general flavor theory - slac indico (indico) · gudrun hiller, tu dortmund 1. general flavor theory...

SLAC, Menlo Park, SSI – August 12+13, 2019

General Flavor Theory

”flavor 2019: (still) puzzling and great opportunity”

Gudrun Hiller, TU Dortmund

1

General Flavor Theory SSI 2019 Slide 2

symmetry, and symmetry-breaking (the same yet not the same)


The Standard Model of Particle Physics

renormalizable QFT in 3+1 Minkowski space w. local symmetry

SU(3)C × SU(2)L × U(1)Y → SU(3)C × U(1)em

LSM = −14F 2 + ψi6Dψ + 1

2(DΦ)2 − ψY Φψ︸︷︷︸

Y ukawa interact.

+µ2Φ†Φ− λ(Φ†Φ)2

ψ: fermions (quarks and leptons) Dµ = ∂µ − ieAµ + . . .

Fµν : gauge bosons ga, γ, Z0,W±

Φ: Higgs doublet

Known fundamental matter comes in generations

ψ → ψi, i = 1, 2, 3,

subject to identical gauge transformations. ”universality”, hard-wired.


They are not the same

Fields in representations under the SM SU(3)C × SU(2)L × U(1)Y

Higgs: Φ(1, 2, 1/2) hypercharge Y = Q− T3

quarks: QL(3, 2, 1/6)i, DR(3, 1,−1/3)i, UR(3, 1, 2/3)i

leptons: LL(1, 2,−1/2)i, ER(1, 1,−1)i L: doublet, R:singlet under SU(2)L

labelled with increasing mass, distinguished by ’flavor’ (mass andmixing, i.e. CKM (quarks), PMNS (leptons)

QL =

u

d

,

c

s

,

t

b

, UR = uR, cR, tR, DR = dR, sR, bR

LL =

νe

e

,

νµ

µ

,

ντ

τ

, ER = eR, µR, τR


Flavor in the Standard Model

Flavor in the SM is sourced only by the Yukawa interactions:

LSM =∑

ψ=Q,U,D,L,E ψii 6Dψi−QLi(Yu)ijΦ

CURj − QLi(Yd)ijΦDRj − LLi(Ye)ijΦERj+Lhiggs + Lgauge, ΦC = iσ2Φ∗

Yu,d,e: Yukawa matrices (3× 3, complex)different Yukawa→ different mass from vev 〈Φ〉 etcoff-diagonal entries open up possibility to mix generations

direct link with Higgs physics: h→ ψψ probes Yu,d,e, flavor!

Program: determine flavor parameters (in SM)


Quark SpectrumLength [m]

10−18 –

10−15 –

10−12 –

10−9 –

10−6 –

–

–

–

–

–

–

–

–

–

nano

visible light

Bohr-Radius

Energy Mass

ΛQCD–

EDeuteron–

ERydberg–

ΛEWK– W Z

2 eV–

t

bτ c

µ s

u de

particle physics

atomic, nuclear physic

mu (2 GeV) md (2 GeV) ms (2 GeV)

2.8± 0.6 MeV 5.0± 1.0 MeV 95± 15 MeV

mc (mc) mb (mb) mt (mt)

1.28± 0.05 GeV 4.22± 0.05 GeV 163± 3 GeV

Spectrum spans five orders of magnitude.


Flavor puzzle

Experimentally (if rotated solely to up-sector)

Yu ∼

10−5 −0.002 0.008 + i 0.003

10−6 0.007 −0.04

10−8 + i 10−7 0.0003 0.94

Yd ∼ diag(10−5, 5 · 10−4, 0.025

)

Ye ∼ diag(10−6, 6 · 10−4, 0.01

)

diag (a,b)=(

a 0

0 b

)

Quark mixing is hierarchal, as well as quark and charged leptonmasses.

Why? ideas, no ”SM” nowhere near, needs BSM to progress


Flavor change

ψ → ψi, i = 1, 2, 3 sounds simple but implies rich phenomenology:flavor change (within same and other generations), CP violation,meson mixing, ...SM flavor change only through weak interaction among left-handedfermions:

Vij = (VCKM)ij. Product of up and down unitary matrices V = VuV†d ,

derived from Yu,d (diagonalization). Not physical each in SM.


Insert: Getting CKM from scratch

Masses from spontaneous breaking of electroweak symmetryΦT (x)→ 1/

√2(0, v + h(x)), Higgs vev 〈Φ〉 = v/

√2 ' 174 GeV

LyukawaSM = −QLYuΦCUR − QLYdΦDR − LLYeΦER

Want mass eigenstates rather than gauge eigenstates QUDLE:perform unitary trafos on quark fields QL = (UL, DL), UR, DR

qA(mass) = VA,q qA(gauge) with VA,qV†A,q = 1, A = L,R, q = u, d.

The 4 unitary matrices VA,q are determined by

diag(mu,mc,mt) = 〈Φ〉 · diag(yu, yc, yt) = 〈Φ〉 · VL,uYuV †R,udiag(md,ms,mb) = 〈Φ〉 · diag(yd, ys, yb) = 〈Φ〉 · VL,dYdV †R,d

i.e., they diagonalize the Yukawas.


CKM from scratch

insert unit matricesLyukawaSM = −UL V †L,uVL,u︸︷︷︸

=1

YuΦC V †R,uVR,u︸︷︷︸

=1

UR + down quarks.

then rewrite term and split upLup−massSM = − ULV †L,u︸︷︷︸

≡ ¯UL

VL,uYuV†R,u︸︷︷︸

diagonal

ΦC VR,uUR︸︷︷︸≡UR

= − ¯ULimui ΦCURi.

The tilde basis are mass eigenstates, down quarks analogously.

What else happened under the basis change in LSM?Lets look at the charged currents W±:

ULγµW+

µ DL = UL (V †L,uVL,u) γµW+µ (V †L,dVL,d) DL

= ¯ULγµW+

µ VL,uV†L,d︸︷︷︸

≡VCKM=V 6=1

DL; Since quarks mix, VL,u 6= VL,d.


CKM

The charged current interaction gets a flavor structure by V

LCC = − g√2

(¯ULγ

µW+µ V DL + ¯DLγ

µW−µ V

†UL

).

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

, V13 = Vub etc

Via W exchange is the only way to change flavor in the SM. SinceCKM is known (more or less precise, see talks), in SM every quarkflavor changing process can be predicted! (TH uncertainties play aninportant role, see talks on hadronic matrix elements).Overconstrain, fits (see talks!)


The Standard Model: CKM properties

V is unitary, is in general complex, and induces CP violationV has 4 physical parameters, 3 angles and 1 phase.

”PDG” parametrization (exact, fully general)

V =

c12c13 s12c13 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13e

iδ s23c13

s12s23 − c12c23s13eiδ −c12s23 − s12c23s13e

iδ c23c13

sij ≡ sin Θij, cij ≡ cos Θij. δ is the CP violating phase.In Nature, δ ∼ O(1) and V is hierarchical Θ13 � Θ23 � Θ12 � 1.Very different – large mixing angles for leptons (PMNS-Matrix):

Θ23 ∼ 45◦, Θ12 ∼ 35◦, Θ13 ∼ O(10◦) all O(1) – anarchy?


CP is violated!.. together with Quark Flavor

Quark mixing matrix has 1 physical CP violating phase δCKM .

Verified in BB mixing sin 2β = 0.672± 0.023 HFAG Aug 2010

δCKM is large, O(1)!

CPX also observed in B-decay ACP (B → K±π∓) = −0.098± 0.013

HFAG Aug 2010

Γ(B → K+π−) 6= Γ(B → K−π+)


Charm is the new Beauty

Betti

∆ACP = ACP (D0 → K+K−)− ACP (D0 → π+π−)


The CKM numerics you can memorize

V is hierarchical Θ13 � Θ23 � Θ12 � 1. Wolfensteinparametrization: expansion in λ = sin ΘC ∼ 0.2, A, ρ, η ∼ O(1)

V =

1− λ2/2 +λ Aλ3(ρ− iη)

−λ 1− λ2/2 +Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4)

beyond lowest order ρ = ρ(1− λ2/2) and η = η(1− λ2/2)

VCKMV†CKM = 1 C = (0, 0) B = (1, 0)

A = (¯, η)

γ β

α∣∣∣∣∣∣∣

VudV∗ub

VcdV∗cb

∣∣∣∣∣∣∣

∣∣∣∣∣∣∣

VtdV∗tb

VcdV∗cb

∣∣∣∣∣∣∣

!

!

"

"

dm#K$

K$

sm# & dm#

ubV

%sin 2

(excl. at CL > 0.95) < 0%sol. w/ cos 2

excluded at CL > 0.95

"

%!

&-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

'

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5excluded area has CL > 0.95

FPCP 13

CKMf i t t e r


Neutral Currents – a window beyond SM

Neutral current gauge interactions γ, Z, g remain unaffected bymisalignement between gauge and mass bases in SM because ofψ → ψi (universality) since they involve the same fields, for instance:ULγ

µAµUL = UL (V †L,uVL,u) γµAµ (V †L,uVL,u) UL

= ¯ULγµAµVL,uV

†L,uUL = ¯ULγ

µAµUL nothing has happend!

Imagine a BSM U(1)′ with generation-dependent charges gi:Ui giγ

µAµUi = ¯UiγµAµ(Vu)ijgj(V

†u )jkUk

Consider 2 generations, Vu orthogonal with mixing angle ϑu between1st and 2nd generation Vu =

(cosϑu sinϑu

− sinϑu cosϑu

)

We obtain FCNC ”flavor changing neutral current” amplitudes

cosϑu sinϑu(g1 − g2) ¯U1γµAµU2


Neutral Currents

FCNC ”flavor changing neutral current” U2 → U1 drop the tilde for mass eigenstates

cosϑu sinϑu(g1 − g2)U1γµAµU2

i) no tree-level FCNC in the SM or other models with universality,where g1 = g2 etc holds.

individual rotations ϑu, ϑd in SM not physical, only V = VLuV†Ld, no

contraint on VRu, VRd.

ii) FCNCs have sensitivity to a) BSM physics and b) origins of flavor(up versus down, it could be that mixing comes only from up-sectorand ϑd = 0)


Exploring Physics at Highest Energies

Length [m]

10−18 –

10−15 –

10−12 –

10−9 –

10−6 –

–

–

–

–

–

–

–

–

–

nano

visible light

Bohr-radius

Energy

ΛQCD–

EDeuteron–

ERydberg–

h

SM/BSM ?

ΛEWK– W Z

2 eV–

t

bτ c

µ s

u de

particle physics

atomic,nuclear physics


Testing the SM with flavor

In SM neutral currents conserve flavor. However, charged currentsinduce FCNCs through quantum loops.

b su, c, t

W±

The upper figure shows an FCNC with flavor number changing inunits of one, ∆F = 1, as in decays, meson mixing has ∆F = 2.


Testing the SM with flavor

Different sectors/couplings presently probed with FCNCs:

s→ d: K0 − K0, K → πνν

c→ u: D0 − D0, ∆ACP , D → π(π)µµ, D → ργ

b→ d: B0 − B0, B → ργ, b→ dγ, B → πµµ

b→ s: Bs − Bs, b→ sγ, B → Ksπ0γ, b→ sll, B → K(∗)ll (precision,

angular analysis, universality), Bs → µµ

t→ c, u, l→ l′: not observed

in red: hot topics

”leaving no stone unturned” (see talks & lectures)


Flavor Changing Neutral Currents

Lets discuss a generic SM FCNC b→ s amplitude

b su, c, t

W±

A(b→ s)SM = VubV∗usAu + VcbV

∗csAc + VtbV

∗tsAt

quantum loop effect induced by weak interaction. Aq = A(m2q/m

2W ).

with CKM unitarity V V † = 1, specifically∑i VibV

∗is = 0:

A(b→ s)SM = VtbV∗ts(At − Ac) + VubV

∗us(Au − Ac)

A vanishes for trivial CKM matrix or if quarks in loop are degenerate.

A(b→ s)SM = VtbV∗ts︸︷︷︸

λ2

(At − Ac) + VubV∗us︸︷︷︸

λ4

(Au − Ac)

amplitude is dominated by first term because of lesser CKM


Flavor Changing Neutral Currents

suppression and because the GIM (Glashow Iliopoulos Maiani)suppression inactive for tops m2

t−m2c

m2W∼ O(1), whereas m2

u−m2c

m2W� 1.

We probe top properties with rare b-decays despite of mt � mb.

CP violation requires interference between the two terms withdifferent phases; for b→ s, this is small, O(λ2).

Generic SM FCNC c→ u amplitudeA(c→ u)SM = V ∗cdVudAd + V ∗csVusAs + V ∗cbVubAb, Aq = A(m2

q/m2W ).

A(c→ u)SM = V ∗cdVud︸︷︷︸−λ

(Ad − Ab) + V ∗csVus︸︷︷︸+λ

(As − Ab) A is

GIM-suppressed; CP violation is suppressed by V ∗cbVubV ∗cdVud

∼ λ4. Verysensitive to corrections beyond the SM. How about∆ALHCbCP ' −1.5 · 10−3 ?


Flavor Changing Neutral Currents in SM

i FCNCs are induced by the weak interaction thru loops.ii FCNCs require V 6= 1.iii FCNCs vanish for degenerate intermediate quarks. Since masssplitting among up-quarks is larger than for down quarks, GIMsuppression is larger with external up-type than down-type quarks.

B(b→ sγ) = 3 · 10−4 (Eγ > 1.6 GeV)

B(b→ sl+l−) = 4 · 10−6 (m2ll > 0.04 GeV2)

SM: B(t→ cg) ∼ 10−10, B(t→ cγ) ∼ 10−12, B(t→ cZ) ∼ 10−13,B(t→ ch) <∼ 10−13 Eilam, Hewett, Soni ’91/99

Lepton flavor violation (LFV) in SM arises through finite neutrinomasses which is so small that LFV observables are ”null tests”.


Flavor Changing Neutral Currents in SM

We see that 3 mechanisms suppress FCNCs in SM: CKM, GIM andabsence at tree level. New physics, which doesnt need to sharethese features, competes with small SM background!

FCNCs feel physics in the loops from energies much higher than theones actually involved in the real process.

They are very useful to look for new physics, in fact, we already nowa lot about new physics from FCNCs!

K0K0 D0D0 B0dB

0d B0

s B0s

ΛNP [TeV] 2 · 105 5 · 103 2 · 103 3 · 102

Table 1: The lower bounds on the scale of new physics from FCNCmixing data in TeV for arbitrary new physics at 95 % C.L.


Sensitivity, Reach, Strategy

Besides statistics, BSM reach is limited by theoretical uncertainties,dominated by hadronic physics.

Use approximate symmetries of SM to improve here: (key in charm,useful in beauty)

– GIM D → ππµ+µ−

– Isospin, or U-spin ∆ACP

– CP ∆ACP , Bs-mixing

– V-A , helicity P ′5

– LFV

– universality RK , RK∗


b→ s`` FCNCs model-independently

Construct EFT Heff = −4GF√2VtbV

∗ts

∑i Ci(µ)Oi(µ) at dim 6

V,A operators O9 = [sγµPLb] [¯γµ`] , O′9 = [sγµPRb] [¯γµ`]

O10 = [sγµPLb] [¯γµγ5`] , O′10 = [sγµPRb] [¯γµγ5`]

S,P operators OS = [sPRb] [¯ ] , O′S = [sPLb] [¯ ] , ONLY O9, O10 are SM, all other BSM

OP = [sPRb] [¯γ5`] , O′P = [sPLb] [¯γ5`]

and tensors OT = [sσµνb] [¯σµν`] , OT5 = [sσµνb] [¯σµνγ5`]

lepton specific CiOi → C`iO

`i , ` = e, µ, τ


Lepton Non-universality?

νe

e

,

νµ

µ

,

ντ

τ

Anomalies in semileptonic B-meson decays:RK = B(B→Kµµ)

B(B→Kee) 2.6σ (LHCb’14,19)

RK∗ = B(B→K∗µµ)B(B→K∗ee) 2.6σ (LHCb’17)

RD(∗) = B(B→D(∗)τντ )

B(B→D(∗)`ν`)∼ 2.7σ (D∗), ∼ 2σ (D)

(LHCb’15,B-factories)


LNU in b→ s FCNCs

RH = B(B→Hµµ)B(B→Hee) , H = K,K∗, Xs,Φ, ...

In models with lepton universality (incl. SM): RH = 1+tiny GH, Kruger ’03

LHCb SMB(B → Kµµ)[1,6] (1.21± 0.09± 0.07) · 10−7 (1.75+0.60

−0.29) · 10−7

B(B → Kee)[1,6] (1.56+0.19+0.06−0.15−0.04) · 10−7 same

RK |[1,6] 0.745±0.0900.074 ±0.036 ' 1


Impact on model building

ψi may be more different than we thought

model space 2002��

��

MSSM MFV

MSSM MFV

low tan large tan

supersoft

effective SUSYβ β

new physics in B data

SUSY breakingdirac gauginos

ED w. SM on

little Higgs w.

SM like B physics

generic Little Higgs

generic ED w. SM in bulk

SUSY GUTs

brane

MFV UV fix

2002: top-down models plot from hep-ph/0207121

2018,19: U(1)-extensions, leptoquarks,...

theory activities how to get these from UV-models 1708.06450, 1708.06350,

1706.05033, 1808.00942 .. see talks during this school!


The situationWe are seeing ∼ 2.6σ hints of new physics in b→ sll, LNU betweene’s and µ’s in both observables RK and RK∗ LHCb ’14, ’17,

RH = B(B→Hµµ)

B(B→Hee) , same cuts e and mu, H = K,K∗, Xs, ...

Lepton-universal models (incl. SM): RH = 1+tiny GH, Kruger, hep-ph/0310219

How can we go on, consolidate and decipher this effect?

1. Which operators are responsible for the deviation? 1411.4773

2. BSM in electrons, or muons, or in both?

3. Side effects from flavor: LFV, τ ’s, or SU(2): ν’s 1411.0565 , 1412.7164,

1503.01084 Charm and Kaons

4. Collider implications (leptoquarks!)


general flavor theory - slac indico (indico) · gudrun hiller, tu dortmund 1. general flavor theory...

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