· The EW ba y ogenesis scena rio The violent Ea rly Universe The Ea rly Universe underw ent to at least 3 imp o rtant phase transitions - 40 - 30 - 20 - 10 0 10 20 Log10 t (s -

Electroweak baryogenesis and New PhysicsG. AuriemmaINFN Sezione di RomaVulcano Workshop 2008G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 1 / 31

Outline1 The EW bayogenesis scenarioThe Higgs mechanismB violationsCP violationsEW phase transition in the SMWhy it fails ?2 Indications of New PhysicsThe Bs anomalyThe Bd → K puzzle3 Models of New PhysicsFourth generation quarksTwo Higgs doublet model of Supersymmetry4 SummaryG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 2 / 31

The EW bayogenesis scenarioOutline1 The EW bayogenesis scenarioThe Higgs mechanismB violationsCP violationsEW phase transition in the SMWhy it fails ?2 Indications of New PhysicsThe Bs anomalyThe Bd → K puzzle3 Models of New PhysicsFourth generation quarksTwo Higgs doublet model of Supersymmetry4 SummaryG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 3 / 31

The EW bayogenesis scenarioThe violent Early UniverseThe Early Universe underwent to at least 3 important phase transitions

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G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 4 / 31


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(1) T ≈ 140 MeV from NuclearMatter to Quark Gluon Plasma(QGP)



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(2) T ≈ 100 GeV from EWbrocken phase to symmetricHiggs phase



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((3) T ≈ 1016 GeV fromSU(3)c×SU(2)L×U(1)Y to theGUT phase.



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GUT BaryogenesysG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 4 / 31


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EW BaryogenesysI The three Sakharov conditions forBaryon-Antibaryon asymmetry where inprinciple realized at T ≈ 100 GeV(t ≈ 2.4× 10−11s)

I Non conservation of baryon numberI CP violationsI Strong rst-order phase transition


The EW bayogenesis scenario The Higgs mechanismThe Higgs mechanismThe entire talk will be aroud this topicPeter Higgs (age 78) visiting LHC tunnel at CERN open day May 2008

An uncommon fact: 3 papers with practically the same title pub-lished in the same volume of the Physical Review LettersG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 5 / 31


I The gauge vector bosons and fermions in the SM acquire anon zero mass from a pervasive complex scalar eld,nicknamed the Higgs eld that has a non zero vacuumexpectation value〈0|φ |0〉 =

v0√2 with v0 =(√2GF)−1/2

= 246 GeV




v0√2 with v0 =(√2GF)−1/2

= 246 GeVI Weak interactions are mediated by gauge bosons withmasses MW± =

g2 v0 and MZ0 =g ′2 v0




v0√2 with v0 =(√2GF)−1/2



I Fermions get mass from Yukawa (adimensional) couplingsto the Higgs eld mf = yf v0with coupling coecients that span fromyν ' 10−14 to ytop ' 1G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 5 / 31



v0√2 with v0 =(√2GF)−1/2



I Fermions get mass from Yukawa (adimensional) couplingsto the Higgs eld mf = yf v0with coupling coecients that span fromyν ' 10−14 to ytop ' 1I The Higgs boson is the only non-detected particle in theSM, due to its large mass (> 115 GeV), originated byself-coupling.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 5 / 31



v0√2 with v0 =(√2GF)−1/2



I Fermions get mass from Yukawa (adimensional) couplingsto the Higgs eld mf = yf v0with coupling coecients that span fromyν ' 10−14 to ytop ' 1I The Higgs boson is the only non-detected particle in theSM, due to its large mass (> 115 GeV), originated byself-coupling.

Higgs physics will be experimen-tally veried at LHC starting thisyear !G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 5 / 31

The EW bayogenesis scenario The Higgs mechanismTwo curious facts1 The Higgs mechanism (if experimentallyconrmed) can account only for ≈ 10% of themass of a hydrogen atom; the remaining 90%comes from the kinetic energy of the connedquarks, thus ultimately from strong forces.


The EW bayogenesis scenario The Higgs mechanismTwo curious facts1 The Higgs mechanism (if experimentallyconrmed) can account only for ≈ 10% of themass of a hydrogen atom; the remaining 90%comes from the kinetic energy of the connedquarks, thus ultimately from strong forces.2 The idea that mass could be not an intrinsicproperty of a body, as postulated by Newton in thefamous Scolium, but the result of the interactionwith an external agent, was anticipated by thefrench philosopher and physicists Descartes(Cartesium), who speculated in the PrincipiaPhilosophiae published in 1647 that the inertiacould be an eect of the friction against the etherG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 6 / 31

The EW bayogenesis scenario The Higgs mechanismSpontaneous Symmetry BreakingA classical analogy with superconductivity (Nambu & Jona-Lasinio 1961)Symmetric

vacuum

True

vacuum

Im(f)Re(f)

f =0

I The spontaneous symmetry breaking that gives to the Higgs eld a nite valueφ 6= 0 is due to the quartic self coupling of the Higgs:Ve = −12µ2|φ|2 +

14λ|φ|4the so-called sombrero-hat potential, that has a minimum for |φ| = µ/√

λ (thered dashed circle).G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 7 / 31


vacuum

True

vacuum

Im(f)Re(f)

f = 0

I At a certain time in the past the Universe had to roll to the minimum of thepotential, choosing a random phase for the eldG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 7 / 31


vacuum

True

vacuum

Im(f)Re(f)

f =0

I Kirzhnits & Linde (1972) observed that in analogy with the Meissner eect insuperconductivity, at high temperatures (T & 100 GeV) the energy density of theeld at equilibrium with the radiation was much greater then the potential well,and thermal uctuations restore the symmetry of the vacuum ShowI The age of the Universe at the transition was ≈ 2.4× 10−11 s and the horizon

. 1 cmG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 7 / 31


vacuum

True

vacuum

Im(f)Re(f)

f =0

I Kirzhnits & Linde (1972) observed that in analogy with the Meissner eect insuperconductivity, at high temperatures (T & 100 GeV) the energy density of theeld at equilibrium with the radiation was much greater then the potential well,and thermal uctuations restore the symmetry of the vacuum ShowI The age of the Universe at the transition was ≈ 2.4× 10−11 s and the horizon

. 1 cmPatchwork. Islands of superconductivity (red, left) may grow and merge as temperature drops. CREDIT: J. SONIER, SIMON FRASER UNIVERSITY (APS 10-14 MARCH, NEW ORLEANS, LOUISIANA)



vacuum

True

vacuum

Im(f)Re(f)

Triumph of the medieval mind G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 7 / 31

The EW bayogenesis scenario The Higgs mechanismB violations in the SMt'Hooft (1975)Symmetric

vacuum

True

vacuum

Im(f)Re(f)

f = 0

I The true vacuum after the symmetry breaking hasnot a single value of the phase, actually itcorresponds to the innite sequenceφ = |φ0|e±i2πnCSof dierent topological states, characterized by atopological quantum number nCS .G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 8 / 31

The EW bayogenesis scenario The Higgs mechanismB violations in the SMt'Hooft (1975)

I All the true vacuums after the symmetry breakingare degenerated, but going from one value of thephase to a dierent one requires energy

Symmetric

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New true

vacuum

Im(f)Re(f)


The EW bayogenesis scenario B violationsB violations in the SMThe periodic structure of EW vacuum (Jackiw & Rebbi 1976)-1

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I In the SM no fundamental symmetry conserve baryon orlepton number;I The divergence of a fermionic current is

∂µJB,Lµ =

nf32π2 (−g2W aµνW aµν + g ′2Bµν Bµν

)6= 0

I The baryon and lepton operators are given respectively bythe space integralsB =

ˆ JB0 d3x L =

ˆ JL0 d3xI From wich follows the selection rule ∆B = ∆L = nf ∆nCSI 6 B+ 6 L reaction must involve at least one member of the 3generations of quarks and lepton and conserve total chargeand neutrality of colors, as for exampleu + d → d + 2s + c + 2b + t + νe + νµ + ντwhere is obviously Bin = 23 and Lin = 0 that is transformedin Bout = − 73 and Lout = −3.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 9 / 31


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I In the SM no fundamental symmetry conserve baryon orlepton number;I The divergence of a fermionic current is

∂µJB,Lµ =

nf32π2 (−g2W aµνW aµν + g ′2Bµν Bµν

)6= 0

I The baryon and lepton operators are given respectively bythe space integralsB =

ˆ JB0 d3x L =

ˆ JL0 d3xI From wich follows the selection rule ∆B = ∆L = nf ∆nCSI 6 B+ 6 L reaction must involve at least one member of the 3generations of quarks and lepton and conserve total chargeand neutrality of colors, as for exampleu + d → d + 2s + c + 2b + t + νe + νµ + ντwhere is obviously Bin = 23 and Lin = 0 that is transformedin Bout = − 73 and Lout = −3.Sphaleron

u

d

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The EW bayogenesis scenario B violationsB violations ratesB violating reactions as transitions in the periodic topological structure-1

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I The transition ∆nCS = 1 must overcomethe potential barrier Esph ≈ 4πg v0f (λ/g2)



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I The transition ∆nCS = 1 must overcomethe potential barrier Esph ≈ 4πg v0f (λ/g2)I In the present Universe T ≈ 0 tunnellingthrough the barrier

Γsph(T = 0) ≈ e− 8π2g2 ' e−170



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Γsph(T = 0) ≈ e− 8π2g2 ' e−170I In the Early Universe when 0 T TEWthermal uctuations drive the eld over thepotential barrier

Γsph(T TEW ) ' gπ32 v70 (T )T 3 e−Esph/TG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 10 / 31


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Γsph(T = 0) ≈ e− 8π2g2 ' e−170I In the Early Universe when 0 T TEWthermal uctuations drive the eld over thepotential barrier

Γsph(T TEW ) ' gπ32 v70 (T )T 3 e−Esph/TI When the temperature is T & TEW wehave v0(TEW ) → 0 and consequently alsothe barrier Esph → 0, thus

Γsph(T & TEW ) ≈( g24πT)4G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 10 / 31

The EW bayogenesis scenario CP violationsQuark mixings and CP violationsCabibbo (1964) Kobayashi & Maskawa (1973)I Masses of fermions are due to couplings with the scalarHiggs elds


The EW bayogenesis scenario CP violationsQuark mixings and CP violationsCabibbo (1964) Kobayashi & Maskawa (1973)I Masses of fermions are due to couplings with the scalarHiggs eldsI Flavor changing processes are due to coupling with theW± vector gauge bosons


The EW bayogenesis scenario CP violationsQuark mixings and CP violationsCabibbo (1964) Kobayashi & Maskawa (1973)I Masses of fermions are due to couplings with the scalarHiggs eldsI Flavor changing processes are due to coupling with theW± vector gauge bosonsmass eigenstates6=weak eigenstates


The EW bayogenesis scenario CP violationsQuark mixings and CP violationsCabibbo (1964) Kobayashi & Maskawa (1973)I Masses of fermions are due to couplings with the scalarHiggs eldsI Flavor changing processes are due to coupling with theW± vector gauge bosonsmass eigenstates6=weak eigenstatesI Weak eigenstates are linked to mass eigenstates by aunitary matrix usually called the CKM matrix

d ′s′b′ =

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

dsb



d ′s′b′ =


dsb

I A ng × ng unitary matrix can be parameterized in the general case with ng (ng − 1) complexparameters, but the phases of the quark elds are irrelevant, therefore the parameterizationmust include 12ng (ng − 1) angles and 12 (ng − 1)(ng − 2) phasesG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 11 / 31


d ′s′b′ =


dsb

I A ng × ng unitary matrix can be parameterized in the general case with ng (ng − 1) complexparameters, but the phases of the quark elds are irrelevant, therefore the parameterizationmust include 12ng (ng − 1) angles and 12 (ng − 1)(ng − 2) phases3 generations ⇒ 3 angles and 1 phaseG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 11 / 31

The EW bayogenesis scenario CP violationsCKM Mechanism

I All the observed CP violations observed up to now are consistent with the CKM paradigm,proposed by Kobayashy & Maskawa in 1973, originated from complex Yukawa coupling ofthe quarks with the Higgs eld.I Masses of quarks are generated by the Yukawa coupling of the Higgs boson, respect to whichDj type quarks are also mixed. Therefore if any pair of the Dj (or of the Ui ) have the samemass the matrix Vjk must be real and there are no CP-violations.ACP ∝ (m2t −m2u)(m2t −m2c)(m2c −m2u)(m2b −m2s )(m2b −m2d)(m2s −m2d) JCPwith JCP ' 10−5.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 12 / 31

The EW bayogenesis scenario EW phase transition in the SMHiggs eld eective potential at nite TColeman & Weinberg (1973) Dolan & Jackiw (1974)The SM eective potential of the Higgs eld VSM is the sum of 3 terms:VSM ' 14M2Hφ2 (1− φ2v20 )The tree level bare potentialH

H

H


The EW bayogenesis scenario EW phase transition in the SMHiggs eld eective potential at nite TColeman & Weinberg (1973) Dolan & Jackiw (1974)The SM eective potential of the Higgs eld VSM is the sum of 3 terms:VSM ' 14M2Hφ2 (1− φ2v20 ) +B [φ4 (ln 2φ2v20 − 12) + φ2v20 ]The tree level bare potential The 1-loop radiative corrections dueto coupling with gauge bosons andfermions,withB =164π2 ∑i gi y4ibeing yi the Yukawa couplings and gi =

(−1)2s (2s + 1) the statistical weights.H H

H H

H H

W,Z0,t

1-Loop

2-Loops +


The EW bayogenesis scenario EW phase transition in the SMHiggs eld eective potential at nite TColeman & Weinberg (1973) Dolan & Jackiw (1974)The SM eective potential of the Higgs eld VSM is the sum of 3 terms:VSM ' 14M2Hφ2 (1− φ2v20 ) +B [φ4 (ln 2φ2v20 − 12) + φ2v20 ]+F (φ,T )The tree level bare potential The 1-loop radiative corrections dueto coupling with gauge bosons andfermions,withB =164π2 ∑i gi y4ibeing yi the Yukawa couplings and gi =

(−1)2s (2s + 1) the statistical weights.The thermodynamical free energy of thethermal bath at constant temperature T .At chemical potential ≈ 0 the free isequal to the thermodynamical potentialΩ = −T∑i gi ´ ln(1∓ e−εi (φ)/T ) d3p

(2π)3with εi =√2y2i φ2 + p2, that is propor-tional to T 4G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 13 / 31

The EW bayogenesis scenario EW phase transition in the SMThe EW phase transition

Higgs Field (GeV)0 20 40 60 80 100 120 140 160

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I For temperature T > Tsp (thepink curve) the unique minimum ofthe potential is at φ ≡ 0 becausethe second derivative is alwaysV ′′e > 0 and the Universe is in astate of false vacuum with 〈φ〉 ≡ 0.



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I For temperature T > Tsp (thepink curve) the unique minimum ofthe potential is at φ ≡ 0 becausethe second derivative is alwaysV ′′e > 0 and the Universe is in astate of false vacuum with 〈φ〉 ≡ 0.I For the temperature T = TC (theblue curve) there are two equalminima of the potential, onecorresponding to the symmetricvacuum 〈φ〉 = 0 and the second tothe SSB vacuum 〈φ〉 = vC/

√2. Atthis temperature the metastablesupercooled symmetric phase cancoexists with the nucleating SSBphase.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 14 / 31


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√2. Atthis temperature the metastablesupercooled symmetric phase cancoexists with the nucleating SSBphase.I When the Universe cools toT < TC the SSB phase isenergetically favoured and rollsrapidly to the present SSB vacuumstate 〈φ〉 → v0/√(2)G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 14 / 31


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√2. Atthis temperature the metastablesupercooled symmetric phase cancoexists with the nucleating SSBphase.I When the Universe cools toT < TC the SSB phase isenergetically favoured and rollsrapidly to the present SSB vacuumstate 〈φ〉 → v0/√(2)A rst order phase transition occurs via nucle-ation, possible if at the critical temperature thetwo phases are energetically equivalentG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 14 / 31

The EW bayogenesis scenario Why it fails ?The build up of the asymmetry|f|>0

|f|>0

|f|>0|f|>0

|f|=0

For details and references see e.g.Cline [hep-ph/0609145] or Buchmuller[arXiv:0710.5857]G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 15 / 31


|f|>0

|f|>0|f|>0

|f|=0I A rst-order phase transition proceedsby nucleation of bubbles of the newphase 〈|φ|〉 > 0, that expand andcoalesce to ll the entire spaceI In the symmetric phase 〈|φ|〉 = 0,outside the bubbles, the B violatingreactions keep B + L = 0 with a rate

Γsph ≈ 4πg T 4I Inside the bubbles B violation reactionsare suppressed to Γsph ≈ T 4e− 4πg v0(T)TI At the bubble walls B and CPviolations create a baryon antibaryonasymmetry, that is incorporated by thebubble's expansionsI The nal asymmetry (for vC/TC 1)will be of the order ofnBs ≈ 90α4w4π2g∗T δwvw εCPwith δw ≈ 1/MH and vw ≈ c bubble'swall thickness and velocity respectivelyG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 15 / 31


|f|>0

|f|>0|f|>0

|f|=0I A rst-order phase transition proceedsby nucleation of bubbles of the newphase 〈|φ|〉 > 0, that expand andcoalesce to ll the entire spaceI In the symmetric phase 〈|φ|〉 = 0,outside the bubbles, the B violatingreactions keep B + L = 0 with a rate

Γsph ≈ 4πg T 4I Inside the bubbles B violation reactionsare suppressed to Γsph ≈ T 4e− 4πg v0(T)TI At the bubble walls B and CPviolations create a baryon antibaryonasymmetry, that is incorporated by thebubble's expansionsI The nal asymmetry (for vC/TC 1)will be of the order ofnBs ≈ 90α4w4π2g∗T δwvw εCPwith δw ≈ 1/MH and vw ≈ c bubble'swall thickness and velocity respectivelyThis mechanism can workout an asymmetry nB/s ≈ 10−10 if1 The transition is strongly rst order v0(TC )TC & 1.32 The CP violations parameter, at a temperature of T ≈ 100GeV, is εCP & 3× 10−3G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 15 / 31

The EW bayogenesis scenario Why it fails ?Why the SM fails?First Problem:vC /TC 6≯ 1.3 The EW baryogenesis in the SM fails to produce the ob-served baryon asymmetry nB/s ≈ 10−10 for two reasons:1 The strenght of the phase transition depends fromthe unknown mass of the Higgs. The LEPexperiment has given a rst indirect indication that114.4 ≤ MH ≤ 144 GeV at 95% C.L.


The EW bayogenesis scenario Why it fails ?Why the SM fails?First Problem:vC /TC 6≯ 1.3 The EW baryogenesis in the SM fails to produce the ob-served baryon asymmetry nB/s ≈ 10−10 for two reasons:1 The strenght of the phase transition depends fromthe unknown mass of the Higgs. The LEPexperiment has given a rst indirect indication that114.4 ≤ MH ≤ 144 GeV at 95% C.L.2 For this mass mass range the EW phase transitionis very weakHiggs Field (GeV)

0 20 40 60 80 100 120 140 160Temperature (GeV) 117

118119

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=124.6 R=1.0C

=120.9 vC

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Fre

e E

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y


The EW bayogenesis scenario Why it fails ?Why the SM fails?First Problem:vC /TC 6≯ 1.3 The EW baryogenesis in the SM fails to produce the ob-served baryon asymmetry nB/s ≈ 10−10 for two reasons:1 The strenght of the phase transition depends fromthe unknown mass of the Higgs. The LEPexperiment has given a rst indirect indication that114.4 ≤ MH ≤ 144 GeV at 95% C.L.2 For this mass mass range the EW phase transitionis very weak3 Numerical computations shows that the EW phasetransition for an Higgs mass >150 GeV isextremely weak if not second orderLEP limit

Higgs Mass (GeV)70 80 90 100 110 120 130 140 150

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0.006

0.008

=92.7 R=0.6C

=146.0 vC

=150 TH

SM: m

Fre

e E

ne

rgy


The EW bayogenesis scenario Why it fails ?Why the SM fails?Second problem: εCP ≯ 10−3I CP violations occurs in interctions involving 4 quarks, like for example annihilationui + d j → uk + d lI The resulting CP asymmetry will be at maximum (Jarskog 1985)

εmaxCP =2Im(αβ∗)

|α|2 + |β|2 with α = VijVkl and β = VkjVilI The larger values of the CP asymmetry will be obtained in interactions involving c,t,s,d thatprovides a large asymmetries |εmaxCP | ≈ 0.41, but this are Boltzmann suppressed attemperature ≈ 100 GeV. Therefore a reasonable estimate of the possible asymmetry will bein the range 10−3 − 10−4I One additional controversial problem is the evolution of the CKM matrix at hightemperature. As a matter of fact it is to be expected that the diagonal element of the matrixshould scale with the temperature as the Higgs vacuum expectation value, vanishing forT → TEW

I According to some estimates (Shaposnikov 1988) a scaling law of the type εCP (T ) ∝ T−12should be expectedI This is probably an overestimated suppression since the VEV of the Higgs eld goes to zero verysharply at T = TEWI Berkooz,Nir,& Volansky (2004) have suggested the possibility that the Yukawa couplings arebigger at high temperatureG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 17 / 31

Indications of New PhysicsOutline1 The EW bayogenesis scenarioThe Higgs mechanismB violationsCP violationsEW phase transition in the SMWhy it fails ?2 Indications of New PhysicsThe Bs anomalyThe Bd → K puzzle3 Models of New PhysicsFourth generation quarksTwo Higgs doublet model of Supersymmetry4 SummaryG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 18 / 31

Indications of New Physics The Bs anomalyMass dierence ∆msMeasured by B0s B0s oscillations

∆ms = 17.77±0.10(stat)±0.07(syst) ps−1(CDF Collaboration 2006)

b b

s,d s,d

u,c,t

u,c,t

W W

b b

s,d s,d

u,cu,c

W

W

(A) (B)

I There are two types of neutral mesons with beauty,the B0s = (sb) and the B0d = (db). Both havebeen observed to oscillate into the respectiveantiparticles, due to the box diagram transitions;G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 19 / 31



b b

s,d s,d

u,c,t

u,c,t

W W

b b

s,d s,d

u,cu,c

W

W

(A) (B)

I The Schrödingher equation of the system will bei ∂

∂t ( B0(t)B0(t) ) =

(M − i Γ2) ( B0(t)B0(t) )where M and Γ are hermitian matrices. The mixingis due to the presence of the o-diagonal elementsin those matrices M12 = M∗12 6= 0 and

Γ12 = Γ∗12 6= 0;G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 19 / 31



b b

s,d s,d

u,c,t

u,c,t

W W

b b

s,d s,d

u,cu,c

W

W

(A) (B)

I The Schrödingher equation of the system will bei ∂

∂t ( B0(t)B0(t) ) =

(M − i Γ2) ( B0(t)B0(t) )where M and Γ are hermitian matrices. The mixingis due to the presence of the o-diagonal elementsin those matrices M12 = M∗12 6= 0 and

Γ12 = Γ∗12 6= 0;I In the box diagram (A) the t-quark channel isdominant, because amplitude isAbs→bs ∝ g4|Vqs |2f ( m2qM2W )G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 19 / 31



b b

s,d s,d

u,c,t

u,c,t

W W

b b

s,d s,d

u,cu,c

W

W

(A) (B)

I In the box diagram (A) the t-quark channel isdominant, because amplitude isAbs→bs ∝ g4|Vqs |2f ( m2qM2W )

I The ratio of mass dierences is predicted to be inthe SM:∆mBs∆mBd =

BBsF 2BsBBs F 2Bd |Vts |2|Vtd |2


Indications of New Physics The Bs anomalyMass dierence ∆msRPP Global t data comparison (Yao et al. 2008)

dB

m∆/sB

m∆

10 20 30 40 50 60

Pro

ba

bilit

y

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

dB

m∆/sB

m∆

10 20 30 40 50 60

Pro

ba

bilit

y

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14CDF

D0

Theory

PBayes<6.5%


Indications of New Physics The Bs anomalyMass dierence ∆msNP search (Ligeti et al. 2006)Presently excluded zone After 1 year of LHCbConclusionsIn a recent analysis by Ligeti et al. (2006) the contribution from NP is searched with adependance

∆mBs = ∆mBs (1 + hNPs e iσNPs )excluding hNPs > 0.3 and 55 ≤ σNPs ≤ 125 at 90% C.L.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 21 / 31

Indications of New Physics The Bs anomalyCP violations in Bs mixingTime (ps)

0 0.2 0.4 0.6 0.8 1

dt

dN

N1

0

0.2

0.4

0.6

0.8

1 a=-5%a=+5%

sX-µ→ s0

B

sX+µ→ s

0B

I Experiments can detect decays into avor specic modes B0 → f , as for examplesemileptonic modes B0q → µ+νµXq and B0q → µ−νµXq with q = d , s that changesthe pattern of B0 B0 oscillations.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 22 / 31


0 0.2 0.4 0.6 0.8 1

dt

dN

N1

0

0.2

0.4

0.6

0.8

1 a=-5%a=+5%

sX-µ→ s0

B

sX+µ→ s

0B

I Experiments can detect decays into avor specic modes B0 → f , as for examplesemileptonic modes B0q → µ+νµXq and B0q → µ−νµXq with q = d , s that changesthe pattern of B0 B0 oscillations.I The CP asymmetry parameter aq , dened aqSL =

∆Γq∆mq tanφq is very small in the SM(Beneke et al. 2003) beingadSL = − (5.0± 1.1) × 10−4 and asSL = (0.21± 0.04) × 10−4G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 22 / 31


0 0.2 0.4 0.6 0.8 1

dt

dN

N1

0

0.2

0.4

0.6

0.8

1 a=-5%a=+5%

sX-µ→ s0

B

sX+µ→ s

0B

I Experiments can detect decays into avor specic modes B0 → f , as for examplesemileptonic modes B0q → µ+νµXq and B0q → µ−νµXq with q = d , s that changesthe pattern of B0 B0 oscillations.I The CP asymmetry parameter aq , dened aqSL =

∆Γq∆mq tanφq is very small in the SM(Beneke et al. 2003) beingadSL = − (5.0± 1.1) × 10−4 and asSL = (0.21± 0.04) × 10−4The D0 collaboration measured the asymmetry parameter asSL = (2.45± 1.93 ± 0.35) × 10−2G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 22 / 31

Indications of New Physics The Bs anomalyClues to NP in Bs decaysM. Bona et al. (UTt Collaboration) 2006 and reference therein.I Almost all the experimental measure of signicative parameters in B0s decays show small nonsignicant deviations from the SM predicted values


Indications of New Physics The Bs anomalyClues to NP in Bs decaysM. Bona et al. (UTt Collaboration) 2006 and reference therein.I Almost all the experimental measure of signicative parameters in B0s decays show small nonsignicant deviations from the SM predicted valuesI From a theoretical point of view CP violations in the B0s decays are an optimal playgroundfor the search of additional NP phases



I UTt group adopted a parameterization of NPeectsCBs e i2φBs = ASMs e−i2βs (1 +ANPsASMs e i2φNPs )with βs = arg (−VtsV ∗tb/VcsV ∗cb) = 0.018 ± 0.001




I Performing a 7 variable t to the experimentalparameters ∆ms ,AsSL,AµµSL , τFSBs , φs , ∆Γs and τBsthey found two possible t1 ANPs /ASMs ≈ 2 and φNPs ≈ −802 ANPs /ASMs ≈ 0.75 and φNPs ≈ −50G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 23 / 31



I Performing a 7 variable t to the experimentalparameters ∆ms ,AsSL,AµµSL , τFSBs , φs , ∆Γs and τBsthey found two possible t1 ANPs /ASMs ≈ 2 and φNPs ≈ −802 ANPs /ASMs ≈ 0.75 and φNPs ≈ −50G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 23 / 31



I Performing a 7 variable t to the experimentalparameters ∆ms ,AsSL,AµµSL , τFSBs , φs , ∆Γs and τBsthey found two possible t1 ANPs /ASMs ≈ 2 and φNPs ≈ −802 ANPs /ASMs ≈ 0.75 and φNPs ≈ −50Sizeable NP contribution with large CPphase at 3.7σ levelG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 23 / 31

Indications of New Physics The Bd → K puzzleDierence between neutral and charged decay of the B mesonsThe BELLE collaboration (Nature, March 20,2008)I The two decays B0 → K+π− and B+ → K+π0 are compared with their CP conjugatedones, with the result that the CP asymmetry of the two decays is dierent by 16.4% at 4.4condence level.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 24 / 31

Indications of New Physics The Bd → K puzzleDierence between neutral and charged decay of the B mesonsThe BELLE collaboration (Nature, March 20,2008)I The diagrams of the two decays dier only for the spectator quark !

b

t

W

s

u

u

u(d) u(d)

K+

p0(p- )

B+(B

0)

b

u

s

u

u(d) u(d)

W

K+

p0 (p- )

B+(B

0)

+G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 24 / 31

Indications of New Physics The Bd → K puzzleDierence between neutral and charged decay of the B mesonsThe BELLE collaboration (Nature, March 20,2008)I The diagrams of the two decays dier only for the spectator quark !

b

t

W

s

u

u

u(d) u(d)

K+

p0(p- )

B+(B

0)

b

u

s

u

u(d) u(d)

W

K+

p0 (p- )

B+(B

0)

+New Physics in the penguin diagramG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 24 / 31

Models of New PhysicsOutline1 The EW bayogenesis scenarioThe Higgs mechanismB violationsCP violationsEW phase transition in the SMWhy it fails ?2 Indications of New PhysicsThe Bs anomalyThe Bd → K puzzle3 Models of New PhysicsFourth generation quarksTwo Higgs doublet model of Supersymmetry4 SummaryG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 25 / 31

Models of New Physics Fourth generation quarksAdditional heavy quarksHou 2008 (arXiv:0803.1234) and references thereinI There are no constraint in the SM to the number ofheavy quarks, with mass higher then the Z0 mass.I Experimental mass limits in direct search for stableare (Acosta et al. CDF Collaboration PRL90,131801) mb′ > 190 GeV and mt′ > 220 GeV at95% C.L.I Precision electroweak measurements suggest

|mt′ −mb′ | ≈ 0I The eventual presence of this additional avor enhances the penguin contributions to the CPviolating decay, that depends from the unknown values of CKM mixing, parametrized

(V ∗t′sVt′b) = rse iφswhere the phase φs introduces additional CP violationsI The observed dierence

∆AKπ = AK+π0 −AK∓π± = +0.164± 0.037can be explained with mt′ & 300 GeV and φs ≈ 90G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 26 / 31

Models of New Physics Fourth generation quarksEW baryogenesis and the 4th familyHiggs Field (GeV)

0 20 40 60 80 100 120 140 160Temperature (GeV) 129130

131132

133134

135136

137138

-0.005

0

0.005

0.01

0.015

=178.8 R=1.3C

=133.0 vC

=100.0 Tb’

=300.0 mt’

4QF: mH=114.4 m

Fre

e E

nerg

y

I The two hypothetical quarks of the 4th family add the the SM Higgs potential terms arisingfrom radiative corrections and thermalization;I The eect of these terms is to increase the strength of the EW phase transition;G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 27 / 31

Models of New Physics Fourth generation quarksEW baryogenesis and the 4th family

(GeV)b’

=Mt’

M

250 300 350 400 450 500

120

140

160

180

200

220

240

4QF Model

vC

TC

Strong Weak

I The two hypothetical quarks of the 4th family add the the SM Higgs potential terms arisingfrom radiative corrections and thermalization;I The eect of these terms is to increase the strength of the EW phase transition;I A numerical calculation of the potential for mt′ = mb′ = 300 GeV shows that the strenghtR = v0(TC )/TC reach the value ∼ 1.3I However it is to observed that the strength of the transition decreases for masses mt′ 300GeVG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 27 / 31

Models of New Physics Two Higgs doublet model of SupersymmetryThe Two Higgs Doublet Model (2HDM)See e.g. Carena & Haber (2003) [hep-ph/0208209] and references thereinI NP eects could be the manifestation of a secondcomplex scalar eld Φ in addition to the Higgs eld

φ of the SM if its mass is large enough to produceonly limited eects at an energy scale ∼ MH of theSM Higgs.



φ of the SM if its mass is large enough to produceonly limited eects at an energy scale ∼ MH of theSM Higgs.I The combination of the two elds leave, after SSB,5 physical Higgs particles:

I 2 scalar neutral with masses MH1 MH2I a pseudoscalar neutral A and a pair of charged H±





I The vacuum expectation values of these elds willbe〈0|φ|0〉 =

( 0v1√2 )〈0|Φ|0〉 =

( uv2e iξ√2 )with v21 + v22 = v20 =√2GF and the ratiov2v1 = tan β with 0 ≤ β ≤ π2 . If the phase

ξ 6= 0, π/2 the eld induces spontaneous CPviolationsG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 28 / 31




I The vacuum expectation values of these elds willbe〈0|φ|0〉 =

( 0v1√2 )〈0|Φ|0〉 =

( uv2e iξ√2 )with v21 + v22 = v20 =√2GF and the ratiov2v1 = tan β with 0 ≤ β ≤ π2 . If the phase

ξ 6= 0, π/2 the eld induces spontaneous CPviolations Limits on the range of masses of chargedHiggs are derived from experiments(Krawczyk & Sokolowska 2007)G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 28 / 31

Models of New Physics Two Higgs doublet model of SupersymmetryThe Two Higgs Doublet Model (2HDM)

Higgs Field (GeV)0 20 40 60 80 100 120 140 160Temperature (GeV)

122

124

126

128130

-0.002

0

0.002

0.004

0.006

0.008

=181.4 R=1.4C

=125.3 vC

2HDM: mH=114.4 T

(GeV)

250 300 350 400 450 500

130

140

150

160

170

180

190

200

Two Higgs Doublet Model

TC

vC

MH1=150

MH1=92.8

Strong

low-mass

Strong

high-mass

MH2=MH

+=MA

Combined limits from LEP, CDF & D0experiments (PDG 2007):MH1 > 92.8 A0 > 93.4


SummaryOutline1 The EW bayogenesis scenarioThe Higgs mechanismB violationsCP violationsEW phase transition in the SMWhy it fails ?2 Indications of New PhysicsThe Bs anomalyThe Bd → K puzzle3 Models of New PhysicsFourth generation quarksTwo Higgs doublet model of Supersymmetry4 SummaryG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 30 / 31

SummarySummaryI Indications for New Physics beyond the SM from the Tevatronexperiments , if conrmed by the coming LHC experiments, support theviability of EW baryogenesis as a reliable model able to quantive explainthe observed baryon asymmetry in the UniverseG. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 31 / 31

SummarySummaryI Indications for New Physics beyond the SM from the Tevatronexperiments , if conrmed by the coming LHC experiments, support theviability of EW baryogenesis as a reliable model able to quantive explainthe observed baryon asymmetry in the UniverseI In particular the clues pointing to a complex multiple structure of theHiggs sector of EW interactions, that are at the moment rather weak,are extremely interesting from the Cosmological point of view.G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 31 / 31

SummarySummaryI Indications for New Physics beyond the SM from the Tevatronexperiments , if conrmed by the coming LHC experiments, support theviability of EW baryogenesis as a reliable model able to quantive explainthe observed baryon asymmetry in the UniverseI In particular the clues pointing to a complex multiple structure of theHiggs sector of EW interactions, that are at the moment rather weak,are extremely interesting from the Cosmological point of view.Thank You for Your attention !G. Auriemma (USB & INFN) EW Baryogenesis Vulcano Workshop 2008 31 / 31

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