Self coupling. Tilman Plehn. why? how? required? when? An Introduction. Tilman Plehn. Universität Heidelberg. Mainz, April 2015

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1 An Introduction Universität eidelber Mainz, April 2015

2 is self couplin Link to fundamental questions Standard Model possibly consistent to Planck scale renormalizable theory tool to probe fundamental physics vacuum stability one of them decision on stability made at TeV scale [Buttazzo et al; Eichorn et al] yt 3 SM couplins m in TeV l 0.0 y b RGE scale m in GeV Fiure 1: Renormalisation of the SM aue couplins 1 = p 5/3 Y, 2, 3, o and couplins (y t, y b, y ), of the is quartic couplin and of the is ma All parameters are defined in the ms scheme. We include two-loop thresholds

3 is self couplin Link to fundamental questions Standard Model possibly consistent to Planck scale renormalizable theory tool to probe fundamental physics vacuum stability one of them decision on stability made at TeV scale [Buttazzo et al; Eichorn et al] runnin couplins Λ 4 Λ 6 3 y RGE scale k in GeV

4 is self couplin Link to fundamental questions Standard Model possibly consistent to Planck scale renormalizable theory tool to probe fundamental physics vacuum stability one of them decision on stability made at TeV scale [Buttazzo et al; Eichorn et al] l l6kuvl=0 l6kuvl=0.1 l6kuvl=0.5 l6kuvl= RG scale in GeV

5 is self couplin Link to fundamental questions Standard Model possibly consistent to Planck scale renormalizable theory tool to probe fundamental physics vacuum stability one of them decision on stability made at TeV scale [Buttazzo et al; Eichorn et al] 1.0 runnin couplins Λ 4 3 y Λ S RG scale k in GeV

6 is self couplin Link to fundamental questions Standard Model possibly consistent to Planck scale renormalizable theory tool to probe fundamental physics vacuum stability one of them decision on stability made at TeV scale [Buttazzo et al; Eichorn et al] usually interpreted as m vs m t only consistency condition on Standard Model strictly speakin λ vs y t seriously hard at colliders [case for 100 TeV?] runnin couplins Λ4 3 y ΛS RG scale k in GeV

7 is self couplin Link to fundamental questions Standard Model possibly consistent to Planck scale renormalizable theory tool to probe fundamental physics vacuum stability one of them decision on stability made at TeV scale [Buttazzo et al; Eichorn et al] usually interpreted as m vs m t only consistency condition on Standard Model strictly speakin λ vs y t seriously hard at colliders [case for 100 TeV?] is portal for dark matter, baryoenesis,... [many papers: Pospelov; Ramsey-Musolf; Lebedev, Enlert] smokin un for stronly interactin is [Contino... ; Grojean...; Gröber, Mühlleitner] we are in EP for fundamental questions! runnin couplins Λ4 3 y ΛS RG scale k in GeV

8 Missin piece Less visionary missin piece in Standard Model LC measurements of XX on the way [rate-based and EFT] is potential V = µ 2 (Φ Φ) + λ(φ Φ) 2 λ = m2 2v 2

9 Missin piece Less visionary missin piece in Standard Model LC measurements of XX on the way [rate-based and EFT] is potential V = µ 2 (Φ Φ) + λ(φ Φ) 2 λ = m2 2v 2 includin D6 operators [Goertz, Papaefstathiou, Yan, Zurita;...] O = µ(φ φ) µ (φ φ) O 6 = 1 3 (φ φ) 3 modified self couplins Feynman rule O G = (φ φ) G µνg µν L self = m2 2v m2 8v 2 i 3m2 v [( 1 f 1v 2 2Λ + 2f ) 2v 4 2 3Λ 2 m 2 [( 1 f 1v 2 + 4f ) 2v 4 Λ 2 Λ 2 m 2 1 f 1v 2 2Λ 2 + 2f 2v 4 3Λ 2 m 2 O f = y f (φ φ) Q L φr R 3 2f ] 1v 2 Λ 2 m 2 µ µ ] 4 4f 1v 2 Λ 2 m 2 2 µ µ + 2f 1v 2 3Λ 2 m 2 3 (p j p k ) j<k

10 Missin piece Less visionary missin piece in Standard Model LC measurements of XX on the way [rate-based and EFT] is potential V = µ 2 (Φ Φ) + λ(φ Φ) 2 λ = m2 2v 2 includin D6 operators [Goertz, Papaefstathiou, Yan, Zurita;...] O = µ(φ φ) µ (φ φ) O 6 = 1 3 (φ φ) 3 O G = (φ φ) G µνg µν is pair production O f = y f (φ φ) Q L φr R [Djouadi, Kilian, Mühlleitner, Zerwas] SM: pp +X LC: σ [fb] WW+ZZ 1 W+Z W:Z 1.6 WW:ZZ M [GeV]

11 LC One-loop amplitude destructive interference convenient effective theory [links vertex to luon self enery for m m t ] ( ) ( L = G µν α s G µν π 12v 2 24v +... = αs 2 12π Gµν G µν lo 1 + ) v threshold behavior [ ] 2 2 3m 2 s m 2 + [3m 2 1 3m 2 1] 0

12 LC One-loop amplitude destructive interference convenient effective theory [links vertex to luon self enery for m m t ] ( ) ( L = G µν α s G µν π 12v 2 24v +... = αs 2 12π Gµν G µν lo 1 + ) v threshold behavior [ ] 2 2 3m 2 s m 2 + [3m 2 1 3m 2 1] 0 Sinal Extraction [Baur etal; Dolan etal] lare top mass approximation useless

13 LC One-loop amplitude destructive interference convenient effective theory [links vertex to luon self enery for m m t ] ( ) ( L = G µν α s G µν π 12v 2 24v +... = αs 2 12π Gµν G µν lo 1 + ) v threshold behavior [ ] 2 2 3m 2 s m 2 + [3m 2 1 3m 2 1] 0 Sinal Extraction [Baur etal; Dolan etal] lare top mass approximation useless kinematics affected by self couplin

14 LC One-loop amplitude destructive interference convenient effective theory [links vertex to luon self enery for m m t ] ( ) ( L = G µν α s G µν π 12v 2 24v +... = αs 2 12π Gµν G µν lo 1 + ) v threshold behavior [ ] 2 2 3m 2 s m 2 + [3m 2 1 3m 2 1] 0 Sinal Extraction [Baur etal; Dolan etal] lare top mass approximation useless kinematics affected by self couplin dσ/dpt,h [fb/gev] λ = 1 λsm λ =0 λsm λ =1 λsm λ =2 λsm mh =125GeV pt,h [GeV]

15 LC One-loop amplitude destructive interference convenient effective theory [links vertex to luon self enery for m m t ] ( ) ( L = G µν α s G µν π 12v 2 24v +... = αs 2 12π Gµν G µν lo 1 + ) v threshold behavior [ ] 2 2 3m 2 s m 2 + [3m 2 1 3m 2 1] 0 Sinal Extraction [Baur etal; Dolan etal] lare top mass approximation useless kinematics affected by self couplin shape analysis necessary and possible dσ/dpt,h [fb/gev] λ = 1 λsm λ =0 λsm λ =1 λsm λ =2 λsm mh =125GeV pt,h [GeV]

16 LC One-loop amplitude destructive interference convenient effective theory [links vertex to luon self enery for m m t ] ( ) ( L = G µν α s G µν π 12v 2 24v +... = αs 2 12π Gµν G µν lo 1 + ) v threshold behavior [ ] 2 2 3m 2 s m 2 + [3m 2 1 3m 2 1] 0 Analysis stratey [Baur etal] search for production [like ATLAS paper] SM: no 5σ sinal tt from is couplins analysis [similarly EFT] limits on anomalous is self couplin exclude λ < 0 with enhanced rate exclude λ 1 from p T which sinatures?

17 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is? m h [GeV] sinal N WWWjj t tw t tz t tj WZ 4j WW 4j t tt t

18 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is?

19 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is? b bγγ: rate limited, but S/B 1

20 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is? b bγγ: rate limited, but S/B 1 at least not as hard as 4b [Spanno s talk]

21 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is? b bγγ: rate limited, but S/B 1 at least not as hard as 4b [Spanno s talk] New attempts: b bτ + τ, b bw + W [Dolan etal, Papaefstathiou etal] b bτ + τ : not very promisin with usual analysis [Baur etal (2003)] but benefittin from fat jets tools [BDRS, Dolan etal] ξ = 0 ξ = 1 ξ = 2 b bττ b bττ [ew] b bw + W ratio to ξ = 1 before cuts reconstructed mττ fatjet cuts reconstructed m b b double b-ta

22 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is? b bγγ: rate limited, but S/B 1 at least not as hard as 4b [Spanno s talk] New attempts: b bτ + τ, b bw + W [Dolan etal, Papaefstathiou etal] b bτ + τ : not very promisin with usual analysis [Baur etal (2003)] but benefittin from fat jets tools [BDRS, Dolan etal] further improved S/B with add l jet?

23 Sinatures Old channels: 4W, b bγγ [Baur etal ( )] 4W : visible mass aainst backrounds and to probe threshold [Σ j,l p µ ) 2 ] (1) small for 2 particle final state (sinal) (2) lare for many backrounds known problem: t tj backround [matrix element versus shower?] only workin for heavier is? b bγγ: rate limited, but S/B 1 at least not as hard as 4b [Spanno s talk] New attempts: b bτ + τ, b bw + W [Dolan etal, Papaefstathiou etal] b bτ + τ : not very promisin with usual analysis [Baur etal (2003)] but benefittin from fat jets tools [BDRS, Dolan etal] further improved S/B with add l jet? b bw + W : not very promisin [Dolan etal] maybe possible [Papaefstathiou etal] t t backround a bi challene where are the experimental studies?

24 Tools Precision predictions LO loop amplitudes in many MC codes approximate NLO available [Dawson, Dittmaier, Spira] NLO with top mass [Grio, off, Melnikov, Steinhauser] NNLO predictions on the way [de Florian, Mazzitelli] remember the distributions! (0) (fb) s (GeV)

25 Linear collider Rate at linear collider: e + e Z very limited number of events low is mass, decays b b measurement of λ throuh total rate (m h = 120 GeV) hard measurement everywhere 0.6 SM Double is-strahlun: e + e - Z σ pol [fb] GeV 1 TeV TeV M [GeV] [Djouadi, Kilian, Mühlleitner, Zerwas]

26 L-LC and Nimatron Make use of 100 TeV and/or 30ab 1 where do we benefit? what is new? pp (b b)+weakly interactin combined with top Yukawa measurement? what is the proress since 2003? where are the experimental studies? why is pairs and not cheaper channels? why billions of dollars? [Papaefstathiou] That looks really hard!