Single Top in the SMEFT Rhea Moutafis July 11, 2019 OVERVIEW - PowerPoint PPT Presentation

Workshop on Standard Model Effective Theory Single Top in the SMEFT Rhea Moutafis July 11, 2019

OVERVIEW Introduction SMEFT Basics Relevant Operators Correlated Uncertainties Results Conclusion 2

INTRODUCTION 3

INTRODUCTION • at LHC: production of new particles or imprints via interferences & virtual effects • single top especially sensitive to electroweak interactions • subset of top sector 
 possibility to focus on the technical side • goal: constrain 7 main dim-6 operators concerning single top with SFitter 4

SMEFT BASICS 5


 
 
 SMEFT BASICS • effects of new heavy BSM particles: 
 N d 6 c i ∑ Λ 2 𝒫 (6) ℒ SMEFT = ℒ SM + + . . . , i i • cross sections: N d 6 N d 6 c i c j c i ∑ ∑ σ SMEFT = σ SM + Λ 2 σ i + Λ 4 ˜ σ ij + . . . , i i , j 6

SMEFT BASICS b = ( 1 + ) 2 c 3 φ q v 2 g 4 ( s − m 2 t ) 2 (2 s + m 2 t ) σ u ¯ d → t ¯ Λ 2 384 π s 2 ( s − m 2 W ) 2 g 2 m t m W ( s − m 2 t ) 2 + c tW 2 π Λ 2 s ( s − m 2 W ) 2 8 g 2 ( s − m 2 t ) 2 (2 s + m 2 t ) + c 3,1 Qq 48 π Λ 2 s 2 ( s − m 2 W ) 7

RELEVANT OPERATORS 8

RELEVANT OPERATORS VERTEX CHANNELS s-channel t-channel W -assoc. Z -assoc. t decay 9

RELEVANT OPERATORS VERTEX CHANNELS OPERATORS ‡ 𝒫 ( ij ) s-channel q i σ μν T A u j ) ˜ φ G A uG = (¯ μν ‡ 𝒫 ( ij ) φ W I uW = (¯ q i σ μν τ I u j ) ˜ μν t-channel ⟷ 𝒫 3( ij ) φ q = ( φ † iD I q i γ μ τ I q j ) μ φ )(¯ W -assoc. ‡ 𝒫 ( ij ) q i σ μν τ I d j ) φ W I dW = (¯ μν ⟷ ‡ 𝒫 1( ij ) φ † iD μ φ )( ¯ φ ud = ( ˜ u i γ μ d j ) Z -assoc. 𝒫 1( ijkl ) = (¯ q i γ μ q j )(¯ q k γ μ q l ) qq t decay 𝒫 3( ijkl ) q i γ μ τ I q j )(¯ q k γ μ τ I q l ) = (¯ qq 10

RELEVANT OPERATORS VERTEX CHANNELS OPERATORS WILSON COEFFICIENTS c tG Re { 𝒫 (33) ‡ 𝒫 ( ij ) s-channel q i σ μν T A u j ) ˜ φ G A uG = (¯ uG } μν c tW Re { 𝒫 (33) ‡ 𝒫 ( ij ) φ W I uW } uW = (¯ q i σ μν τ I u j ) ˜ μν t-channel ⟷ c 3 𝒫 3(33) 𝒫 3( ij ) φ q = ( φ † iD I q i γ μ τ I q j ) μ φ )(¯ φ q φ q W -assoc. c bW Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν τ I d j ) φ W I dW } dW = (¯ μν ⟷ Re { 𝒫 (33) c φ tb ‡ 𝒫 1( ij ) φ † iD μ φ )( ¯ φ ud } φ ud = ( ˜ u i γ μ d j ) Z -assoc. + 1 c 3,1 𝒫 1( ijkl ) 𝒫 3( ii 33) 6( 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) = (¯ q i γ μ q j )(¯ q k γ μ q l ) ) qq qq qq qq Qq t decay c 3,8 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) 𝒫 3( ijkl ) q i γ μ τ I q j )(¯ q k γ μ τ I q l ) = (¯ qq qq qq Qq 11

RELEVANT OPERATORS VERTEX CHANNELS OPERATORS WILSON COEFFICIENTS c tG Re { 𝒫 (33) ‡ 𝒫 ( ij ) s-channel q i σ μν T A u j ) ˜ φ G A uG = (¯ uG } μν c tW Re { 𝒫 (33) ‡ 𝒫 ( ij ) φ W I uW } uW = (¯ q i σ μν τ I u j ) ˜ μν t-channel ⟷ c 3 𝒫 3(33) 𝒫 3( ij ) φ q = ( φ † iD I q i γ μ τ I q j ) μ φ )(¯ φ q φ q W -assoc. c bW Wtb Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν τ I d j ) φ W I dW } dW = (¯ μν ⟷ Re { 𝒫 (33) c φ tb ‡ 𝒫 1( ij ) φ † iD μ φ )( ¯ φ ud } φ ud = ( ˜ u i γ μ d j ) Z -assoc. + 1 c 3,1 𝒫 1( ijkl ) 𝒫 3( ii 33) 6( 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) = (¯ q i γ μ q j )(¯ q k γ μ q l ) ) qq qq qq qq Qq t decay c 3,8 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) 𝒫 3( ijkl ) q i γ μ τ I q j )(¯ q k γ μ τ I q l ) = (¯ qq qq qq Qq 12

RELEVANT OPERATORS VERTEX CHANNELS OPERATORS WILSON COEFFICIENTS c tG Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν T A u j ) ˜ φ G A s-channel uG = (¯ uG } μν c tW Re { 𝒫 (33) ‡ 𝒫 ( ij ) φ W I uW } uW = (¯ q i σ μν τ I u j ) ˜ μν t-channel ⟷ c 3 𝒫 3(33) 𝒫 3( ij ) φ q = ( φ † iD I q i γ μ τ I q j ) μ φ )(¯ φ q φ q W -assoc. c bW qq’q’’t Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν τ I d j ) φ W I dW } dW = (¯ μν ⟷ Re { 𝒫 (33) c φ tb ‡ 𝒫 1( ij ) φ † iD μ φ )( ¯ φ ud } φ ud = ( ˜ u i γ μ d j ) Z -assoc. + 1 c 3,1 𝒫 1( ijkl ) 𝒫 3( ii 33) 6( 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) = (¯ q i γ μ q j )(¯ q k γ μ q l ) ) qq qq qq qq Qq t decay c 3,8 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) 𝒫 3( ijkl ) q i γ μ τ I q j )(¯ q k γ μ τ I q l ) = (¯ qq qq qq Qq 13

RELEVANT OPERATORS VERTEX CHANNELS OPERATORS WILSON COEFFICIENTS c tG Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν T A u j ) ˜ φ G A s-channel uG = (¯ uG } μν c tW Re { 𝒫 (33) ‡ 𝒫 ( ij ) φ W I uW } uW = (¯ q i σ μν τ I u j ) ˜ μν t-channel ⟷ c 3 𝒫 3(33) 𝒫 3( ij ) φ q = ( φ † iD I q i γ μ τ I q j ) μ φ )(¯ φ q φ q W -assoc. c bW ttg Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν τ I d j ) φ W I dW } dW = (¯ μν ⟷ Re { 𝒫 (33) c φ tb ‡ 𝒫 1( ij ) φ † iD μ φ )( ¯ φ ud } φ ud = ( ˜ u i γ μ d j ) Z -assoc. + 1 c 3,1 𝒫 1( ijkl ) 𝒫 3( ii 33) 6( 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) = (¯ q i γ μ q j )(¯ q k γ μ q l ) ) qq qq qq qq Qq t decay c 3,8 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) 𝒫 3( ijkl ) q i γ μ τ I q j )(¯ q k γ μ τ I q l ) = (¯ qq qq qq Qq 14

RELEVANT OPERATORS VERTEX CHANNELS OPERATORS WILSON COEFFICIENTS c tG Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν T A u j ) ˜ φ G A s-channel uG = (¯ uG } μν c tW Re { 𝒫 (33) ‡ 𝒫 ( ij ) φ W I uW } uW = (¯ q i σ μν τ I u j ) ˜ μν t-channel ⟷ c 3 𝒫 3(33) 𝒫 3( ij ) φ q = ( φ † iD I q i γ μ τ I q j ) μ φ )(¯ φ q φ q W -assoc. c bW ttZ, tt γ Re { 𝒫 (33) ‡ 𝒫 ( ij ) q i σ μν τ I d j ) φ W I dW } dW = (¯ μν ⟷ Re { 𝒫 (33) c φ tb ‡ 𝒫 1( ij ) φ † iD μ φ )( ¯ φ ud } φ ud = ( ˜ u i γ μ d j ) Z -assoc. + 1 c 3,1 𝒫 1( ijkl ) 𝒫 3( ii 33) 6( 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) = (¯ q i γ μ q j )(¯ q k γ μ q l ) ) qq qq qq qq Qq t decay c 3,8 𝒫 1( i 33 i ) − 𝒫 3( i 33 i ) 𝒫 3( ijkl ) q i γ μ τ I q j )(¯ q k γ μ τ I q l ) = (¯ qq qq qq Qq 15

CORRELATED UNCERTAINTIES 16

CORRELATED UNCERTAINTIES • theoretical: identical predictions 
 averaging (alternative nuisance parameters, but we get too many) • systematic: build matrix of uncertainties, write correlated ones in same column • all handled with DataPrep 17

CORRELATED UNCERTAINTIES 2 2 contributions for correlated uncertainties contributions for correlated uncertainties χ χ 2 s-channel χ t-channel tW tZ 25 W helicity 20 15 10 5 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 c tW 18

CORRELATED UNCERTAINTIES 2 2 contributions for uncorrelated theoretical uncertainties contributions for uncorrelated theoretical uncertainties χ χ 2 s-channel χ t-channel 45 tW tZ 40 W helicity 35 30 25 20 15 10 5 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 c tW 19

CORRELATED UNCERTAINTIES 2 2 2 2 contributions for uncorrelated systematic uncertainties contributions for uncorrelated systematic uncertainties contributions for uncorrelated theoretical uncertainties contributions for uncorrelated theoretical uncertainties χ χ χ χ 2 2 s-channel s-channel χ χ t-channel t-channel 45 45 tW tW tZ tZ 40 40 W helicity W helicity 35 35 30 30 25 25 20 20 15 15 10 10 5 5 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 c c tW tW 20

RESULTS 21

RESULTS Bounds at standard dataset & theory Bounds at standard dataset & theory ] all coefficients: 68% conf. int. -2 [TeV all coefficients: 95% conf. int. 4 one coefficient: 68% conf. int. one coefficient: 95% conf. int. reference (all coefficients): 95% conf. int. 2 Λ 3 8.7 / i c 2 1 0 -1 -2 -3 -4 -27 3,1 3,8 3 c c c c c c c q tG tW bW φ tb Qq Qq φ 22

RESULTS Bounds without kinematic distributions Bounds without kinematic distributions ] standard (all coefficients): 68% conf. int. -2 standard (all coefficients): 95% conf. int. [TeV all coefficients: 68% conf. int. 2 all coefficients: 95% conf. int. one coefficient: 68% conf. int. one coefficient: 95% conf. int. 2 Λ / i c 1 0 -1 -2 -3 -4 3,1 3,8 3 c c c c c c c φ q tG tW bW φ tb Qq Qq 23

RESULTS Bounds without measurements at 7 TeV Bounds without measurements at 7 TeV ] standard (all coefficients): 68% conf. int. -2 standard (all coefficients): 95% conf. int. [TeV all coefficients: 68% conf. int. 2 all coefficients: 95% conf. int. one coefficient: 68% conf. int. one coefficient: 95% conf. int. 2 Λ / i c 1 0 -1 -2 -3 -4 3,1 3,8 3 c c c c c c c φ q tG tW bW φ tb Qq Qq 24

RESULTS Bounds without NLO corrections Bounds without NLO corrections ] standard (all coefficients): 68% conf. int. -2 standard (all coefficients): 95% conf. int. [TeV all coefficients: 68% conf. int. 8 all coefficients: 95% conf. int. one coefficient: 68% conf. int. one coefficient: 95% conf. int. 2 Λ / i c 6 4 2 0 -2 -4 3,8 c 3,1 3 c c c c c c Qq q tG tW bW φ tb Qq φ 25