Download - G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries
![Page 1: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/1.jpg)
Guido MartinelliSISSA & INFN
From the Standard Model to DarkMatter and beyond: Symmetries,Masses and Misteries
NIS, Serbia 29/08/2011
![Page 2: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/2.jpg)
Plan of the Talk
1) The UT analysis within the SM2) Beyond the SM: the case of Bs3) Outlook
![Page 3: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/3.jpg)
Lquarks = Lkinetic + Lweak int + Lyukawa
In the Standard Model the quark massmatrix, from which the CKM Matrix andCP originate, is determined by the YukawaLagrangian which couples fermions andHiggs
CP invariant
CP and symmetry breaking are closely related !
![Page 4: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/4.jpg)
Two accidental symmetries:
Absence of FCNC at tree level (& GIMsuppression of FCNC in quantum effects @loops)
NO CP violation @tree level
Flavour Physics is extremely sensitiveto new physics
![Page 5: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/5.jpg)
QUARK MASSES ARE GENERATED BY DYNAMICAL SYMMETRY BREAKING
Charge -1/3 ∑i,k=1,N [ mu
i,k (uiL uk
R )
+ mdi,k (di
L dkR) + h.c. ]
Charge +2/3
Lyukawa ≡ ∑i,k=1,N [ Yi,k (qi
L HC ) UkR
+ Xi,k (qiL H ) Dk
R + h.c. ]
![Page 6: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/6.jpg)
Diagonalization of the Mass Matrix Up to singular cases, the mass matrix can always be
diagonalized by 2 unitary transformationsui
L UikL uk
L uiR Uik
R ukR
M´= U†L M UR (M´)† = U†
R (M)† ULLmass ≡ mup (uL uR + uR uL ) + mch(cL cR + cR cL )
+ mtop(tL tR + tR tL )
![Page 7: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/7.jpg)
N(N-1)/2 angles and (N-1)(N-2) /2 phases
N=3 3 angles + 1 phase KMthe phase generates complex couplings i.e. CPviolation;6 masses +3 angles +1 phase = 10 parameters
Vud Vus Vub
Vcd Vcs Vcb
Vtb Vts Vtb
![Page 8: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/8.jpg)
CP Violation is natural with three quarkgenerations (Kobayashi-Maskawa)
With three generations all CPphenomena are related to the same
unique parameter ( δ )
NO Flavour Changing Neutral Currents (FCNC)at Tree Level
(FCNC processes are good candidates forobserving NEW PHYSICS)
![Page 9: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/9.jpg)
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
Quark masses &Generation Mixing
NeutronProton
νe
e-
downup
W
| Vud |
| Vud | = 0.9735(8)| Vus | = 0.2196(23)| Vcd | = 0.224(16)| Vcs | = 0.970(9)(70)| Vcb | = 0.0406(8)| Vub | = 0.00409(25)| Vtb | = 0.99(29) (0.999)
β-decays
![Page 10: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/10.jpg)
1 - 1/2 !2 ! A !3(" - i #)
- ! 1 - 1/2 !2 A !2
A !3 $
(1- " - i #) -A !2 1
+ O(λ4)
The Wolfenstein Parametrization
λ ~ 0.2 A ~ 0.8 η ~ 0.2 ρ ~ 0.3
Sin θ12 = λSin θ23 = A λ2
Sin θ13 = A λ3(ρ-i η)
Vtd
Vub
![Page 11: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/11.jpg)
a1
a2
a3
b1
b2
b3
d1
e1
c3
The Bjorken-Jarlskog Unitarity Triangle| Vij | is invariant under
phase rotationsa1 = V11 V12
* = Vud Vus*
a2 = V21 V22* a3
= V31 V32*
a1 + a2 + a3 = 0(b1 + b2 + b3 = 0 etc.)
a1
a2a3
α β
γOnly the orientation dependson the phase convention
![Page 12: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/12.jpg)
Physical quantities correspond to invariantsunder phase reparametrization i.e.|a1 |, |a2 |, … , |e3 | and the area of theUnitary Triangles
a precise knowledge of themoduli (angles) would fix J
Vud*Vub+ Vcd
* Vcb+Vtd
* Vtb = 0
CP ∝ J
J = Im (a1 a2 * ) = |a1 a2 | Sin β
Vud*Vub Vtd
*Vtb
Vcd*Vcb
α
γ βγ = δCKM
![Page 13: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/13.jpg)
13
VubVud+ VcbVcd+VtbVtd = 0* **
![Page 14: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/14.jpg)
From A. StocchiICHEP 2002
![Page 15: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/15.jpg)
For details see:UTfit Collaboration
http://www.utfit.org
![Page 16: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/16.jpg)
sin 2β is measured directly from B J/ψ Ksdecays at Babar & Belle
Γ(Bd0 J/ψ Ks , t) - Γ(Bd
0 J/ψ Ks , t)AJ/ψ Ks =Γ(Bd
0 J/ψ Ks , t) + Γ(Bd0 J/ψ Ks , t)
AJ/ψ Ks = sin 2β sin (Δmd t)
![Page 17: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/17.jpg)
DIFFERENT LEVELS OF THEORETICALUNCERTAINTIES (STRONG INTERACTIONS)
1) First class quantities, with reduced or negligible theor.uncertainties
2) Second class quantities, with theoretical errors of O(10%)or less that can be
reliably estimated
3) Third class quantities, for which theoretical predictionsare model dependent (BBNS, charming, etc.)
In case of discrepacies we cannottell whether is new physics orwe must blame the model
![Page 18: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/18.jpg)
K0 - K0
mixing
UnitaryTriangle SM
B0d,s - B0
d,s mixing Bd Asymmetry
2005
semileptonic decays
![Page 19: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/19.jpg)
Classical Quantities used in the Standard UT Analysis
beforeonly a lower bound
Inclusive vs ExclusiveOpportunity for lattice QCDsee later
Vub/Vcb εK Δmd Δmd/Δms
levels @68% (95%) CL
f+,F
BK
fBBB1/2 ξ
![Page 20: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/20.jpg)
New Quantities used in the UT Analysis
sin 2β cos 2β α γ sin (2β + γ)
B→J/Ψ K0 B→J/Ψ K*0 B→ππ,ρρ B→D(*)K B→D(*)π,Dρ
![Page 21: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/21.jpg)
![Page 22: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/22.jpg)
![Page 23: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/23.jpg)
![Page 24: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/24.jpg)
Repeat with several fCP final states
![Page 25: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/25.jpg)
THECKM
![Page 26: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/26.jpg)
Global Fit within the SM SM Fit
CKM matrix is the dominant source of flavour mixing and CP violation
In thehadronicsector,the SMCKMpatternrepresentstheprincipalpart of theflavourstructureand of CPviolation
ρ = 0.132 ± 0.020
η = 0.353 ± 0.014
Consistence on anover constrained fit
of the CKM parameters
α = (88 ± 3)0
sin2β = 0.695 ±0.025??
β = (22 ±1)0
γ= (69 ± 3)0
![Page 27: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/27.jpg)
Vincenzo Vagnoni ICHEP 06, Moscow, 28th July 2006
The The UT-angles fit does not depend UT-angles fit does not depend onontheoretical calculations theoretical calculations ((treatement treatement ofof
errors is not an issueerrors is not an issue))
η = 0.340± 0.016
η = 0.404 ± 0.039
ANGLES VS LATTICE 2011
ρ = 0.129 ± 0.027
Still imperfectagreement in η dueto sin2β and Vubtension
Comparable accuracydue to the precise sin2βvalue and substantialimprovement due tothe new Δmsmeasurement
Crucial to improvemeasurements of theangles, in particular γ(tree level NP-freedetermination)
UT-angles UT-lattice
ρ = 0.155 ± 0.038
![Page 28: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/28.jpg)
SM predictionsof Δms
SM expectationΔms = (18.3 ± 1.3 ) ps-1
agreement between the predicted values and the measurements at better than :
6σ
5σ3σ
4σ
1σ
2σ
Legenda
Δms
10
Prediction “era” Monitoring “era”
ExpΔms = (17.77 ± 0.12 ) ps-1
![Page 29: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/29.jpg)
Theoretical predictions of Sin 2 βin the years predictions
exist since '95
experiments
sin 2 βUTA = 0.65 ± 0.12Prediction 1995 fromCiuchini,Franco,G.M.,Reina,Silvestrini
![Page 30: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/30.jpg)
1) Possible tensions in the present SM Fit ?2) Fit of NP-ΔF=2 parameters in a Model “independent” way3) “Scale” analysis in ΔF=2
Is the present picture showing a Model StandardissimoStandardissimo ?
An evidence, an evidence, my kingdom for an evidence From Shakespeare's Richard III
![Page 31: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/31.jpg)
Compatibility plotsThey are a procedure to ``measure” the agreement of a singlemeasurement with the indirect determination from the fit
αexp = (91 ± 6)0 γexp = (76 ± 11)0
![Page 32: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/32.jpg)
![Page 33: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/33.jpg)
![Page 34: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/34.jpg)
εΚ
-1.5 σ devation
Three “news” ingredients
(6)
12Imsin
i
K
Me
m
!
!
"
#! " $% &
= +' ()* +
K
1) Buras&Guadagnoli BG&Isidori corrections
Decrease the SM prediction by 6%
2) Improved value for BK BK=0.731±0.07±0.35
3) Brod&Gorbhan charm-top contribution at NNLO enhancement of 3% (not included yet)
![Page 35: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/35.jpg)
![Page 36: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/36.jpg)
VUB PUZZLE
Inclusive: uses non perturbative parameters most not from lattice QCD (fitted from the lepton spectrum)
Exclusive: uses non perturbative form factors from LQCD and QCDSR
![Page 37: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/37.jpg)
Vcb & Vub
Vub (excl) = (3.26 ± 0.30) 10-3
Vub (inc) = (4.40 ± 0.31) 10-3
Vub (com) = (3.83 ± 0.57) 10-3
~2σ difference
Vcb (excl) = (39.5 ± 1.0) 10-3
Vcb (inc) = (41.7 ± 0.7) 10-3
Vcb (com) = (41.0 ± 1.0) 10-3
2.4% uncertainty
AFTER EPS-HEP2011
15% uncertainty
![Page 38: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/38.jpg)
sin2β(excl) = 0.740 ± 0.041 1.6 σ from direct measurement
sin2β(incl) = 0.809 ± 0.036 3.2 σ from direct measurement
no B → τν
![Page 39: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/39.jpg)
σMeasurementPrediction
+1.318 ±113.55 ±0.28Br(Bll ) 10-9
1.40.731 ±0.0360.88 ±0.09ΒK [103]
0.33.83 ±0.573.63±0.15Vub [103]
2.31.64±0.340.83±0.08Br(Bτ ν) 10-4
1.017.70±0.0819.1±1.5Δms (ps-1)
2.30.667±0.0210.795±0.051sin2β
0.7(91 ± 6)°(85 ± 4)°α
0.9(79 ±10)°(69 ±3)°γ
Summary Table of the Pulls
![Page 40: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/40.jpg)
What for a ``standardissimo” CKMwhich agrees so well with theexperimental observations?
New Physics at the EWscale is “flavor blind”-> MINIMAL FLAVORVIOLATION, namely flavouroriginates only from theYukawa couplings of the SM
New Physics introduces newsources of flavour, thecontribution of which, atmost < 20 % , should befound in the present data,e.g. in the asymmetries ofBs decays
![Page 41: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/41.jpg)
INCLUSIVE Vub = (43.1 ± 3.9) 10-4
Model dependent in the threshold region(BLNP, DGE, BLL)But with a different modelling ofthe threshold region [U.Aglietti et al.,0711.0860] Vub = (36.9 ± 1.3 ± 3.9) 10-4
EXCLUSIVE Vub = (34.0 ± 4.0) 10-4
Form factors from LQCD and QCDSR
![Page 42: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/42.jpg)
…. beyond the Standard Model
![Page 43: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/43.jpg)
Only tree level processes Vub/Vcb and B-> DK(*)
CP VIOLATION PROVEN IN THESM !!
degeneracy of γbroken by ASL
![Page 44: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/44.jpg)
![Page 45: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/45.jpg)
In general the mixing mass matrix of the SQuarks(SMM) is not diagonal in flavour space analogouslyto the quark case We may eitherDiagonalize the SMM
z , γ , g
QjLqj
L
FCNC
or Rotate by the samematrices the SUSY partners ofthe u- and d- like quarks(Qj
L )´ = UijL Qj
LUj
LUiL dk
L
g
![Page 46: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/46.jpg)
In the latter case the Squark MassMatrix is not diagonal
(m2Q )ij = m2average 1ij + Δmij2 δij = Δmij2 / m2average
![Page 47: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/47.jpg)
New local four-fermion operators are generatedQ1 = (bL
A γµ dLA) (bL
Bγµ dLB) SM
Q2 = (bRA dL
A) (bRB dL
B)Q3 = (bR
A dLB) (bR
B dLA)
Q4 = (bRA dL
A) (bLB dR
B)Q5 = (bR
A dLB) (bL
B dRA)
+ those obtained by L ↔ R
Similarly for the s quark e.g.(sR
A dLA) (sR
B dLB)
![Page 48: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/48.jpg)
Bs mixing , a road to New Physics (NP) ?
The Standard Model contributionto CP violation in Bs mixing iswell predicted and rather small
The phase of the mixing amplitudes can be extractedfrom Bs ->J/Ψ φ with a relatively small th.
uncertainty. A phase very different from 0.04 impliesNP in Bs mixing
2009
![Page 49: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/49.jpg)
Main Ingredients and General Parametrizations
Neutral Kaon Mixing
![Page 50: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/50.jpg)
Bd and Bs mixing
CqPen and φq
Pen parametrize possible NP contributions to Γq
12 from b -> s penguins
![Page 51: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/51.jpg)
Physical observables
![Page 52: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/52.jpg)
Experimental measurements
![Page 53: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/53.jpg)
![Page 54: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/54.jpg)
XXACP (J/Ψ Κ)
XXASL(Bs)
XXεK
XXτ(Βs), ΔΓs/Γs
XXXXACH
CεK
X
ϕs
XXACP (Dπ(ρ),DKπ)
XXASL
XXα (ρρ,ρπ,ππ)
Xγ (DΚ)
~XACP (J/Ψ φ)
XΔms
ϕd
X
Cd Csρ , η
XΔmd
XVub/VcbTree
processes
1↔3 family
2↔3 family
1↔2familiy
0
( , , , ..)
( / , ) sin(2 2 ) ( , , )
( , , )
| | | |
d d
d d
d d
EXP SM
d B d B
CP B B
EXP SM
B B
EXP SM
K K
m C m f C QCD
A J K f
f
C!
" #
$ % " # %
& & % " # %
! !
' = '
( = +
= )
= ( , , , ..)
( , , , ..)
( / , ) sin(2 2 ) ( , , )
...
s
s s
EXP SM
s B s Bs
CP s B B
f C QCD
m C m f C QCD
A J f
!" #
" #
% $ % " # %
' = '
( = )
ΔF=2NP model independent Fit
Parametrizing NP physics in ΔF=2 processes
2 2 2
2
NP SM
i B B
SM
B
A Ae
A
! = ! =
! =
+=
qC döCBqe2iφBq
![Page 55: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/55.jpg)
η = 0.346 ± 0.015
ρ = 0.129 ± 0.022
η = 0.389 ± 0.054
ρ = 0.145 ± 0.045
SM analysis NP-ΔF=2 analysis
ρ,η fit quite precisely in NP-ΔF=2 analysis and consistent with the one obtained on the SM analysis
[error double](main contributors tree-level γ and Vub)
5 new free parameters Cs,ϕs Bs mixing Cd,ϕd Bd mixing CεK K mixing
Today : fit is overcontrained
Possible to fit 7 free parameters (ρ, η, Cd,ϕd ,Cs,ϕs, CεK)
Please consider these numbers when you want to get CKM parametersin presence of NP in ΔF=2 amplitudes (all sectors 1-2,1-3,2-3)
![Page 56: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/56.jpg)
![Page 57: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/57.jpg)
Effective Theory Analysis ΔF=2
2( )
( )
j
j
j
jC
LF F
C
L= !" ="
""
L is loop factor and should be : L=1 tree/strong int. NPL=α2
s or α2W for stron/weak perturb. NP
C(Λ) coefficients are extracted from data
F1=FSM=(VtqVtb*)2
Fj=1=0 MFV
|Fj | =FSMarbitrary phases NMFV
|Fj | =1 arbitrary phases
Flavour generic
Effective Hamiltonian in the mixing amplitudes
![Page 58: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/58.jpg)
From Kaon sector @ 95% [TeV]
~14000~47000~470000Generic
3.211107NMFV
MFV
αW loopαs loopStrong/treeScenario
From Bd&Bs sector @ 95% [TeV]
1003303300Generic
0.250.88NMFV
MFV
αW loopαs loopStrong/treeScenario
Main contribution to present lower bound on NP scale come fromΔΦ=2 chirality-flipping operators ( Q4) which are RG enhanced
![Page 59: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/59.jpg)
b s & τ µγ in SUSY GUTS
ΔMs msq=500 GeV
Φs
Limits from Belle and Babar <4.5 & 6.8 10-8
![Page 60: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/60.jpg)
![Page 61: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/61.jpg)
We can consider simultaneously LFV, g-2e EDM,e.g. Isidori, Mescia, Paradisi, Temes in MSSM
![Page 62: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/62.jpg)
FCNC in rare K decays
![Page 63: G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries](https://reader034.vdocuments.us/reader034/viewer/2022051818/549487dab47959654d8b4b2a/html5/thumbnails/63.jpg)
1) CKM matrix is the dominant source of flavour mixing and CPviolation σ(ρ)~15% & σ(η) ~4%
2) There are tensions that should be understood : sin2β, εK , Br(Bτ ν)
3) Estraction of SM predictions with different possibilities:inclusive vs exclusive
4) The suggestion of a large Bs mixing phase has survived formore than two years but could be killed by LHCbmeasurements.
CONCLUSIONS