BSM round-up
Riccardo Rattazzi, EPFL
Annual Theory Christmas Meeting, 2015, IPPP Durham
Monday, December 21, 2015 1 Weak Scale Naturalness:
Ideology, Ingenuity & Reality
Riccardo Rattazzi, EPFL
Annual Theory Christmas Meeting, 2015, IPPP Durham
Monday, December 21, 2015 2 In QM whatever is possible is also compulsory
selection rules
= n1i nki O Oi i = ci λ1 ...λk i O dim = ∆ dim = ∆
If max it seems we are missing something O|exp |Oi|
Un-Naturalness = failure of dimensional analysis and selection rules
Monday, December 21, 2015 3 Mass Hierarchies
ΛUV
∼ scale invariant dynamics
∼ fixed point of RG L
ΛIR
Naturalness of Λ Λ stability of fixed point IR UV
3 options
Monday, December 21, 2015 4 1. Marginality
ΛUV the fixed point theory does not possess scalar operators with dimension strictly less than 4
ΛIR
mass = c Λ 4 L UV O − 1/ ΛIR = c ΛUV ΛIR = c ΛUV
algebraica y small c and is enough to produce hierarchy
Rattazzi, Zaffaroni 01 Ex: Yang-Mills, TechniColor, Randall-Sundrum model Strassler 03
Monday, December 21, 2015 5 2. Symmetry
ΛUV = Λ2 Lmass UV O2
small parameter protected by symmetry ΛIR
ϵ Λ = √ Λ • must be hierarchica y small IR UV • how does this smallness originate?
Ex: QCD, Supersymmetry
Monday, December 21, 2015 6 3. Sequestering
ΛUV
ΛIR
Monday, December 21, 2015 7 3. Sequestering
ΛUV
ΛIR
Monday, December 21, 2015 7 3. Sequestering SFT2
() ΛUV SFT1 O
ΛIR
Monday, December 21, 2015 7 3. Sequestering SFT2
() ΛUV SFT1 O
D1 D2 D1+2 Dilations × → by small coupling
ΛIR Λ Λ technically natural IR ∼ UV
Monday, December 21, 2015 7 3. Sequestering SFT2
() ΛUV SFT1 O
D1 D2 D1+2 Dilations × → by small coupling
ΛIR Λ Λ technically natural IR ∼ UV
• SFT2 = ‘UV completion of gravity’ = ΛUV /MP
Ex. a-gravity • not clearly compatible with basic principles Salvio, Strumia 2012 • but imagine there was a gorgeous candidate for SFT1? ....well there isn’t: Giudice, Isidori, Salvio, Strumia 2014
Monday, December 21, 2015 7 The Standard Model
ΛUV ≣ fixed point LSM ∼ Lfree
H†H ≣ relevant and unprotected Λ m IR ∼ W
Naturalness demands not too large ΛUV
How large ΛUV can we tolerate compatibly with Naturalness?
What can we broadly say about the physics at ΛUV ?
Monday, December 21, 2015 8 But notice:
a seemingly un-natural hierarchy Λ m offers a remarkable bonus UV W
(d 4) 1 (5) 1 (6) SM = ≤ + + 2 + ... L L ΛUV L ΛUV L
• Accidenta y possesses all the symmetries we observe in Nature: B, L, Flavor,... • Not the case in any natural completion of the SM, where we have to resort to extra ad hoc assumptions
Monday, December 21, 2015 9 ΛUV
Λ m IR ∼ W
How large ΛUV can we tolerate compatibly with Naturalness?
What can we broadly say about the physics at ΛUV ?
Monday, December 21, 2015 10 3y2 9g2 3g 2 δm2 = t Λ2 Λ2 Λ2 + ... h 4π2 t − 32π2 g − 32π2 g
1 1 1 Λt < 0.45 TeV Λg < 1.1 TeV Λg < 3.7 TeV
Ingenuity • so models high scale susy breaking, eg. SUGRA • superso models composite Higgs, low scale susy breaking,...
• hyperso models neutral naturalness: twin Higgs, ...
Monday, December 21, 2015 11 Soft Models: MSSM (and variants) with high scale mediation
Λ soft term injection S m m˜ m g˜ −→ t ←→ H RG m m˜ g˜ ∼ t 2 2 3yt ΛS 2 2 δmh 2 ln mt˜ mt˜ ∼ 4π × mS × ∼ mS
g˜ LEP scale SUSY expected Z t˜ χ˜+ χ˜0
2 2 mh with O(ε) tuning m t˜ ∼
Monday, December 21, 2015 12 125 GeV Higgs, within MSSM pushes stops above TeV
direct bounds similarly imply tuning to better than 1%
Monday, December 21, 2015 13 SuperSoft Models
low scale mediation Dirac gauginos
ΛS ΛS
m m˜ m g˜ −→ t ←→ H
mS mS
3y2 4π2 m2 2 t 2 m2 h δmh 2 mt˜ t˜ 2 ∼ 4π ∼ 3yt g˜ t˜ + roughly LHC scale SUSY expected Z χ˜ χ˜0
Monday, December 21, 2015 14 SuperSoft Models
low scale mediation Dirac gauginos
ΛS
m m˜ m g˜ −→ t ←→ H
ΛmSS mS
3y2 4π2 m2 2 t 2 m2 h δmh 2 mt˜ t˜ 2 ∼ 4π ∼ 3yt g˜ t˜ + roughly LHC scale SUSY expected Z χ˜ χ˜0
Monday, December 21, 2015 14 already pressed by data, requiring tuning of order 10%
Monday, December 21, 2015 15 Modern Composite Higgs
ΛUV gauge H-sector ~CFT SM
proto-Yukawa m ∗ 2 3yt 2 m mh 4π ∗ ∼
H = composite pseudo-NGB from CFT symmetry broken by SM couplings
Simplest option H SO(5)/SO(4) Georgi, Kaplan ’84 ∈ Arkani-Hamed, Cohen, Katz, Nelson ’02 Agashe, Contino, Pomarol ‘04
Monday, December 21, 2015 16 • give up search for explicit gauge theory incarnations of CFT • just characterize CFT in terms of the needed operator spectrum • holographic realizations via warped compactifications do exist • simplest option: low energy theory broadly described by 2 parameters Giudice, Grojean, Pomarol, RR, 2007
m resonance mass scale ∗ g overall coupling ∗
4π g ∗ ∼ √N large N m m f ∗ √N ∗ ∼ g ∼ 4π pseudo-NGB decay const ∗
v2 4π2 m2 F h Measures of tuning 2 2 2 ∼ f ∼ 3yt m Monday, December 21, 2015 ∗ 17 Top mass and Higgs potential
= y Q¯ + y t¯ Q t Lmix L LOR R ROL L R y y y L R t ∼ g ∗
2 2 3yt 2 V (H)= + ... mh m ∼ 4π2 ∗
T L,R 0 fermionic resonances with given q-numbers: | ≡O | the Top Partners
T X 5/3 Expected in the most plausible cases B ⊕ T
Monday, December 21, 2015 18 mX > 950 GeV ∼
EWPT m > 2 TeV but notice indirect bounds ∗ ∼ Flavor m g > 5 TeV ∗ × ∗ ∼
Monday, December 21, 2015 19 Hypersof Models: Twin Higgs Chacko, Goh, Harnik 2005
Z2 SM SM
states with SM color and charge m g f ∗ ∼ ∗ ˜ t m˜ y f t ∼ t
t h if g yt ∗ colored resonances outside LHC reach !! ΛQCD ΛQCD Contino, Greco, Mahbubani, RR to appear Monday, December 21, 2015 20 γγ at 750
arXiv:1512.04933
Roberto Franceschini, Gian F. Giudice, Jernej F. Kamenik, Matthew McCullough, Alex Pomarol, Riccardo Rattazzi, Michele Redi, Francesco Riva, Alessandro Strumia, Riccardo Torre
Monday, December 21, 2015 21 Monday, December 21, 2015 22 Subtle is the Lord?
Monday, December 21, 2015 22 Subtle is the Lord?
or Malicious is He?
Monday, December 21, 2015 22 Christmas 2011: the Higgs Christmas 2015: ...
Monday, December 21, 2015 23 ATLAS M 750 GeV Γ 45 GeV favored ∼
∼ 14 events 3.9 σ local 2.3 σ including LEE
CMS M 760 GeV narrow width favored
∼ 10 events 2.6 σ local 1.2 σ including LEE
• No significant ETmiss, leptons or jets in the events • No γγ resonance at 8 TeV but small upward fluctuation
Monday, December 21, 2015 24 partonic distribution coeffs
σ [C /s] r ¯ r r r ¯ r r r = 13 TeV = gg 13 TeV bb cc¯ ss¯ dd uu¯ gg σ8TeV [Cgg/s]8TeV 5.45.14.32.72.54.7
r 5 makes 8 TeV and 13 TeV mutually compatible
Monday, December 21, 2015 25 Spin 0 resonance in gg-fusion Γ =0.06 M
Γγγ Γgg 6 Γ 8 1.1 10− 6 10− M M ≈ × M ≈ ×
If large width true need extra decay channel S f dominate
Monday, December 21, 2015 → 26 if S f dominates →
Γgg Γf Γgg Γγγ Γgg 8 σ(pp S f) 6 10− =fixed → → ∝ M Γ ∼ M M M ≈ ×
Γγγ 1 M ∝ σ(pp S f) → →
Γγγ 3 > 2 10− M ∼ ×
Γγγ 4 > 2 10− M ∼ ×
Monday, December 21, 2015 27 A taste of the necessary parameters
Ex: αs λ µν µν N color fundamentals b3 Gµν G or Gµν G ∼ 8π MΨ with charge Q Dynkin index b3 = N
α λ 2 µν µν bQ =2NQ bQ Fµν F or Fµν F ∼ 8π MΨ
as a rule of thumb estimate λ g 1 ∗ b3,Q N correct also in composite models MΨ → m ≡ f ∼ ∗
Monday, December 21, 2015 28 1 g ∗ Ex: η in large Nc QCD mη m = m m ∼ √N ∗ 4π ∗ ∗
α 1 Nc √ fη N c ∼ 8π fη ∝
Monday, December 21, 2015 29 2 2 Γgg 5 2 M Γγγ 8 2 M = 10− b =0.75 10− b M × 3 f M × × Q f
Assuming narrow width (dominated by gg): easy to explain
Ex: one vectorlike quark Q=5/3 b3 =1 M 1 Ψ =(3, 0, 5/3) bQ = 15 f ∼
Assuming Γ = 45 GeV η × M b3 < 5 Γ from t t¯ or invisible f M b > 150 √η Q f
stretchedly compatible with composite model with N 10 (g 3) ∼ ∗ ∼ η < 0.1 would give much more realistic numbers
Monday, December 21, 2015 30 Final Comments
• Naturalness: Symmetries & Selection Rules
• Natural Hierarchy (business as usual): new states around the weak scale
• Unnatural Hierarchy: history and a landscape enter particle physics •cosmological constant: first blatant case of fine tuning •global symmetries : tuned SM structurally superior to its natural extensions •the neatest incarnations of naturalness have since long missed their appointment
• Well motivated model building remains our only way to give shape to the unknown and guide experimental searches
• But we just had a taste of how exciting is to be guided by experiments...
Monday, December 21, 2015 31