Bridging the UV and the IR at the loop level ERC workshop on - PowerPoint PPT Presentation

c e r n eth zurich Adrián Carmona Supported by a Marie Skłodowska-Curie Individual Fellowship MSCA-IF-EF-2014 September 13, 2016 Slide 1/26 Bridging the UV and the IR at the loop level ERC workshop on Effective Field Theories for Collider Physics฀ Flavor Phenomena and EWSB

The LHC has proven another model to be right, the Kübler-Ross one 1 Denial They did not publish yet the spin-2 analysis! 2 Anger Damned experimentalists! Enough of ambulance-chasing! 3 Bargaining 4 Depression The fjeld is dying! 5 Acceptance The 750 Stages of Grief A simple 2 σ anomaly would be enough!

The LHC has proven another model to be right, the Kübler-Ross one 1 Denial They did not publish yet the spin-2 analysis! 2 Anger Damned experimentalists! Enough of ambulance-chasing! 3 Bargaining 4 Depression The fjeld is dying! 5 Acceptance There are plenty of reasons for NP; it could just be beyond the direct LHC reach! The 750 Stages of Grief A simple 2 σ anomaly would be enough!

The LHC has proven another model to be right, the Kübler-Ross one 1 Denial They did not publish yet the spin-2 analysis! 2 Anger Damned experimentalists! Enough of ambulance-chasing! 3 Bargaining 4 Depression The fjeld is dying! 5 Acceptance There are plenty of reasons for NP; it could just be beyond the direct LHC reach! The 750 Stages of Grief A simple 2 σ anomaly would be enough! KEEP CALM AND SEARCH FOR NP

allows us to search for NP in a model independent way! compatible with the observed symmetries and dof the bottom-up approach EFT as a discovery tool • In its search for NP, the LHC indicates the existence of a non-negligible mass gap v ≪ Λ • We can therefore write the most general non-renormalizable L L eff = L (4) + 1 Λ L (5) + 1 Λ 2 L (6) + 1 Λ 3 L (7) + . . . • Mapping experimental observables to the Wilson coeffjcients in L eff • We dispose nowadays of an impressive fjt of the SM EFT to data (EWPD, LHC data, …) Ciuchini, Franco, Mishima, Silvestrini, '13; de Blas, Chala, Santiago, '13,'15; Pomarol, Riva, '14, Pruna, Signer, '14; Falkowski, Riva, '15; Buckley, Englert, Ferrando, Miller, Moore, Russel, White, '15; Berthier, Trott, '15; Aebischer, Crivellin, Fael, Greub, '15; Ghezzi, Gomez-Ambrosio, Passarino, Uccirati, '15; Hartman, Trott, '15; David, Passarino, '15; Boggia, Gomez-Ambrosio, Passarino, '16; de Blas, Ciuchini, Franco, Mishima, Pierini, Reina, Silvestrini, '16;…

the top-down approach EFT as a discovery tool matching running

automated one-loop matching in efgective fjeld theories Outline • UV/IR tree-level dictionary • UV/IR one-loop dictionary • Efgective Lagrangian at one loop: functional methods and matching • MatchMaker Anastasiou, AC, Lazopoulos, Santiago, to appear soon • Conclusions

We can perform the tree-level matching for the following Lagrangian by using equations of motion and which leads to Tree Level Matching − D 2 − m 2 Φ+ O (Φ 3 ) L UV ( φ, Φ) = L SM ( φ )+[Φ † F ( φ )+ h . c . ]+Φ † [ ] φ − U ( φ ) D 2 + m 2 Φ c = F ( φ ) + O (Φ 2 [ ] Φ + U ( φ ) c ) 1 1 Φ c = Φ + UF = D 2 + m 2 Φ ( D 2 + U ) 1 + m − 1 m 2 [ ] F Φ 1 1 ( D 2 + U ) 1 1 ( D 2 + U ) 1 ( D 2 + U ) 1 = − F + F + . . . m 2 m 2 m 2 m 2 m 2 m 2 Φ Φ Φ Φ Φ Φ L tree eff = L UV ( φ, Φ c (Φ))

N Y D U N Dirac Dirac/Majorana Dirac D U X Dirac Dirac Dirac/Majorana D Irrep We already have a tree-level dictionary for non-mixed contributions! Spinor U X Irrep Leptons D U N D U E Y Tree Level Matching     ( ) ( ) ( ) Q ( m )     (3 , 1) 2 (3 , 1) − 1 (3 , 2) 1 (3 , 2) 7 (3 , 2) − 5 (3 , 3) 2 (3 , 3) − 1 3 3 6 6 6 3 3 New Quarks: del Aguila, Perez-Victoria, Santiago, '00 E +     E − ( N ) ( ) E − E − E −−     E − E −− (1 , 1) 0 (1 , 1) − 1 (1 , 2) − 1 (1 , 2) − 3 (1 , 3) 0 (1 , 3) − 1 2 2 New Leptons: del Aguila, de Blas, Perez-Victoria, '08

Irrep Irrep Vector Scalars Scalars Irrep Colored Scalars Irrep We already have a tree-level dictionary for non-mixed contributions! Colorless Irrep Colored Vector Tree Level Matching B 1 W 1 G 1 B µ W µ G µ H µ L µ µ µ µ (1 , 1)0 (1 , 1)1 (1 , Adj )0 (1 , Adj )1 ( Adj , 1)0 ( Adj , 1)1 ( Adj , Adj )0 (1 , 2) − 3 2 U 2 U 5 Q 1 Q 5 Y 1 Y 5 X µ µ µ µ µ µ µ (¯ (¯ (3 , 1) 2 (3 , 1) 5 (3 , 2) 1 (3 , 2) − 5 (3 , Adj ) 2 6 , 2) 1 6 , 2) − 5 3 3 6 6 3 6 6 New Vectors: del Aguila, de Blas, Perez-Victoria, '10 S S 1 S 2 ϕ Ξ0 Ξ1 Θ1 Θ3 (1 , 1)0 (1 , 1)1 (1 , 1)2 (1 , 2) 1 (1 , 3)0 (1 , 3)1 (1 , 4) 1 (1 , 4) 3 2 2 2 Π1 Π7 ω 1 ω 2 ω 4 ζ (3 , 1) − 1 (3 , 1) 2 (3 , 1) − 4 (3 , 2) 1 (3 , 2) 7 (3 , 3) − 1 3 3 3 6 6 3 Ω1 Ω2 Ω4 Υ Φ (6 , 1) 1 (6 , 1) − 2 (6 , 1) 4 (6 , 3) 1 (8 , 2) 1 3 3 3 3 2 New Scalars: de Blas, Chala, Perez-Victoria, Santiago, '15

eff at tree level contributions Tree Level Matching • Dimensionful couplings imply that particles with difgerent spin can simultaneously contribute to L d =6 κφ 1 φ 2 φ 3 + κ ′ V µ D µ φ + κ ′′ V µ V ′ µ + . . . . . . • Only a subset of the irreps in the previous lists contributes • Work in progress: de Blas, Chala, Criado, Perez-Victoria, Santiago, to appear soon • Then, the tree-level UV/IR dictionary will be complete!

generated at the quantum level appear at loop level in specifjc models account for these cases seems compulsory. One loop matching • Many contributions to the efgective Lagrangian can be only • Even contributions that can potentially arise at tree-level only • The dictionary should be extended to one loop if we want to • The number of possibilities increases dramatically!! Automation • The matching can be performed • Diagrammatically Anastasiou, AC, Lazapoulos, Santiago • By functional methods Henning, Lu & Murayama, '14; Drozd, Ellis, Quevillon, You, '15; Henning, Lu, Murayama, '16; Ellis, Quevillon, You, Zhang, '16; Fuentes-Martin, Portoles, Ruiz-Femenia, '16

where leads at one-loop order in the saddle-point approximation to The efgective action One loop matching by functional methods ∫ e iS eff ( φ ) = D Φ e iS UV ( φ, Φ) ( ) − δ 2 S UV ( φ, Φ) � � S eff ( φ ) = S UV ( φ, Φ c ( φ )) + i � 2 log det δ Φ 2 � Φ c � δ S ( φ, Φ) � = 0 ⇒ Φ c ( φ ) � δ Φ � Φ c φ φ . . . Φ Φ

U obtaining where One loop matching by functional methods Henning, Lu & Murayama, '14 resuscitated the Covariant Derivative Expansion (CDE) Gaillard, '86; Cheyette, 86 for the calculation of ( ) − δ 2 S UV ( φ, Φ) � D 2 + m 2 � [ ] ∆ S eff ( φ ) = ic s Tr log = ic s Tr log Φ − U ( φ ) � δ Φ 2 � Φ c [ ) 2 ] d 4 q ∫ ∫ ( ∂ q µ + ˜ Φ + ˜ d 4 x + m 2 ∆ S eff ( φ ) = ic s − G µν (2 π ) 4 tr log ∂ q ν ∞ n + 1 ∂ n ˜ ∑ G µν = ( n + 2)! [ P α 1 , [ . . . [ P α n , [ D µ , D ν ]]]] ∂ q α 1 ∂ q α 2 · · · ∂ q α n n =0 ∞ 1 ∂ n ˜ ∑ U µν = n ! [ P α 1 , [ . . . [ P α n , U ]]] ∂ q α 1 ∂ q α 2 · · · ∂ q α n n =0

for all! U U U U d q d q or One loop matching by functional methods Henning, Lu & Murayama, '14 After expanding in ∆ = ( q 2 − m 2 Φ ) − 1 one obtains (for d q = d 4 q /(2 π ) 4 ) ∫ ∫ 1 d m 2 ∆ L eff = − ic s Φ tr [ ({ } )] q µ , ˜ + ˜ G σµ ˜ ν ∂ µ ∂ ν − ˜ ∆ − 1 1 + ∆ G µν ∂ µ G σ ∫ ∫ [ ( G 2 − ˜ ) { q , ˜ G } + ˜ d m 2 ∆ L eff = − ic s ∆ − ∆ ∆ Φ tr ( G 2 − ˜ ) ( G 2 − ˜ ) ] { q , ˜ G } + ˜ { q , ˜ G } + ˜ +∆ ∆ ∆ + . . . In the case m Φ ∝ 1 , [∆ , [ P α 1 , [ . . . , [ P α n , [ D µ , D ν ]]]]] = [∆ , [ P α 1 , [ . . . , [ P α n , U ]]]] = 0 so the d q integrals factor out of the trace and can be computed once and

U c s One loop matching by functional methods Henning, Lu & Murayama, '14 { L eff , 1 − loop = (4 π ) 2 tr log m 2 [ − 1 µ 2 − 3 )] ( + m 4 2 2 log m 2 [ ] ( ) + m 2 − µ 2 − 1 [ ] log m 2 2 log m 2 − 1 µν − 1 ( ) + m 0 G ′ 2 µ 2 U 2 µ 2 − 1 12 [ ] 1 − 1 ) 2 − 1 σµ − 1 12 ( P µ U ) 2 − 1 6 U 3 − 1 P µ G ′ 90 G ′ µν G ′ νσ G ′ 12 UG ′ µν G ′ + ( µν µν m 2 60 [ 1 24 U 4 + 1 1 1 ) 2 + 1 ) 2 + ( ) P 2 U U 2 G ′ µν G ′ + ( ( P µ U µν m 4 12 U 120 24 ] 1 1 G ′ U [ U , G ′ G ′ [ ] [ ] ( P µ U ) , ( P ν U ) µν ] − µν − µν 120 120 [ ] 1 − 1 60 U 5 − 1 ) 2 − 1 20 U 2 ( ) 2 ( + P µ U UP µ U m 6 30 [ 1 ]} 1 120 U 6 where P µ A = [ P µ , A ] , G ′ + µν = [ D µ , D ν ] m 8