today's menumarco ciuchini page 1 international school niccolò cabeo 2015 – ferrara – may...
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![Page 1: Today's menuMarco Ciuchini Page 1 International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015 Today's menu 1. Indirect searches for New Physics - Effective Field](https://reader035.vdocuments.net/reader035/viewer/2022081622/6135a8050ad5d206764783fa/html5/thumbnails/1.jpg)
Marco Ciuchini Page 1
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
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Marco Ciuchini Page 2
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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”
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Marco Ciuchini Page 3
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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
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Marco Ciuchini Page 4
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 5
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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
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Marco Ciuchini Page 6
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 7
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 8
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
New physics inΔF=2 processes
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Marco Ciuchini Page 9
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 10
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 11
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
CKM matrix in the presence of New Physics
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Marco Ciuchini Page 12
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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Marco Ciuchini Page 13
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
(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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Marco Ciuchini Page 14
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
SM
NP1NP2
NP3
Using: |Vub/Vcb|, g e, Dmd, sin 2b
SM+NP1
NP2+NP3
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Marco Ciuchini Page 15
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
Using: |Vub/Vcb|, g
e, Dmd, sin 2b
a, b, ASL
NP2
SM
SM
NP2
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Marco Ciuchini Page 16
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 17
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 18
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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
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Marco Ciuchini Page 19
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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
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Marco Ciuchini Page 20
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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 Page 21
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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Marco Ciuchini Page 22
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 23
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
* 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
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Marco Ciuchini Page 24
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 25
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
Minimal FlavourViolation
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Marco Ciuchini Page 26
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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)
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Marco Ciuchini Page 27
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 28
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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)
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Marco Ciuchini Page 29
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 30
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 31
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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
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Marco Ciuchini Page 32
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 33
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
Minimal FlavourViolation
at large tanb
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Marco Ciuchini Page 34
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 35
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 36
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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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Marco Ciuchini Page 37
International School Niccolò Cabeo 2015 – Ferrara – May 25th – 29th, 2015
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
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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)
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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)
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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