P, T LR 2 5 Consider a (weak interaction) V – A neutrino-electron current in the relativistic limit:
μμμ1 uV()−= Auν uγγ()1 − uννν γ =+() u γ u u = u u ee2 5,,,,, eLeRLeLL It proj ects upon t he lfhleft han ddhliiided helicities, an dhd hence v iliolates P maxillimally, as requ id!ired !
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 29 P and C Violation in Weak Interaction
Weak interaction violates both C and P symmetries
μ −−→++νν Consider the collinear decay of a polarized muon: polarized e μ e
P
The preferred emission handedness of the electron: P transformation (i.e. direction of the light reversing all three left-handed electron is directions in space) opposite to the muon suppressed yields constellation that polarization. is suppressed in nature. CC Similar situation for C Applying CP, the resulting transformation (i.e. reaction—in which an replace all particles with antimuon preferentially their antiparticles). suppressed emits a positron in the same direction as the polarization—is observed. handedness of the positron: B. Cahn, LBL
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 30 … and tomorrow, we will see
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 31 CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 32 CP Vio lat ion
CP Symmetry requires that processes and their anti-processes have the same rates
1. Due to the CPT theorem, CP symmetry also requires T symmetry 2. CP violation would enable us to distinguish between particles and antiparticles, and between past and future in an absolute way !
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 33 Dipole moments
Can there be CP violation in the electromagnetic or neutral weak current ?
Le t’s mo dify the Stan dar d Mo de l Lagrang ian to a llow for CP viltiiolation throug h electromagnetic and weak dipole moments:
i μν EM weak LdFdZ=−σγ() μνμν + CP 2 ll5 ll
where Fμν and Zμν are electric and weak field strength tensors.
In the nonrelativistic limit one obtains the Pauli equation with the additional terms:
r r A shift in the energy of the system when LdEdZ→+EMσσr weak r CP ll applying an external electric or weak field
But…. why do these dipole moments violate CP symmetry ?
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 34 Dipole Moments and CP Violation
Spin is the only explicit “direction” of an elementary particle. Hence the dipole moment must be proportional to it r ds∝ r
The electric dipole moment is the average of a charge density distribution Æ polar vector r ddxxx=⋅⋅∫ 3 ρ()r r dipole The spin has the form of angular momentum Æ axial vector spin moment
r ∝×rr srp P + – – + r =−rrr =r = PParitarity transformationtransformation g giives: es Pd d, Ps s⇒{ d 0 P invariance
r ==rrr −r = Time reversal transformation gives: Td d, Ts s⇒{ d 0 T T invariance + + – – Non-vanishing electric or weak dipole moments require the presence of a P- and T-violating (=CP-violating) interaction
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 35 CERN Summer Student Lectures 2008
Experimental Limit on dEM (e.cm) 10 10 10 10 10 10 -30 -28 -26 -24 -22 -20 progress History oftheexperimental h esrmn fEDMs: of Measurement The 9017 9019 2000 1990 1980 1970 1960
Measurement e neutron: ltl ec
t of ron: A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) & and Antimatter (1 between Matter Symmetry Violation The of Höcker: A.
EDMs:
10 10 10 10 10 10 10 10 Higgs Multi -22 -38 -36 -34 -32 -30 -24 -20 Left-Right magnetic Electro- SUSY tnadModel Standard None of this seen yet, why ? None ofthisseen yet,why present experimentallimits d d d d (electron) <1.6 (electron) 3 < (neutron) (proton) 7 < (muon)
Model < 5 × × 10 × 10 10 × –19 –24 10 –26 e –27 cm 36 digression: CP Violation in the QCD Lagrangian
It was found in 1976 that the perturbative QCD Lagrangian was missing a term Lθ θμναβ α μν μνα1 β =+ ==θεs aa,,, a a LLQCD pQCD Lθ , where: L GGμν %%, and G G { 82π 14243 perturbative{ QCD PT,-violating Gluon field tensors 144424443 dual field tensor
that breaks through an axial triangle anomaly diagram the U(1)A symmetry of LpQCD , which iiss notnot observedobserved in naturenature when classical symmetries are broken on the quantum level, it is denoted an anomaly
aaμν , aaμν , The term GG μν contained in LpQCD is CP-even, while GG μν % is P-and T-odd, since:
22 22 ∝+⎯⎯⎯r rrrPT, →+ Relativistic invariants, GG∑∑() Eaa B () E aa B aasimilar to electric field tensors: FFμν , FF% μν r r PT, r r μνμν GG% ∝⋅⎯⎯⎯(EB) →− ( E ⋅ B ) μνμν ν ∑ aa ∑ aa ∂=∂=μμFj, F% 0 aa 14444244443 Maxwell equations color electric and magnetic fields θ This CP-violating term contributes to the EDM of the neutron:
⋅× −16 θ den 510 cm, so that tiny or zero 144444444424444444443 "Strong CP (finetuning) Problem"
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 37 digression: The Strong CP Problem
Remarks:
If at least one quark were massless, Lθ could be made to vanish; if all quarks are massive, one has uncorrelated contributions, which have no reason to disappear
Peccei-Quinn suggested a new global, chiral UPQ(1) symmetry that is broken, with the φ “axion” as pseudoscalar Goldstoneθμν boson; the axion field, a ,compensates the contribution from Lθ : θ φ α ⎛⎞a μν ,a axion coupling to SM particles is LGG=−⎜⎟ a s % f 8π suppressed by symmetry-breaking ⎝⎠a scale (= decay constant)
φ φ θ ⋅ QCD nonperturbative effects (“instantons”) induce a potential for a with minimum at a = fa
The axion mass depends on the UPQ(1) symmetry-breaking scale fa
7 ≈×⎛⎞10 GeV ∝ ma ⎜⎟0.62 eV , and axion coupling strength: gmaa ⎝⎠fa (GeV)
If fa ofhdfhEWl(f the order of the EW scale (v), ma~250 ke V Æ exclu de d by co llider exper iments
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 38 digression: The Search for Axions (a dark matter candidate !)
The axion can be made “invisible” by leaving scale and coupling free, so that one has: –12 ma ~ 10 eV up to 1 MeV Æ 18 orders of magnitude !
AiAxion sca le an d mass, toget her with the exclusion ranges from experimental non-observation
γ f γ π0 a Axion decays to 2 ,j, just as for the ,g, or in a static magnetic field: γ
Schematic view of CAST experiment at CERN:
Axion source Axion detection (LHC dipole magnet)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 39 The Discovery of CP Violation
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 40 Ingredients … Strange Particles
Strange mesons have an “s” valence quark
πρ − Non-strange particles: (,,K )I=1 : ud, ( uu dd )/2 Neutral particles are ηω ++eigenstates of C operator (, ,KK )I=0 : (uu dd )/2 ∗+−====00 Strange particles: (KK , ,K )I=1/ 2 : K usK, usK, dsK, ds
Neutral strange particles are not eigenstate of C operator
Prod uc tion o f st range parti cl es vi a s trong or el ec tromagneti c i n terac tion has to respect conservation of the S (“strangeness”) quantum number (Strange particles are “eigenstates” of these interactions)
− 0 ()()π =p =→Λ =−K =+ SS00SS==00 S 1 S 1 () ++0 π==p → ()pK = =+=− K SS00SS==00 S 0 S 1 S 1 +−00 −+ ()pp= =→ (ππ = K =− K =+) , ( = K =+ K =− ) SS00S=0 S 0 S 1 S 1SS==00 S 0 S 1 S 1 −+ 00 ()ee==→→φ =()K =+=− K SS00SS==00S 0 S 1 S 1 Kaons are lightest s-particles Æ can only decay via s-changing weak interaction
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 41 The Discovery of CP Violation
Empirically (in the experiment) one does however not observe the neutral “flavor 0 0 eigenstates” K and K but rather long- and short-lived neutral states: KL and KS
0 0 → (ππ ) → (πππ ) Larger phase space of Their observed pionic decays are: K S and KL 2π decay: And it was believed that: CP K =+ K and CP K=− K ⇒ ττ/580 SS LL KKLS
→ ππ+− However, Cronin, Fitch et al. (BNL) discovered in 1964 the CP-violating decay KL
Measurement of oppggpening angle of pion Today’ s most precise tracks and their invariantK →π mass:+π– events Jim Cronin L measurement of ampli- tude ratio: ε AK()→ ππ+− = L ()→ +− AKS ππ = (2. 282±× 0. 017) 10−3
Val Fitch
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 42 The KLOE experiment at the φ Factory DAΦNE (Frascati, Italy) can detect single CP-violating decays:
+−→→φ 00 +−→→φ ee KK and equivalently: eeSL KK
→ ππ+− KS → ππ+− KL
Note that the quantum coherence is broken after the decay of one of the two K0’s
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 43 The Discovery of CP Violation in the Charged Weak Current
To understand the observed CP violation from the flavour perspective, let us construct CP eigenstates with CP eigenvalues 1:
1 KKKCP=+()00 , [] =+ 1 1 2 1 KKKCP=−()00 , [] =− 1 2 2
While the flavour eigenstates are defined by the production, the CP eigenstates are distinguished by their decay into an even and odd number of pions. Since there is CP viiltiolation, the p hys ica l s tttates (“mass e igens tttates ”) are not exactly the same as the CP eigenstates:
0 ⎛⎞KKK ⎛+ ε ⎞ pq ⎛⎞K S ==1112 ⎛⎞ ⎜⎟ε ⎜ ⎟ ⎜⎟o ⎜⎟ ⎜⎟KKK+ 2 ⎜−+ε ⎟2 pq− ⎜⎟0 ⎝⎠L 1 ⎝12 ⎠ ⎝⎠⎝⎠K
where: qp / =− ()() 1 εε / 1 + 0.995 ≠ 1 (!)
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 44 CP Violation and Neutral Kaon Mixing
CPLEAR (CERN) measured the rates of KKt 00 ,() → ππ +− (using initial state strangeness tagging) as a function of the decay time, and finds quite a surprise:
s-tagging at production: after acceptance correction and background subtraction −+π 0 ⎪⎪⎧⎫KK ± ppK→ charge of ⎨ +− 0 ⎬ ⎩⎭⎪⎪KKπ
Kt0 ()→ ππ+− Rates are different for the tfltttwo flavor states
Kt0 ()→ ππ+− Also T violation measured Thereby looking is a non-exponentialat time-dependent asymmetrycomponent of(?) KKt00/()()→ e+− //πν −+
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 45 Neutral Kaon Mixing
Neutral kaons “mix” through the charged weak current, which does not conserve strangeness, neither P nor C. Weak interaction cannot distinguish K 0 from K 0
Simple picture: they mix through common virtual states:
(ππ )0
K0 K0 ()πππ 0
These oscillations are described in QCD by ΔS = 2 Feynman “box” diagrams:
Δ s [ S=2] d + 0 W 0 K tc, tc, K d W − s
× –12 0 Because Δm(K) = m(KL) – m(KS) = 3.5 10 MeV > 0, a K will change with time into a K 0 and vice versa
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 46 Neutral Kaon Mixing
An initially pure K0 state, will evolve into a superposition of states:
Kt()=+ gt () K00 ht () K
The time dependence is obtained from the time-dependent Schrödinger equation:
With 2 ×2 matrices M, Γ, of which the off - ⎛⎞Kt00() ⎛⎞ Kt () ∝ Γ d diagonals Δm, Δ govern the mixing i ⎜⎟=−()M i Γ ⎜⎟ ⎜⎟002 ⎜⎟ dt ⎜⎟Kt() ⎜⎟ Kt () ⎝⎠ ⎝⎠ IT()/(0) I After several KS lifetimes, only KL are left The respective time-dependent intensities 0 are ffdtb(ltiound to be (neglecting CP viilti)olation): K
−Γ−Γ − Γ +Γ ∝++SSLttLt ()/2 Δ⋅ It0 () e e2cos e mt ( ) K K 0 −Γ−Γ − Γ +Γ L It()∝+− eSSLtt eLt 2cos e()/2 Δ⋅ mt ( ) K 0 0 cos terms caused K by interference = τ Tt/ S
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 47 Observing K 0 Mixing
The s in the K+ is transferred to the K0
The s in the K0 mixes to a s making a K0
The s is transferred to a Λ0 (uds baryon)
1971, Graham Thompson
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 48 Neutral Kaon Mixing and CP Violation
Since KS and KL are not CP eigenstates, the time dependence has to be slightly modified by the size of ε, giving rise to an additional sine term.
00+− +− Γ→(KKππ ππ) −Γ→( ) Neggglecting other =∝Δ⋅−π+π– ε ( ϕ) sources of CP violation Let’sAsymmetry: get back Atoππ the decay+− rates: +− cos mt Γ→()KK00ππ ππ +Γ→()& assuming arg(ε) = π/4.
CPLEAR 1999 →π+π– dominated by KS
Kt0()→ ππ+−
Aππ →π+π– →π+π– ∝ ε N(KS ) ~ N(KL amplitude) | | Æ Large interference with opposite sign
→π+π– dominated by KL Kt0 ()→ ππ+−
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 49 There are in Fact Four Meson Systems with Mixing
Pairs of self-conjugate mesons that can be transformed to each other via flavor changing weak interaction transitions are:
0 = 0 = 0 = 0 = All measured Ksd Dcu Bbdd Bbss by now !
They have very different oscillation frequencies that can be understood from the “CKM couplings” (Æ tomorrow !) occurring in the box diagrams
[ΔS=2] s for the plotd + NT()/ N 00 xsD == 150.02 0 → W 0 BBss y == 0.100 0 tc, sD K − tc, δ K sD == 00 d BB000000→→→W s KKDDss00→ BBdd mixing probability: χχ~ ~=2 ×50%18%10–6
0 KL
00 BB→ 00 ddKK→
T
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 50 Three Types of CP Violation
The CP violation discovered by Cronin, Fitch et al. involves two types of CPV:
CP Violation in mixing:
Prob(KK00→≠ ) Prob( KK 00 → )
also called: CP Violation in interference of decays with and without mixing: “indirect CPV”
Prob(Kt00 ( )→≠ ππππ +− ) Prob( Kt ( ) → +− )
There is another, conceptually “simpler” type of CP violation:
CP Violation in the decay:
also called: Prob(Kf→≠ ) Prob( Kf → ) “direct CPV”
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 51 “Direct” CP Violation = CP Violation in Decay
General signature: rate differences between CP-conjugated processes:
Γ→(if) ≠Γ→ ( i f)
It must involve interference of amplitudes contributing to the processes. To obtain interference, we need phases that change sign under CP { φ ∈ } Example: if the decay amplitudes are given by: a1,2, 1,2
iiθφ θ φ i i φ Alters sign under CP A(if→=) aeeaee11 + 2 2 j 12 (“weak phase”) θφ−−−− θ φ ξξ Ai()→= f () aeeii11 + aee i 2 i 2 e2( iif ) θ CP invariant 12 14243 j unphysical phase (“strong phase”)
2 2 where: Γ→()if ∝ Aif() → and Γ→()if ∝ Aif() →
We can d e fine the foll ow ing CP asymmetry ACP:
Γ→−Γ→()if() if 2sinaa ()()θθ−− φφ sin A ==12 1 2 1 2 CP 22++(θθ −) φφ( −) Γ→+Γ→(if) ( if) aa122 aa 1212cos cos 12
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 52 CP Violation in the Kaon Decay
We have seen that at least two amplitudes with different weak and strong phases must contribute to the decay for direct CPV. This suppresses this type of CPV, so that the observable effect should be small compared to ε.
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 53 The Discovery of CP Violation in the Decay
It took several experiments and over 30 years 00 +−εε′ Γ→()ππ ππ Γ→()} KKLL ⎛⎞′ ()()16−×Re of effort to establish the existence of direct CPV Γ→00 Γ→+− ⎜⎟ KKSSππππ ⎝⎠
Feynman graphs: u Experimental average π − ε W − d Indeed, a very small CPV effect ! s ε 0 u π + K d d “Tree” (born-level) − amplitudes W s u 0 0 u π K d d π 0 d
(16.7 ± 2.3)×10–4 Interference
W − tcu,, “Penguin” s d π − (loop-level) 0 g u amplitude K d u π + d
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 54 And the Theory ?
Direct CP violation is in general very hard to calculate due to its sensitivity to the relative size and phase of different amplitudes of similar size
Many theoretical groups have put efforts into this. All agree that the effect is much smaller than the indirect CPV (a success for the Standard Model !), but the theory uncertainties are larger than the measurement errors
plot not updated ! retical t)dictions oo ss The ...the ball is on pre(po the theory side courtesy: G. Hamel de Monchenault
e n d o f L e c t u r e 1 & 2
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 55 Conclusions of the first two Lectures
No CP violation without antimatter !
CP violation is a vital ingredient for the creation of a matter universe
CPT Symmet ry i s a f und ament al propert y of quant um fi eld theori es
P, C, T are good symmetries of electromagnetic and strong interactions
P, C are maximally violated in weak interaction
CP, T are broken symmetries of weak interaction
CP violation has been first discovered in the kaon system, and both, direct and indirect CP violation have been observed
No other source of CP violation has been found so far
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 56 Cartoon shown by N. Cabibbo in 1966 … since then, there was tremendous progress in the understanding (better: describing) CP violation Æ next lecture !
CERN Summer Student Lectures 2008 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 57