today's menumarco ciuchini page 1 international school niccolò cabeo 2015 – ferrara – may...

Marco Ciuchini

International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015

Today's menu

1. Indirect searches for New Physics- Effective Field Theory approach and the

“flavour problem”

2. New physics in ΔF=2 transitions- NP amplitudes and generalized CKM fit- EFT analysis

3. Minimal Flavour Violation- EFT & phenomenology- small and large tanβ

Marco Ciuchini


The road toNew Physics

NewPhysicsp

g̃

q̃L

q

q

l̃∓χ̃ 20

χ̃ 10

l± l∓

pStandardModel

-- the “energy frontier”-- the “intensity frontier”-- the “cosmic frontier”

“The space detour”

“The relativistic highway”

“The quantum path”

Marco Ciuchini


Indirect searches look for new physics through virtual effects of new particles in loop corrections

* SM FCNCs and CP-violating processes occur at the loop level

* SM quark FV and CPV are governed by the weak interactions and suppressed by small mixing angles

* SM quark CPV comes from a single source (neglecting θQCD)

New Physics does not necessarily share the SM pattern of FV and CPV: very large NP effects are possible

Beyond the SM with flavour physics: why?

Past (SM) successes: 1970: charm from K0 →+- (GIM) 1973: 3rd generation from єK (Kobayashi & Maskawa)

80s-90s: heavy top from ∆mB

Marco Ciuchini


Flavour physics confronts NP searchesThe problem of today particle physics: where is the NP scale ΛNP? 0.5, 1, 10, 1013, 1016 TeV?

The quantum stabilization of the weak scale suggests ≤ 1 TeV (naturalness argument)

Standard Model

E (GeV)

ΛQCD ΛEW ΛNP ΛGUT ΛPlank

1 102 ? 1016 1019⇦MWIMP

MR⇨

* LHC searches in this range...

mH2 mH

2 mH2

mH2=

3G F

22 mt2NP

2~0.3 NP

2

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Two approaches

* Effective field theory (bottom-up)- correlations are not fully included- results up to O(1) unknown coefficients- not always viable/useful

* Explicit model (top-down)- full correlations among observables- fully calculable- possibly (likely?) wrong

Marco Ciuchini


ℒeff=ℒSM +∑k(∑i Cik Qi

(k+4))/Λk

EFT approach to New Flavour Physicsa game of scale and couplings

NP flavour effects are governed by two players: ii) the value of the new physics scale Λii) the effective flavour-violating couplings C's

In explict models:Λ ~ mass of virtual particles (Fermi th.: MW) C ~ loop coupling x flavour coupling

(SM/MFV: w x CKM)

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Pictorially : - exp. constraints give a bound on Λ for any given C and vice-versa - curves correspond to different assumptions on C

Λ

excl

uded

CAnticipating today's discussion:- NP scales < 1 TeV produces far too large

FCNC and CP violation for natural flavour couplings: the so-called “flavour problem”

- A prototype solution in EFT: the class of models with Minimal Flavour Violation

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New physics inΔF=2 processes

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New Physics in the mixing amplitudes

1. find out how much room is left for NP in ΔF=2 transitions

- add most general NP to all sectors- use all available experimental info

- fit simultaneously for the CKM andthe NP parameters (generalized UT fit)

2. perform an EFT analysis to putbounds on the NP scale

- consider different choices of the FVand CPV couplings UTfit collaboration

hep-ph/0509219, arXiv:0707.0636

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1. parameterization of NP contributionsto the mixing amplitudes

K mixing amplitude (2 real parameter):

Bd and Bs mixing amplitudes (2+2 real parameters):

ReAK=CmKReAK

SM ImAK=C ImAKSM

Aqe2iq =CBq

e2iBqAq

SMe2iqSM

= 1 AqNP

AqSM e

2iqNP−q

SM AqSMe2i q

SM

ΦdSM = -β, Φs

SM = βs

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CKM matrix in the presence of New Physics

Marco Ciuchini


Marco Ciuchini


(1) 3-generations unitarity(2) no new physics in tree-level processes

Assumptions:

Using only tree-level: g and |Vub/Vcb|. Results:

In any NP model, theseconstraints must be satisfied

UTfit coll., hep-ph/0501199;Botella et al., hep-ph/0502133

Checking the Unitarity Clock

r = 0.134 0.049

h = 0.368 0.050

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SM

NP1NP2

NP3

Using: |Vub/Vcb|, g e, Dmd, sin 2b

SM+NP1

NP2+NP3

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Using: |Vub/Vcb|, g

e, Dmd, sin 2b

a, b, ASL

NP2

SM

SM

NP2

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UT parameters in the presence of NP

Model-independent fitof the CKM parameters

(neglecting NP in tree decays)

In the SM is:ρ = 0.159 ± 0.045 η = 0.363 ± 0.049

--

l = 0.2253 ± 0.0009A = 0.802 ± 0.02

ρ = 0.159 ± 0.045 η = 0.363 ± 0.049

--

l = 0.2253 ± 0.0009A = 0.802 ± 0.02

ρ = 0.132 ± 0.023

η = 0.352 ± 0.014

--

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Ce = 1.05±0.16 CBd = 1.07±0.17 fBd [°] = -2.0±3.2

SM SMSM

Constraints on NP parameters

CBs = 1.05±0.08 fBs [°] = 0.7±2.1

SMSM

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In general: ANP/ASM ~ 10-20% @ 95% prob.more when NP is aligned to SM

Sizeable NP contributions toDF=2 transitions still allowed

Bounds on ANP/ASM and fNP

Aqe2iϕq =( 1+Aq

NP

AqSM e

2i(ϕqNP−ϕq

SM)) AqSMe2iϕq

SM

ΦdSM = -β, Φs

SM = βs

Marco Ciuchini


Q 1=q L b L

q L b L

(SM/MFV)

Q 2=q R b L

q R b L

Q 3=q R b L

q R b L

Q 4=q R b L

q Lb R

Q 5=q R b L

q Lb R

Q 1=q R b R

q R

b R

Q 2=q Lb R

q Lb R

Q 3=q Lb R

q Lb R

2. the ΔF=2 effective Hamiltonian

7 new operators beyond SM/CMFV involvingquarks with different chiralities

H eff B=2

=∑i=1

5

C i Qi ∑i=1

3

C i Qi

Aq e2iq=⟨M q∣H eff

F=2∣M q⟩The mixing amplitudes

Marco Ciuchini


Heff can be recast in terms of the high-scale Ci(L)

- Ci(L) can be extracted from the data (one by one)- the associated NP scale L can be defined as

= LF i

C i

Generic FV

- |Fi| ~ 1- arbitrary phases

tree/strong interact. NP: L ~ 1perturbative NP: L ~ as

2, aW

2

MFV

- F1 = FSM~ (VtqVtb*)2

- Fi1 = 0

Flavour structures:

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Marco Ciuchini


Lower bound on the NP scale from ΔF=2 transitions (TeV @95%)

FC~1 FC~SM

Λ (TeV) K D Bd Bs

FC~1 5x105 3.5x104 3.3x103 880FC~SM 113 8.5 21 27

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* ΔF=2 chirality-flipping operators are RGenhanced and thus probe larger NP scales

* when these operators are allowed, the NP scale is easily pushed beyond the LHC reach

(manifestation of the flavour problem)

* suppression of the 1 2 transitions strongly ↔weakens the lower bound on the NP scale

Marco Ciuchini


ΔF=2 processes occur at the loop level,thus could receive O(1) NP corrections

but effects > ~20% are excluded

Does this result point to MFV?(or even establishes MFV)

NP scale ~ O(1 TeV)* suppression of flavour- violating couplings required in all sectors possibly pointing to MFV

* stabilizing the Fermi scale requires “mild” fine-tuning

NP scale ~ O(10-100 TeV)* suppression of flavour- violating couplings needed in sector 1-2 only. No strong indication of MFV

* stabilizing the Fermi scale requires “moderate” fine-tuning

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Minimal FlavourViolation

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ℒSM=ℒgauge+ℒHiggs+ℒYukawa

Minimal Flavour Violation (i)

ℒgauge+ℒHiggs invariant under the global symmetry

U (3)5=U (3)QL×U (3)U R

×U (3)D R× .. .

ℒYukawa= QL YU UR+QL YD DR+... is formallyinvariant if YU = (3,3,1) and YD= (3,1,3) (spurions)

_ _~- -

MFV hypothesis: NP operators (built out of theSM fields and spurions) must be

invariant under the global symmetry

D'Ambrosio et al., NPB645 (2002)

Marco Ciuchini


Minimal Flavour Violation (ii)

Basis choice:

Neglecting all diagonal Yukawa couplings but Ytop, the only off-diagonal flavour structure is YuYu

†

- flavour-changing transitions in the up sector are suppressed

- flavour-changing transitions in the down sectorare governed by

powers of YuYu† are proportional to FC

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Minimal Flavour Violation (iii)

All flavour-invariant dimension-six operators built out of quark fields and one Higgs doublet:

Two basic bilinears:

ΔF=1

ΔF=2

D'Ambrosio et al., NPB645 (2002)

Marco Ciuchini


Minimal Flavour Violation (iv)After EW-symmetry breaking and using the EOM

- SM operators only: 6 QCD penguins, 4 EW penguins, 2 (chromo-) magnetic-dipole, 3 quark-lepton + 1 ΔF=2 operator

- flavour-violating couplings fixed by the MFVassumption, while the NP scale is unknown

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Minimal Flavour Violation (v)

- unknown real, O(1) Wilson coefficients a's shift the SM Inami-Lim functions

- MFV NP corrections to different flavoursectors are correlated

In terms of flavour-changing amplitudes:

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Comparing with flavour data, one can put a lower bound on the NP scale and make

predictions for channels not measured yet

- the ΔF=2 operator contributes to mixing amplitudes giving Mloop> 200 GeV (Λ>5.5 TeV)

- (chromo-) magnetic dipole operators contribute to B X→ s giving Mloop> 450 GeV (Λ>12 TeV)

- quark-lepton operators contribute to B X→ s l+l- giving Mloop> 100 GeV (Λ>3 TeV)

- EWP operators contribute to B K→ π and ℇ'/ℇ with no significant bounds

- sensitivity to NP of QCD penguin operators is reduced by the mixing with Q1 and Q2

Marco Ciuchini


MFV: upper bounds on the deviationsfrom the SM

Bobeth et al., hep-ph/0505110

- maximum effects in FCNC are O(10%) or less- hardly detectable given the SM uncertainties and

experimental errors- correlations among flavour sectors might help

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Minimal FlavourViolation

at large tanb

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MFV at large tanβ (i)Two Higgs doublets:

U(1) symmetry avoids tree-level FCNC: Hd d,e H↔ u u ↔

U(1) cannot be exact: U(1)-breaking terms are generated

additional spurion,non-negligible for

large tanβ ~20-60

O(1) corrections to FCNC arise for εi tanβ ~ O(1)

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MFV at large tanβ (ii)An additional rotation is required to diagonalizedown-type masses

Masses and off-diagonal terms (including the CKM matrix) in the down sector get O(1) corrections

Formally the up sector is modified in the same way, but corrections are not tanβ-enhanced

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MFV at large tanβ (iii)After the diagonalization:

- tree-level exchange of heavy neutral Higgsesmediate loop-generated, but tanβ-enhancedscalar FCNC interactions

- charged Higgs FCNC receive O(1) corrections for large tanβ

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MFV at large tanβ (iv)New non-negligible flavour-violating structures

ΔF=1:

ΔF=2:

new bilinears contributing to b transitions → B and K physics are no longer correlated

1.

2.new FC scalar operator

suppressed by a light quark mass

Marco Ciuchini


The four musketeers of large tanβ

∝ tan4β ∝ tan6β ∝ mstan2β ∝ tan2β,tan3β

Large deviations from the SMwith a definite pattern are possible…

for MH=0.5 TeV & tanβ=50

Isidori, Paradisi, hep-ph/0605012

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… but not found in the data

Misiak et al., hep-ph/0609232

ΔmsB→ Bs→

B X→ sg

Agreement with the SM at the ~1.5s level

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No new sources of flavourand CP violation beyond the SM

- NP contributions governed by SM Yukawa couplingsex.: small-tanβ CMSSM and mSUGRA, Universal χDim, LHM

- NP only modifies SM top contribution to FCNC & CPVunless other Yukawa couplings are enhanced; for examplelarge tanβ in 2HDM enhances bottom contributions

1HDM/2HDM at small tanbsame operators as in Heff

SM

NP in K and B correlatedsmall effects < O(10%)

2HDM at large tanbnew operators wrt Heff

SM

NP in K and B uncorrelatedlarge effects excluded

Minimal Flavour Violation Summary

Chivukula,Giorgi, PLB188(1987)Hall,Randall, PRL65 (1990)

Gabrielli,Giudice, NPB433 (1995)Gabrielli,MC,Giudice, PLB388 (1998)

Buras et al., NPB500 (2001)D'Ambrosio et al., NPB645 (2002)

Marco Ciuchini


Messages from this lecture (i)

1.large NP contributions to FCNC and CP violation are “natural” for NP at the TeV scale – the “flavour problem”

2.the CKM matrix can be determined in the presence of NP with O(10-20%) accuracy – crucial tool for NP searches

3.NP amplitudes contributing to B and K mixing can be O(10-20%) of the SM amplitudes at most (unless they are aligned)

Marco Ciuchini


Messages from this lecture (ii)

4.MFV can be defined using the flavour symmetry of the SM as a guiding principle. It solves the flavour problem, if it is there

5.MFV models with 1 HD (2 HD with small tanβ) predict highly correlated, but <10% corrections. Experimentally challenging

6.2HDM MFV models at large tanβ predict a possible pattern of measurable corrections, unfortunately not found in the data

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