Baryogenesis and New Physics

How many baryons?

The abundances of the primordial elements and the height of the peaks of the CMB power spectrum dependC.E.M. on the ratio Wagner of baryons-to-photons. EFI & KICP , Univ.Strumia of Chicago HEP Division, Argonne National Lab.

Fields, Sarkar

KICP Colloquium, Univ. of Chicago, February 3rd, 2015 1 Anti-Matter • An inevitable prediction of the marriage of Quantum Mechanics and Special Relativity. Its existence was first postulated by Dirac, in order to make sense of the negative energy states appearing as solutions of the Dirac equation

Dirac, 1930

Positrons discovered by C. Anderson in 1932

• Holes of negative energy : Positive energy positrons. • Antiparticles carry the same mass and spin as particles, but opposite charges. Every particle has its antiparticle. Symmetry C (and CP) relates them. Under reasonable assumptions, CPT is a symmetry of nature. • No symmetry prevents the annihilation of matter and anti-matter. So, they don’t coexist easily together.

2 Matter-Antimatter Annihilation

3 The Puzzle of the Matter-Antimatter asymmetry

• Anti-matter is governed by the same interactions as matter.

• Observable Universe is composed of matter.

• Anti-matter is only seen in cosmic rays and particle physics accelerators

• The rate observed in cosmic rays consistent with secondary emission of antiprotons

n P "10!4 n P

4 Theory vs. Observation

Baryons annihilate with anti-baryons via strong interactions mediated by mesons This is a very efficient annihilation channel and the equilibrium density is

nB¯ nB 20 = 10 n n How does this compare to experiment ? First of all, we have the problem of the unobserved antimatter. Secondly, from the analysis of BBN and CMBR, one obtains, consistently

5 BaryonBaryon AbundanceAbundance inin thethe UniverseUniverse

! Information on the baryon abundance comes from two main sources: ! Abundance of primordial elements. When combined with Big Bang Nucleosynthesis tell us

n B 421 " = , n! = 3 n! cm ! CMBR, tell us ratio

%B !5 2 GeV $#B , %c "10 h 3 %c cm ! There is a simple relation between these two quantities

"8 2 # =2.68 10 !Bh

6 How many baryons?

The abundances of the primordial elements and the height of the peaks of the CMB power spectrum depend on the ratio of baryons-to-photons.

Strumia

Fields, Sarkar

How to explain the absence of antimatter and the appearance of such a small asymmetry ?

7 SmallMatter Asymmetry and may Anti-Matterbe generated dynamically, at temperaturesEarly belowUniverse the reheating one : Baryogenesis

NB=30 000 000 001 NB =30 000 000 000

1,000,000,001 1,000,000,000 t 10−6 s

Matter Anti-matter

Murayama 54 Assuming the existence of a small primordial asymmetry solves the puzzle. Indeed, matter-antimatter annihilation can now occur efficiently and finally the small asymmetry will lead to observable matter in the Universe

8

8 Matter and Anti-Matter Small Asymmetry may be generated primordially : EarlyBaryogenesis Universe

NB=1 NB =0 NB=30 000 000 001 NB =30 000 000 000

1,000,000,001 1,000,000,000 t 10−6 s now

Matter Anti-matter

Murayama 54 Assuming the existence of a small primordial asymmetry solves the puzzle. Indeed,Now matter-antimatterthe question annihilation is: why can was now there occur efficiently in the and very finally early the small asymmetry will lead to observable matter in the Universe Universe an excess of baryons 9 BaryogenesisBaryogenesisBaryogenesis 9 Baryogenesis ConditionsBaryogenes ifors at Baryogenesisthe weak scale

! Under natural assumptions, there are three conditions, enunciated by Sakharov, that need to be fulfilled for baryogenesis. The SM fulfills them :

! Baryon number violation: Anomalous Processes

! C and CP violation: Quark CKM mixing

! Non-equilibrium: Possible at the electroweak phase transition.

10 Anomalous processes in the SM Non-equivalent Vacua and Static Energy in Field Configuration Space

The sphaleron is a static configuration with non-vanishing values of the Higgs and gauge boson fields.

Its energy may be identified with the height of the barrier separating vacua with different baryon number

The quantity v is the Higgs vacuum expectation value, < H > = v. 8! v E = This quantity provides an order parameter which sph distinguishes the electroweak symmetry gW preserving and violating phases. . N &µ j B,L = g Tr( $ µ#!" F F ) µ 32 % 2 µ# !" B =L =3 Instanton configurations (mBay be rLeg)=0arded as semiclasical configurampationslitudes for tunelling effect between vacuum states with different baryon number 11 2" Sinst = #%B$0 " exp(!Sinst ) !W

Weak interactions: Transition amplitude exponentially small. No observable baryon number violating effects at T = 0 .. At high temperatures,B,L theN barrier can be crossed &µ j = g Tr( $ µ#!" F F ) µ 32 % 2 µ# !" Baryon Number Violation at finite T n AnomalousIns tprocessesanton config uviolaterations mbothay b ebaryon regarde dand as s eleptonmiclasi cnumber,al but configurampationslitudes for tunelling effect between vacuum states with preserve d Biff e–re L.nt bRelevantaryon num forber the explanation of the Universe baryon asymmetry. 2" Sinst = #%B$0 " exp(!Sinst 2) !W n At zero T baryon number violating processes highly suppressed Weak interactions: Transition amplitude exponentially small. No observable baryon number violating effects at T = 0 n At finite T, only Boltzman suppression

4MW T

T>T EW Tet

AtAt largelarge temperatures,temperatures,Klinkhamer and Manton transitionstransitions ’85, Arnold and Mc violatingviolating Lerran ’88 B+LB+L

(and(and preservingpreserving B-L)B-L) occuroccur veryvery often.often. 12

SPHALERONS Just toRelevance summarize: of Sphaleron Processes:

In SU(5) there existSU(5) gauge Example bosons Xµ whose SU(3), SU(2) and U(1)y quantum numbers are (3, 2,−5/6 ), as well as Higgs• In bosonsSU(5) GrandY with Unification quantum Theories, numbers there(3, 1, are 1/3 24 ), and whosegauge couplings bosons, are only similar 12 of to which those belong of the to vectors the SM.

Taken from arXiv:hep-ph/0609145 17

13 Baryon number is violated

If C and CP are violated,

Mean net baryon number produced in the decay of X

Mean net antibaryon number produced in the decay of X

The resulting baryon asymmetry is:

BX ++BX¯ =(r r¯)

14 Lepton Number

In order for this baryon asymmetry to be preserved, there must be departure from thermal equilibrium. Otherwise

(X Y )=(Y X) ! ! No baryon asymmetry will be generated

Thermal equilibrium broken due to the expansion of the universe, at temperatures below the heavy gauge boson masses

Net baryon number will be generated

What about lepton number ?

L = (1 r),L¯ =(1 r¯) X X L = L + L ¯ =(r r¯) X X

15 Sphaleron erasure of B

Sphaleron processes are in thermal equilibrium at high energies. Since they violate B + L, the sphaleron processes will suppress this quantity But since we started from an initial condition with B - L = 0, and this is preserved, then

B + L =0=2B = B =0 )

Generated baryon number is erased ! GUT baryogenesis in SU(5) or other B-L preserving GUT theory doesn’t work.

16 Leptogenesis

Baryon asymmetry could be generated if the generated asymmetry carries non-zero B-L charge Sphaleron could be used to our advantage, and we could generate a non-zero baryon charge starting from a net lepton number charge at high energies. Lepton number violation is naturally associated with heavy Majorana right-handed neutrinos. Such particles can a) Explain the smallness of the observed neutrino masses b) Lead to the necessary generation of lepton number via the decay of the Majorana neutrinos. Sphaleron processes convert this lepton number into Baryon number !

17 Type I see-saw mechanism: Introduce heavy right-handed neutrinos (at least two).

it!! See-sawThat 'mechanisms

TheAs itmost is well general known, Lagrangian after adding compatible the right-handed with the neutrinos Standard to theModel SM gaugemodel, symmetry one is allowed is: to write Majorana mass terms for these particles

Minkowski’77, Yanagida’80, Gell-Man, Ramond, Slansky’80

Naturally small due to the suppression For Yukawa couplings of order one, by smallness the large ofright-handed neutrino massesneutrino may masses be explained by large values of M

18 Lepton number generation 1- Generation of the lepton asymmetry Fukugita, Yanagida’86 At tree level, the total decay rate is:

c c The rate for N1  lH and N1  l H are identical. No CP asymmetry:

19 1- Generation of the lepton asymmetry 1- Generation of the lepton asymmetry 1- GenerationAt one of theloop ,lepton new diagrams asymmetry contribute to the decay rate: Generation of a lepton Asymmetry At one loop, new diagrams contribute to the decay rate: At one loop, new diagrams contribute to the decay rate:

Interference with the wave-function correction

Interference with the vertex correction Tricky! Calculable only when Mi -M1  Gi-G1

    Enhanced,Enhancement when of massesthe CP asymmetry are when the

closeright-handed (resonant neutrinos leptogenesis) are almost degenerate A lepton (and therefore a B-L) asymmetry is generated by

the heavy Majorana neutrino decays. Complex phases necessary

20 Baryon number generation • Several relevant processes in equilibrium at high temperatures, including weak sphalerons (essential), strong sphalerons, gauge and Yukawa processes • The condition of equilibrium leads to a relation between the chemical potential of the Higgs, quark and lepton species 8N +4 Harvey, Turner’90 B = f (B L)in 22Nf + 13 14N +9 L = f (B L)in 22Nf + 13 • Then, for three families of quark and leptons one gets

(B L)in nB 2 B 10 ✏1 ' 3 n '

21 A global fit to neutrino oscillation data Neutrino Masses and Mixing

Forero, Tortola, Valle (2014)

22 Parametrization of the “lost” parameters:

Work in the basis where the right-handed neutrino mass matrix is diagonal:

Relation with Neutrino Phenomenology The most general Yukawa coupling which solves this equation is:

Fermion Mass Spectrum Casas,Casas, AI Ibarra’01

Right-handed “Fixed” by neutrino masses experiments 3 real parameters

3 real parameters and 3 phases

Ulep

23 1- Upper bound on the CP asymmetry

1- Upper boundConsider on the the scenario CP asymmetry with hierarchical right-handed neutrinos. In this limit, the CP asymmetry produced in the decay of the Consider the lightestscenario right-handed with hierarchical neutrino right-handed is: neutrinos. In this limit, the CP asymmetry produced in the decay of the lightest right-handed neutrino is:

In the limit of hierarchical right-handed neutrinos M1Μ2, Μ3

In the limit of hierarchical right-handed neutrinos M1Μ2, Μ3 Bound on the Majorana masses • Assuming non-resonance behavior, and using the above parameterization, it is easy to show that Substituting the previous parametrization of the neutrino Yukawa coupling: Substituting the previous parametrization of the neutrino Yukawa coupling:

And therefore which• is bounded from above by: Davidson, AI which is bounded from above by: Davidson, AI Davidson, Ibarra’02 • So, the asymmetry would go to zero in the case of degenerate neutrinos. Taking the maximum value of the mass difference, one obtains 9 M1 > 10 GeV

9 • For thermal leptogenesis then also the rehating T, TR > 10 GeV 24 ImplicationsBounds foron theinflation Majorana Neutrino Masses and on the Reheating Temperature for Thermal Leptogenesis. To produceNo new thermally physics the apart right-handed from the neutrinosthree heavy the neutrinosUniverse must have been very hot in the past:

Giudice et al.

Inflation must have reheated the Universe to temperatures

larger than 109-1010 GeV  constraint on inflationary models 25 2- Flavour effects provide a new insight in the connection between leptogenesisCP-Violation and low energy CP violation. LetTake me the emphasize most general that Yukawa the previous coupling formula compatible for thewith the • low energy neutrino observations. asymmetry contains no dependence on the active neutrino mixing Ulep ! This means a disconnection between leptogenesis and the • Taking flavours properly into account: CP-violating effect in neutrino oscillation • However, it is well known that for temperatures as the ones considered here, the tau-lepton Yukawa is in equilibrium and one has to recalculate the asymmetries : Flavor matters

There is still a dependence on UAbadalep! If et CP al’06, violation Nardi iset observed al’ 06 • Consideringin the neutrino flavor sector, effects, leptogenesis the interrelation will gain support. between low energy experiments and leptogenesis is reestablished !

26 Hierarchy Problem ? • The heavyAn explicit neutrinos hierarchy induce a correction problem to the Higgs massThe parameter see-saw Lagrangian that in is: the see-saw mechanism case may be easily computed The Higgs doublet interacts with heavy degrees of freedom

Quadratic divergence!

• Some people argue that then the large neutrino masses necessary for leptogenesis call for supersymmetry :-) • I will not expand on that, but in such a case, one could see effects in charged lepton flavor experiments like µ e (also gravitino problem associated with high reheating! T). 27 Predictions of this leptogenesis picture

• Neutrinos are Majorana particles. Best probes of this idea in neutrinoless double beta decays

• imgres

• CP-violation in neutrino sector. Best probe in oscillation experiments, which test its presence on Ulep. If it is measured, necessary ingredient proved.

28 Baryogenesis at the Weak Scale

29 Baryon Asymmetry Preservation

If Baryon number generated at the electroweak phase transition,

Kuzmin, Rubakov and Shaposhnikov, ’85—’87 Baryon number erased unless the baryon number violating processes are out of equilibrium in the broken phase. Therefore, to preserve the baryon asymmetry, a strongly first order phase transition is necessary:

30 Electroweak Phase Transition

Higgs Potential Evolution in the case of a first order

Phase Transition

31

31 Finite Temperature Higgs Potential in the SM

D receives contributions at one-loop proportional to the sum of the couplings of all bosons and fermions squared, and is responsible for the phenomenon of symmetry restoration

E receives contributions proportional to the sum of the cube of all light boson particle couplings

Since in the SM the only bosons are the gauge bosons, and the quartic coupling is proportional to the square of the Higgs mass,

32 Yukawa couplings) than δhR, because they give a zero contribution at this order , we can easily obtain:

b ∗ 2 b ∗ 2 δhR = αwλiλf KliKlf IR(Ml ), δhL = αw KliKlf IL(Ml ) (5.15) !l !l and

λf ∗ 2 c = KliKlf Im(Ml ), (5.16) mi !l where we have defined π I (M 2) = H(M , M ), I (M 2) = λ2I (M 2), I (M 2) = πλ M C(M , M ). (5.17) R l − 2 l W L l l R l m l l l l W

2 It then follows that the first effect in the asymmetry appears at O(αw) and it comes only from the interference of the O(α ) effects in δhb and δhb . Consequently, there is no effect w R-22 L 2 5. 10 b a t-5O(αw) at leading order in T , because at this order δhR = 0. It is interesting to analyze 3. 10 -22 the expression for the non-integrated asymm4.e t10ry at this order, where the GIM mechanism -5 2. 10is explicitly operative: -22 3. 10 -5 -22 1. 10 2. 10 † † † ∆(2) T r[ r(1) r ( 1) + -22r(2) r(0) + r(0) r(2) antiparticles ] CP-ViolationCP 1. 10 sources 0 ≡ − r0 m ((r0 )2 (r0 )2) r0 1 1 b b 0 ∗ jj j 0ii − jj jj Im[ δhL)jiδhR)ij] Im rii [ 2 + + ( + ) ] . 47.9∼ 48 48.1 48.2× 48.3{ 48.4dij 2d20iidijd30ji 40 dii50dij 60dji 70} 80 Another problem!i,j for the realization| | of the SM electroweak (5.18) baryogenesis scenario:(a) (b) ∆(2) can be shown to have the following structure: Figure C7P: (a) shows the non-integrated CP asymmetry (∆CP ) produced by down quarks in the narrow energy range which dominates for zero damping rate, when masses are neglected ∆(2) α2 (2iJ) T int T ext, (5.19) Absencein the inte rofnal sufficientlyloop. (b) show strongs the draC mCP-violatingP a∼tic weffect of tu sourcesrning on the damping rate effects, in the sawmheraepJp,rToxinimt aantdionT.ext contain the expected “`a la Jarlskog” behaviour of the asymmetry as a function of the weak angles (J), the internal quark (T int) and the external quark masses Eventhe o(t Thassumingeexrt)h.aTndh,e icno ntpreservationhnecctiaosne bγet=we0ena n(ofd5.1 in8baryon)tahnedli(m5. i1tasymmetry,9m) is<< γ 23, th baryone express ionumbern for the peak ̸ generationvalue of the a sseveralymmetry orderbeautif uoflly magnituesreduces to lower than required b b 2 ∗ ∗ 2 2 2 2 Im[δhL)jiδhR)ij] = αwλiλj2i Im[KliKljKl′jKl′i](λl λl′ )IR(Ml′ )IR(Ml ) l,l′ − 3 ! 2 2 2 2 2 2 2int 2 2 2 2 2 2 max 3π αW T (mt mc )(mt αwmλiuλ)j((mc2iJ)mTu) ,(mb ms)(ms md)(mb m(5d.)20) ∆CP = J − ≡ − ± − − − − ⎡# 2 32 α ⎤ M 6 (2γ)9 with √ s W ⎣ ⎦ (5.26) ∗ ∗ 2 This was expected from naJive ordIemr-[oKf-mKagKnit′ uKde′ ]ar=gucmcecntss.s s s , ≡ ± li lj l j l i 1 2 3 1 2 3 δ Finally, the results (5.25) show that non-leading effects in T give the main contribution and to t:heQuarasymmketDamry in pthine gcasreateof non-vanishing damping rate and, in contrast with [11], the up-sector dominates the asymminettry. 2 2 2 T (λl λl+1)IR(Ml )IR(Ml+1). (5.21) Very recently, Huet and Sather≡[28l] have−analyzed the problem. These authors state that they confirm our conclusions. As we!haGavela,d done in Hernandez,ref. [1], they s tOrloff,ress tha Penet the d aandmpi nQuimbay’94g rate is 12 a source for quantum decoherence, and use as well an effective Dirac equation whic33h takes it Thursday,into Augustaccou 19,nt .2010They discuss a nice physical analogy with the microscopic theory of reflection 33 of light. They do not use wave packets to solve the scattering problem, but spatially damped waves, as in our heuristic treatment at the begin3n1ing of Sect. 4.

5.4 Wall thickness. Notice that the derivation in sect. 4 is totally independent of the shape of the function r(k). The only requirement was a singularity structure limited to a cut in the region of total reflection. This is quite generic: only for very special wall shapes can other singularities be expected. For instance, when the wall is not monotonous, a pole with an imaginary part may express the decay of a quasi-bound state trapped in a potential well. The thin wall approximation used in this paper is valid only for wall thickness l 1/6γ, while perturbative estimates suggest l .1GeV−1 1/6γ. The CP asymmetry, gene≪rated in ≥ ≥ 23This is valid for down external quarks, the case we considered

34 Preservation of the Baryon Asymmetry n EW Baryogenesis would be possible in the presence of new boson degrees of freedom with strong couplings to the Higgs. n Supersymmetry provides a natural framework for this scenario. Huet, Nelson ’91; Giudice ’91, Espinosa, Quiros,Zwirner ’93. n Relevant SUSY particle: Superpartner of the top n Each stop has six degrees of freedom (3 of color, two of charge) and coupling of order one to the Higgs

M. Carena, M. Quiros, C.W. ’96, ‘98 n Since

Higgs masses up to 120 GeV may be accomodated

34 Comments Stop particles have explicit soft mass terms and acquire temperature dependent masses at high T The effective coupling is reduced due to the presence of mixing. For left-handed stops much heavier than the right handed ones (m m ) Q U 4g2 A2 m2 m2 + 3 T 2 + .. + h22 1 t t˜1 U t 2 ' 9 mQ !

This is the object entering in the cubic term In order to strengthen the phase transision the mixing must be small and the right-handed stop mass parameter must be negative. One stop is lighter than the top ! But mixing and stop masses controls the Higgs mass !

35 The upper bound on the Higgs comes from the impossibility of obtaining larger Higgs masses for the chosen parameters

Carena, Quiros, C.W.’98 Figure 2: Region of the mh–m t parameter space for which a strongly first order phase transition takes place is shown within solid lines. The short-dashed lines demark the But regionphase for whichtransition a two-step phasecan! transition still be may strong, occur. The rifegion one on the includes right of the the dashed line and left of themetastable short-dashed may lead regions. to a metastable vacuum state.

For larger values of mQ, however, large logarithmic contributions must be resummed.

36 21 technical framework for the treatment of the light stop scenario, in the presence of a very heavy stop, was defined by using an effective theory approach and it was subsequently applied to the EWBG scenario in Ref. [23]. For completeness, and in order to define a few representative updated points, we present the results of such an analysis here. In order to properly analyze the issue of EWBG we have complementedthezerotem- perature results with the two-loop finite temperature effective potential [12]. Light stops may be associated with the presence of additional minima in the stop–Higgs V (t,˜ h)po- tential, and therefore the question of vacuum stability is relevant and should be considered by a simultaneous analysis of the stop and Higgs scalar potentials. All points shown in Fig. 1 fulfill the vacuum stability requirement 1. For values of the heavy stop massFinalmQ Resultsbelow a few tens of TeV, the maximal Higgs mass that can be achieved consistent with a strong first order phase transition is about 122 GeV.(Meta)stability The main reason isof that Color larger valuesBreaking of the Higgs Minima boson masassumeds would demand large values of the mixing parameter Xt, for which the effective coupling ghht˜t˜ of the Point A B C D E F G lightest stop to the Higgs is suppressed,A /m 0.5 0 turning0 0 the0.3 0.4 electroweak0.7 phase transition too | t Q| weak. In the effective theory thetan couplingβ 15 15ghh2.0t˜t˜ is1.5 given1.0 1.0 by 1.0 6 Table 1: Values of the fundamental parameters at the scale mQ =10 TeV corresponding to the 6 benchmark points shown in the left panel of Fig. 1. mQ ≤ 50 TeV mQ ≤ 10 TeV 120 120 D 115 115 2 C 2 Xt E g ˜˜ h 1 (1 + ∆g) (2.1) hhtt t 2 110 110 ≃ ! − mQ " B where ∆g contains one-loop threshold and radiative corrections (see Ref. [31] and Fig. 1 105 105 F [GeV] of Ref. [33]). Such Higgs mass values, below 122[GeV] GeV, would not lead to an explanation

of the Higgs signal observed at the LHC [24–30]. 100 ˜ ˜ t 100 t For larger values of the heaviest stop mass the logarithmic corrections to the Higgs m m mass increase and larger values of the Higgs mass95 may be obtained for the same value 95 of Xt/mQ, preserving the strength of the phase transition. In this paper we shall focus 6 90 on benchmark points where mQ =10TeV. This is represented in the right panel of 90 G A 114 117Fig. 120 1, where 123 it is126 shown that129 values 132 of the Higgs114 mass as 117 large as 120 132 GeV 123 may126 be 129 132 obtained for this value of m and (relatively large values of) tan β 15, corresponding to mh [GeV] Q mh [GeV] ≃ 6 point A. However any given point inside the EWBG region calculated at mQ =10 TeV and moderate tan β can also be conveniently obtained by decreasing m and increasing Figure 1: The window with φ(Tn) /Tn ! 1foragluinomassM3 =700GeV,Q mQ 50 TeV tan β.Evenfortan6 ⟨ β 1⟩ values of the Higgs mass about 125 GeV may be obtained ≤ (left panel) and mQ 10 6 TeV (right≃ panel). for mQ≤=10 TeV, as it is represented by point G in Fig. 1. The largest values of the Higgs mass areM. obtained Carena, for the G. largest Nardini, possible M. values Quiros, of the HiggsC.W.’13 mixing parameter, which in turn leads to the smallest values of the lightest stop mass consistent with a strong electroweak phase transition. Points A and B have tan β 15 while the rest of ≃ 1There is an apparentthe points losshave ofsmaller perturbativity values of tan β inas the shown thermal in Tab. correct 1, whichions defines to the valuest˜ potential of associated 2 with the longitudinalthe fundamental modes of parameters the gluon. for In the our benchmark work wepoints considered used in this t workhat, due. Finally to their let us large tempera- 37 stress that, although in this paper we concentrate on the MSSM case, the value of m ture dependent masses, the terms proportional to the third power of their thermal massesQ in the high can be considerably lowered in some non-minimal UV completions of the LSS [36]. temperature expansion are efficiently screened and do not lead to any relevant contribution to the t˜ potential. 3 Light Neutralinos and the EWBG Scenario

In this section, we shall study the effects of light neutralinos on the Z and Higgs in- visible width, as well as on the stop phenomenology within the EWBG scenario. As it was discussed in section 1, a light stop with relevant couplings to the Higgs (leading to

2 Notice that the parameters At Xt as µ = (100 GeV) mQ in the LSS. ≃ O4 ≪

5 LHC Higgs Physics CombiningBut we all cannot channels determine the LHC experiments the Higgs foundcouplings a best very fit to accurately the Higgs production The propertiesrate consistent of the recently with that discovered one of a HiggsSM Higgs boson of aremass close close to to the 125 SM GeV ones Large Variations of Higgs couplings are still possible

As these measurements become more precise, they constrain possible extensions of the SM, and they could lead to the evidence of new physics.

It is worth studying what kind of effects one could obtain in well motivated 38 extensions of the Standard Model, like SUSY. Monday, August 26, 2013 (for an extensive review, see Christensen, Han and Su’13)

2 The stop masses, for X m and m m , are approximately given by t ' Q3 Q3 u3 2 2 2 2 Xt m˜ m + m 1 , (3) t1 ' u3 t m2 Q3 ! 2 2 2 2 Xt m˜ m + m 1+ , (4) t2 Higgs' Q 3Physicst Constraintsm2 Q3 ! Chung, Long, Wang’12 where X =(A µ/ tan ). The value of the light stop mass is then given approximately t t Light Stop Contribution to Higgs Loop Processes by m and the value of heavier stop mass by m . For stop masses larger than the Higgs u3 • In a normalization in which theQ 3stops contribute a factor 4 to the mass, their loop contributionsamplitude, the to stops the contributeor gg amplitude like are approximately proportional to [58] 2 t˜ mt 2 2 2 A m˜ + m˜ X . (5) ,gg / m2 m2 t1 t2 t t˜1 t˜2 For the diphoton rate, the2 SM contribution2 2 to the amplitude Hence, for values• of the mixing parameter Xt > (<)(m˜ +m˜ ), the stops lead to a reduction would be approximately (-15) and governedt1 t2 by W contributions. (enhancement) of the gluon-gluon Higgs production and an enhancement (reduction) of the In the limit of light stops we are considering, one can see the Higgs to diphoton• decay width. In particular, in the presence of a large hierarchy for the soft appearance of the light stop coupling we discuss before. masses, mQ mu , and for large values of tan , the stop loop e↵ects depend dominantly on 3 • 3This contribution grows for light stops and small mixing, and can the relative magnitudecause of importantAt with respect enhancement to mQ3 . of Eq. the (5) gluon provides fusion a process good parametrization rate. of the stop e↵ects,• The but diphoton it underestimates decay branching the stop ratio contributions will be affected when in their a negative masses are of the order of or smallerway. than the Higgs mass. Specifically for stop masses of the order of a 100 GeV, they are approximately 30% larger than the value suggested by Eq. (5). 39 For reference, we note that we use a normalization in which the SM contributions to these amplitudes are At 4andAW,t 13. The stop contributions to the gluon fusion gg ' ' t˜ amplitude are approximately given by A,gg, Eq. (5), while those to the amplitude are t˜ approximately given by (8/9 A,gg). Two comments are in order:

If the stop contribution is of the same sign as the top contribution, it adds to the gluon • fusion amplitude; however it will then contribute to the suppression of the dominant W amplitude in , and vice versa;

Comparing the relative magnitudes of the SM and stop contributions, we note that • the stop e↵ects on the gluon fusion amplitude are approximately a factor of 3.5 larger than their e↵ects on the amplitude, normalized to their SM values.

8 SM SM Γgg / Γgg , M = 10 TeV, tanβ = 5 Γgg / Γgg , M = 10 TeV, tanβ = 15 160 4 160 4

150 150 3.5 3.5 140 140

130 3 130 3 (GeV) (GeV) 1 1 t 120 2.5 t 120 2.5 m m 110 110 2 2 100 100

90 1.5 90 1.5 110 115 120 125 130 135 110 115 120 125 130 135 Higgs Signaturesmh0 (GeV) put a strong constraintm h0on (GeV) this scenario

SM SM σBR / σBR , M = 10 TeV, tanβ = 5 σBR / σBR , M = 10 TeV, tanβ = 15 160 A. Menon 1.6 and D. Morrisey’09 160 1.6 SM SM Γgg / Γgg , M = 1000 TeV, tanβ = 5 Γgg / Γgg , M = 1000 TeV, tanβ = 15 150 1.55 150 1.55 160 Phase Transition 4 160vs. Higgs Rates 4 140 140 150 1.5 150 1.5 3.5 3.5 130 130 140 1.45 140 1.45 (GeV) (GeV) 1 1 t 120 3 t 120 3

m 130 m 130 1.4 1.4

110 (GeV) (GeV) 110 1 1 t 120 2.5 t 120 2.5 m 1.35 m 1.35 100 110 100 110 2 2 90 100 1.3 90100 1.3 110 115 120 125 130 135 110 115 120 125 130 135 90 1.5 90 1.5 mh0 (GeV) mh0 (GeV) 110 115 120 125 130 135 110 115 120 125 130 135 mh0 (GeV) Diphoton Production mh0 (GeV) SM SM σBR / σBR , M = 1000 TeV, tanβ = 5 σBR / σBR , M = 1000 TeV, tanβ = 15 Figure 160 2: Higgs boson decay width to 1.6 gluons Γ(h0 160 gg)relativetotheSMasafunctionof 1.6 1500 1.55 150→ 1.55 mh and mt˜1 for M =10, 1000 TeV and tan β =5, 15. 140 140 1.5 1.5 130 130 0 1.45 1.45 (GeV) (GeV) 1 1 Γt (120h gg)computedintheLSTrelativetothevalueintheSMwiththesat 120 me value of the m 1.4 m 1.4 → 0 Higgs 110 boson mass as a function of mh and mt˜1 for 110 tan β =5, 15 and M =10, 1000 TeV. In 2 2 2 generating 100 these figures we scan over 1.35 the ranges 100(150 GeV) m (0 GeV) and 1.35 0 − ≤ U3 ≤ ≤ X 90t/M 0.9. These parameter ranges 1.3 are a superset 90 of the values that areconsistentwitha 1.3 | 110 | ≤ 115 120 125 130 135 110 115 120 125 130 135 strongly first-ordermh0 (GeV) phase transition required for EWBG.[Cohen, (Wealsoexhibitthedependenceof DM,m Pierceh0 (GeV) ’12] 0 the physical massesSimilarmt˜1 results,and mh byon Cohen, the underlying Morrissey Lagrangian and Pierce’12 parameters showed in Appendix A.) Higgs 0physics testability of this model at the LHC FigureFrom 4: Inclusive Fig. 2 we•pp seeInconsistent a significanth γγ enhancementproduction with rate in measured the at decay the LHC width Higgs relativeto gluons torates. relative the SM to as the a SM byMoreover, as much0 as other a factor→ authors of→ four. found Since these this decayresults width to be is nearinconsistently proportional with LHC to the data Higgs function of mh and mt˜1 for M =10, 1000 TeV and tan β =5, 15. production rate through[Curtin, gluon Jaiswal, fusion at Meade hadron ’12; colliders Katz at+ leadingPerelstein order ’14] (LO), including the Tevatron at √s =1.96 TeV and the LHC at √s =10 14 TeV, our results imply a strong 40 0 3 − functionenhancement of mh inand thismt˜1 production.Asabove,weconsidertan mode. The enhancementβ =5, 15 is and greatestM =10 for, 1000 smaller TeV, values and 2 2 2 2 scanof theover Higgs the ranges boson m(1500 and GeV) stop m˜ mmasses,3 (0 corresponding GeV) and 0 to smallerXt/M values0. of9.m Weand also −h ≤t1 U ≤ ≤ | | ≤ U3 assumeXt /m thatQ3 .Indeed,itisforthesesmallermassvaluesthattheelectro gluon fusion makes up 83% of the inclusive production rateweak before phase including transition the enhancement|can| be strong from enough a light to stop, allow which viable is approximately EWBG. The recent the ex analysipectedsofRef.[27]findsthat fraction contributing to the inclusive signal for a light SM Higgs boson at the LHC with √s =14TeV[56,57].From 3 Our computation of the Γ(h0 gg)widthisatLO.WhileNLOcorrectionsaresignificant,their Figs.effect 2 and is to 3 rescale we know both that the SM the and Higgs→ squark boson LO production contributions rate to the thro productionugh gluon rate fusion in nearly is enhanced the same whileway the[41, 53, branching 54]. Thus, ratio we expect into the diphotons bulk of these is higher-ord suppressed.er corrections The total to cancel rate in is the approximately ratios of decay proportionalwidths, interpreted to the as product ratios of gluonof these fusion quantities. production This rates, produthat wect display. is ultimately enhanced in the light stop scenario because the stop loop interferes constructively with the top quark loop in the production rate and destructively with a more dominant W ± loop in the decay width to diphotons. In the region of parameter space7 consistent with a strongly first-order phase transition, the inclusive production rate is enhanced by a factor between 1.4and1.6. The light stop in the MSSM EWBG scenario will also lead to modifications of other Higgs boson search channels. There will be an enhancement in all channels for which gluon fusion is the dominant production mechanism. For example, the rate for inclusive pp h0 ZZ∗ at the LHC (assuming the gluon fusion makes up 83% of the total rate) is increased→ → by a factor of 1.75–3 within the parameter region consistent withviableEWBG.Ontheother hand, the suppression in the h0 γγ branching fraction reduces proportionally the signal →

9 only about 1σ above the SM predictions. Similar results are obtained at ATLAS, which shows central values of order 2 times the SM cross sections in both production channels. In the ZZ channel, ATLAS and CMS are in good agreement with SM predictions [24–29], +0.5 but with rates about (1.3 0.6) and 0.7− times the SM one, and hence also consistent ± 0.4 with slight suppressions or enhancements of these rates. Similarly, the best fit to the ! " +0.5 ATLAS and CMS WW production rates [24–30] are about (1.4 0.5) and (0.6− )times ± 0.4 the SM one, respectively. CMS also shows a large suppression of WW production in the vector boson fusion channel, but with a very large error. CMS also reports a suppression of ττ production in the vector boson fusion channel [25,29]. No suchsuppressionisseen in the gluon fusion channel. Overall, considering all the production and decay channels explored at the LHC, the best fit performed at CMS shows a suppression of the vector boson fusion induced rates with respect to those expected in the SM and gluon fusion induced rates that are consistent with the SM ones. As we will show, such overall behavior is consistent with the predictions of the LSS in the presence of light neutralinos. 0 ! As it is highlighted in Fig. 3, for mχ1 63GeV the Higgs cannot decay into neutralinos. In such a case the Higgs production via gluon fusion is enhancedbyafactorlargerthan two. Then the subsequent Higgs decay into weak bosons, whose rate is unmodified by light stops at leading order, is enhanced by the same factor oftwo.Thisenhancement factor is instead suppressed by 25% if the Higgs decays into photons because of the stop ∼ 0 " destructive-interference contribution. If mχ1 63GeV the Higgs invisible width increases. HoweverAlternative for relatively large : Increase values of tan Higgsβ, as pointInvisible B, and Width for µ = M2 = 200 GeV, the coupling gh11 is suppressed, and opening kinematically the Higgs decay channel into neutralinos reducesM. Carena, the G. visible Nardini, branching M.Quiros, ratios C.W., by JHEP at most 130210%. (2013) In conclusion, 001 for point (σ × BR) Point G BR Point G M =200 GeV µ=200 GeV M2=200 GeV µ=200 GeV 2 4

qq,ll,VV (ggF) 1.4 WW bb qq,ll,VV (VBF) gg γγ (ggF) 1.2 0 0 3 γγ (VBF) χ 1 χ 1 + χ mass χ 1 1 m 0 SM

100 GeV mass χ 2 0.8

BR 2 BR) × σ × 0.6 σ (

1 0.4 BR

0.2

0 0 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 0 m 0 [GeV] mχ1 [GeV] χ1

Figure 4: The same asLHC Fig. Data 3 but put for pointstrong G constraints and M2 = µon= this 200 possibility. GeV. The Higgs mass is about 125Only GeV. a narrow band, of neutralino masses close to threshold would be allowed in this case The invisible width would be of order 50 percent and then, again, could be tested. Weak Boson Fusion processes would be suppressed. This model is in agony. 14

41 RelicRelic DensityDensity ConstraintsConstraints ((A r g ( M 1 , 2 µ ) = ! / 2 ))

! O n Lightly CP-v iStopolating andphase Relicwe con sDensityider is the oConstraintsne relevant for In the presence of a light stop, the most relevant annihilation the generation of the baryon asymmetry, namely : Arg( M1,2 µ ) = ! / 2 channel is the coannihilation between the stop and the neutralino ! Neutralinoat small massco-an differences.nihilation w Relicith s tdensityops eff imaycien bet f onaturallyr stop-n ofeu thetral ino massobserved differences size in of this order region 15-20 of parameters. GeV . Light Higgs resonant annihilation may be relevant (here Higgs mass is about 115 GeV)

tan ! = 7

C. Balazs, M. Carena, A. Menon, D. Morrissey, C.W. 05 Ciriglliano, Profumo, Ramsey-Musolf 07, Martin’06--’07

42 Stop Bounds

In the region of parameters of interest, they may be avoided when different decays become competitive or if there are, for instance, light staus or tau sneutrinos. Another challenge for this scenario.

43 mt˜1 /GeV = 110 130 150 170 190 210 230 ∆m/GeV = 10 1920 1716 1585 1360 1056 1015 845 20 1170 1085 948 877 717 676 570 30 762 746 676 679 548 551 433 40 559 516 514 507 442 444 348 50 437 449 422 428 364 343 279

−1 Table 2: Number of signal events in the jet+E/ T channel for 100 fb and for various combinations of m ˜ and ∆m = m ˜ m 0 . The event numbers in the table have an intrinsic t1 t1 − χ˜1 statistical uncertainty of a few tens from the Monte Carlo error. Alternative Channel at the LHC calibrated from jZ with JetsZ l+l −plus[28], and missingfor similar reaso nsEneras in thegyphoton case, the → SUSY background has been assumed to be small. M. Carena, A. Freitas, C.W.’08 When Intheord estopsr to pro candeed w itneutralinoh this analysis, masswe have udifferencesed the same c uists small,as in Ref .the[28]: jets will be soft. 1. Require one hard jet with pT > 100 GeV and η < 3.2 for the trigger. | | One can2. L alookrge mi sforsing ethenerg yproductionE/ T > 1000 GeV .of stops in association with jets

or photons.3. Veto a gSignature:ainst electrons wJetsith pT (or> 5 photons)GeV and muo npluss with missingpT > 6 Ge Venergyin the visible region ( η < 2.5). | | M. Carena, A. Freitas, C.W. ‘08 4. Require the second-hardest jet to go in the opposite hemisphere as the missing mo- mentum (i.e. the first and second jet shouldIncludinggo in rou gsystematicshly the same associateddirection): 200 ∆φ(pT,j2 , ⃗pγ) > 0.5. This cut reduces background from W τν where the tau decay 200 with jet and→ missing energy products are emitted mostly i−n1 the opposite direction as the hard initial-state jet. fb 30 -1 determination. Dominant missing 100− 1 fb Application of these cuts leads to ba SM Background of about 7 fb, corresponding to 700 -1 0 f energy background, coming from 30 fb−1 10 150eve150nts for 100 fb [28]. − 1 -1 ] 300fb fb Z’s, calibrated with the electron V 00 e ˜ ˜∗ 3 G The NLO corrections to t1t + j are not available channel.in the literature. However, experience [ 1 -1 0 1 ˜ frχ om tt¯j [30] suggests that8t hfbe K-factor should be close to one. Therefore, contrary to what

m(neu) 100 −1

m Tevatron 8 fb 100was done in the photo n c a-1se, we shall not include a K-factor for the signal. 2 fb Tevatron 2 fb−1 Excellent reach until masses of the order of 220 GeV and larger. U50sing the above dDefi1nfebd−1cuts, the expected number of signal events is listed in Tab. 2 for -1 ∅ 50varioD0us s1t ofbp and neutralino mass values. Fig. 3 shows the projected 5σ discovery reach with the statistical significance estimated by S/√B and inFullcludi nregiong syste mconsistentatic errors. withIn or dEWBGer to estim0ate the systematic errors, we have explored the fwillollo wbeing probedtwo stra tbyegi ecombinings, (a) and (b the): 100 120 140 160 180 200 220 LHC with the Tevatron searches. (a) The first strategmy˜d[eGteerVm] ines the dominant SM backgrounds directly from data [28]. In 0 t1 54 100 pa120rticula140r, the j160Z bac180kgroun200d with220Z νν¯, which contributes about 75% of the SM m(stop) 44 Figure 3: Projected LHC 5bσacdkigscrovuenrdyarfetaecrhcuints,thceanjebte+iE/nfTercrheadnfn→roelm. FjZorwciotmhpZarisoln+lt−h,el = e, µ. The Z l+l− → → current and future Tevatronc9a5li%brCat.iLon. ecxhcalunsnieolnisboaubnodust fsoervelinghttimsteospssmaarlelearlstohashnotwhne.Z νν¯ background in the 44 Figure 2: Projected reach in jet+E/ channel. → signal region (pT,ll > 1 TeV), thuTs leading to the error estimate δsysB = √7B. A 5% error on E/ T induces a 36% uncertainty on the background, as determined • by simulating(bjZ) AwlittehrnZativeνlyν¯,. similar to the previous section, individual systematic error sources can was done in the photon case, websehidaellntn→ifioetdi:nclude a K-factor for the signal. Using the above The PDFs can be extracted from reference SM processes, e.g. jZ with Z l+l−. defined cuts, Fi•g. 2 shows the projected 5σ discovery reach with the statistica→l significance Thus the uncertainty is mainly limited by the statistical8error for the standard estimated by S/√B, and where systematic erros have been included. candle process. For the region of high transverse momenta (pT > 500 GeV), which is relevant for the present analysis, this leads to relatively small error of 3%. In order to estimate the systematic errors, we have used the following two strategies, (a) and Systematic uncertainties associated with the lepton veto are negligible, since this (b): • cut plays a role mainly for the jW background with W eν or W µν, which → → (a) Determine baccokngtriobuutneds odnilryecabtloyutfr5o%mtodtahteato[1ta3l].SMThbaisckwgrooruknsd.for jZ with Z νν¯, which → contributes aIbnosuutm7m5a%ry,otfhtishestrSaMtegbyaycikelgdrsoauntodtaalfteestrimcauttesd, asynsdtemcaanticbeerrionrfeorfraebdoufrto3m6%j,Z with + − + − Z l l , l =streo,nµgl.y TdohmeinZated bly lthecuanlicbertaatiinotyn ocfhtahnenmeilssiisngabE/oumt esaesvuernemteinmt.es smaller than the → → T Z νν¯ background in the signal region (pT,ll > 1 TeV), thus leading to the error estimate → I√t is evident that the data-driven method (a) for determining the systematic error of the SM δsysB = bac7kBgr.ounds leads to better results. This is different from the photon case in section 3, in (b) Detewrhmicihnemienthdoidvi(dbu)aplrosvyesstteombaetciconevrernoiernts.ouTrhceeism: provement in the results associated with method (a) in the jet case is due to the larger statistics, while on the other hand a much E/laTr:ge5r%bacekrgrroorunodnunEc/erTta: in3t6y%is ienffduecetdofnor bmaecthkogdro(ub)ndby, tahse derertoerrimn itnhedmibssyinsgimenuerlgayting jZ • widtheteZrminaνtiνo¯n.. The→results presented in Fig. 3 make use of method (a). Searches in the jet plus E/ T PDchFasnnferlomturnreofuertetnocbeeSmMoreprporocmesisiensg, teh.agn. inγ t+heZphwotiotnh pZlus E/ Tl+chl−an:ne3l%. T(hsetyata.lloewrror for • to test the co-annihilation region up to relatively large values o→f the stop mass, of about pT2>00 5G0e0VGoerVla)r.ger. Moreover, when complemented with Tevatron search analyses, they Lepton veto: negligible error, since this cut plays a role mainly for the jW back- • ground with W eν or W µν, whic9h contributes only about 5% to the total SM background. → →

Total: 36%.

The results presented in Fig. 2 make use of method (a). Searches in the jet plus E/ T

6 Baryon Number Generation

n Baryon number violating processes out of equilibrium in the broken phase if phase transition is sufficiently strongly first order.

Cohen, Kaplan and Nelson, hep-ph/9302210; A. Riotto, M. Trodden, hep-ph/9901362; Carena, Quiros, Riotto, Moreno, Vilja, Seco, C.W.’97--’03, Konstantin, Huber, Schmidt,Prokopec’00--’06 Cirigliano, Profumo, Ramsey-Musolf’05--06

45 In general we will relate particle number changing, or fermion number violating, rates ΓX with the corresponding rates per unit volume γX ,as, 6 γ Γ = X . (4.2) X T 3 The involved weak and strong sphaleron rates are: 8 Γ =6κ α5 T, Γ =6κ α4T, (4.3) ws ws w ss ss 3 s respectively, where κ =20 2[44]andκ = (1). The particle number changing ws ± ss O rates that will be considered both in the symmetric and in the broken phase are: ΓY2 , corresponding to all supersymmetric and soft breaking trilinear interactions arising from

the htH2QT term in the superpotential, ΓY1 ,whichcorrespondstothesupersymmetric trilinear scalar interaction in the Lagrangian involving the third generation squarks and the Higgs H1,andΓµ,whichcorrespondstotheµcH˜1H˜2 term in the Lagrangian. There are also the Higgs number violating and axial top number violation processes, induced by the Higgs self interactions and by top quark mass effects, with rates Γh and Γm,respectively, that are only active in the broken phase.

We will write now a set of diffusion equations involving nQ, nT , nH1 (the density of ˜ ¯ ¯ ¯˜ H1 (h1, h1)) and nH2 (the density of H2 (h2, h2)), and the particle number changing rates≡ and CP-violating source terms discussed≡ above. In the bubble wall frame, and ignoring theThe curvature diffusion of the bubble equations wall, all quantities for the become evaluation functions of ofz ther + v baryont, ≡ ω where vω densityis the bubble takes wall velocity. into account The diffusion the equations interaction are: rates and sources n n n + ρ n n n v n′ =D n′′ Γ Q T H h Γ Q T ω Q q Q − Y k − k − k − m k − k ! Q T H " ! Q T " n n n + n 6Γ 2 Q T +9 Q T +˜γ (4.4) − ss k − k k Q ! Q T B "

n n n + ρ n n n v n′ =D n′′ + Γ Q T H h + Γ Q T ω T q T Y k − k − k m k − k ! Q T H " ! Q T " n n n + n No Baryon number +3Γ 2 Q T +9 Q T γ˜ (4.5) ss k − k k − Q ! Q T B " violation: Chiral charges generated In general we will′ relate′′ particlenQ numbernT nH + changing,ρ nh ornH fermion numberfrom violating, CP-violating rates sources vωnH =DhnH + ΓY Γh +˜γH+ (4.6) kQ − kT − kH − kH (gamma’s) ΓX with the corresponding rates! per unit volume"γX ,as, n n n + n /ρ # n v n′ =D n′′ + ρ Γ Q T H h (Γ +4Γ ) h +˜γ (4.7) ω h h h Y k − k − k − h µ k H− ! Q T 6 γHX " H ΓX = 3 . # (4.2) where all derivatives are with respect to z,TDq 6/T and Dh 110/T are the cor- respondingHere di fftheusion ki’s constants are statistical in the quark andfactors∼ Higgs sectorrelatings[46],∼ then densitiesn + n , to chemical In general we will relateH ≡ particleH2 numberH1 changing, or fermion number violating, rates The involvedn weakn andn , strongk k sphaleron+ k , Γ ratesΓ + Γ are:and ρ Γ Γ Γ .Theparameter h potentialsH2 H1 H andH1 theH2 GammasY Y2 Γ Yare1 with rates theY corresponding perY2 unitY1 ratesvolume. per unit In volume particular,γ ,as, ρ is≡ in the− range 0 ≡ ρ 1. In previous≡ analysesX [30, 31,≡ 40] the− limit Γ was X ≤ ≤ µ →∞ 5 8 4 6 γX Γws =6κws α T, Γss =6κss α T, Γ = (4.3). (4.2) w 12 3 s X T 3 The involved weak and strong sphaleron rates are: respectively, where κws =20 2[44]andκss = (1). The particle number changing ± O 46 rates that will be considered both in the symmetric and in the broken phase5 are: ΓY2 , 8 4 Γws =6κws α T, Γss =6κss α T, (4.3) corresponding to all supersymmetric and soft breaking trilinear interactions arisingw from 3 s the htH2QT term in the superpotential, ΓY1 ,whichcorrespondstothesupersymmetricrespectively, where κws =20 2[44]andκss = (1). The particle number changing ± O trilinear scalar interaction in the Lagrangian involvingrates that will the be third considered generation both in squarks the symmetric and and in the broken phase are: ΓY2 , corresponding to all supersymmetric and soft breaking trilinear interactions arising from the Higgs H1,andΓµ,whichcorrespondstotheµcH˜1H˜2 term in the Lagrangian. There are the htH2QT term in the superpotential, ΓY1 ,whichcorrespondstothesupersymmetric also the Higgs number violating and axial top numbertrilinear scalar violati interactionon processes, in the Lagrangian induced by involving the the third generation squarks and ˜ ˜ Higgs self interactions and by top quark massthe effects, Higgs withH1,and raΓtesµ,whichcorrespondstotheΓh and Γm,respectively,µcH1H2 term in the Lagrangian. There are that are only active in the broken phase. also the Higgs number violating and axial top number violation processes, induced by the We will write now a set of diffusion equationsHiggs involving self interactionsn , andn , byn top(the quark density mass effects, of with rates Γh and Γm,respectively, that are only activeQ in theT brokenH1 phase. ˜ ¯ ¯ ¯˜ H1 (h1, h1)) and nH2 (the density of H2 (h2,Weh2)), will and write the now particle a set of dinumberffusion equations changing involving nQ, nT , nH1 (the density of ≡ ≡ ˜ ¯ ¯ ¯˜ rates and CP-violating source terms discussedH1 above.(h1, h1)) In and thenH2bubble(the density wall of frame,H2 (h2 and, h2)), and the particle number changing rates≡ and CP-violating source terms discussed≡ above. In the bubble wall frame, and ignoring the curvature of the bubble wall, all quantities become functions of z r + vωt, ignoring the curvature of the bubble wall,≡ all quantities become functions of z r + vωt, where vω is the bubble wall velocity. The diffusion equations are: ≡ where vω is the bubble wall velocity. The diffusion equations are:

′ ′′ nQ nT nH + ρ nh ′ nQ′′ nT nQ nT nH + ρ nh nQ nT vωnQ =DqnQ ΓY vωnQΓm=DqnQ ΓY Γm − k − k − k − k −− k kQ − kT − kH − kQ − kT ! Q T H " ! Q T! " " ! " nQ nT nQ + nT nQ nT nQ + nT 6Γss 2 +9 +˜γQ (4.4) 6Γ 2 +9 +˜γ − kQ − kT kB(4.4) − ss k − k k Q ! " ! Q T B "

′ ′′ nQ nT nH + ρ nh nQ nT vωnT =DqnT + ΓY + Γm kQ − kT − kH kQ − kT ′ ′′ nQ nT nH + ρ nh nQ nT! " ! " vωnT =DqnT + ΓY + Γm nQ nT nQ + nT k − k − k +3Γkss 2− k +9 γ˜Q (4.5) Q T H Q k −T k k − ! " ! ! Q " T B " nQ nT nQ + nT +3Γss 2 +9 γ˜Q (4.5) kQ − kT kB − n n n + ρ n n ! "v n′ =D n′′ + Γ Q T H h Γ H +˜γ (4.6) ω H h H Y k − k − k − h k H+ ! Q T H " H n n n + n /ρ # n v n′ =D n′′ + ρ Γ Q T H h (Γ +4Γ ) h +˜γ (4.7) ′ ′′ nQ nT nH + ρ nh ω h nHh h Y h µ H− kQ − kT − kH − kH vωnH =DhnH + ΓY Γh +˜γH+ ! (4.6)" kQ − kT − kH − kH # ! where" all derivatives are with respect to z, D 6/T and D 110/T are the cor- # q h ′ ′′ nQ nT nH + nh/ρ nh ∼ ∼ responding diffusion constants in the quark and Higgs sectors[46],nH nH2 + nH1 , vωnh =Dhnh + ρ ΓY (Γh +4Γµ) +˜γH− (4.7) ≡ kQ − kT − kHnh nH2− nH1 , kH kH1 k+HkH2 , ΓY ΓY2 + ΓY1 and ρ ΓY ΓY2 ΓY1 .Theparameter ! ρ is≡ in" the− range 0 ≡ ρ 1. In previous≡ analyses [30, 31,≡ 40] the− limit Γ was ≤ ≤ # µ →∞ where all derivatives are with respect to z, D 6/T and D 110/T are the cor- q ∼ h ∼ responding diffusion constants in the quark and Higgs sectors[46],n n 12+ n , H ≡ H2 H1 nh nH2 nH1 , kH kH1 + kH2 , ΓY ΓY2 + ΓY1 and ρ ΓY ΓY2 ΓY1 .Theparameter ρ is≡ in the− range 0 ≡ ρ 1. In previous≡ analyses [30, 31,≡ 40] the− limit Γ was ≤ ≤ µ →∞

12 with with ∞ 2 ∞ −ζλ+ λ = dζ γ˜ (ζ) e 2 2 2 H− −ζλ+ A v =+4Γ1Dh + v +4Γ2Dh 0 dζ γ˜ (ζ) e λω 2 ω 2 " H− A ∞vω +4Γ1Dh + vω +4Γ2Dh 0# with 1 −ζλ+ " 0 =! dζ f+∞(!z) e # (4.28) 1 −ζλ+ A Dλ0+=!0 dζ f+(!z) e ∞ (4.28) " 2 − A Dλ+ = 0 dζ γ˜ (ζ) e ζλ+ λ 2 2 H− A " v +4Γ1D + v +4Γ2D 0 and ω h ω h " and 1 ∞ # ! ! −ζλ+ 0 =1 dζ 2f+(z) e (4.28) λ±A= Dλ+vω 0 vω +4Γ D . (4.29) 2D "1± 2 λ± $= %vω vω +4& Γ D . (4.29) and 2D ± Since we assume theOnce sphalerons the chiral are inactivecharge$ inside is %obtained, the bubbl wees,& can the baryoncompute density is constant inSince the broken we assume phase the and sphalerons satisfies, inare the inactive1 symmetric inside p2hase, the bubbl an equationes, the baryon where n densityL is the baryon numberλ± =generationvω viav +4sphaleronΓ D . effects (4.29) acts asconstant a source in [30] the and broken there phase is an and explicit satisfies, sphaleron-indu2D in the± symmetriccedω relaxation phase, term an equation [45, 42] where n $ % & L acts as a source [30] and there is an explicit sphaleron-induced relaxation term [45, 42] Since we′ assume the sphalerons are inactive inside the bubbles, the baryon density is vωnB(z)= θ( z)[nF ΓwsnL(z)+ nB (z)] (4.30) constant in the broken′− phase− and satisfies, inR the symmetric phase, an equation where nL vωnB(z)= θ( z)[nF ΓwsnL(z)+ nB (z)] (4.30)z where n =3isthenumberoffamiliesandacts as a source [30] and there− is− anis the explicit relaxation sphaleron-indu coeR fficientced [45], relaxation term [45, 42] F R where nF =3isthenumberoffamiliesandHere R is the relaxation′ coefficientis the relaxation coeSymmetricfficient [45], Broken vωnB(5z)= θ( Rz)[nF ΓwsnL(z)+ nB (z)] (4.30) = nF Γ−ws −. R Phase(4.31) Phase R 4 5 where nF =3isthenumberoffamiliesand= nF Γws . is the relaxation coefficient [45],(4.31) Eq. (4.30) can be solved analytically and gives,R 4 in the brokeR nphasez 0, a constant baryon asymmetry, 5 ≥ Eq. (4.30) can be solved analytically and gives,= innF theΓws broke. nphasez 0, a constant(4.31) The solution to this equationR 4 gives the final baryon≥ baryon asymmetry, 0 n Γ Eq. (4.30)number cann = be solveddensityF ws analytically in thedz n broken( andz) e gives,zR /vphase,ω . in the namely brokenphasez(4.32)0, a constant B L0 − vω −∞ ≥ baryon asymmetry, "nF Γws zR/vω nB = dz nL(z) e . (4.32) − vω −∞ 0 Using now the explicit solutions for nH and nh given in Eqs. (4.25) and (4.22), we can n"F Γws zR/vω cast the explicit solution for the baryonn asymmetryB = as, dz nL(z) e . (4.32) Using now the explicit solutions for−n vandω n−∞given in Eqs. (4.25) and (4.22), we can H "h cast the explicit5 solutionk k +8 fork k the baryon9k k asymmetry+ as, D Using nowQ B the explicitT B solutionsQ T forHnH andh nh givenH in Eqs. (4.25) and (4.22), we can nB = nF Γws − A A + B 2 (4.33) cast the explicitkH (kB solution+9kQ +9 fork theT ) baryon+ asymmetryvωα+ D as,+ v 5kQkB +8kT kB $9kRQkT H + Rh ω &D H nB = nF Γws − A A + B 2 (4.33) where all symbols used in Eq. (4.33)kH (kB have+9k beenQ +9 previouslykT ) defi+ vned.ωα+ D + vω 47 5kQkB +8kT kB 9$kQRkT H + h R D &H nB = nF Γws − A A + B 2 (4.33) The validity of our analytical approximationkH (kB +9kQ is+9 guaranteedkT ) by+ v theωα+ dominanceD + v of nH where all symbols used in Eq. (4.33) have been previously$R defined. R ω & over nh,whichinturnisrelatedtothetanβ suppression ofγ ˜H− and the presence of The validity of our analytical approximation is guaranteed by the dominance of nH Γµ.Infactwereweworkinginthelimitwhere all symbols used in Eq.Γµ (4.33) havewe would been previously find that defi thened. density nh is over nh,whichinturnisrelatedtothetan→∞ β suppression# ofγ ˜ and the presence of negligible. On theThe other validity hand, of in our the analytical limit Γµ approximation0andtanβ is1wewouldreallyexpect guaranteedH− by the dominance of nH Γ .Infactwereweworkinginthelimit→ Γ we≃ would find that the density n is n >n µ,duetothedominanceof˜over nh,whichinturnisrelatedtothetanγ overγ ˜ ,atleastforlargevaluesofµ β suppression ofmγ ˜H−whereand the the presenceh of h H H− H+ →∞ # A ∆β suppressionnegligible.Γ ofµ.Infactwereweworkinginthelimit Onγ ˜ theis more other severe. hand, in However the limit smallΓµ valuesΓµ0andtan of tanweββ,aswenoticedearlier would1wewouldreallyexpect find that the density nh is H+ → →∞ ≃ # n >n ,duetothedominanceof˜negligible. On the other# hand,γ in#over theγ ˜ limit,atleastforlargevaluesofΓµ 0andtanβ 1wewouldreallyexpectm where the in this paper,h H are strongly disfavored in ourH− scenarioH by+ recent→ LEP bounds≃ on the HiggsA nh >n# H ,duetothedominanceof˜γ overγ ˜ ,atleastforlargevaluesofmA where the mass.∆ Hence,β suppression we have offoundγ ˜H+ thatis more the severe. analytical However approximatioH− smallH+ valuesnisaccuratewithanerror of tan β,aswenoticedearlier ∆β suppression ofγ ˜ is more# severe. However# small values of tan β,aswenoticedearlier whichin depends this paper, on the are chosen strongly values disfavoredH+ of the supersymmetric in our scenario by par recameters,ent LEP but bounds it is always on the Higgs # # # much smallermass. Hence, thanin this the we paper, other have are found uncertainties strongly that disfavored the involved analytical in in our the approximatio scenario final calculation. by recnisaccuratewithanerrorent LEP In section bounds 5on the Higgs mass. Hence, we have# found that the analytical approximationisaccuratewithanerror we willwhich provide depends explicit on comparison the chosen with values the of numerical the supersymmetric result, while parall plotsameters, will but be done it is always which depends on the chosen values of the supersymmetric parameters, but it is always using themuch numerical smaller solution than the of other system uncertainties (4.12). involved in the final calculation. In section 5 much smaller than the other uncertainties involved in the final calculation. In section 5 we will provide explicit comparison with the numerical result, while all plots will be done we will provide explicit comparison with the numerical result, while all plots will be done using the numerical solution of system (4.12). using the numerical solution of16 system (4.12).

16 16 Generation of Baryon Asymmetry n Here the Wino mass has been fixed to 200 GeV, while the phase of the parameter µ has been set to its maximal value. Necessary phase given by the inverse of the displayed ratio. Baryon asymmetry linearly decreases for large

Carena,Quiros,Seco,C.W.’02

M2 = 200GeV

M. Carena, M. Quiros, M. Seco, C.W. ‘02 Balazs, Carena, Menon, Morrissey, C.W.’05

48 Electric Dipole Moments (EDM)

• Two loop: [Cirigliano, Li, Profumo, Ramsey-Musolf ’09] [Chang, Keung, Pilaftsis ’98; ...]

Electron electric dipole moment

n Asssuming that sfermions are sufficiently heavy, dominant contribution comes from two-loop effects, which depend on the same phases necessary to generate the baryon asymmetry.

n Chargino mass parameters scanned over their allowed values. The • Does notelectric decouple! dipole moment is constrained to be Electric smaller than Dipole Moments (EDM) 29 • ACME: de < 8.7 10 ecm Balazs, Carena, Menon, Morrissey, C.W.’05⇥ • Two loop: [Cirigliano, Li, Profumo, Ramsey-Musolf ’09] [Chang, Keung, Pilaftsis ’98; ...]

Chang, Keung, Pilaftsis ‘99, Pilaftsis ‘99 Chang, Chang, Keung ‘00, Pilaftsis ‘02 • Does not decouple! 49 29 • ACME: de < 8.7 10 ecm ⇥ Electric Dipole Moments (EDM)

• Two loop: [Cirigliano, Li, Profumo, Ramsey-Musolf ’09] [Chang, Keung, Pilaftsis ’98; ...]

17

• ComparingDoes not decouple! bino- and wino-driven EWB 29 • ACME: de < 8.7 10 ecm • Electron EDM: ⇥

M 95GeV, M 190GeV, | | 200GeV, tan 10, m 0 300GeV Ref. point: 1 ! 2 ! # ! " ! A ! Cirigliano, Profumo, Ramsey-Musolf’06 YL, S. Profumo, M. Ramsey-Musolf, arXiv:0811.1987

50 e.g.1: {N}MSSMBaryogenesis[Pietroni beyond’92; Davies etthe al. ’96; MSSM Huber+Schmidt ’00; Menon et al. ’04; ...] e.g.1: {N}MSSM [Pietroni ’92; Davies et al. ’96; Huber+Schmidt ’00; Menon et al. ’04; ...] • {N}MSSM = MSSM + singlet (S): • {N}MSSM = MSSMW + singletSH (S):H + ... u · d W SHu Hd + ... • Singlet VEV: µeff= S · h i • Singlet VEV: µeff = S • The singlet can induce ha stronglyi first-order EWPT • The driven singlet partly can by induce tree-level a strongly effects first-order with: [Carena,EWPT Shah, C.W.’12] [Huang et al. ’14; Kozaczuk et al. ’14] • drivenm h partly125 GeV by .tree-level effects with: ' [Huang et al. ’14; Kozaczuk et al. ’14] • m h 125 GeV . • Higgs' rate corrections consistent with data. •• HiggsViable rate Bino-Singlino corrections dark consistent matter. with data. • •HiggsViable rate Bino-Singlino corrections darkare still matter. expected.

• Higgs rate corrections are still expected. 51 ( Electroweak Phase Transition

Defining

2 2 2 2 2 (ts +˜a ) ˜2 2 Ve↵ =( m + AT ) 2 2 2 + ms +

Non-renormalizable potential controlled by m s . Strong first order phase transition induced for small values of m s . Contrary to the MSSM case, this is induced at tree level.

52 Instead of analyzing the potential of a specific model, one can try to analyze the generic potential with non-renormallizable operators 2 2 2 4 6 8 10 Ve↵ =( m + AT ) + + +  + ⌘ + ... Perelstein, Grojean et al Here, 1/⇤2,  1/⇤4 and ⌘ 1/⇤6. / / / One of the relevant characteristics of this model is that the self interactions of the Higgs are drastically modified.

For instance, the trilinear coupling of the Higgs, coming from the third derivative of the Higgs potential at the minimum can be enhanced with respect to the SM.

10 Joglekar, Dashed line : c 240 Critical temperture Huang, Li, C.W.’15 15 Green and dark blue 230 regions lead to a first order P.T. with a cutoff 220 larger than 400 and 20 500 GeV, respectively. 210 Enhancements of order 5 to 8 may be obtained. 15 200 53 3 4 5 6 7 8 SM ghhh/ghhh 53 Unfortunately, the test of this possibility is hard at the LHC.

Frederix et al’14

HH production at 14 TeV LHC at (N)LO in QCD

MH=125 GeV, MSTW2008 (N)LO pdf (68%cl) 102 pp →HH (EFT loop-improved)

1 pp 10 →HHjj (VBF) [fb] (N)LO σ pp→ttHH 100

pp→WHH

-1 10 tjHH pp→ZHH pp→ MadGraph5_aMC@NLO

-4 -3 -2 -1 0 1 2 3 4

λ/λSM Very few events in the SM case after cuts are implemented. Figure 3: Total cross sections at the LO and NLO in QCD for HH production channels, at the √s =14 TeV LHC as a function of the self-interactionThe number coupling λ.Thedashed(solid)linesandlight-(dark-)colourbandsco of events does not improverrespond to thedramatically LO (NLO) results and to thein scale gluon and PDFfusion uncertainties processes added linearly. The SM valueseven of the crossforsections enhancements are obtained at λ/λSM =1. of order 5. In addition, Grantgain Agreement is in numbers region PITN-GA-2010-264564 of parameters (LHCPhe- [11] where M. Gouzevitch, acceptance A. Oliveira, J. Rojo, R. Rosenfeld, is low. G. P. Salam, noNet) and PITN-GA-2012-315877 (MCNet). The work of et al., JHEP 1307,148(2013), arXiv:1303.6636 [hep-ph] . [12] T. Plehn, M. Spira, and P. Zerwas, Nucl.Phys. B479,46(1996), FM and OM is supported by the IISN “MadGraph” con- arXiv:hep-ph/9603205 [hep-ph] . 54 vention 4.4511.10, by the IISN “Fundamental interactions” [13] S. Dawson, S. Dittmaier, and M. Spira, Phys.Rev. D58,115012 convention 4.4517.08, and in part by the Belgian Federal (1998), arXiv:hep-ph/9805244 [hep-ph] . Science Policy Office through the Interuniversity Attrac- [14] T. Binoth, S. Karg, N. Kauer, and R. Ruckl, Phys.Rev. D74, 54 113008 (2006), arXiv:hep-ph/0608057 [hep-ph] . tion Pole P7/37. OM is "Chercheur scientifique logistique [15] J. Baglio, A. Djouadi, R. Gröber, M. Mühlleitner, J. Quevillon, postdoctoral F.R.S.-FNRS". et al., JHEP 1304,151(2013), arXiv:1212.5581 [hep-ph] . [16] R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.-S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, to appear . References [17] The code can be downloaded at: https://launchpad.net/madgraph5,http://amcatnlo.cern.ch. [1] F. Englert and R. Brout, Phys.Rev.Lett. 13,321(1964). [18] U. Baur, T. Plehn, and D. L. Rainwater, Phys.Rev.Lett. 89, [2] P. W. Higgs, Phys.Rev.Lett. 13,508(1964). 151801 (2002), arXiv:hep-ph/0206024 [hep-ph] . [3] CMS-HIG-13-003. CMS-HIG-13-004. CMS-HIG-13-006. CMS- [19] V. Hirschi et al., JHEP 05,044(2011), arXiv:1103.0621 [hep-ph] HIG-13-009. (2013). . [4] ATLAS-CONF-2013-009. ATLAS-CONF-2013-010. ATLAS- [20] A. Denner, S. Dittmaier, M. Roth, and D. Wackeroth, CONF-2013-012. ATLAS- CONF-2013-013. (2013). Nucl.Phys. B560,33(1999), arXiv:hep-ph/9904472 [hep-ph] . [5] E. Asakawa, D. Harada, S. Kanemura, Y. Okada, and [21] A. Denner, S. Dittmaier, M. Roth, and L. Wieders, Nucl.Phys. K. Tsumura, Phys.Rev. D82,115002(2010), arXiv:1009.4670 B724,247(2005), arXiv:hep-ph/0505042 [hep-ph] . [hep-ph] . [22] Q. Li, Q.-S. Yan, and X. Zhao, (2013), arXiv:1312.3830 [hep- [6] S. Dawson, E. Furlan, and I. Lewis, Phys.Rev. D87,014007 -ph] . (2013), arXiv:1210.6663 [hep-ph] . [23] P. Maierhöfer and A. Papaefstathiou, (2013), arXiv:1401.0007 [7] R. Contino, M. Ghezzi, M. Moretti, G. Panico, F. Piccinini, [hep-ph] . et al., JHEP 1208,154(2012), arXiv:1205.5444 [hep-ph] . [24] J. Grigo, J. Hoff,K.Melnikov,andM.Steinhauser,Nucl.Phys. [8] G. D. Kribs and A. Martin, Phys.Rev. D86,095023(2012), B875,1(2013), arXiv:1305.7340 [hep-ph] . arXiv:1207.4496 [hep-ph] . [25] D. de Florian and J. Mazzitelli, Phys. Rev. Lett. 111, 201801 [9] M. J. Dolan, C. Englert, and M. Spannowsky, Phys.Rev. D87, (2013), 10.1103/PhysRevLett.111.201801, arXiv:1309.6594 055002 (2013), arXiv:1210.8166 [hep-ph] . [hep-ph] . [10] M. J. Dolan, C. Englert, and M. Spannowsky, JHEP 1210,112 [26] D. Y. Shao, C. S. Li, H. T. Li, and J. Wang, JHEP07,169 (2012), arXiv:1206.5001 [hep-ph] . (2013), arXiv:1301.1245 [hep-ph] .

6 In all the baryogenesis mechanisms I discussed in my talk, one question remains unanswered :

What explains the factor five difference between the baryon and Dark Matter contributions to the energy budget of the Universe ?

It could be orders of magnitude difference, but they are of the same order !

55

55 Asymmetric Dark Matter and Baryon Number

The idea is to explain the intriguing relation between the abundances of ordinary matter and Dark Matter

Dark Matter, could carry a conserved quantum number; it could be a baryon of a different neutral sector Nusinov’85, Barr’91, Kaplan’92, Dodelson et al’92 Dark Matter and baryon (or leptons) can proceed from similar processes, like the decay of a heavy neutral state

The number densities would be related. What about the masses ?

Beautiful idea by Bai and Schwaller’12, relying on IR fixed points, relating the QCD scale to the Dark Sector QCD. States charged under both sectors, with masses of a few TeV needed (experimental tests)

Many other models exist. See review by Petraki and Volkas ’13.

56 Conclusions • The origin of the matter-antimatter asymmetry is one of the fundamental open questions in particle physics and cosmology • Several proposals exist for its dynamical generation, and lead to very different physical phenomena • The resolution of this question will involve experiments in the high energy, intensity and cosmic frontiers. • Of particular relevance are the Majorana nature of neutrinos and the presence of CP-violation, as well as the search for electric dipole moments, for instance, of the electron and the neutron. • Collider physics is already constraining some scenarios. • The relation between the baryon and Dark Matter contributions to the Universe energy budget may be a clue towards the resolution of this puzzle.

57 Parameters with strongly first order transition

n All dimensionful parameters n Values constrained by perturbativity varied up to 1 TeV up to the GUT scale.

Maximum value of n Small values of the singlet singlet mass mass parameter selected

Menon,Morrissey,C.W.’04

58 the cut cos φ > 0.7 is useful. Finally, two of the jets have to combine to the invariant aco,lj − mass of the Z boson, while the other two jets have to combine to W mass, mj1j2 MZ < 10 0 0 | − | GeV and mj3j4 MW < 10 GeV. This removes most of χ˜2χ˜4 background and is also effective on tt¯. | − | After application of these cuts, the SM background is removed to a negligible level, while 0 0 still a sizeable contamination of background from χ˜3χ˜4 is left. In total B = 245 background events remain, compared to S = 186 events for the signal. Since the cross-section for the neutralino process can be measured independently, as described above, it can be subtracted, but the additional error from this procedure needs to be taken into account. The resulting expected precision for the χ˜1±χ˜2∓ cross-section is δσ1±2 = 13%. For the chargino signal, the spectrum of the 4-jet invariant mass has an upper limit of minv,j,max = m m 0 , which can be used to extract information about the heavy chargino χ˜2± χ˜1 mass. The neutr−alino background typically leads to slightly smaller 4-jet invariant masses, so that this upper edge is not contaminated. From a fit to the data, one obtains +5.4 minv,j,max = 287.2 4.2 GeV, (49) − + which together with the m 0 mass measurement from the analysis of χ˜ χ˜− production di- χ˜1 1 1 rectly translates into +5.5 mχ˜± = 319.5 4.3 GeV. (50) 2 − 3.3.8 Combination of sparticle measurements at ILC

+ Feeding in the precise measurement of the neutralino mass from the analysis of χ˜1 χ˜1− produc- 0 0 0 0 tion, the masses of the heavier neutralinos from χ˜2χ˜4 and χ˜3χ˜4 production can be determined much more accurately, +1.1 +2.5 mχ˜0 = 106.6 1.3 GeV, mχ˜0 = 181.5 4.9 GeV, mχ˜0 = 278.0 3.5 GeV. (51) 2 − 3 ± 4 − For the lightest neutralino and the charginos, the expected errors given in the previous sections are not improved by combining with the other neutralino observables, so that one obtains +0.4 +5.5 0 0 mχ˜ = 33.3 0.3 GeV, mχ˜± = 164.98 0.05 GeV, mχ˜ = 319.5 4.3 GeV. (52) 1 − 1 ± 4 − From a χ2 fit to all mNeutralinoass and cross-section Massobservable sMatrix, constraints on the underlying neu- tralino and chargino parameters can be extracted. For completeness, we also allow a tripe- singlet coupling κ as in the NMSSM. In the nMSSM, κ must be zero, but it is interesting not to impose this requirement a priori, but see how well it can be checked from an experimental analysis. The parameter κ enters in the (5,5)-entry of the neutralino mass matrix, M 0 c s M s s M 0 1 − β W Z β W Z 0 M c c M s c M 0 ⎛ 2 β W Z − β W Z ⎞ Mχ˜0 = c s M c c M 0 λv λv , (53) ⎜− β W Z β W Z s 2⎟ ⎜ ⎟ ⎜ sβsWMZ sβcWMZ λvs 0 λv1⎟ ⎜ − ⎟ ⎜ 0 0 λv2 λv1 κ ⎟ ⎜ ⎟ ⎝ ⎠ 27

In the nMSSM, = 0.

59

59 Upper bound on Neutralino Masses

Values of neutralino masses below dotted line consistent with perturbativity constraints.

Maximum value of Lightest neut. mass

Perturbative limit

Menon,Morrissey,C.W.’04

60 Relic Density and Electroweak Baryogenesis

Region of neutralino masses selected when perturbativity constraints are impossed. Z-boson and Higgs boson contributions shown to guide the eye. Neutralino masses between 35 GeV and 45 GeV. Higgs decays aected by presence of light neutralinos. Large invisible decay rate.

Proper relic density

Z-width constraint

Menon,Morrissey,C.W.’04

61 Direct Dark Matter Detection

Since dark matter is mainly a mixing betwen singlinos (dominant) and Higgsinos, neutralino nucleon cross section is governed by the new, -induced interactions, which are well defined in the -6 relevant regime of parameters 10

CDMS II 2005 -7 10 XENON10 Recent results from the CDMS II 2007 -8 Xenon 100kg

(pb) 10 SI

XENON 100 experiment ! XENON tends to disfavor this scenario -9 SuperCDMS 25kg 10 Xenon 1000kg SuperCDMS 100kg Balazs,Carena, Freitas, C.W. ‘07 -10 Zeplin 4 10 30 31 32 33 34 35 36 37 38 39 40 See also m~ (GeV) Z1 Barger,Langacker,Lewis,McCaskey, Input model Shaughnessy,Yencho’07 LHC scan, excluded LHC scan, allowed ILC scan, ± 1 ! ILC scan, ± 2 !

62 Singlet Mechanism for the generation of µ in the NMSSM

One could break the symmetry by self interactions of the singlet

W = ⇥SH H S3 + h QUH + ... u d 3 u u

No dimensionful parameter is included. The superpotential is protected by a Z3 symmetry, ⇥ exp(i2/3)⇥ This discrete symmetry would be broken by the singlet v.e.v. Discrete symmetries are dangerous since they could lead to the formation of domain walls: Different volumes of the Universe with different v.e.v.’s separated by massive walls. These are ruled out by cosmology observations.

One could assume a small explicit breakdown of the Z3 symmetry, by higher order operators, which would lead to the preference of one of the three vacuum states. That would solve the problem without changing the phenomenology of the model.

63 c c c Hˆ1 Hˆ2 Sˆ Qˆ Lˆ Uˆ Dˆ Eˆ Bˆ Wˆ gˆ WnMSSM

U(1)R 0 0 2 1 1 1 1 1 0 0 0 2

U(1)PQ 1 1 -2 -1 -1 0 0 0 0 0 0 0

Table 1: Charges of fields under the Abelian U(1)R and U(1)PQ symmetries of the super- potential.

yf lead to one physical phase in the CKM quark mixing matrix, which however is constrained to be relatively small by present data from many heavy-flavor experiments. The phase of m12 will be addressed below. Beyond the superpotential, new complex phases can appear in through supersymmetry breaking. The soft supersymmetry breaking Lagrangian reads

2 2 2 2 = m H†H + m H†H + m S + (t S + a SH H + h.c.) Lsoft 1 1 1 2 2 2 s | | s λ 1 · 2 + (M1BB + M2W W + M3 g˜g˜ + h.c.) · (5) 2 2 2 2 ˜ 2 2 ˜ ˜ 2 2 + m q˜† q˜ + m u˜R + m ˜ dR + m˜ l† l + m e˜R q˜ L!·! L "u˜| "| d| | l L · L e˜| | + (y A q˜ H u˜∗ + y A q˜ H d˜∗ + h.c.). u u L · TCP-Violating2 R d d L · 1 R Phases

Here Hi, S, q˜L, u˜R, d˜R, ˜lL, e˜R are the scalar components of the superfields Hˆi, Sˆ, Qˆ, Uˆ, Dˆ, Lˆ, Eˆ, where the quark and lepton fields exist in three generations (the generation index has been suppressed in the formuThela). conformalB, W, g˜ de (massnote independent)the fermionic sectorcom pofone then tstheoryof the is gauge super- invariant under an R-symmetry and a PQ-symmetry, with multiplets. Among the soft breaking parameters, aλ, ts, M1,2,3 and Au,d can be complex. However not all their phases ar!e p"hysical. To see this, one can observe that the superpotential ˆ ˆ ˆ ˆ ˆ ˆ c ˆ c ˆc ˆ ˆ is invariant under an U(1)R symmHe1tryH, 2withS tQhe LchargeU sDlisteEd iBn TWab.gˆ1. WInnMaSSddition,M it obeys an approximate Peccei-QuUi(n1n)R sym0 me0try2 U(11)PQ1 , 1whic1h is1 b0roke0n 0by th2e singlet tadpole term m2 . Both U(1) Ua(1n)dPQ U(11) 1 ar-2e b-1rok-e1n b0y som0 e0of 0the0su0persy0mmetry breaking ∝ 12 R PQ parameters. Table 1: Charges of fields under the Abelian U(1)R and U(1)PQ symmetries of the super- potential. With the help of the TheseU(1)R symmetriesand U(1)PQ allow, th toe fiabsorveelds ca phasesn be ro intotate redefinitiond so that the phases two parameters become rofea fields.l. By Theana remaininglyzing th ephasescharg emays, it beca absorvedn be see nintoth athet t he following products remain yinf levadaritoanonet upnhydseicralbphasothe inR-theandCKMPQ-quarktransformations:mixing matrix, which however is constrained to be relatimassvely sm parameters.all by present datOnlya fr physicalom many heaphasesvy-flav oremain,r experim givenents. Tbyhe phase of m12 will be addressed below. Beyond the suapregrp(omten1∗2titasl,anλe)w, complex phases can appearTextin t h rHiggsough s uSectorpersymmetry breaking. The soft supersymmetry breaking Lagrangian reads arg(m1∗2tsMi), i = 1, 2, 3, Chargino-Neutralino Sector 2 2 2 2 (6) = m H†H + m H†H + m S + (t S + a SH H + h.c.) Lsoftarg(1m1∗2t1sAu)2, 2 (32 generationss | | s ), λ 1 · S-up2 sector + (M1BB + M2W W + M3 g˜g˜ + h.c.) arg(m1∗2tsAd), (3· generations), S-down sector (5) 2 2 2 2 2 2 2 2 † ˜ ˜† ˜ + mq˜ q˜L q˜L + mu˜ u˜R + md˜ dR + m˜l lL l L + me˜ e˜R !·! "| "| | | · | | corresponding to 10 physical CP+-v(yioAlatq˜ingHpu˜h∗a+seysAinq˜adHdidt˜∗io+nht.co.).the CKM phase. Without u u L · 2 R d d L · 1 R 64 loss of generality, the phases of m12 and ts can be chosen real, so that the physical phases Here Hi, S, q˜L, u˜R, d˜R, ˜lL, e˜R are the scalar components of the superfields Hˆi, Sˆ, Qˆ, Uˆ, Dˆ, Lˆ, Eˆ, are transferred inwtoheraeλt,heMqu1a,2r,k3 aandnd lepAtoun,dfi.elds exist in three generations (the generation index has been In this work, sfuorpprseismsedplicin itthye,fogauginormula). B,unificW, g˜ deationnote theis faersmsuionicmed,comspoonethatnts ofMthe1 :gaugeM2 :suMper-3 1 : ≈ multiplets. Among the soft breaking parameters, aλ, ts, M1,2,3 and Au,d can be complex. 2 : 6. In this case, the gaugino masses carry one common phase, φM1 = φM2 = φM3 φM. However not all their phases ar!e p"hysical. To see this, one can observe that the superpotential≡ To simplify the analysis further, the phases in Au,d and aλ are set to zero. is invariant under an U(1)R symmetry, with the charges listed in Tab. 1. In addition, it obeys an approximate Peccei-Quinn symmetry U(1)PQ, which is broken by the singlet tadpole 2 term m12. Both U(1)R and U(1)PQ4are broken by some of the supersymmetry breaking param∝eters. With the help of the U(1)R and U(1)PQ, the fields can be rotated so that the phases two parameters become real. By analyzing the charges, it can be seen that the following products remain invariant under both R- and PQ-transformations:

arg(m1∗2tsaλ),

arg(m∗ tsMi), i = 1, 2, 3, 12 (6) arg(m1∗2tsAu), (3 generations),

arg(m1∗2tsAd), (3 generations), corresponding to 10 physical CP-violating phases in addition to the CKM phase. Without loss of generality, the phases of m12 and ts can be chosen real, so that the physical phases are transferred into aλ, M1,2,3 and Au,d. In this work, for simplicity, gaugino unification is assumed, so that M : M : M 1 : 1 2 3 ≈ 2 : 6. In this case, the gaugino masses carry one common phase, φ = φ = φ φ . M1 M2 M3 ≡ M To simplify the analysis further, the phases in Au,d and aλ are set to zero.

4