Flavour Physics
Tim Gershon
University of Warwick
1 April 2014
Outline
●
Lecture 2
– predictions of CKM theory
●
●
–
mixing
●
●
●
–
unitarity triangles
discoveries of charm, bottom and top
neutral meson mixing
categories of CP violation
time-reversal invariance
kaon physics
●
–
direct CP violation
charm physics
CKM Matrix / KM mechanism
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3x3 matrix of complex numbers ⇒ 18 parameters
●
Unitary ⇒ 9 parameters
●
Quark fields absorb unobservable phases ⇒ 4
parameters
–
3 mixing angles and 1 phase (VCKM complex)
CKM Matrix : parametrizations
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3 mixing angles and 1 phase
Standard (PDG) parametrization; Chau & Keung PRL 53 (1984) 1802
s12 ~ 0.2
●
s23 ~ 0.04
s13 ~ 0.004
Exploit hierarchy – Wolfenstein parametrization
– expansion parameter λ ~ sin θ ~ 0.22
c
Hierarchy in quark mixing
Unitarity
|Vud|2 + |Vus|2 + |Vub|2 = 1
VudVus* + VcdVcs* + VtdVts* = 0
|Vcd|2 + |Vcs|2 + |Vcb|2 = 1
VudVub* + VcdVcb* + VtdVtb* = 0
|Vtd|2 + |Vts|2 + |Vtb|2 = 1
VusVub* + VcsVcb* + VtsVtb* = 0
|Vud|2 + |Vcd|2 + |Vtd|2 = 1
VudVcd* + VusVcs* + VubVcb* = 0
|Vus|2 + |Vcs|2 + |Vts|2 = 1
VudVtd* + VusVts* + VubVtb* = 0
|Vub|2 + |Vcb|2 + |Vtb|2 = 1
VcdVtd* + VcsVts* + VcbVtb* = 0
Unitarity triangles
VudVus* + VcdVcs* + VtdVts* = 0
λ
λ
λ5
VudVub* + VcdVcb* + VtdVtb* = 0
λ3
λ3
λ3
VusVub* + VcsVcb* + VtsVtb* = 0
λ4
λ2
λ2
See also Harrison, Dallison, Scott, PLB 680, 328 (2009)
DISCLAIMER : THESE ARE NOT TO SCALE!
Jarlskog
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All unitarity triangles have the same area
–
A = J/2
–
J is the Jarlskog invariant
–
J = c12 c23 c132 s12 s23 s13 sin δ ~ 4 10-5
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invariant measure of CP violation in the quark sector
–
|J| = Im( Vij Vkl Vkj* Vil*), for any choice of ijkl (i≠k; j≠l)
–
J related to commutator of mass matrices
●
[M,M'] = iC
det(C) = -2 F F' J
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F = (mt – mc)(mt – mu)(mc – mu)
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F' = (mb – ms)(mb – md)(ms – md)
The Unitarity Triangle
●
Convenient method to illustrate (dis-)agreement
of observables with CKM prediction
All measurements must agree
Predictive nature of KM mechanism
Im
α
γ J/2 β
Re
Plot by A.Hoecker
Discovery of charm
●
J/ψ discovery, Nov. 1974 (“November revolution”)
–
J : Samuel Ting, BNL
–
ψ : Burton Richter, SLAC
Discovery of J/ψ
●
2 observations & 1 confirmation in the same
edition of Physical Review Letters
Discovery of charmonium (J)
Brookhaven National Laboratory
p + Be → e+ e- X
Discovery of charmonium (ψ)
Stanford Linear Accelerator Center
e+e- → hadrons, e+e- , μ+μ-
Confirmation of charmonium (J/ψ)
Laboratori Nazionale di Frascati
e+e- → hadrons, e+e- , μ+μ-
Flavour physics machines
●
Previous examples illustrate the two main tools
used to study quark flavour physics
–
–
●
hadron machines
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symmetric colliders
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fixed target
electron-positron machines
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symmetric colliders
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asymmetric colliders
Very roughly, the former are good for discoveries
of particles, while the latter are good for
precision studies of those particles
Discovery of bottomonium (Υ)
Fermilab National Accelerator Laboratory
p + {Cu,Pt} → μ+ μ- X
Discovery of bottomonium (Υ)
Fermilab National Accelerator Laboratory
p + {Cu,Pt} → μ+ μ- X
Discovery of bottomonium (Υ)
Fermilab National Accelerator Laboratory
p + {Cu,Pt} → μ+ μ- X
Discovery of Υ(4S)
Cornell University
e+e- collisions
Quarkonia & mesons
●
●
●
J/ψ identified as JPC = 1- - charmonium (cc)
–
produced in e+e- collisions
–
decays to e+e-, μ+μ-, etc. (clean signatures)
–
narrow: width ~ 90 keV
Charmonia above DD threshold are wide
–
no OZI suppression
–
discovery of the D0 (cu), D+ (cd), Ds+ (cs), ... mesons
Charmonia with other quantum numbers take a
bit longer to discover
–
ηc (0-+), χc{0,1,2} ({0,1,2}++), and more (still active area)
Quarkonia & mesons
●
PC
Υ identified as J = 1 bottomonium (bb)
–
●
narrow: width ~ 50 keV
Bottomonia above BB threshold are wide
–
–
–
●
--
no OZI suppression
discovery of the B0 (db), B+ (ub), Bs0 (sb), ... mesons
Υ(4S) ~ 100% decay to B0B0, B+B-
Bottomonia with other quantum numbers take a
bit longer to discover
–
ηb (0-+) discovered recently (PRL 101, 071801 (2008))
–
χb{0,1,2} ({0,1,2}++), and more (still active area)
WARNING: NOT ALL “DISCOVERIES” ARE REAL
WARNING: NOT ALL “DISCOVERIES” ARE REAL
Discovery of the top quark
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The top quark decays too quickly to hadronise
–
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no (tt) “toponium” resonance (no top mesons at all)
top pairs produced from g in hadronic collisions
–
–
tt → W+bW-b
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W+- can give high pt leptons
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b quarks have displaced vertices
single top production (W+ → tb) also possible
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first observed in 2009 (CDF/D0), now giving good
measurement of |Vtb| (CMS arXiv:1403.7366)
–
|Vtb| = 0.998 ± 0.038 (exp.) ± 0.016 (theo.)
Discovery of the top quark
CDF collaboration
PRL 74, 2626 (1995)
D0 collaboration
PRL 74, 2632 (1995)
Current mt World Average
ATLAS + CDF + CMS + D0
arXiv:1403.4427 [hep-ex]
Mixing
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Various mixings
–
quark mixing (CKM)
–
flavour SU(2)
–
flavour SU(3)
–
neutral meson mixing
Mixing in flavour SU(2) – isospin
●
Four meson combinations of u & d quarks
–
●
●
ud, ud, uu, dd
Under SU(2) symmetry
–
π0 is member of isospin triplet
–
η is isosinglet
–
π0 = (uu – dd)/√2
m(π0) ~ 0.135 GeV
η = (uu + dd)/√2
m(η) ~ 0.550 GeV
Mixing in flavour SU(3)
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Now 3 quarks: u,d,s
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SU(3) symmetry → octuplet & singlet
●
●
–
π0 = (uu – dd)/√2
–
η1 = (uu + dd + ss)/√3
η8 = (uu + dd – 2ss)/√6
Physical states η,η' are further mixtures
–
η = η1 cos θP + η8 sin θP
–
η' = -η1 sin θP + η8 cos θP
Pseudoscalar mixing angle θP determined from
masses or from partial widths
CPT theorem
●
●
So far, considering mixing of particles with no
flavour quantum numbers
Now move to neutral kaons:
–
●
●
K0 (sd) & K0 (sd)
CPT theorem → particle & antiparticle have
–
equal and opposite charges
–
identical masses
–
identical lifetimes
Mixed states (eg. KS & KL) can have Δm, ΔΓ ≠ 0
Time evolution
●
Consider arbitrary mixture: a|K0> + b|K0>
governed by time-dependent Schrodinger eqn.
 
 
i
a
a
a
∂
i
=H
= M− 
∂t b
2
b
b
●
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H is Hamiltonian; M and Γ are 2x2 Hermitian
matrices
CPT theorem: M11 = M22 & Γ11 = Γ22
Time evolution
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Physical states : eigenstates of effective Hamiltonian
|KS,L> = p|K0> ± q|K0>
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Eigenvalues
λS,L = mS,L – ½iΓS,L = (M11 – ½iΓ11) ± (q/p)(M12 – ½iΓ12)
Δm = mL – mS
ΔΓ = ΓS – ΓL
(Δm)2 – ¼(ΔΓ)2 = 4(|M12|2 + ¼|Γ12|2)
ΔmΔΓ = 4Re(M12Γ12*)
q/p = – (Δm – ½iΔΓ)/2(M12 – ½iΓ12)
= – 2(M12* – ½iΓ12*)/(M12 – ½iΓ12)
What do we expect?
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mixing occurs via box diagrams
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SM predictions for
–
neutral kaon system
–
neutral D meson system
–
Bd0 system
–
Bs0 system
What do we observe?TG, arXiv:1306.4588
significant recent progress (numbers already out-of-date)
some recent progress and more anticipated
Categories of CP violation
●
Consider decay of
neutral particle to a CP
eigenstate
qA
CP =
pA
q
∣ ∣≠1
p
A
∣ ∣≠1
A
qA
ℑ
≠0
pA
 
CP violation in mixing
CP violation in decay (direct CPV)
CP violation in interference
between mixing and decay
CP violation in mixing
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Observed first in KL decays in 1964
–
KL → π+π-
–
KL → π0π0
–
δL(μ) = (Γ(KL → π-μ+ν) - Γ(KL → π+μ-ν))/SUM
–
δL(e) = (Γ(KL → π-e+ν) - Γ(KL → π+e-ν))/SUM
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Due to CPT theorem, CP violation = T violation
●
Is it possible to observe T violation directly?
CPLEAR experiment
P  K  K  −P  K  K

A T=
0
0
0
0
P  K  K  P  K  K 
0
●
0
0
Tag strangeness of initial kaon using charge of
associated kaon from production
+
0
-
-
0
pp → K K π / K K π
●
0
+
Tag strangeness of neutral kaon from charge of
lepton in semileptonic decay (ΔS = ΔQ rule)
T violation in the B system
–
B0→B–
–
B0→B+
B+→B0
BaBar
PRL 109 (2012) 211801
Generalisation of usual
sin(2β) analysis allowing
for separate CP, T and CPT
violating terms
B–→B0
No significant sign of CPT
violation in any test
–0
e.g. AT(B →B–) between (l– tag, J/ψKS, Δt>0)
and (l+ tag, J/ψKL, Δt<0)
~ ½( ΔST+sin(ΔmdΔt) + ΔCT+cos(ΔmdΔt) )
39
Comment on T violation
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●
●
We can never run experiments backwards in
time, so we never really compare a process with
its T conjugate
Nonetheless, certain observables are sensitive
to T violation
–
electric dipole moments
–
transverse polarizations in semileptonic decay
–
triple product correlations in P → VV decays
CPT conservation : T violation = CP violation
Direct CP violation in neutral kaons
●
●
Superweak models (Wolfenstein, 1964) predict
CP violation occurs only in mixing
KM mechanism: CPV in decay also possible
–
●
eg. A(K2 → π+π-) ≠ 0
Experimental test:
–
if CPV in KL → π+π- ≠ CPV in KL → π0π0 ↔ CPV
cannot be in mixing only
R = (KL → π0π0)/(KS → π0π0)/(KL → π+π-)/(KS → π+π-)
R = 1 – 6 Re(ε'/ε)
Measurement of Re(ε'/ε)
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●
Long running saga to establish Re(ε'/ε) ≠0
–
NA31 (CERN) : (23.0 ± 6.5) x 10-4
–
E731 (FNAL) : (7.4 ± 5.9) x 10-4
Next generation of experiments to confirm or
-4
refute the effect at level of 2 x 10
–
●
NA48 (CERN) & KTeV (FNAL)
Final results from NA48 in 2002, KTeV in 2008
NA48 technique
●
Precise measurement – need control of
systematic errors
–
use simultaneous KL and KS beams
–
take data in all four modes together
–
make acceptance as similar as possible
–
perform analysis in bins on kaon energy
●
–
correct for differences in KL and KS energy spectra
weight KL events according to KS decay distribution
NA48 beams
NA48 acceptance
NA48 detector
NA48 detector
NA48 – KL weighting
NA48 result
Re(ε'/ε) = (14.7 ± 2.2) x 10-4
1997-1999 data set
2001 data set
Re(ε'/ε) World Average