Embed Size (px)
Citation preview
Flavor Physics LandscapeZoltan Ligeti
SLAC Summer Institute 2019
The Menu of Flavors:Quarks, Charged Leptons, Neutrinos
Aug 12–23, 2019
What is particle physics?
• Central question of particle physics:
L = ?
... What are the elementary degrees of freedom and how do they interact?
• Most experimentally observed phenomena consistent with the “standard model”(Michelson 1894: “... it seems probable that most of the grand underlying principles have been firmly established ...”)
• Standard Model (SM)of particle physics:
fermions ∼ matter
(3 generations)
bosons ∼ forces
Standard Modelof cosmology:
• Inconsistent: Two very successful theories, but they cannot be the full story
Z L – p. 1
What is particle physics?
• Central question of particle physics:
L = ?
... What are the elementary degrees of freedom and how do they interact?
• Most experimentally observed phenomena consistent with the “standard model”(Michelson 1894: “... it seems probable that most of the grand underlying principles have been firmly established ...”)
• Clearest empirical evidence that SM is incomplete:
– Dark matter Maybe at
– Baryon asymmetry of the Universe TeV scale
– Neutrino mass
– Inflation in the early universe [have a plausible theoretical picture]
– Dark energy [cosmological constant? need to know more to understand?]
Z L – p. 1
The Universe: matter vs. antimatter
• Gravity, electromagnetism, strong interaction are same for matter and antimatter
• As the early Universe cooled,quarks and antiquarks annihilated
N(baryon)
N(photon)∼ 10
−9 ⇒ Nq −Nq
Nq +Nq
∼ 10−9
t < 10−6 s (T > 1013 K ∼ 1 GeV)
• The SM prediction is ∼1010 times smaller
[Nonzero! Sakharov conditions: (i) baryon number
violation; (ii) charge (C) and charge-parity (CP )
violation; (iii) deviation from thermal equilibrium]
• BSM source(s) of CP violation are requiredWhat is the microscopic theory of CP violation? How precisely can we probe it?
Z L – p. 2
The standard model + neutrino mass
• Gauge symmetry: SU(3)c × SU(2)L × U(1)Y parameters
Gauge symmetry: 8 gluons W±, Z0, γ 3 (+θQCD)
• Particle content: 3 generations of quarks and leptons
Particle content: QL(3, 2)1/6, uR(3, 1)2/3, dR(3, 1)−1/3 10
Particle content: LL(1, 2)−1/2, `R(1, 1)−1 12 or 10 ∗
Particle content: quarks:(u c t
d s b
)leptons:
(νe νµ ντ
e µ τ
)• Symmetry breaking: SU(2)L × U(1)Y → U(1)EM
symmetry breaking: φ(1, 2)1/2 Higgs, with vev: 〈φ〉 =
(0
v/√
2
)2
∗Not known: LY = −Y ije LILi φ e
IRj −
YijνΛ LILiL
ILj φφ violates lepton number
Y ijν LILi φ ν
IRj requires νR fields
• We do not know what is the Lagrangian that describes the observed particles
Z L – p. 3
What is flavor physics?
• Flavor≡what distinguishes generations? [breakU(3)Q×U(3)u×U(3)d×U(3)L×U(3)e]
Flavor ≡ rich and sensitive ways to probe the SM and search for NP
• SM flavor: hierarchy of masses and mixing angles? why 3 generations?SM flavor: Flavor in SM is simple: only Higgs – fermion couplings break flavor symmetries
• BSM flavor: TeV scale (hierarchy problem) � “naive” flavor & CP viol. scaleBSM flavor: Most TeV-scale new physics contain new sources of CP and flavor violation
BSM flavor: E.g., SUSY: ∼10× increase in flavor parameters (CP and flavor problems?)
BSM flavor: Generic TeV-scale flavor structure excluded ⇒ new mechanisms to reduce signals
• Flavor sector will be tested a lot better, many NP models have observable effects
• Any new particle that couples to quarks or leptons⇒ new flavor parameters(Understanding these param’s can be crucial; e.g., Higgs, or squark & slepton couplings [if exists])
Z L – p. 4
Quark and lepton mixing
• Fermions with same quantum numbers mix, Yukawas define mass eigenstates:
M =
Ma1 Ma2 Ma3
Mb1 Mb2 Mb3
Mc1 Mc2 Mc3
=
1
c23 s23
−s23 c23
c13 s13e
−iδ
1
−s13eiδ c13
c12 s12
−s12 c12
1
• If neutrinos are Majorana, multiply by: diag (eiα1/2, eiα2/2, 1)
The additional phases α1,2 don’t affect oscillation experiments, only lepton # viol.
Always think about mass eigenstates: if neutrino masses were larger, we wouldhave gotten used to thinking of π → µν2 and π → µν3, instead of π → µνµ
• Leptons (PMNS): θ12 ≈ 34◦ (solar), θ23 ≈ 48◦ (atm), θ13 ≈ 9◦, δ unknown
• Quarks (CKM): θ12 ≈ 13◦, θ23 ≈ 2.4◦, θ13 ≈ 0.2◦, δ ≈ 68◦
Z L – p. 5
Spectacular track record
• Uncertainty principle ⇒ heavy particles, which cannot be produced, affect lowerenergy processes, E2/M2 suppressed if interference ⇒ probe very high scales
• High mass-scale sensitivity due to suppressed SM predictions
– Absence of KL → µµ⇒ charm quark (Glashow, Iliopoulos, Maiani, 1970)
– εK ⇒ 3rd generation (t, b quarks) (Kobayashi & Maskawa, 1973)
– ∆mK ⇒ mc ∼ 1.5 GeV (Gaillard & Lee; Vainshtein & Khriplovich, 1974)
Why is ∆mK/mK ≈ 7× 10−15 so small?
SM: ∆mK/mK ∼g4
2
16π2|VcsVcd|2
m2c
m4W
f2K �� � � � �
� � �� � � �� � �
�
������ �
� � � �� � �
� � � �� � �
��� � �
� ����� �
� �
– ∆mB ⇒mt >∼ 100 GeV (bound in 1987: 23 GeV)⇒ large CP violation & FCNC
• Critical in developing SM — it is only unambiguous since 1998 that mν 6= 0
What can future data tell us about BSM physics?
Z L – p. 6
Very high scales probed
• Scales of dim-6 operators probed — various mechanisms devised to let TeV-scaleNP obey these bounds (Pattern and orders of magnitudes matter more than precise values)
[Abramowicz @ DPF 2019]
• Mu2e is probably the largest increase in mass-scale sensitivity in next 10–15 yrs
Z L – p. 7
Some flavor-related questions
• Will LHC see new physics beyond the Higgs?
• Will NP be seen in the quark sector?Current data: several hints of lepton flavor universality violation (see later)
• Will NP be seen in charged lepton sector? µ→ eγ, µ→ eee, τ → µγ, τ → µµµ?
• Neutrinos: Is 3 flavor oscillation paradigm OK? What is the nature of ν mass?
• No one knows — an exploratory era!(n.b.: 2 generations + superweak is “more minimal” to accommodate CPV, than 3 generations...)
• Near future: “anomalies”, both in quark & lepton sector, might first be established
Long term: large increase in discovery potential in many modes
Z L – p. 8
Outline
• Lepton flavor
Basic open questions, some processes very clean, quark flavor more broad
• Quark flavor
– Mode / model independent: Large improvements in NP sensitivity
NP <∼ (few × SM) → NP <∼ (0.3 × SM) → NP <∼ (0.04 × SM)(−15 yrs) (now) (+15 yrs)
– Mode / model specific: recent 2 – 4σ tensions⇒ lots of exp. & theory work
• Many exciting areas: Higgs & top, charged lepton flavor violation, EDM searches,
BSM scenarios may have nontrivial flavor: dark sectors, long lived particles, ...
(I’ll focus on the quark sector, richest in SM, leptons equally important, especially if there is NP)
Z L – p. 9
Lepton flavor
Neutrino oscillation measurements
• Three mixing angles have been measured
• Oscillation between two flavors (δm2 = m21−m2
2)
Posc = sin2(2θ) sin
2
(1.27
δm2
eV2
L
km
GeV
E
)• Atmospheric neutrinos:
1 ∼ (10−3)×(101...4) / (100±1)
half of up-going νµ get lost
• Solar neutrinos: δm2L/E � 1
• Two mass-squared differences are measured,but not the absolute mass scale
(Short baseline anomalies not easy to fit, e.g., w/ 4 flavors)
© ©©
Z L – p. 10
Neutrinos — a history of surprises
• Most theorists’ expectations around late 80’s – early 90’s:
– Solar neutrino problem will go away, we do not understand the Sun Wrong
– If it does not, solution must be small angle MSW, since it’s cute Wrong
– Expect ∆m223 ∼ 10− 100eV2, since it’s cosmologically interesting Wrong
– Expect θ23 ∼ Vcb ' 0.04, motivated by simplest GUTs Wrong
– Atmospheric neutrino anomaly will go away, because it requires large Wrongmixing angle — the first that became compelling (⇒ Nobel, 2002)
– Tribimaximal mixing ansatz predicted θ13 near zero Wrong
sin2 2θ13 ∼ 0.1 not too small — helps CP violation searches[inspired by H. Murayama]
• Experiments crucial, independent of prevailing theoretical “guidance”(Recall that CP violation was a surprise, as was B0 –B0 mixing, etc.)
Z L – p. 11
Lepton vs. quark mixing
• Are the origin of quark and lepton masses & mixings related?
• Some lepton processes are especially clean; quark sector observables more rich
• Cannot directly measure neutrino mass eigenstates (possible for e, µ, τ and quarks)
• Neutrino FCNCs seem impossible to search for; e.g., νi → νj γ, X → νiνj(Y )
• Magnitudes of mixing matrix elements, assuming 3-generation unitarity:
UPMNS =
0.820± 0.008 0.552± 0.011 0.150± 0.002
0.367± 0.041 0.574± 0.034 0.712± 0.020
0.410± 0.038 0.591± 0.033 0.681± 0.021
[νfit 2019, 3σ, converted]
VCKM =
0.97446± 0.00010 0.22452± 0.00044 0.00365± 0.00012
0.22438± 0.00044 0.97359+0.00010−0.00011 0.04214± 0.00076
0.00896+0.00024−0.00023 0.04133± 0.00074 0.999105± 0.000032
[PDG 2018]
• SM flavor puzzle extended: why lepton & quark masses and mixings so different?
Z L – p. 12
Neutrinos — many unknowns
• Are neutrinos = their own antiparticles?(Different than all other known particles? Theoretically favored, most leptogenesis models)
• What is the absolute mass scale?
We know two mass-squared differences
At least one state has mνi>∼ 50 meV
Cosmology:∑mi<0.12− 0.3 eV [Planck 2018]
(depends on assumptions; can relax, e.g., [1901.04352])
• Value of CP violating phase δ ?
• Is the mass hierarchy “normal” or “inverted”?
If inverted hierarchy: planned 0νββ experiments will beIf inverted hierarchy: able to determine if ν = ν or ν 6= ν
Normal hierarchy: may or may not see 0νββ, even in Majorana case
Z L – p. 13
Charged lepton flavor violation (CLFV)
• Expect 104 better sensitivity (Mu2e, COMET)⇒ 10× higher mass scales probed!
• mν 6= 0 ⇒ lepton flavor is violated, no reason to impose it as a symmetry on NP
If there are new TeV-scale particles that carry lepton number (e.g., sleptons), thenthey have their own mixing matrices⇒ charged lepton flavor violation (CLFV)
• In many SUSY models (& other scenarios), NP in the quark and lepton sectorsmay originate from the same underlying physics
• Experimental sensitivity is at exciting level for complementarity with LHC searches
• Flavor vs. naturalness: heavier NP⇒ less constraints on its flavor structureFlavor vs. naturalness: “naturalness’ loss — flavor’s gain”
• CLFV measurements can discover NP signals due to TeV-scale NP with SM-likeflavor structure, or 10–1000 TeV NP with generic flavor⇒ cast a wide net
Z L – p. 14
Operators, patterns, connections
• More sensitive: µ→ eγ or µ→ eee? (Mu2e also sensitive to tree-level LQ exchange)
Depends on NP: L =mµ
(κ+ 1)Λ2µRσαβF
αβeL +
κ
(κ+ 1)Λ2(µLγ
αeL)(eLγαeL)
κ→ 0 : µ→ eγ at tree level, µ→ eee at order ακ� 1 : µ→ eee at tree level, µ→ eγ at order α
• Flavor: µ→ eγ and (g − 2)µ operators are similar: mµ
Λ2µσαβF
αβe ,
mµ
Λ2µσαβF
αβµ
If coefficients are comparable, µ→ eγ gives much stronger bound already
If (g− 2)µ is due to NP, large hierarchy of coefficients (⇒ model building lessons)
• Lepton number violation: search for ppµ− → nne+
in simplest scenario sensitive to |Σ3i=1miUeiUµi|
similar to 0νββ measuring |mee| = |Σ3i=1miU
2ei|
• Patterns would tell us about underlying structuresu
µ�
u
d
e+
d
Z L – p. 15
Bounds on κ− Λ
10 3
10 4
10-2
10-1
1 10 102
!
" (T
eV)
EXCLUDED (90% CL)
B(µ # e$)=10-13
B(µ # e$)=10-14
B(µ # e conv in 27Al)=10-16
B(µ # e conv in 27Al)=10-18
a [de Gouvea & Vogel, 1303.4097]
Z L – p. 16
Many complementary CLFV processes
• SM predictions incredibly small TeV-scale loop-level NP may be observable
rates ∝ m4ν
m4W
< 10−50
[diagrams: hep-ph/9501334]
• Many interesting processes; NP-dependent which is most sensitive:µ→ eγ, µ→ eee, µ+N → e+N (′), µ−pp→ e+nn, τ → µγ, τ → eγ, τ → µµµ,τ → eee, τ → µµe, τ → µee, τ → µπ, τ → eπ, τ → µKS, eN → τN
• τ decays: µ→ eγ, eee vs. τ → µγ, µµµ
Either can “win”, huge NP model depen-dence: B(τ → µγ)/B(µ→ eγ) ∼ 104±3
• Belle II: improve 2 orders of magnitude
• Any discovery⇒ broad program to mapout the detailed structure
γ - eγ - µ0 π - e0 π - µη - eη - µ'η - e'η - µ
0 S K- e
0 S K- µ
0 f- e
0 f- µ
0ρ - e0ρ - µ K*
- e K
*- µK
* - eK
* - µ
φ - eφ - µω - eω - µ
- e+
e- e-
e+ e- µ
- µ + µ - e- µ + µ - µ-
e+ µ - e- µ +
e- µ- π + π - e- π + π - µ-
K+ π - e-
K+ π - µ- π +
K- e- π +
K- µ-
K+ K- e
- K+
K- µ0 S
K0 S
K- e0 S
K0 S
K- µ- π +
e- π- π + µ - π-
K+ e- π
- K+ µ - π
- K+
e-K
- K+ µ -
KΛ - πΛ - πΛ -
KΛ -
K
dec
ays
τ90
% C
.L. u
pper
lim
its fo
r LF
V
-1010
-910
-810
-710
-610
-510
CLEOBaBarBelleLHCbBelle II
γl 0lP 0lS 0lV lll lhh hΛ
Z L – p. 17
Electric dipole moments
• SM + mν: CPV can occur in: (i) quark mixing; (ii) lepton mixing; and (iii) θQCD
Only observed δKM 6= 0, baryogenesis implies there must be more
• Neutron EDM bound: “the strong CP problem”, θQCD < 10−10 — axion?θQCD is negligible for CPV in flavor-changing processes
• EDMs from CKM: vanish at one- and two-loopEDMs from CKM: large suppression at three-loop level
• E.g., SUSY: quark and lepton EDMs can be generated at one-loop
Generic prediction (TeV-scale, no small param’s) above cur-rent bounds; if mSUSY ∼ O(10 TeV), may still discover EDMs
• Expected 102–103 improvements: complementary to LHCDiscovery would give (rough) upper bound on NP scale
Z L – p. 18
Quark flavor
Precision CKM tests with kaons
• CPV in K system is at the right level (εK accommodated with O(1) KM phase)
• Hadronic uncertainties preclude precision tests (ε′K notoriously hard to calculate)
Cannot yet rule out (nor prove) that the measured value of ε′K is dominated by NP(N.B.: bad luck in part — heavy mt enhanced hadronic uncertainties, but helps for B physics)
• With lattice QCD improvements, εK has become more sensitive, hopes for ε′/ε
• K → πνν : Theory error ∼ few %, but very small rates 10−10 (K±), 10−11 (KL)
A ∝
(λ5m2
t) + i(λ5m2t) t : CKM suppressed
(λm2c) + i(λ5m2
c) c : GIM suppressed(λΛ2
QCD) u : GIM suppressed
� �� �
��������� �� ���
� �
� � � �� �
So far O(1) uncertainty in K+ → π+νν, and O(103) in KL → π0νν
• CERN NA62: aim ∼100 K+ → π+νν events at SM levelJ-PARC KOTO: aim to observe K0
L → π0νν at SM level
}Far from theory limits
Z L – p. 19
Quark mixing and unitarity triangle
• The (u, c, t) W± (d, s, b) couplings: (Wolfenstein parm., λ ∼ 0.23)
VCKM =
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
︸ ︷︷ ︸
CKM matrix
=
1− 12λ
2 λ Aλ3(ρ− iη)
−λ 1− 12λ
2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+ . . .
9 complex couplings depend on 4 real parameters⇒ many testable relationsOne complex phase in VCKM: only source of CP violation in quark mixing
• Unitarity triangle: visualize SM constraints and compare measurements
CPV in SM ∝ Area
Vud V∗ub + Vcd V
∗cb + Vtd V
∗tb = 0
Sides and angles measurable in many ways
Goal: overconstrain by many measurementssensitive to different short distance physics
Z L – p. 20
Learned a lot, plenty of room for new physics
• Spectacular progress in last 20 years
• The implications of the consistency ofmeasurements is often overstated
• Larger allowed region if there is NP
γ
γ
Kε
Kε
α
α
dm∆
sm∆ & dm∆
ubV
βsin 2
(excl. at CL > 0.95)
< 0βsol. w/ cos 2
exclu
ded a
t CL >
0.9
5
α
βγ
ρ
1.0 0.5 0.0 0.5 1.0 1.5 2.0
η
1.5
1.0
0.5
0.0
0.5
1.0
1.5
excluded area has CL > 0.95
ICHEP 16
CKMf i t t e r
Z L – p. 21
Learned a lot, plenty of room for new physics
• Spectacular progress in last 20 years
• The implications of the consistency ofmeasurements is often overstated
• Larger allowed region if there is NP
• Compare tree-level (lower plot) andloop-dominated measurements
• LHCb: constraints in the Bs sector(2nd–3rd gen.) caught up with Bd
γK
ε
α
α
dm∆
sm∆ & dm∆
ubV
βsin 2(excl. at CL > 0.95)
< 0βsol. w/ cos 2
α
βγ
ρ
0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0
η
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
exclu
ded a
rea h
as C
L >
0.9
5
ICHEP 16
CKMf i t t e r
γ
ubV
α
βγ
ρ
0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0
η
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
exclu
ded a
rea h
as C
L >
0.9
5
ICHEP 16
CKMf i t t e r
• O(20%) NP contributions to most loop-level processes (FCNC) are still allowed
Z L – p. 21
LHCb — LHC at CERN
• Major LHCb upgrade in LS2 (raise instantaneous luminosity to 2× 1033/cm2/s)
Major ATLAS and CMS upgrades in LS3, for HL-LHC
• LHCb, 2017, Expression of Interest for an upgrade in LS4 to 2× 1034/cm2/s
Not yet approved — an integral part of the full exploitation of the LHC
Z L – p. 22
Belle II — SuperKEKB at Tsukuba
• First collisions 2018 (unfinished detector), with full detector starting spring 2019Goal: 50× the Belle and nearly 100× the BABAR data set
• Discussions started about physics case and feasibility of a factor ∼ 5 upgrade,similar to LHCb Phase-II upgrade aiming 50/fb→ 300/fb, in LHC LS4
Z L – p. 23
Recent surprise: CMS “B – parking” in 2018
• Collected 1010 B-s; hope to compete w/ LHCb on RK(∗) anomaly [CMS @ LHCC, Nov 2018]
B-Parking
Effort in 2018 paid off, 12B triggered events on tape
Up to 5.5 kHz in the second part of the fill where events are smaller
Now studying processing strategy
1.1B events were already fully processed in order to help development of trigger/reconstruction !16
7.6 PB on tape Avg event size is 0.64 MB (1MB for standard events)
Z L – p. 24
Model independent
(1) Discovery potential at HL-LHC
• Figure of merit ∼ mass-scale vs. coupling sensitivity
• Consider: ATLAS/CMS 300/fb→ 3000/fb and LHCb 50/fb→ 300/fb
ATLAS & CMS searches for high-mass states: parton luminiosities fall rapidly
LHCb Phase-2 upgrade compared to Phase-1: 4√
6 ∼ 1.6 mass scale (conservative)
• 4√
6 ∼ 1.6 improvement @ LHCb vs. mass-scale increase at 14 TeV, 300→ 3000/fb
• Increase in sensitivity >1.6, iff (w/ caveats)limit with 300/fb at 14TeV is <∼1 TeV
I.e., weakly produced particles (H±, ...) ordifficult decays — not the typical Z ′, q, g !
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8
syst
em
mass
[Te
V]
for
14
.00
TeV
, 3
00
0.0
0 f
b-1
system mass [TeV] for 14.00 TeV, 300.00 fb-1
http
://cern
.ch/co
llider-re
ach
by G
.P. Sala
m a
nd
A. W
eile
r
q q
Σi qi q-
iq gg g
[http://collider-reach.web.cern.ch/]
Z L – p. 25
At fixed energy, 1/√L is about the best
• It is often said that what’s excluded at300/fb, cannot be discovered at 3000/fb
... so why keep going?
– Holds for many heavy particle searches
– Exception: light or weakly coupled par-ticles, often with large backgrounds(e.g., charged Higgs)
– IF program @ HL-LHC: refine Higgscouplings, SM particle properties, flavorobservables (uncert. ∼1/
√L)
• Statistics ×10 can make 1.5σ →∼5σ, even without analysis improvements(No one knows how many measurements are 1.5σ from SM expectation... which also improve)
Z L – p. 26
(2) New physics in B mixing
• Meson mixing:
Meson mixing:
General parametrization:
M12 = MSM12 × (1 + h e2iσ)
NP parameters↑ ↗
SM: ∼CSM
m2W
NP: ∼CNP
Λ2
What is the scale Λ? How different is the CNP coupling from CSM?
If deviation from SM seen⇒ upper bound on Λ
• Assume: (i) 3× 3 CKM matrix is unitary; (ii) tree-level decays dominated by SM
• Modified: loop-mediated (∆md, ∆ms, β, βs, α, ...)
Unchanged: tree-dominated (γ, |Vub|, |Vcb|, ...)
(Importance of these constraints is known since the 70s, conservative picture of future progress)
Z L – p. 27
Sensitivity to NP in B mixing
• At 95% CL: NP<∼ (0.3× SM)⇒ NP < (0.05 × SM)
• Scale: h ' |Cij|2|V ∗tiVtj|2
(4.5 TeV
Λ
)2
⇒ Λ ∼{
2.3× 103 TeV
20 TeV (tree + CKM)2 TeV (loop + CKM)
• Similar to LHC mg reach
• Sensitivity would continue toincrease beyond 300/fb
Complementary to high-pT
Now LHCb 50/fb + Belle II 50/ab
dh0.0 0.1 0.2 0.3 0.4 0.5
dσ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0pvalue
excluded area has CL > 0.95
2013
CKMf i t t e r
HFAG 2014s
φ
dh0.0 0.1 0.2 0.3 0.4 0.5
dσ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0pvalue
excluded area has CL > 0.95
Stage II
CKMf i t t e r
[color: 2σ, dotted: 3σ] M(q)12 = MSM
12 (1+hqe2iσq)
dh0.0 0.1 0.2 0.3 0.4 0.5
sh
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0pvalue
excluded area has CL > 0.95
2013
CKMf i t t e r
HFAG 2014s
φ
dh0.0 0.1 0.2 0.3 0.4 0.5
sh
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0pvalue
excluded area has CL > 0.95
Stage II
CKMf i t t e r
[1309.2293]
Z L – p. 28
Mode / model dependent
The current B “anomalies”
• Lepton non-universality would be clear evidence for NP
1) RK and RK∗ (B → Xµ+µ−)/(B → Xe+e−) ∼ 20% correction to SM loop �
� �
��
� �
��� � � ���� � ��
2) R(D) and R(D∗) (B → Xτν)/(B → X(e, µ)ν) ∼ 20% correction to SM tree ν
�����
Scales: RK(∗) <∼ few× 101 TeV, R(D(∗)) <∼ few× 100 TeV Would bound NP scale!
• Theor. less clean: 3) P ′5 angular distribution (B → K∗µ+µ−)
Theor. less clean: 4) Bs → φµ+µ− rate
Can fit 1), 3), 4) with one operator: C(NP)9,µ /C
(SM)9,µ ∼ −0.2 , C9,µ = (sγαPLb)(µγ
αµ)
• Viable BSM models... leptoquarks? No clear connection to DM & hierarchy puzzle
(Is the hierarchy problem or the flavor problem more pressing for Nature?)
• What are smallest deviations from SM, which can be unambiguously established?
Z L – p. 29
RK and RK∗: theoretically cleanest
• LHCb: RK(∗) =B → K(∗)µ+µ−
B → K(∗)e+e−< 1 both ratios ∼2.5σ from lepton universality
2.6σ 2.2σ 2.5σ
• Theorists’ fits quote 3 – 5σ (sometimes including P ′5 and/or Bs → φµ+µ−)
• Modifying one Wilson coefficient in Heff gives good fit: δ C9,µ ∼ −1
Z L – p. 30
The B → D(∗)τ ν decay rates
• BABAR, Belle, LHCb: R(X)=Γ(B → Xτν)
Γ(B → X(e/µ)ν)
3.1σ from SM predictions — robust due to heavyquark symmetry + lattice QCD (only D so far)
more than statistics: R(D∗) with τ → ν3π [1708.08856]
more than statistics: Bc → J/ψ τν [1711.05623]
• Imply NP at a fairly low scale (leptoquarks, W ′, etc.), likely visible at ATLAS / CMSSome of the models Fierz (mostly) to the same (SM) operator: distributions, τ polarization = SM
• Tree level: three ways to insert mediator: (bν)(cτ), (bτ)(cν), (bc)(τν)
Tree level: overlap with ATLAS & CMS searches for b, leptoquark, H±
• Models built to fit these anomalies have impacted many ATLAS & CMS searches
Z L – p. 31
Exciting future
• LHCb: RK(∗) sensitivity with existing Run 1–2 data can still improve a lot
• LHCb and Belle II: increase pp→ bb and e+e− → BB data sets by factor ∼50
• LHCb:Belle II (50/ab, at SM level):
δR(D) ∼ 0.005 (2%)
δR(D∗) ∼ 0.010 (3%)
Measurements will improve a lot!
(Even if central values change, plenty of
room for establishing deviations from SM)
• Competition, complementarity, cross-checks between LHCb and Belle II
Z L – p. 32
Lepton universality→ lepton flavor violation
quark sector
New charged current interactionsgenerically introduce new FCNCs
Hope: new physics at LHC, couples toquarks somehow (production, decays)
However, no NP effect seen yet inflavor-changing neutral currents
Puzzle: How does NP “know” aboutthe rotation between the quark massand weak interaction eigenstates
Solution: Some symmetry of NP, min-imal flavor violation, natural in GMSB
lepton sector
New lepton-nonuniversal interactionsgenerically introduce LFV
Hope: some of the hints for leptonnon-univerality survive
However, no lepton flavor violationseen yet in meson or lepton decays
Puzzle: Same for leptons question forwhatever mediates the BSM interac-tion
Solution: Same, maybe... Want dataon many processes to give clues
Z L – p. 33
E.g., leptoquark flavor structures
• Leptoquarks are some of the most often discussed models for RK(∗) and R(D(∗))
A-priori no reason for the leptoquark couplings to be (approx.) flavor conserving
Need this to explain b→ s`+`− data Need to worry about all b→ q`+1 `−2 couplings
λ =
λde λdµ λdτ
λse λsµ λsτ
λbe λbµ λbτ
• RK implies: 0.7 <∼ Re(λseλ∗be − λsµλ
∗bµ)
(24 TeV)2
M2<∼ 1.5
• Search for LFV in B → K(∗)µ±e∓, B → K(∗)µ±τ∓, etc.,
similarly in D and K decays, and LFV in purely leptonic processes
• Leptoquarks — almost by definition — connect quark and lepton flavor
Z L – p. 34
A possible pattern of couplings
• Let’s assume: λ =
ρd κ ρd ρd
ρ κ ρ ρ
κ 1 1
rows = quarkscolumns = leptons
[de Medeiros Varzielas, Hiller, 1503.01084]
Allow for extra suppression of lighter quark couplings, e.g., ρ ∼ ε2, ρd ∼ ε3 or ε4
Can be arranged using flavor symmetries (Froggatt-Nielsen mechanism, ε ∼ 0.2, Cabibbo angle)
• Predictions:
• For first generation couplings, kaon decays give the strongest bounds at presentMu2e and COMET will beat these
Z L – p. 35
Richness of directions
Some key measurements, done much better
CP violation in Bs → ψφ
now consistent with SM
)0
(BSLA0.02 0.01 0 0.01 0.02
)s0
(BS
LA
0.02
0.01
0
0.01
HFLAV
Summer 2017
B factoryaverage
LHCbXµ
(*)
(s) D→
0
(s)B
0DXµ
(*)
(s) D→
0
(s)B0D
muons
0Daverage
10×Theory
World average
= 12χ∆
DØ
ASL: important, indep.of DØ anomaly
0
0.2
0.4
0.6
0.8
1
CL
−1
0 50 100 150]° [γ
GLW
ADS
GGSZ
Combined
GLW
ADS
GGSZ
Combined
68.3%
95.5%
HFLAVLate 2017
Measurements of γ crucial,LHCb is now most precise
• Uncertainty of predictions� current experimental errors (⇒ seek lot more data)
• Breadth crucial, often have to combine many measurements and theory(“The interesting messages are not simple, the simple messages are not interesting”)
Z L – p. 36
B → µ+µ−: interesting well beyond HL-LHC
• Bd → µ+µ− in SM, 10−10 : LHCb expects 10% (300/fb), CMS expects 15% (3/ab)
SM uncertainty, as of now ' (2%)⊕ f2Bq⊕ CKM [Bobeth, FPCP’15]
)−
µ+µ → 0
sBF(B
0 2 4 6 8
9−10×
)−
µ+
µ →
0B
F(B
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.99−
10×
68.2
7%
95.4
5%
99.7
3%
99.9
9%
SM
LHCb
• Theoretically cleanest |Vub| I know, only isospin: B(Bu → `ν)/B(Bd → µ+µ−)
• A decay with mass-scale sensitivity (dim.-6 operator) that competes w/ K → πνν
Z L – p. 37
The LHC is a top factory: top flavor physics
• FCNC top decays not yet strongly constrained
t→ cZ, cγ, cH, uZ, uγ, uH
SM predictions: < 10−12
Best current bound: <∼ few× 10−4[ATLAS, CMS]
• Sensitivity will improve ∼2 orders of magnitude
l
ν
tW
Z
u, c
t
l
l
b
• Indirect constraints: tL ↔ bL⇒ tight bounds fromB decays
– Strong bounds on operators with left-handed fields
– Right-handed operators could give rise to LHC signals
• If top FCNC is seen, LHC & B factories will both probe the NP responsible for it
Z L – p. 38
The LHC is a Higgs factory
• Many production and decay channels: richness due to fermion couplings
Yukawa matrices determine these, just like K, B, and D physics
• Higgs flavor param’s: 3rd gen: κt, κb, κτ 2nd gen: κc, κµ Do κtc, κτµ vanish?
Z L – p. 39
Higgs flavor physics
Future precision of flavor-diagonal couplings [Heinemann & Nir, 1905.00382]
• Fermion masses and mixing angles all originatefrom the Yukawa matrices
Z L – p. 40
• Dark matter, with flavor:
Baryogenesis, dark matter, B decays
• Ann Nelson: many brilliant and groundbreaking contributions to baryogenesis,flavor physics, CP violation, GMSB and SUSY breaking, dark sectors, etc.
• E.g., recently: Post-sphaleron baryogenesis, at few MeV, oscillations of baryons,mesons, mesinos; new interplays of cosmology, DM, model building, flavor[A. Nelson & different collaborators, 1907.10612, 1901.08141, 1810.00880, 1708.01259, 1512.05359, 1508.05392, 1407.8193]
• Potentially spectacular signals — hardly any constraints on some:
– Search for neutral heavy baryon oscillation
– Search for baryon number violation in heavy baryon decays
– Search for invisible modes, even baryonic, e.g., B → N + invis. [+mesons]
– Novel DM searches in B decays
Z L – p. 40
Final remarks
Very broad program: many directions
• Better tests of (exact or approximate) conservation laws
• Maximize sensitivity to τ → 3µ, τ → hµµ, etc.
• Exhaustive list of dark / hidden sector searches
• LFV meson decays, e.g., M0 → µ−e+, B+ → h+µ−e+, etc.
• Invisible modes, even baryonic, B → N + invis. [+mesons] [1708.01259]
• Hidden valley inspired scenarios, e.g., multiple displaced vertices, even with `+`−
• Exotic Higgs decays, e.g., high multiplicity, displaced vertices (H → XX → abab)
• Search for “quirks” (non-straight “tracks”) at LHCb using many velo layers
• I do not know how many CP violating quantities have been measured...neither how many new hadronic states discovered by BABAR, Belle, LHCb ...
Z L – p. 41
What are the largest useful data sets?
• No one has seriously explored it! (Recall, Sanda, 2003: the question is not 1035 or 1036...)
• Which measurements will remain far from being limited by theory uncertainties?
– γ, theory limit only from higher order electroweak
– Bs,d → µµ, B → µν and other leptonic decays (lattice QCD, [double] ratios)
– CP violation in D mixing (firm up theory)
– Ad,sSL (work on exp. syst. issues)
– CLFV, EDM, etc.
• In some decay modes, even in 2030 we’ll have: (exp. bound)/
SM >∼ 103
E.g., B → e+e−, τ+τ− — can build models... (I hope to be proven wrong!)
• My guess: until 100× (Belle II & LHCb Phase 2), sensitivity to NP would improve
• FCC-ee in tera-Z phase could be the ultimate B factory!
Z L – p. 42
10 points to conclude
• Flavor physics probes scales�1 TeV; sensitivity limited by statistics, not theory
• New physics in FCNCs may still be >∼ 20% of the SM
• Few tensions with SM; some of these (or others) could soon become decisive
• Precision tests of SM will improve in the next decade by 10–104 (esp. Mu2e)
• Discovering lepton universality violation would focus much more attention on LFV
• Discovering CLFV⇒ broad program to map out operator and generation structure
• Many interesting theoretical questions relevant for optimal experimental sensitivity
• Ample physics reasons to aim for data sets far beyond what’s envisioned so far
• We’ll learn a lot, whether NP is discovered or not (I’d like to know the Lagrangian!)
• If new physics is discovered, many new questions about its flavor structure
Z L – p. 43
Extra slides
The Universe: a not understood superconductor
• Electromagnetism: Coulomb’s law F ∝ 1/r2... infinite range... mγ = 0
Weak interaction: Exponential fall-off... short range... mW±,Z0 6= 0
Gauge symmetry forbids W,Z masses, understandthem the same way as Meissner effect: exponentialfall-off of B field (spontaneous symmetry breaking)
• mW,Z 6= 0: ground state of the Universe (“vacuum”) is in a superconducting state
Higgs mechanism ∼ nonabelian Ginzburg–Landau theory of superconductivityHiggs mechanism = penetration depth: λ−1 ∼ mW , coherence length: ξ−1 ∼ mh
• The microscopic theory (BCS): Cooper pairs, scale of “new physics” connected
• Is electroweak superconductivity similar? LHC may still find mBSM/mh ∼ O(10)
• As in BCS, microscopic explanations involve phenomena at related scales(supersymmetry, little higgs, extra dimensions, strongly interacting sectors, etc.)
Z L – p. i
Theory challenges / opportunities
• New methods & ideas: recall that the best α and γ measurements are in modesproposed in light of Belle & BABAR data (i.e., not in the BABAR Physics Book)
– Better SM upper bounds on Sη′KS − SψKS, SφKS − SψKS, and Sπ0KS− SψKS
– And similarly in Bs decays, and for sin 2β(s) itself
– How big can CP violation be in D0 –D0 mixing (and in D decays) in the SM?
– Better understanding of semileptonic form factors; bound on SKSπ0γ in SM?
– Many lattice QCD calculations (operators within and beyond SM)
– Inclusive & exclusive semileptonic decays
– Factorization at subleading order (different approaches), charm loops
– Can direct CP asymmetries in nonleptonic modes be understood enough to– make them “discovery modes”? [SU(3), the heavy quark limit, etc.]
• We know how to make progress on some + discover new frameworks / methods?
Z L – p. ii
D –D mixing and CP violation
• CP violation in D decay
LHCb, Nov 2011: ∆ACP ≡ AK+K− −Aπ+π− = −(8.2± 2.4)× 10−3
LHCb, Mar 2019: ∆ACP = −(1.82± 0.33)× 10−3 ↖(a stretch in the SM, imho)
• I think we still don’t know how big an effect could (not) be accommodated in SM
• Mixing generated by down quarksor in SUSY by up-type squarks
• Value of ∆m? Not even 3σ yet
• Connections to FCNC top decays
•SM
•no mixing
• SUSY: interplay of D &K bounds: alignment, universality, heavy squarks?
Z L – p. iii
The holy grail: K → πνν
• Long history of ingenious experimental progress (huge backgrounds)
E787/E949: 7 events observed, B(K → π+νν) = (1.73+1.15−1.05)× 10−10
SM: B(K+ → π+νν) = (0.78± 0.08)× 10−10, B(K0L → π0νν) = (0.24± 0.04)× 10−10
• Theoretically clean:
– Top quark loops dominate
– K0L → π0νν is (mostly) CP violating
• CERN NA62: aim ∼ 100 K+ → π+νν
events at SM level
• J-PARC KOTO: observe K0L → π0νν
at SM level
Z L – p. iv
(3) Sensitivity to vector-like fermions
• Add one vector-like fermion: mass term w/o Higgs, hierarchy problem not worse11 models in which new particles can Yukawa couple to SM fermions and Higgs⇒ FCNC Z couplings to leptons or quarks [Ishiwata, ZL, Wise, 1506.03484; Bobeth et al., 1609.04783]
Upper (lower) rows are current (future, 50/fb LHCb & 50/ab Belle II) sensitivities
ModelQuantum Bounds on M/TeV and λiλj for each ij pair
numbers ij = 12 ij = 13 ij = 23
∆F = 1 ∆F = 2 ∆F = 1 ∆F = 2 ∆F = 1 ∆F = 2
V (3, 1,−1/3) 66d [100]e {42, 670}f 30g 25h 21i 6.4j
280d {100, 1000}f 60l 61h 39k 14j
VII (3, 3,−1/3) 47d [71]e {47, 750}f 21g 28h 15i 7.2j
200d {110, 1100}f 42l 68h 28k 16j
XI (3, 2,−5/6) 66d [100]e {42, 670}f 30g 25h 18k 6.4j
280d {100, 1000}f 60l 61h 39k 14j
Strongest bounds arise from many processes, nominally 1-2 generation most sensitive, large variation across models
• LHCb 50/fb + Belle 50/ab increase mass scale sensitivity by factor ∼2.5 ∼ 4√
50
Z L – p. v
Dark sectors: broad set of searches
• Started with bump hunting in B → K∗µ+µ−
Nearly an order of magnitude improvement due to dedicated LHCb analysis
In axion portal models, scalar couples as (mψ/fa) ψγ5ψ a (mt coupling in loops)
) [MeV]−µ+µ(m1000 2000 3000 4000
0.5
1
1
2
)=10 T
eVh(
m [PeV
], β 2
)tanχ(
f
)=1
TeV
h(m
[Pe
V],
β2
)tan
χ(f
hadrons) = 0→χ(B
hadrons) = 0.99→χ(B
LHCb
4
1 TeV
2 TeV3 TeV
5 TeV
10 TeV20 TeV
30 TeV
1 TeV
2 TeV3 TeV
5 TeV10 TeV20 TeV30 TeV
50 TeV
0 1 2 3 4 5 60
200
400
600
800
1000
1200
1400
tan Β
mH!GeV"
Bound on fa
FIG. 1: Bounds on fa as a function of tan β and mH for n = 1in Eq. (8), for m2
a ≪ m2B. For each displayed value of fa there
are two contour lines, and the region between them is allowedfor fa below the shown value. The bound disappears alongthe dashed curve, and gets generically weaker for larger tan β.
that LHCb should be able to carry out a precise mea-surement [40]. Interestingly, since the B → Ka signal isessentially a delta function in q2, the bound in Eq. (15)can be improved as experimental statistics increase byconsidering smaller and smaller bin sizes, without beinglimited by theoretical uncertainties in form factors [41](or by nonperturbative contributions [42]). The boundon fa will increase compared to the results we obtain inthe next section, simply by scaling with the bound on1/
√Br(B → Ka).
V. INTERPRETATION
We now derive the bounds on fa using the calculatedB → Ka branching ratio in Eq. (14) and the experimen-tal bound in Eq. (15). We start with the axion portalscenario with Br(a → µ+µ−) ∼ 100% and where sin θ isdefined in terms of fa by Eq. (8). We will then look atthe bound on more general scenarios, including the lightHiggs scenario in the NMSSM.
For the axion portal, Fig. 1 shows the constraints on fa
as a function of the charged Higgs boson mass mH andtanβ. For concreteness, we take n = 1; other values of ncorrespond to a trivial scaling of fa. In the mass rangein Eq. (1), the dependence on ma is negligible for settinga bound. The bound on fa is in the multi-TeV range forlow values of tanβ and weakens as tanβ increases. Ateach value of tanβ, there is a value of mH for which the
0 200 400 600 800 1000 1200 14000
20
40
60
80
100
mH !GeV"
f atan2Β!TeV"
Bound on fa tan2Β !Large tan Β"
FIG. 2: The shaded regions of fa tan2 β are excluded in thelarge tan β limit. To indicate the region of validity of thelarge tan β approximation, the dashed (dotted) curve showsthe bound for tan β = 3 (tanβ = 1).
b → sa amplitude in Eq. (12) changes signs, indicated bythe dashed curve in Fig. 1, along which the bound dis-appears. Higher order corrections will affect where thiscancellation takes place, but away from a very narrow re-gion near this dashed curve, the derived bound is robust.The region tanβ < 1 is constrained by the top Yukawacoupling becoming increasingly nonpertubative; this re-gion is included in Figs. 1 and 3, nevertheless, to providea clearer illustration of the parametric dependence of thebounds.
As one goes to large values of tanβ, the X1 pieceof Eq. (12) dominates, and sin(2β)/2 = 1/ tanβ +O(1/ tan3 β). In this limit, the constraint takes a par-ticularly simple form that only depends on the combi-nation fa tan2 β, as shown in Fig. 2. Except in the re-gion close to mH ∼ 550 GeV, the bound is better thanfa tan2 β >∼ few × 10 TeV.
These B → Ka bounds are complementary to thoserecently set by BaBar [30] in Υ(nS) → γ a → γ µ+µ−:
fa>∼ (1.4 TeV) × sin2 β . (16)
For example, for mH ≃ 400 GeV, the Υ bound dominatesfor tanβ >∼ 5, while B → Ka dominates for tanβ <∼ 5.
The bounds in Figs. 1 and 2 apply for a generic axionportal model where mH and tanβ are free parameters.One would like some sense of what the expected valuesof mH and tanβ might be in a realistic model. Ref. [8]considered a specific scenario based on the PQ-symmetricNMSSM [31]. In that model small tanβ is preferred,since large tanβ requires fine-tuning the Higgs potential.In addition, mH is no longer a free parameter and isapproximately related to the mass of the lightest CP -even scalar s0 via
m2H ≃ m2
W +
(2
sin2 2β
ms0fa
vEW
)2
. (17)
Freytsis, Ligeti, Thaler[0911.5355]
LHCb, m(a) = 600 MeV[1508.04094]
0
140
280
420
560
700
mH± (GeV)[LHCb, 1508.04094]
• Many other current / future LHCb dark photon searches [Ilten et al., 1603.08926, 1509.06765]
Z L – p. vi
New particles, e.g., supersymmetry
• Any new particle that couples to quarks or leptons⇒ new flavor parameters
The LHC will measure: masses, production rates, decay modes (some), etc.
Details of interactions of new particles with quarks and leptons will be important
• New physics flavor structure can be: new physics mass scale:
– Minimally flavor violating (mimic the SM)– Related but not identical to the SM– Unrelated to the SM, or even completely anarchic
↑↓ can be “light”
must be heavy
Some aspects will be understood from ATLAS & CMS data (masses, decays, etc.)
• New sources of CP violation: squark & slepton couplings, flavor diagonal pro-cesses (e, n EDM), neutral currents; may enhance FCNCs (B(s) → `+`−, µ→ eγ)
Z L – p. vii
Can probe very high scales
• Example: ∆mK/mK ' 7× 10−15 — huge suppressions
• In SM: ∆mK/mK ∼ α2W |VcsVcd|
2 m2c
m4W
f2K (several small factors)
�� � � � �� � �
� � � �� � �
�
������ �
� � � �� � �
� � � �� � �
��� � �
� ����� �
� �
• Hypothetical particle X:
��
� �
��
��
��
���
� � �� �� � �� � � �
�� �
� �
��
� �� ��
∣∣∣∣∆m(X)K
∆mK
∣∣∣∣ ∼ ∣∣∣∣ g2 Λ3QCD
M2X ∆mK
∣∣∣∣ ⇒ MX
g>∼ 2× 10
3TeV
(The bound from εK is even stronger)
• Measurements probe{
TeV scale with SM-like CKM and loop suppressions∼103 TeV scale with generic flavor structure
Kaon bounds on NP are often the strongest, since so are the SM suppressionsThis has been an input to (and not output from) model building — suppression mechanisms devised to be viable
• We do not know where NP will show up⇒ sensitivity to highest scales is crucial
Z L – p. viii
Example: SUSY in K0 –K0 mixing
• (∆mK)SUSY
(∆mK)exp∼ 10
4
(1 TeV
m
)2 (∆m2
12
m2
)2
Re[(K
dL)12(K
dR)12
](oversimplified)
KdL(R): mixing in gluino couplings to left-(right-)handed down quarks and squarks
• Constraint from εK: replace 104 Re[(Kd
L)12(KdR)12
]with ∼ 106 Im
[(Kd
L)12(KdR)12
]
(44 CPV phases: CKM + 3 flavor diagonal + 40 in mixing of fermion-sfermion-gaugino couplings)
• Classes of models to suppress each terms (structures imposed to satisfy bounds)
(i) Heavy squarks: m� 1 TeV (e.g., split SUSY)
(ii) Universality: ∆m2Q,D� m2 (e.g., gauge mediation)
(iii) Alignment: |(KdL,R)12| � 1 (e.g., horizontal symmetry)
• All models incorporate some of the above — known since the ’70s
Z L – p. ix
The MSSM parameters and flavor
• Superpotential: [Haber, hep-ph/9709450]
W =∑
i,j
(Y uijHuQLiULj + Y d
ijHdQLiDLj + Y `ijHdLLiELj
)+ µHuHd
• Soft SUSY breaking terms: (S = QL,˜DL,
˜UL, LL,˜EL)
Lsoft = −(AuijHuQLi
˜ULj + AdijHdQLi
˜DLj + A`ijHdLLi
˜ELj + BHuHd
)−∑
scalars
(m2S)ij SiSj −
1
2
(M1BB +M2WW +M3gg
)3 Y f Yukawa and 3 Af matrices — 6×(9 real + 9 imaginary) parameters5 m2
S hermitian sfermion mass-squared matrices — 5×(6 real + 3 imag.) param’s
Gauge and Higgs sectors: g1,2,3, θQCD,M1,2,3,m2hu,d
, µ, B — 11 real + 5 imag.
Parameters: (95 + 74) − (15 + 30) from U(3)5 × U(1)PQ × U(1)R → U(1)B × U(1)L
• 44 CPV phases: CKM + 3 in M1,M2, µ (set µB∗,M3 real) + 40 in mixing matrices44 CPV phases: of fermion-sfermion-gaugino couplings (+80 real param’s)
Z L – p. x
History of surprises: CP violation
⇒ Cronin & Fitch, Nobel Prize, 1980
⇒ 3 generations, Kobayashi & Maskawa, Nobel Prize, 2008
Near misses: CP violation
“At that stage the search was terminated by administration of the Lab.”
[Okun, hep-ph/0112031]
