Download - Symmetries and their Violation in Particle Physics

Symmetries and their Violation inParticle Physics

Dezso Horváth

[email protected].

RMKI, Budapest and ATOMKI, Debrecen, Hungary

Dezso Horváth: Symmetries in Particle Physics Symmetry Festival 2006 Budapest, 12-18 August 2006 – p.1

Outline

Symmetries in Particle Physics

Symmetries in the Standard Model

Parity and its Violation

Antiparticles and CPT Invariance

Lost Symmetries?

Search for Supersymmetry

Apropos:50 years of parity violation


SymmetriesDeeper microstructure ⇒ greater role of symmetries

More basic role in particle physics than inchemistry or solid state physics (origin!)

Field theory: Noether’s theoremGlobal symmetry ⇒ conserving quantity

Spatial displacement ⇒ momentumTime displacement ⇒ energyRotation ⇒ angular momentumMirror reflection ⇒ parityGauge invariance ⇒ charge (electric, color, fermion)

Popular journal of Fermilab and SLAC:symmetry — dimensions of particle physics


The Standard ModelElementary particles

fermion doublets (S= 1/2)

leptons

νe

e

L

νµ

µ

L

ντ

τ

L

quarks

u

d′

L

c

s′

L

t

b′

L

colored quarks ⇒ colorless composite hadronshadrons = mesons (qq) + baryons (qqq)

Nucleons (I = 12): p = (uud) n = (udd) p = (uud)


InteractionsDerived from local gauge invariance: no masses, divergence

Standard Model:Free Dirac (point-like) fermion

+ local U(1)⊗SU(2) symmetry⇒ electroweak interaction (γ, Z, W±)

+ local SU(3) symmetry⇒ strong interaction (8 gluons)

+ Higgs field with spontaneous symmetry breaking⇒ masses, convergence (+ Higgs boson)

Fundamental job of particle physics: study symmetries

Pioneer of particle symmetries: Yuval Ne’eman


Glory Road of Standard ModelMeasurement Fit |Omeas−Ofit|/σmeas

0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02758 ± 0.00035 0.02766

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874

ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4957

σhad [nb]σ0 41.540 ± 0.037 41.477

RlRl 20.767 ± 0.025 20.744

AfbA0,l 0.01714 ± 0.00095 0.01640

Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1479

RbRb 0.21629 ± 0.00066 0.21585

RcRc 0.1721 ± 0.0030 0.1722

AfbA0,b 0.0992 ± 0.0016 0.1037

AfbA0,c 0.0707 ± 0.0035 0.0741

AbAb 0.923 ± 0.020 0.935

AcAc 0.670 ± 0.027 0.668

Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1479

sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314

mW [GeV]mW [GeV] 80.392 ± 0.029 80.371

ΓW [GeV]ΓW [GeV] 2.147 ± 0.060 2.091

mt [GeV]mt [GeV] 171.4 ± 2.1 171.7

Summer 2006 statusIncludes hundreds of

measurements of all

experiments

Slightly deviating quantity

changes from year to year

Now it is forward-backward

asymmetry of

e+e− → Z → bb

LEP Electroweak Working Group:

http://lepewwg.web.cern.ch/


Spontaneous Symmetry Breaking


Higgs-boson?

The by-product of spontaneous symmetry breaking

The most wanted particle of physics as it is

the only missing particle of the Standard Model

Experimentally not observed yet?

Theory: it must exist

It was in 1972 ... that my life as a boson really began(Peter Higgs: Int. J. Mod. Phys. A 17 Suppl. (2002) 86-88.)


Mirror symmetries

Charge conjugation: C|p(r, t)> = |p(r, t)>Space reflection: P|p(r, t)> = |p(−r, t)>Time reversal: T|p(r, t)> = |p(r,−t)>

All three symmetries are trivial ...

C charge: electromagnetic & strong invariant

P parity: e-m & strong: spherical potential

T time: why should it bother?

Weak interaction???


Spatial Reflection: Parity

Cartesian systemwith all axes

reversed

right handed⇓

left handedcoordinate system

(mirror reflection)


Parity Violation in β DecayThe τ−θ paradox:

Two identical particles with different parities: τ+→2π ⇔ θ+→3π(JP(π) = 1−)

Tsung-Dao Lee és Chen-Ning Yang:Question of Parity Conservation in Weak InteractionsPhys. Rev. 104 (1956) 254-258. (50 years ago!)

All exp. evidence for parity conservation for electromagneticphenomena

Weak interaction violates parity, τ+ ≡ θ+(≡ K+)

Proposals for experimental tests

Experimental verification:Chien-Shiung Wu et al. (and Richard L. Garwin et al.), 1957

Nobel Prize: Lee and Yang, 1957


The Wu experiment

C.S. Wu et al.:

Experimental Test of Parity Conservation in Beta

Decay

Phys. Rev. 105 (1957) 1413-1414

Beta decay of 60Co in magnetic field (T < 0,1 K)

(n→p+e− +νe)60Co → 60Ni∗ +e− +νe

J = 5 J = 4 +12 +1

2

−→ −→ → →

Maximal violation of mirror (parity) symmetry!


The Garwin experiment

R.L. Garwin, L.M. Lederman, M. Weinrich:Observations of the Failure of Conservation of Parity and

Charge Conjugation in Meson Decays: the MagneticMoment of the Free Muon

Phys. Rev. 105 (1957) 1415-1417

Pion decay:π+→µ+νµ

Only B realized ⇒ maximal parity violation


Parity Violation in Weak Decay

Muon formation:π+→µ+νµ

Muon decay:µ+→e+νeνµ

Basis of µSR method

νµ µ+

π+

µ+

νe

νµ

e+

J = 0_

Parity violation of weak interaction: (V-A theory)Left-handed particles ⇔ right-handed antiparticles

W. Pauli:I cannot believe that God is left-handed!


Discovery of Parity Violation

Phys. Rev. 105 (1957) 1413-1414 Phys. Rev. 105 (1957) 1415-1417

Wonderful example of scientific ethics and colleagiality:

Wu’s group worked many months on their experimentGarwin et al. measured 1 day, analysed 1 week, then waited for

Wu to finishDezso Horváth: Symmetries in Particle Physics Symmetry Festival 2006 Budapest, 12-18 August 2006 – p.15

CPT Invariance

Basic assumption of field theory:CPT|p(r, t)> = |p(−r,−t)> = |p(r, t)>

meaning free antiparticle ∼ particlegoing backwards in space and time.

Giving up CPT one has to give up:

locality of interactions ⇒ causality, or

unitarity ⇒ conservation of matter, information, ... or

Lorentz invariance

Motivation to doubt:

Asymmetric Universe: no antimatter galaxies


How to testCPT?

Particle = – antiparticle ?

|m(K0)−m(K0)|/m(average) < 10−18

proton ∼ antiproton? (compare m, q,~µ)

hydrogen ∼ antihydrogen (antipro-ton+positron)? (2S−1S)


Antihydrogen (antiproton+positron)

12

3

BohrDiracLambHFS

1S2P

1/2

1/2

2S1/2

2P3/2

F=0

F=1

ANTIHYDROGEN

1

2

3

Bohr Dirac Lamb HFS

1S

2P

1/2

1/2

2S1/2

2P3/2

F=0

F=1

HYDROGEN

2-photon 2S−1S transition:

Slow transition ⇒ narrow lineTwo counter-propagating photons ⇒ Doppler-free


The Antiproton Decelerator at CERNis built to test CPT invariance

Three experiments test CPT:

ATRAP: q(p)/m(p) ↔ q(p)/m(p)

H(2S−1S) ↔ H(2S−1S)

ATHENA ⇒ ALPHA:

H(2S−1S) ↔ H(2S−1S)

ASACUSA: q(p)2m(p) ↔ q(p)2m(p)

µℓ(p) ↔ µℓ(p)

H ↔ H HF structure

RED: done, GREEN: planned c©Ryugo S. Hayano

Lots of H produced, spectroscopy is ahead


Lost symmetries?„.. the fundamental equations of physics have more symmetry

than the actual physical world does”Frank Wilczek: In search of symmetry lost, Nature 433 (2005) 239

CPT invariance: fundamental, absolute, no violationSU(3) gauge invariance

conserves color chargegives rise to strong interactionsno violation

U(1)×SU(2) gauge invariancespontaneously broken by Higgs fieldgives rise to electroweak interactionproduces Higgs boson

What else?


Supersymmetry (SUSY): motivationTheoretical problems of Standard Model:

Naturalness (hierarchy): Mass of Higgs bosonquadratically diverges due to radiative corrections.Eliminated if fermions and bosons exist in pairs.

Dark matter and energy is dominant mass of Universe.What is it that we observe its gravity only?

Gravity: does not fit in system of gauge interactions(strong, electromagnetic, weak)

Convergence of interactions: in SM the three gaugecouplings converge at ∼ 1016 GeV but do not meet

All these would be solved by a universalfermion ⇔ boson supersymmetry.


Supersymmetry: partner particles

Charges (electric, color, fermion) identical

SUSY partners of fermionsLeptons (S= 1

2) scalar leptons (S= 0)

e, µ, τ e, µ, τνe, νµ, ντ νe, νµ, ντ

Quarks (S= 12) scalar quarks (S= 0)

u, d, c, s, t, b u, d, c, s, t, b

Antiparticle ↔ antipartner

XL, XR ↔ X1, X2


SUSY partners of bosons

Elementary boson spin SUSY partner spinphoton: γ 1 photino: γ 1

2

weak bosons: 1 zino: Z 12

Z, W+, W− 1 wino: W+, W− 12

gluons: g1, ... g8 1 8 gluinos: g1, ... g812

Higgs fields 0 higgsinos 12

H01, H0

2, H+1 , H−

2 H01, H0

2, H+1 , H−

2

graviton 2 gravitino 32

Two Higgs doublets ⇒ 5 Higgs bosons: h, H, A, H+, H−


Supersymmetry?

Supersymmetry is obviously broken:no such particles,

or maybe with much larger masses

What is a broken symmetry good for?

Higgs mechanism:symmetry violating field ⇒ masses, renormalisation

Higgs field violates an existing symmetrym

SUSY introduces a non-existing one

All this for a rational, cosistent theory


Unification of gauge interactions

Standard Model:Gauge couplings get closebut do not converge at high

energies

SUSY:Perfect convergence at

∼ 1016 GeV

Difference:extra particles ⇒ more

corrections

Frank Wilczek: Nature 433 (2005) 239


Supersymmetry: + and−

+

naturalness of theory

cold dark matter of the Universe (23 %) = LSP

unification of interactions

includes gravitation

BUT:

−Mechanism of SUSY breaking ??

Many different models

Many new parameters

Not seen below m∼ 100GeV


Search for SUSY particles

Creation in pairs, decay to ordinary and SUSY particles

Properties depend on models and parameters

Lightest SUSY particle (LSP) unobservable⇒ missing energy observed

Which one is LSP? Model dependent.

SUSY (and Higgs) search at CERN:Large Electron-Positron collider (LEP), 1989 – 2000;

Large Hadron Collider (LHC), 2008 –


The Large Hadron Collider at CERN


Accelerators at CERN


SUMMARY–1

LHC starts in 2007 with low luminosityWe hope for discoveries from 2008

14 TeV collision energy is enough for everything:Higgs boson(s), SUSY particles

For precise studies one needs e+e− collider:International Linear Collider (ILC)

LHC design started before LEP constructionILC plans are developing worldwide


SUMMARY–2

"There is a theory which states that if ever anyonediscovers exactly what the Universe is for and why it is here,it will instantly disappear and be replaced by somethingeven more bizarre and inexplicable.

"There is another theory which states that this has alreadyhappened."

Douglas Adams: The Restaurant at the End of the Universe


Thanks for your attention


Fitting Higgs mass

0

1

2

3

4

5

6

10030 300

mH [GeV]

∆χ2

Excluded Preliminary

∆αhad =∆α(5)

0.02758±0.00035

0.02749±0.00012

incl. low Q2 data

Theory uncertainty

Summer 2006 status

Sensitivityof SM parameters

to Higgs mass

114< MH < 166GeV(95 % confidence)

LEP Electroweak Working Group: http://lepewwg.web.cern.ch/LEPEWWG/


Exception: antigravity?

ATHENA home page

(http://cern.ch/athena/)

CPT: particle – Earth ∼ antiparticle – antiEarth

weak equivalence:particle – Earth ∼ antiparticle – Earth


CPT Invariance: violation?Theoreticians in general: CPT is NOT violated

CPT-violating theories:(Alan Kostelecký, F.R. Klinkhamer, N.E. Mavromatos et al)

Standard Model valid up to Planck scale (∼ 1019 GeV).Above Planck scale new physics ⇒Lorentz violation possible

Quantum gravity: fluctuations ⇒ Lorentz violationloss of information in black holes ⇒ unitarity violation

Motivation for testing CPT at low energy

Quantitative expression of Lorentz and CPT invarianceneeds violating theory

low-energy tests can limit possible high energyviolation


Accelerators at CERNUntil 1996 From 2007


Search for SUSY particles at LEPDifficult: hard to distinguish from SM reactions.

Scalar lepton formation e+e− → ℓ+ℓ−

Decay e.g. ℓ±→χ01ℓ

±, model-dependent cross sections

Look for e+e−→ ℓ+ℓ− + missing energy

Main background: e+e− → W+W−→ ℓ+νℓ−ν

LEP result (ALEPH + DELPHI + L3 + OPAL):

No supersymmetric particle below m∼ 90−100GeV(kinematic limit: LEP worked up to 200 GeV)

Statistical analysis ⇒ excluded parameter regions


Compact Muon Solenoid (CMS)


The CMS detector of LHC(Compact Muon Solenoid)

Weight: 12500 tons, more iron, than in Eiffel tower

> 2000participants

Largest (superconducting) solenoid on Earth:13 m long, 5.8 m inner diameter , B = 4 Tesla

Proton bunches collide at 40 MHz (25 ns!)(uud + uud) ⇒ many hadrons

Each event contains 10-15 p-p interactions

Event filter: ≈ 4000PC, 500 GBit/secEvent storage: ≈ 10 PB data, 10 PB MC per yearData handling: LHC Computing Grid (> 100sites)

Signal: lepton or jet orthogonal to beam,Larger mass easier to identify


Simulated H→ ZZ → eeqq at CMS


SUSY search with CMSSignal: Particles of SUSY pair → fermions + lighter SUSY→ ... → fermions + LSP

Fermion cascade with missing transverse momentum

g → bb → χ02 b b→ ℓ+ ℓ− b b→ χ0

1 ℓ+ ℓ− b b

Measurements for all parameter values of all models??

Collaboration with theorists:check benchmark points in parameter space

Given model and parameters ⇒quantitative prediction of SUSY properties

and reaction probabilities ⇒can be tested experimentally
