EFFECTIVE FIELD THEORY FOR BSM Roberto Contino Scuola Normale - PowerPoint PPT Presentation

EFFECTIVE FIELD THEORY FOR BSM Roberto Contino Scuola Normale Superiore, Pisa INFN, Pisa pre-SUSY2018 school, 17-20 July, 2018, Barcelona

SMEFT Lagrangian

Effective Lagrangian for a Higgs doublet Buchmuller and Wyler NPB 268 (1986) 621 ... Grzadkowski et al. JHEP 1010 (2010) 085 X c i O i ≡ L SM + ∆ L SILH + ∆ L cc + ∆ L dipole + ∆ L V + + ∆ L 4 ψ L = L SM + ¯ i 16 operators Best operator basis to test light composite Higgs (12 CP even, 4 CP odd) Giudice, Grojean, Pomarol, Rattazzi JHEP 0706 (2007) 045 ∆ L SILH = ¯ c H + ¯ c T − ¯ c 6 λ H † ← → ⇣ ⌘⇣ H † ← → ⌘ � 3 2 v 2 ∂ µ � H † H H † H D µ H H † H � � � � ∂ µ D µ H 2 v 2 v 2 ⇣ ¯ q L H c u R + ¯ q L Hd R + ¯ c u c d c l ⌘ v 2 y l H † H ¯ v 2 y u H † H ¯ v 2 y d H † H ¯ + L L Hl R + h . c . + i ¯ ( D ν W µ ν ) i + i ¯ c B g � c W g H † σ i ← → H † ← → ⇣ ⌘ ⇣ ⌘ D µ H D µ H ( ∂ ν B µ ν ) 2 m 2 2 m 2 W W + i ¯ µ ν + i ¯ c HB g � c HW g ( D µ H ) † σ i ( D ν H ) W i ( D µ H ) † ( D ν H ) B µ ν m 2 m 2 W W c γ g � 2 c g g 2 + ¯ H † HB µ ν B µ ν + ¯ S H † HG a µ ν G aµ ν m 2 m 2 W W + i ˜ µ ν + i ˜ c HB g � c HW g ( D µ H ) † σ i ( D ν H ) ˜ ( D µ H ) † ( D ν H ) ˜ W i B µ ν m 2 m 2 W W c γ g � 2 c g g 2 + ˜ B µ ν + ˜ H † HB µ ν ˜ µ ν ˜ S H † HG a G aµ ν m 2 m 2 W W 3

Effective Lagrangian for a Higgs doublet Buchmuller and Wyler NPB 268 (1986) 621 ... Grzadkowski et al. JHEP 1010 (2010) 085 X c i O i ≡ L SM + ∆ L SILH + ∆ L cc + ∆ L dipole + ∆ L V + + ∆ L 4 ψ L = L SM + ¯ i 6 current-current operators i ¯ c � ∆ L cc = i ¯ c Hq H † ← → H † σ i ← → Hq q L γ µ q L ) � � � q L γ µ σ i q L � � � (¯ + ¯ D µ H D µ H v 2 v 2 � ¯ + i ¯ + i ¯ c Hu c Hd H † ← → H † ← → u R γ µ u R ) d R γ µ d R � � � � � (¯ D µ H D µ H v 2 v 2 ✓ i ¯ ◆ c Hud H c † ← → u R γ µ d R ) � � + (¯ + h . c . D µ H v 2 + i ¯ c HL H † ← → � ¯ L L γ µ L L � � � D µ H v 2 4

Effective Lagrangian for a Higgs doublet Buchmuller and Wyler NPB 268 (1986) 621 ... Grzadkowski et al. JHEP 1010 (2010) 085 X c i O i ≡ L SM + ∆ L SILH + ∆ L cc + ∆ L dipole + ∆ L V + + ∆ L 4 ψ L = L SM + ¯ i 8 dipole operators c uB g 0 c uW g c uG g S ∆ L dipole = ¯ q L H c σ µ ν u R B µ ν + ¯ µ ν + ¯ q L σ i H c σ µ ν u R W i q L H c σ µ ν λ a u R G a y u ¯ y u ¯ y u ¯ µ ν m 2 m 2 m 2 W W W c dB g 0 c dW g c dG g S + ¯ q L H σ µ ν d R B µ ν + ¯ µ ν + ¯ q L σ i H σ µ ν d R W i q L H σ µ ν λ a d R G a y d ¯ y d ¯ y d ¯ µ ν m 2 m 2 m 2 W W W c lB g 0 c lW g + ¯ L L H σ µ ν l R B µ ν + ¯ L L σ i H σ µ ν l R W i y l ¯ y l ¯ µ ν + h . c . m 2 m 2 W W 5

Effective Lagrangian for a Higgs doublet Buchmuller and Wyler NPB 268 (1986) 621 ... Grzadkowski et al. JHEP 1010 (2010) 085 X c i O i ≡ L SM + ∆ L SILH + ∆ L cc + ∆ L dipole + ∆ L V + + ∆ L 4 ψ L = L SM + ¯ i 22 four-fermion operators 7 operators built with gauge fields only (5 CP even, 2 CP odd) ∆ L V = ¯ ( D µ W µ ν ) i ( D ρ W ρν ) i + ¯ ( ⇥ µ B µ ν ) ( ⇥ ρ B ρν ) + ¯ c 2 W c 2 B c 2 G ( D µ G µ ν ) a ( D ρ G ρν ) a m 2 m 2 m 2 W W W c 3 W g 3 c 3 G g 3 + ¯ + ¯ � ijk W i ν µ W j ρ ν W k µ S f abc G a ν µ G b ρ ν G c µ m 2 m 2 ρ ρ W W c 3 W g 3 c 3 G g 3 + ˜ + ˜ ˜ ν ˜ � ijk W i ν µ W j ρ W k µ S f abc G a ν µ G b ρ G c µ m 2 m 2 ν ρ ρ W W In total: 59 dim-6 operators for 1 SM family For a review see: RC, Ghezzi, Grojean, Muhlleitner, Spira JHEP 07 (2013) 035 6

Naive estimate at the matching scale (SILH power counting): m ∗ ✓ v 2 ✓ m 2 ✓ m 2 ◆ ◆ ◆ W W c H , ¯ c T , ¯ c 6 , ¯ c ψ ∼ O , c W , ¯ c B ∼ O , c HW , ¯ c HB , ¯ c γ , ¯ c g ∼ O ¯ ¯ ¯ f 2 M 2 16 π 2 f 2 m ∗ ✓ m 2 ! λ 2 v 2 v 2 ✓ λ u λ d ◆ ◆ ψ W c 0 c H ψ , ¯ H ψ ∼ O , c Hud ∼ O , c ψ W , ¯ c ψ B , ¯ c ψ G ∼ O ¯ ¯ ¯ g 2 f 2 g 2 f 2 16 π 2 f 2 ⇤ ⇤ where f ≡ m ∗ /g ∗

Processes with 0, 1, 2, ... Higgses related Q: Which operators are already constrained by experiments w/o Higgs ? In total: 59 dim-6 operators Elias-Miro, Espinosa, Masso, Pomarol 17 involve the Higgs JHEP 1311 (2013) 066 Pomarol, Riva JHEP 01 (2014) 151 8 affect Higgs physics only 8

Operators that affect Higgs physics only Elias-Miro, Espinosa, Masso, Pomarol JHEP 1311 (2013) 066 Pomarol, Riva JHEP 01 (2014) 151 shifts all Higgs couplings O H = ( ∂ µ | H | 2 ) 2 O BB = g 0 2 | H | 2 B µ ν B µ ν modify inclusive rates O W W = g 2 | H | 2 W µ ν W µ ν (constrained by fit to O GG = g 2 s | H | 2 G µ ν G µ ν Higgs couplings) O y d = y d | H | 2 ¯ q L Hd R q L ˜ O y u = y u | H | 2 ¯ Hu R shift h ψψ O y e = y e | H | 2 ¯ L L He R O 6 = λ | H | 6 9

Operators that affect Higgs physics only Elias-Miro, Espinosa, Masso, Pomarol JHEP 1311 (2013) 066 Pomarol, Riva JHEP 01 (2014) 151 O H = ( ∂ µ | H | 2 ) 2 O BB = g 0 2 | H | 2 B µ ν B µ ν h → γγ modify inclusive rates O W W = g 2 | H | 2 W µ ν W µ ν (constrained by fit to h → Z γ Higgs couplings) gg → h O GG = g 2 s | H | 2 G µ ν G µ ν O y d = y d | H | 2 ¯ q L Hd R q L ˜ O y u = y u | H | 2 ¯ Hu R O y e = y e | H | 2 ¯ L L He R O 6 = λ | H | 6 10

Alloul, Fuks, Sanz arXiv:1310.5150 2000 Operators that affect Higgs physics only 1800 SM 1600 1400 Arbitrary Units 1200 1000 c W =0 . 1 ¯ 800 600 O H = ( ∂ µ | H | 2 ) 2 c HW =0 . 1 ¯ 400 200 O BB = g 0 2 | H | 2 B µ ν B µ ν 0 modify also differential 200 300 400 500 600 700 800 900 m (GeV) Vh O W W = g 2 | H | 2 W µ ν W µ ν rates, can be probed by: O GG = g 2 s | H | 2 G µ ν G µ ν decays h → WW*, h → ZZ* ( angular distributions) ─ O y d = y d | H | 2 ¯ q L Hd R Higgs associated production hV (Higgs p T , ─ m Vh , and angular distributions) q L ˜ O y u = y u | H | 2 ¯ Hu R single-Higgs production via VBF O y e = y e | H | 2 ¯ ─ L L He R O 6 = λ | H | 6 11

Operators that affect Higgs physics only Elias-Miro, Espinosa, Masso, Pomarol JHEP 1311 (2013) 066 Pomarol, Riva JHEP 01 (2014) 151 O H = ( ∂ µ | H | 2 ) 2 O BB = g 0 2 | H | 2 B µ ν B µ ν O W W = g 2 | H | 2 W µ ν W µ ν O GG = g 2 s | H | 2 G µ ν G µ ν modifies p T spectrum of gg → h + jet [ top loop vs point-like interaction ] O y d = y d | H | 2 ¯ q L Hd R q L ˜ O y u = y u | H | 2 ¯ Hu R O y e = y e | H | 2 ¯ L L He R h h vs O 6 = λ | H | 6 Azatov, Paul JHEP 1401 (2014) 014 Grojean, Salvioni, Schlaffer, Weiler JHEP 1405 (2014) 022 12

Operators that affect Higgs physics only Elias-Miro, Espinosa, Masso, Pomarol JHEP 1311 (2013) 066 Pomarol, Riva JHEP 01 (2014) 151 O H = ( ∂ µ | H | 2 ) 2 O BB = g 0 2 | H | 2 B µ ν B µ ν O W W = g 2 | H | 2 W µ ν W µ ν O GG = g 2 s | H | 2 G µ ν G µ ν O y d = y d | H | 2 ¯ q L Hd R q L ˜ O y u = y u | H | 2 ¯ Hu R O y e = y e | H | 2 ¯ L L He R yet un-probed gg → hh O 6 = λ | H | 6 13

Renormalization of EFT

RG evolution of coefficients UV theory matching • Loops of light (SM) particles induce the RG m ∗ ¯ c i ( m ∗ ) flow (and mixing) of the coefficients ¯ c i RG range of validity ✓ α SM ( µ ) ◆ evolution log µ δ ij + γ (0) of eff. Lagrangian ¯ c i ( µ ) = c j ( m ∗ ) ¯ ij 4 π m ∗ c i ( µ ) ¯ µ Elias-Miró et al. JHEP 1308 (2013) 033; JHEP 1311 (2013) 066 low-energy scale Jenkins et al. JHEP 1310 (2013) 087; JHEP 1401 (2014) 035 (exp’s done here) Alonso et al. JHEP 1404 (2014) 159 • No big hierarchy between and EW scale, 1-loop m ∗ corrections to SMEFT are generally small 15

Do we need to go beyond tree level ? • The bulk of the 1-loop effect (RG running) can be effectively included by setting limits on the value of the coefficients at the low-energy scale • Knowledge of the RG running is however needed when it comes to make assumptions on the coefficients at the scale (ex: to m ∗ simplify the analysis by neglecting some of the operators) 1-loop effects important if: [in setting limits] Some loosely bound coefficients appears in a Ex: in ¯ gg → h c t precisely measured observable at 1-loop level [in constraining physics at ] m ∗ A larger coefficient renormalizes a smaller one (for a given power counting). RG effects can be sizeable if UV dynamics is strongly coupled 16

RG evolution of coefficients • In case of strong dynamics, leading effects come from loops of composite particles (i.e. Higgs, top quarks, ...) Examples: ig � ig µ ν ( H † σ i ← → ∂ ν B µ ν ( H † ← → 1. Running of D ν W i D µ H ) + D µ H ) O W + B = ¯ c W + B 2 m 2 2 m 2 W W ✓ µ ◆ c W + B ( m ∗ ) − 1 α 2 ¯ c W + B ( µ ) = ¯ 4 π log c H ( m ∗ ) ¯ 6 m ∗ ¯ c H c W ( m ∗ ) , c B ( m ∗ ) ∼ m 2 W ¯ m 2 g 2 ✓ m ∗ ◆ ∆ ¯ ∗ c W + B ∗ 16 π 2 log ∼ c H ( m ∗ ) ∼ v 2 g 2 = m 2 g 2 ¯ c W + B µ W ¯ ∗ ∗ m 2 m 2 g 2 ∗ ∗ 1-loop correction can be large if the UV dynamics is strongly-interacting ( large) g ∗ 17