Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Operators involving top trilinear interactions q Li D µ u Rj ) D µ ˜ O ( 3 , i + j ) = 1 / 2 [ O ( 3 , ij ) + ( O ( 3 , ji ) ) † ] O ij i ≤ j Du = (¯ φ φ q φ q φ q q Li u Rj ) D µ ˜ O ( 1 , i + j ) = 1 / 2 [ O ( 1 , ij ) + ( O ( 1 , ji ) O ij ) † ] Du = ( D µ ¯ φ i ≤ j ¯ φ q φ q φ q q Li D µ d Rj ) D µ φ O ij φφ = i (˜ φ † D µ φ )(¯ u Ri γ µ d Rj ) O ij Dd = (¯ q Li d Rj ) D µ φ O i + j φ u = 1 / 2 [ O ij φ u + ( O ji φ u ) † ] O ij i ≤ j Dd = ( D µ ¯ ¯ q Li σ µν τ I u Rj )˜ q Li γ µ τ I D ν q Lj W I O ij φ W I O ij uW = (¯ qW = ¯ µν µν O ij q Li σ µν τ I d Rj ) φ W I O ij q Li γ µ D ν q Lj B µν dW = (¯ qB = ¯ µν q Li σ µν u Rj )˜ O ij O ij u Ri γ µ D ν u Rj B µν uB φ = (¯ φ B µν uB = ¯ O ij q Li λ a σ µν u Rj )˜ φ G a O ij q Li λ a γ µ D ν q Lj G a uG φ = (¯ qG = ¯ µν µν O ij u φ = ( φ † φ )(¯ q Li u Rj ˜ O ij u Ri λ a γ µ D ν u Rj G a φ ) uG = ¯ µν redundant combinations O ij φ q − ( O ji φ q ) † [JAAS NPB ’09] and O ij φ u − ( O ji φ u ) † dropped J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Frequently asked questions Q: You are using the equations of motion. What you do is process-dependent, valid only for on-shell particles. A: No. Using the gauge-invariant EOM amounts to a field redefinition which leaves the path integral invariant up to higher-order terms. Q: You are changing the basis of Buchmüller & Wyler by some other, to simplify top interactions. A: No. I’m just dropping operators from that basis without introducing new ones. Q: Then, are there several redundant operators in the B & W basis? A: Indeed. Let’s see. J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij O ij qW , qB , uB , qG , uG int. by parts & gauge field EOM x = 1 + 1 � x ) † � � x ) † � O ij O ij x + ( O ji O ij x − ( O ji 2 2 g + g + g h ) † i O ij qW + ( O ji qW ) † O ( 3 , ij ) + ( O ( 3 , ji ) 4 O ( 3 , kkij ) 3 O ( 1 , 1 , ikkj ) = qq φ q φ q lq 4 + g − g 2 O ( 8 , 1 , ikkj ) 2 O ( 1 , 1 , ijkk ) qq qq − g ′ qe + g ′ g h ) † i + g ′ O ikkj O ( 1 , ij ) + ( O ( 1 , ji ) 4 O ( 1 , kkij ) O ij qB + ( O ji qB ) † 6 O ( 1 , 1 , ijkk ) = qq φ q φ q lq 4 − 2 g ′ − g ′ + g ′ − g ′ 9 O ( 1 , ikkj ) 3 O ( 8 , ikkj ) 9 O ( 1 , ikkj ) 6 O ( 8 , ikkj ) qu qu qd qd J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij O ij qW , qB , uB , qG , uG int. by parts & gauge field EOM x = 1 + 1 � x ) † � � x ) † � O ij O ij x + ( O ji O ij x − ( O ji 2 2 + g ′ lu − g ′ eu − g ′ g h φ u ) † i O ij uB + ( O ji uB ) † O ij φ u + ( O ji 2 O kjik 2 O kkij 18 O ( 1 , kjik ) = qu 4 − g ′ + 2 g ′ − g ′ 12 O ( 8 , kjik ) 3 O ( 1 , ijkk ) 6 O ( 1 , ijkk ) qu uu ud J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij O ij qW , qB , uB , qG , uG int. by parts & gauge field EOM x = 1 + 1 � x ) † � � x ) † � O ij O ij x + ( O ji O ij x − ( O ji 2 2 g s − 8 g s + g s − 8 g s O ij qG + ( O ji qG ) † 2 O ( 8 , 1 , ijkk ) 9 O ( 1 , ikkj ) 6 O ( 8 , ikkj ) 9 O ( 1 , ikkj ) = qq qu qu qd + g s 6 O ( 8 , ikkj ) qd − 8 g s + g s − g s O ij uG + ( O ji uG ) † 9 O ( 1 , kjik ) 6 O ( 8 , kjik ) + g s O ( 1 , ikkj ) 3 O ( 1 , ijkk ) = qu qu uu uu + g s 4 O ( 8 , ijkk ) ud J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij O ij qW , qB , uB , qG , uG dual fields & quark EOM & Bianchi x = 1 + 1 � x ) † � � x ) † � O ij O ij x + ( O ji O ij x − ( O ji 2 2 − 1 h dW ) † i uW ) † − Y d † O ij qW − ( O ji qW ) † Y u jk O ik uW + Y d jk O ik dW − Y u † ki ( O jk ki ( O jk = 4 − 1 h uB φ ) † − Y d † dB φ ) † i O ij qB − ( O ji qB ) † Y u jk O ik uB φ + Y d jk O ik dB φ − Y u † ki ( O jk ki ( O jk = 4 1 h uB φ ) † i O ij uB − ( O ji uB ) † Y u ki O kj uB φ − Y u † jk ( O ki = 4 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij O ij qW , qB , uB , qG , uG dual fields & quark EOM & Bianchi x = 1 + 1 � x ) † � � x ) † � O ij O ij x + ( O ji O ij x − ( O ji 2 2 − 1 h dG φ ) † i uG φ ) † − Y d † O ij qG − ( O ji qG ) † Y u jk O ik uG φ + Y d jk O ik dG φ − Y u † ki ( O jk ki ( O jk = 4 1 h uG φ ) † i O ij uG − ( O ji uG ) † Y u ki O kj uG φ − Y u † jk ( O ki = 4 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij Du , Du , Dd , ¯ ¯ Dd int. by parts & scalar EOM Dx = 1 ± 1 � � � � O ij O ij Dx + O ij O ij Dx − O ij Dx , ¯ ¯ ¯ Dx Dx 2 2 q Li u Rj ˜ lq + Y u † kl O ( 1 , ijkl ) kl O ( 1 , ijkl ) O ij Du + O ij − m 2 ¯ φ + λ O ij u φ + Y e kl O ijkl + Y d = ¯ qu qq Du qde ) † + Y u O ij Dd + O ij − m 2 ¯ q Li d Rj φ + λ O ij d φ + Y e † kl ( O lkji kl O ( 1 , klij ) + Y d † kl O ( 1 , ijkl ) = ¯ qq qd Dd J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ij O ij O ij O ij Du , Du , Dd , ¯ ¯ Dd int. by parts & algebra Dx = 1 ± 1 � � � � O ij O ij Dx + O ij O ij Dx − O ij Dx , ¯ ¯ ¯ Dx Dx 2 2 uW + g ′ − g uB φ − 1 h ) † − ( O ( 1 , ki ) ) † i 2 Y u † ( O ( 3 , ki ) O ij Du − O ij 4 O ij 4 O ij = ¯ φ q φ q Du jk φ u ) † − Y d † + Y u † ki ( O jk ki ( O jk φφ ) † dW − g ′ − g 4 O dB φ − 1 h i 2 Y d † O ( 3 , ik ) + O ( 1 , ik ) O ij Dd − O ij 4 O ij = ¯ jk φ q φ q Dd − Y u † ki O kj φφ − Y d † ki O kj φ d J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ( 3 , ij ) O ( 1 , ij ) O ij , , φ q φ q φ u int. by parts & quark EOM u φ ) † + Y d † O ( 3 , ij ) − ( O ( 3 , ji ) ) † Y u jk O ik u φ − Y d jk O ik d φ − Y u † ki ( O jk ki ( O jk d φ ) † = φ q φ q u φ ) † + Y d † O ( 1 , ij ) − ( O ( 1 , ji ) ) † d φ + Y u † d φ ) † − Y u jk O ik u φ − Y d jk O ik ki ( O jk ki ( O jk = φ q φ q O ( ij ) φ u − ( O ( ji ) φ u ) † Y u ki O kj u φ − Y u † jk ( O ki u φ ) † = J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ( 3 , ij ) O ( 1 , ij ) O ij , , φ q φ q φ u Not all i , j flavour combinations independent! O ij Instead of i , j = 1 , 2 , 3 x = 1 � x ) † � O i + j O ij x + ( O ji i ≤ j = 1 , 2 , 3 use ➙ x 2 = 1 � x ) † � O i − j O ij x − ( O ji and drop i ≤ j = 1 , 2 , 3 x 2 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Technical details for fans O ( 3 , ij ) O ( 1 , ij ) O ij , , φ q φ q φ u Independent operators: i φ † ( τ I D µ − ← − O ( 3 , i + j ) � � D µ τ I ) φ q Li γ µ τ I q Lj ) = (¯ φ q 2 2 ( φ † ← → i O ( 1 , i + j ) D µ φ )(¯ q Li γ µ q Lj ) = φ q 2 ( φ † ← → i O i + j D µ φ )(¯ u Ri γ µ u Rj ) = φ u J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Reminder This is not a change of basis: operators in blue included in BW list O ( 1 , 1 , ijkl ) O ( 8 , 1 , ijkl ) q Li γ µ q Lj )(¯ q Li γ µ λ a q Lj )(¯ q Lk γ µ λ a q Ll ) = 1 / 2 (¯ q Lk γ µ q Ll ) = 1 / 2 (¯ qq qq O ( 1 , ijkl ) = (¯ O ( 3 , ijkl ) = (¯ l Li γ µ l Lj )(¯ l Li γ µ τ I l Lj )(¯ q Lk γ µ τ I q Ll ) q Lk γ µ q Ll ) lq lq O ( 1 , ijkl ) u Ri γ µ u Rj )(¯ O ijkl e Ri γ µ e Rj )(¯ = 1 / 2 (¯ u Rk γ µ u Rl ) eu = (¯ u Rk γ µ u Rl ) uu O ( 1 , ijkl ) u Ri γ µ u Rj )(¯ O ( 8 , ijkl ) u Ri γ µ λ a u Rj )(¯ d Rk γ µ λ a d Rl ) = (¯ d Rk γ µ d Rl ) = (¯ ud ud lu = (¯ O ijkl O ijkl l Li u Rj )(¯ u Rk l Ll ) qe = (¯ q Li e Rj )(¯ e Rk q Ll ) O ( 1 , ijkl ) O ( 8 , ijkl ) q Li λ a u Rj )(¯ u Rk λ a q Ll ) = (¯ q Li u Rj )(¯ = (¯ u Rk q Ll ) qu qu O ( 1 , ijkl ) q Li d Rj )(¯ O ( 8 , ijkl ) q Li λ a d Rj )(¯ d Rk λ a q Ll ) = (¯ d Rk q Ll ) = (¯ qd qd O ijkl qde = (¯ l Li e Rj )(¯ O ( 1 , ijkl ) q Lk ǫ ) T d Rl ˆ ˜ d Rk q Ll ) = (¯ q Li u Rj ) (¯ qq O ijkl (¯ l Lk ǫ ) T e Rl ˆ ˜ lq = (¯ q Li u Rj ) J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Reminder This is not a change of basis: operators in blue included in BW list O ij q Li σ µν d Rj ) φ B µν O ij q Li λ a σ µν d Rj ) φ G a dB φ = (¯ dG φ = (¯ µν φ d = i ( φ † D µ φ )(¯ d φ = ( φ † φ )¯ O ij d Ri γ µ d Rj ) O ij q Li d Rj φ J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Can redundant operators just be dropped? One can write any dim 6 operator Certainly ☞ in terms of the reduced “basis” Many redundant operators already discarded in [Buchmuller, Wyler NPB ’86] Using a redundant operator or an equivalent expression are two ways of writing (parameterising) the same quantity, up to dim 8 terms The contributions to amplitudes are the same at this order (dim 6) ☞ Explicitly checked in several examples [JAAS NPB ’08 ’09] J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Which is the “right” set for the top quark? Dropping O ij qW , O ij qG , O ij Du , O ij Dd , . . . top trilinear interactions are simplified several interesting process involve less diagrams Dropping for example 4f operators many calculations (e.g. top decay) unchanged: 4f are not involved still lots of 4f operators remain, little improvement J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Four-fermion operators contributing to single top ( t , s -channel) ( i , j , k , l are flavour indices) O ( 1 , 1 , ijkl ) q Li γ µ q Lj )(¯ O ( 8 , 1 , ijkl ) q Li γ µ λ a q Lj )(¯ q Lk γ µ λ a q Ll ) = 1 / 2 (¯ q Lk γ µ q Ll ) = 1 / 2 (¯ qq qq O ( 1 , ijkl ) u Ri γ µ u Rj )(¯ O ( 8 , ijkl ) u Ri γ µ λ a u Rj )(¯ d Rk γ µ λ a d Rl ) = (¯ d Rk γ µ d Rl ) = (¯ ud ud O ( 1 , ijkl ) O ( 8 , ijkl ) q Li λ a u Rj )(¯ u Rk λ a q Ll ) = (¯ q Li u Rj )(¯ u Rk q Ll ) = (¯ qu qu O ( 1 , ijkl ) q Li d Rj )(¯ O ( 8 , ijkl ) q Li λ a d Rj )(¯ d Rk λ a q Ll ) = (¯ d Rk q Ll ) = (¯ qd qd O ( 1 , ijkl ) q Lk ǫ ] T d Rl ) O ( 8 , ijkl ) q Li λ a u Rj )([¯ q Lk ǫ ] T λ a d Rl ) = (¯ q Li u Rj )([¯ = (¯ qq qq � 10 for ub → dt ➙ total = 20 operators 10 for cb → st J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses If you think I’m missing four-fermion operators note that, for example 1 O ( 1 , 3 , ijkl ) q Li γ µ τ I q Lj )(¯ q Lk γ µ τ I q Ll ) ≡ 2 (¯ qq 2 3 O ( 1 , 1 , ilkj ) + O ( 8 , 1 , ilkj ) − O ( 1 , 1 , ijkl ) = qq qq qq 1 O ( 8 , 3 , ijkl ) q Li γ µ λ a τ I q Lj )(¯ q Lk γ µ λ a τ I q Ll ) ≡ 2 (¯ qq 32 − 2 9 O ( 1 , 1 , ilkj ) − O ( 8 , 1 , ijkl ) 3 O ( 8 , 1 , ilkj ) = qq qq qq using λ a , τ I completeness relations and Fierz rearrangements ☞ several four-fermion operators in BW list are redundant J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings O ij O ij O ij O ij O ij qW , qB , uB , qG , uG O ij O ij O ij O ij Du , Du , Dd , I choose to drop ¯ ¯ Dd O ( 3 , i − j ) O ( 1 , i − j ) O i − j , , φ q φ q φ u and will show how top interactions (and some selected observables) are simplified J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Wtb vertex - before − g b γ µ ( V L P L + V R P R ) t W − ¯ L Wtb = √ µ 2 b i σ µν q ν − g ¯ ( g L P L + g R P R ) t W − √ µ M W 2 � q µ ( f 1 L P L + f 1 R P R ) + k µ � − g ¯ t W − √ ( f 2 L P L + f 2 R P R ) b µ M W M W 2 q 2 − g ¯ b γ µ ξ W L P L t W − √ µ M 2 2 W − g 1 � k µ − k · q γ µ ) h W ¯ L P L t W − √ b ( q µ + h.c. M 2 2 W J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Wtb vertex - without redundant operators More − g b γ µ ( V L P L + V R P R ) t W − ¯ L Wtb = √ µ 2 b i σ µν q ν − g ¯ ( g L P L + g R P R ) t W − √ µ + h.c. M W 2 � q µ ( f 1 L P L + f 1 R P R ) + k µ � − g ¯ t W − √ ( f 2 L P L + f 2 R P R ) b µ M W M W 2 q 2 − g ¯ b γ µ ξ W L P L t W − √ µ M 2 2 W − g 1 � k µ − k · q γ µ ) h W ¯ L P L t W − √ b ( q µ + h.c. M 2 2 W J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Ztt vertex - before − g t γ µ � X L tt P L + X R tt P R − 2 s 2 ¯ � L Ztt = W Q t t Z µ 2 c W t i σ µν q ν − g d Z V + id Z ¯ � � A γ 5 t Z µ 2 c W M Z � q µ 1 R P R ) + k µ g � ¯ ( f Z 1 L P L + f Z ( f Z 2 L P L + f Z − 2 R P R ) t t Z µ 2 c W M Z M Z q 2 g t γ µ ( ξ Z ¯ L P L + ξ Z − R P R ) t Z µ M 2 2 c W Z g 1 � k µ − k · q γ µ )( h Z ¯ L P L + h Z − t ( q R P R ) t Z µ M 2 2 c W Z J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Ztt vertex - without redundant operators More − g t γ µ � X L tt P L + X R tt P R − 2 s 2 ¯ � L Ztt = W Q t t Z µ 2 c W t i σ µν q ν − g d Z V + id Z ¯ � � A γ 5 t Z µ 2 c W M Z � q µ 1 R P R ) + k µ g � ¯ ( f Z 1 L P L + f Z ( f Z 2 L P L + f Z − 2 R P R ) t t Z µ 2 c W M Z M Z q 2 g t γ µ ( ξ Z ¯ L P L + ξ Z − R P R ) t Z µ M 2 2 c W Z g 1 � k µ − k · q γ µ )( h Z ¯ L P L + h Z − t ( q R P R ) t Z µ M 2 2 c W Z J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings γ tt vertex - before t i σ µν q ν ( d γ V + id γ − eQ t ¯ t γ µ t A µ − e ¯ L γ tt = A γ 5 ) t A µ m t − e q 2 t γ µ ( ξ γ L P L + ξ γ ¯ R P R ) t A µ m 2 t − e 1 � k µ − k · q γ µ )( h γ L P L + h γ ¯ t ( q R P R ) t A µ m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings γ tt vertex - without redundant operators More t i σ µν q ν ( d γ V + id γ − eQ t ¯ t γ µ t A µ − e ¯ L γ tt = A γ 5 ) t A µ m t − e q 2 t γ µ ( ξ γ L P L + ξ γ ¯ R P R ) t A µ m 2 t − e 1 � k µ − k · q γ µ )( h γ L P L + h γ ¯ t ( q R P R ) t A µ m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings gtt vertex - before t λ a t λ a i σ µν q ν ( d g V + id g 2 γ µ t G a A γ 5 ) t G a − g s ¯ µ − g s ¯ L gtt = µ m t q 2 t λ a γ µ ( ξ g L P L + ξ g ¯ R P R ) t G a − g s µ m 2 t 1 � k µ − k · q γ µ )( h g L P L + h g ¯ t λ a ( q R P R ) t G a − g s µ m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings gtt vertex - without redundant operators More t λ a t λ a i σ µν q ν ( d g V + id g 2 γ µ t G a A γ 5 ) t G a − g s ¯ µ − g s ¯ L gtt = µ m t q 2 t λ a γ µ ( ξ g L P L + ξ g ¯ R P R ) t G a − g s µ m 2 t 1 � k µ − k · q γ µ )( h g L P L + h g ¯ t λ a ( q R P R ) t G a − g s µ m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Htt vertex - before − 1 ¯ � Y V t + iY A � L Htt = √ t γ 5 t t H 2 − 1 q µ ¯ t γ µ � ω L tt P L + ω R � √ tt P R t H m t 2 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Htt vertex - without redundant operators More − 1 ¯ � Y V t + iY A � L Htt = √ t γ 5 t t H 2 − 1 q µ ¯ t γ µ � ω L tt P L + ω R � √ tt P R t H m t 2 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Ztc vertex - before − g c γ µ � X L ct P L + X R � L Ztc = ¯ ct P R t Z µ 2 c W c i σ µν q ν − g κ L ct P L + κ R � � ¯ ct P R t Z µ 2 c W M Z � q µ 1 R P R ) + k µ g � ( f ct 1 L P L + f ct ( f ct 2 L P L + f ct − ¯ 2 R P R ) c t Z µ 2 c W M Z M Z q 2 g c γ µ ( β Z L P L + β Z − ¯ R P R ) t Z µ M 2 2 c W Z g 1 � k µ − k · q γ µ )( θ Z L P L + θ Z − ¯ c ( q R P R ) t Z µ + h.c. M 2 2 c W Z J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Ztc vertex - without redundant operators More − g c γ µ � X L ct P L + X R � L Ztc = ¯ ct P R t Z µ 2 c W c i σ µν q ν − g κ L ct P L + κ R � � ¯ ct P R t Z µ + h.c. 2 c W M Z � q µ 1 R P R ) + k µ g � ( f ct 1 L P L + f ct ( f ct 2 L P L + f ct − ¯ 2 R P R ) c t Z µ 2 c W M Z M Z q 2 g c γ µ ( β Z L P L + β Z − ¯ R P R ) t Z µ M 2 2 c W Z g 1 � k µ − k · q γ µ )( θ Z L P L + θ Z − ¯ c ( q R P R ) t Z µ + h.c. M 2 2 c W Z J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings γ tc vertex - before c i σ µν q ν � λ L ct P L + λ R � L γ tc = − e ¯ ct P R t A µ m t − e q 2 c γ µ ( β γ L P L + β γ ¯ R P R ) t A µ m 2 t − e 1 � k µ − k · q γ µ )( θ γ L P L + θ γ ¯ c ( q R P R ) t A µ + h.c. m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings γ tc vertex - without redundant operators More c i σ µν q ν � λ L ct P L + λ R � L γ tc = − e ¯ t A µ + h.c. ct P R m t − e q 2 c γ µ ( β γ L P L + β γ ¯ R P R ) t A µ m 2 t − e 1 � k µ − k · q γ µ )( θ γ L P L + θ γ ¯ c ( q R P R ) t A µ + h.c. m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings gtc vertex - before c λ a i σ µν q ν � ζ L ct P L + ζ R � t G a L gtc = − g s ¯ ct P R µ m t q 2 c λ a γ µ ( β g L P L + β g R P R ) t G a − g s ¯ µ m 2 t − e 1 � k µ − k · q γ µ )( θ g L P L + θ g c λ a ( q R P R ) t G a ¯ µ + h.c. m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings gtc vertex - without redundant operators More c λ a i σ µν q ν � ζ L ct P L + ζ R � t G a L gtc = − g s ¯ µ + h.c. ct P R m t q 2 c λ a γ µ ( β g L P L + β g R P R ) t G a − g s ¯ µ m 2 t − e 1 � k µ − k · q γ µ )( θ g L P L + θ g c λ a ( q R P R ) t G a ¯ µ + h.c. m 2 t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Htc vertex - before − 1 � η L ct P L + η R � L Htc = √ ¯ c ct P R t H 2 − 1 q µ c γ µ � ω L ct P L + ω R � √ ¯ t H + h.c. ct P R m t 2 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses A minimal set of top anomalous couplings Htc vertex - without redundant operators More − 1 � η L ct P L + η R � L Htc = √ ¯ t H + h.c. c ct P R 2 − 1 q µ c γ µ � ω L ct P L + ω R � √ ¯ t H + h.c. ct P R m t 2 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses In summary: ➀ Gauge interactions: only γ µ and σ µν q ν terms ➁ Higgs: only scalar and pseudo-scalar terms This is general for any fermion and process, ☞ not only the top quark! � phenomenological analyses This simplifies Monte Carlo building J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Q & A: Q: Why is this new? I’ve been using only γ µ and σ µν q ν all my life! A: Yes, but possibly you were using top on-shell. This is valid for top off-shell, light quarks off-shell and bosons off-shell J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Top interactions tested at LHC involve general off-shell vertices Single top tW : Wtb with t / b off-shell t ¯ tZ : Ztt with one t off-shell t ¯ t γ : γ tt with one t off-shell Zt production: Ztc with t / c off-shell γ t production: γ tc with t / c off-shell . . . The effort to obtain a minimal set of operators pays off: ☞ description completely general but much simpler J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Q & A: Q: And what’s wrong with having a few extra parameters? A: If you rename a single parameter ‘ a ’ as ‘ b + c ’, you will not measure b nor c individually with your observables, which all depend on b + c J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Top-charm-Higgs vertex with redundant operators L Htc = − 1 t H − 1 q µ � η L ct P L + η R � c γ µ � ω L ct P L + ω R � √ ¯ √ ¯ c ct P R ct P R t H m t 2 2 H t ct | 2 + | η R � | η L ct + ω R ct + ω L ct | 2 � Γ = A c c H c H c ct | 2 + | η R + � | η L ct + ω R ct + ω L ct | 2 � σ = B t g t g t Suspicious coincidence . . . ω vertex is q -dependent! J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Minimal top-charm-Higgs vertex L Htc = − 1 t H − 1 q µ � η L ct P L + η R � c γ µ � ω L ct P L + ω R � √ ¯ √ ¯ c ct P R ct P R t H m t 2 2 H t ct | 2 + | η R � | η L ct | 2 � Γ = A c c H c H c ct | 2 + | η R + � | η L ct | 2 � σ = B t g t g t 4 parameters → 2 parameters J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses ( q = u , c ) Some FCN Processes mediated by gtq g t t → qg q q t gq → t g q Z q Z t + gq → Zt q g g t t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Lagrangians for gtu interactions Dropping O ij qG , O ij uG c λ a i σ µν q ν ζ L ut P L + ζ R t G a � � L gtu = − g s ¯ µ + h . c . ut P R m t √ √ 2 vm t 2 vm t with ζ L C 31 ∗ Λ 2 , ζ R C 13 ut = ut = uG φ uG φ Λ 2 g s g s [JAAS NPB’09] Dropping 4f operators gtu = i α tu uG + i α ut uG + β tu uG φ + β ut L ′ Λ 2 O 31 Λ 2 O 13 Λ 2 O 31 Λ 2 O 13 uG φ + h . c . [Ferreira, Santos PRD ’06 − 09] J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Some observables for gtu anomalous couplings Γ( t → ug ) = 4 ut | 2 + | ζ R | ζ L ut | 2 � � 3 α s m t √ » – 2 vm t im t β ∗ ( α ∗ ζ L ut = tu + tu + α ut ) √ g s Λ 2 2 2 v √ » – 2 vm t im u ζ R ( α ut + α ∗ ut = β ut + tu ) √ g s Λ 2 2 2 v m 3 ut | 2 + 16 ˆ | β tu | 2 + | β ut | 2 � t m 2 t | α tu + α ∗ v 2 � � Γ( t → ug ) = 12 π Λ 4 vm t Im β tu ( α ∗ + 8 ˆ tu + α ut ) } = [Ferreira, Santos PRD ’06] J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Some observables for gtu anomalous couplings ut | 2 + | ζ R σ ( gu → t ) = 2 . 162 × 10 6 � | ζ L ut | 2 � pb √ » – 2 vm t im t β ∗ ( α ∗ ζ L ut = tu + tu + α ut ) √ g s Λ 2 2 2 v √ » – 2 vm t im u ζ R ( α ut + α ∗ ut = β ut + tu ) √ g s Λ 2 2 2 v 1 ut | 2 + 5413 | β tu | 2 + | β ut | 2 � 342 | α tu + α ∗ � � σ ( gu → t ) = Λ 4 + 2722 Im β tu ( α ∗ tu + α ut ) } pb ≃ [Ferreira, Santos PRD ’06] J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Some observables for gtu anomalous couplings ut | 2 + 2 . 378 × 10 4 | ζ R ut | 2 pb σ ( gu → Zt ) = 2 . 321 × 10 4 | ζ L √ » – 2 vm t im t β ∗ ( α ∗ ζ L ut = tu + tu + α ut ) √ g s Λ 2 2 2 v √ » – 2 vm t im u ζ R ( α ut + α ∗ ut = β ut + tu ) √ g s Λ 2 2 2 v 1 ut | 2 + 61 . 3 | β tu | 2 + 62 . 8 | β ut | 2 3 . 88 | α tu + α ∗ � σ ( gu → Zt ) = Λ 4 + 30 . 8 Im β tu ( α ∗ tu + α ut ) } pb ≃ [Ferreira, Santos PRD ’06] J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Extracting the Lagrangian from experiment ★ Identification of relevant observables ★ Comparison of sensitivities to anomalous couplings given their experimental uncertainties (syst and stat) ☞ example: Wtb vertex J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Observables for Wtb anomalous couplings Present CDF & D0 analyses Use W helicity fractions in t → Wb F R , F L , F 0 sensitive to anomalous couplings [Kane, Ladinsky, Yuan PRD ’92] Dependence on couplings: simple analytical expressions up to corrections of order m b / m t ∼ 0 . 03 [Chen, Larios, Yuan PLB ’05] Combination of F and single top σ barring cancellations among anomalous couplings [Chen, Larios, Yuan PLB ’05] But. . . at LHC we can and must do better! combined effort of theorists and experimentalists ☞ J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses New observables for Wtb anomalous couplings LHC precision determined ☞ investigate new observables by systematic uncertainties New observables ρ R , L = F R , L , A ± asym. F 0 [JAAS et al. EPJC ’08] smaller systematics enhanced sensitivity Expected limits for ATLAS, 10 fb − 1 / V L = 1, V R = 0 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses W rest frame observables ℓ distribution in W rest frame d Γ 1 = 3 ℓ ) 2 F L + 3 4 sin 2 θ ∗ 8 ( 1 − cos θ ∗ ℓ F 0 d cos θ ∗ Γ θ ∗ ℓ l ν W ℓ + 3 ℓ ) 2 F R 8 ( 1 + cos θ ∗ ( F i = Γ i / Γ) t [Kane, Ladinsky, Yuan PRD ’92] b F L , F R , F 0 partial widths to W with helicity − 1, + 1, 0 in top rest frame, F L + F R + F 0 = 1 by definition they depend on Wtb couplings V L , V R , g L , g R good for ➙ distribution independent of top spin t ¯ t production J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses W helicity fractions and related observables 0.8 Analytical 0.7 MC simulation 0.6 * 1 / Γ d Γ / d cos θ l 0.5 0.4 0.3 0.2 0.1 0 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 cos θ l * J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses W helicity fractions and related observables ➙ fit F 0 , F L , F R (with F 0 + F L + F R = 1) 0.8 Analytical 0.7 MC simulation 0.6 * 1 / Γ d Γ / d cos θ l 0.5 0.4 0.3 0.2 0.1 0 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 cos θ l * J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses W helicity fractions and related observables ➙ fit F 0 , F L , F R (with F 0 + F L + F R = 1) 0.8 ρ R ≡ F R F 0 , ρ L ≡ F L Analytical ➙ 0.7 fit MC simulation F 0 0.6 * 1 / Γ d Γ / d cos θ l 0.5 (independent parameters) 0.4 ρ R best limit on V R , g L ☞ 0.3 0.2 0.1 0 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 cos θ l * J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses W helicity fractions and related observables ➙ fit F 0 , F L , F R (with F 0 + F L + F R = 1) 0.8 ρ R ≡ F R F 0 , ρ L ≡ F L Analytical ➙ 0.7 fit MC simulation F 0 0.6 * 1 / Γ d Γ / d cos θ l 0.5 (independent parameters) 0.4 ρ R best limit on V R , g L ☞ 0.3 0.2 A + A − 0.1 0 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 cos θ l * ➙ count events A ± asym. around ∓ ( 2 2 / 3 − 1 ) A + ☞ best limit on g R J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Use accurate theoretical expressions for observables LHC excellent precision are m b / m t effects relevant? ☞ F ’s with anomalous couplings linear terms ∝ m b / m t g L V L quadratic terms ∝ g 2 L ☞ of the same order! Expected limits for ATLAS, 10 fb − 1 V L = 1, V R = 0 / J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Use accurate theoretical expressions for observables Top partial widths to polarised W g 2 | � (h m 2 q | | V L | 2 + | V R | 2 i “ | g L | 2 + | g R | 2 i “ 1 − x 2 W + x 2 ” t h 1 − x 2 W − 2 x 2 b − x 2 W x 2 b + x 4 ” Γ R , L = + b b M 2 32 π W m t ˜ “ 1 − x 2 W − x 2 ” − 4 x b Re V L V ∗ R − 4 x b Re g L g ∗ ˆ V L g ∗ R + V R g ∗ R − 2 Re L b M W m t ”ff ˜ “ 1 + x 2 W − x 2 ˆ V L g ∗ L + V R g ∗ + 2 x b Re R b M W g 2 m 3 | V L | 2 − | V R | 2 i | g L | 2 − | g R | 2 i “ t n − x 2 h h 1 − x 2 ” ± + W b M 2 64 π W ˜¯ “ 1 − 2 x 2 W − 2 x 2 b + x 4 W − 2 x 2 W x 2 b + x 4 ” + 2 x W Re ˆ V L g ∗ R − V R g ∗ ˜ + 2 x W x b Re ˆ V L g ∗ L − V R g ∗ L R b g 2 | � ( m 2 q | | V L | 2 + | V R | 2 i “ | g L | 2 + | g R | 2 i “ t h 1 − x 2 W − 2 x 2 b − x 2 W x 2 b + x 4 ” h 1 − x 2 W + x 2 ” Γ 0 = + b b M 2 32 π W m t ˜ “ 1 − x 2 W − x 2 ” − 4 x b Re V L V ∗ R − 4 x b Re g L g ∗ ˆ V L g ∗ R + V R g ∗ R − 2 Re L b M W m t ”ff ˜ “ 1 + x 2 W − x 2 ˆ V L g ∗ L + V R g ∗ + 2 x b Re R b M W x b = m b / m t , x W = m W / m t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Allowing for cancellations fit the four Wtb couplings Model-independent analysis ☞ using many observables σ , F insufficient to constrain V R , g L simultaneously ☞ find new observables spin asymmetry ratio r bl = A b A l easily improves combined limits J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Top rest frame observables p b � � s Polarised top decay in top rest frame θ b 1 d Γ = 1 + α X cos θ X θ ℓ Γ d cos θ X θ ν 2 � p ℓ t [Jezabek, Kuhn PLB ’94] p ν � α ℓ + , α ν , α b called ‘spin analysing power’ of ℓ + , ν , b they depend on Wtb couplings V L , V R , g L , g R α ℓ + = 1 α ν = − 0 . 32 α b = − 0 . 41 tree level SM values α ℓ + = 0 . 998 α ν = − 0 . 33 α b = − 0 . 39 one loop [Bernreuther et al. NPB ’04] look for spin ➙ top spin not directly measurable asymmetries J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Top spin asymmetries tj production: spin asymmetries ➙ X = top decay product � p X = momentum in t rest frame � p j = jet momentum in t rest frame N ( Q > 0 ) − N ( Q < 0 ) A X ≡ ➙ Q = cos ( � p X ,� p j ) N ( Q > 0 ) + N ( Q < 0 ) 1 [ P = 0 . 95 ( t ) P = − 0 . 93 (¯ = 2 P α X t )] [Mahlon, Parke PLB ’00] J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Ratios of top spin asymmetries Ratios of asymmetries depend only on α ˜ A bj A bj = α b t ¯ ➙ = ≡ r b ℓ t production ˜ A ℓ j α ℓ A ℓ j = α b A b tj / t ¯ ➙ = r b ℓ bj production A ℓ α ℓ Guessed precision in plot . . . hope it’s realistic r bl = − 0 . 406 ± 0 . 032 SM central value, relative error 8% J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Summary: observables to fit Wtb vertex ➀ Single top cross sections L + κ V R V 2 R + κ V L V R V L V R + κ g L g 2 L + κ g R g 2 � V 2 � σ = σ SM R + . . . ➁ W helicity observables in t → Wb → ℓν b helicity fractions F R , F L , F 0 and ratios ρ R , L angular asymmetries A ± . . . ➂ Spin asymmetry ratios in single and pair production single top: A b , A ℓ . . . top pair: A ll , A ℓ j . . . ratios independent of production mechanism r bl = A b = A bj , r ν l , . . . A ℓ A ℓ j ➃ More to come . . . J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses TopFit : the global fit to the Wtb vertex After the reduction in the number of meaningful parameters, we can obtain model-independent measurements and limits (or with very few assumptions) General Wtb vertex − g b γ µ ( V L P L + V R P R ) t W − ¯ L Wtb = √ µ 2 b i σ µν q ν − g ¯ ( g L P L + g R P R ) t W − √ µ + h . c . M W 2 q = p t − p b = p W ★ either we find Wtb anomalous couplings no-lose bet: ★ or we clean the room to probe NP in production J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses TopFit : the global fit to the Wtb vertex An example: the input Exact expressions for W helicity ratios and spin analysing powers in top decay t → Wb → f f ′ b Their expected ATLAS precision with 10 fb − 1 Expressions for single top xsec with anomalous couplings including theoretical uncertainty Expected ATLAS precision for tW xsec with 10 fb − 1 Guesstimated ATLAS precision for A ℓ , A b and other new asymmetries with 10 fb − 1 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Coming soon . . . Estimated limits for LHC (8-dimensional region) ( V L , Re V R ) ( Re g L , Re g R ) ➙ Many cancellations possible in single observables life is not easy ➙ All of them allowed in the fit reduced by combination Model-independent measurement of W tb vertex and single top P J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Coming soon . . . Estimated limits for LHC (8-dimensional region) ( Re V R , Im V R ) ( Re g L , Im g L ) ( Re g R , Im g R ) ➙ Many cancellations possible in single observables life is not easy ➙ All of them allowed in the fit reduced by combination Model-independent measurement of W tb vertex and single top P J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Protos : Monte Carlo with anomalous couplings Generator Protos (PROgram for TOp Simulations) for ➀ Single top and t ¯ t production with anomalous Wtb couplings ➁ Top FCNC production and decay Includes the minimal sets of top anomalous couplings arising from dim 6 effective operators J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Protos : simplification using minimal set Vertices simpler, and amplitudes also involve less diagrams Example: tW − production with Wtb anomalous couplings new diagram s -channel t -channel b W b W b W b t g g g t t t gWtb required by gauge symmetry if redundant operators included J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Protos : simplification using minimal set Vertices simpler, and amplitudes also involve less diagrams Example: tW − production with Wtb anomalous couplings new diagram s -channel t -channel not needed b W b W b t g g t t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Equivalent parameterisations of the same new physics One can either Use for example O ij Du − O ij Du , which involves Wtb couplings ¯ and an associated gWtb vertex ➙ The extra diagram with the quartic vertex must appear Replace O ij Du − O ij Du by an equivalent expression (up to dim 8) ¯ which involves γ µ , σ µν q ν already present from other operators and does not have any gWtb vertex The contribution to the amplitudes is the same ➙ but the parameterisation is much simpler J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Gauge invariance at work: an example Contributions to gb → tW γ µ , σ µν q ν k µ b W b W t t b W g g t t g µν = b W b W g b t b γ µ , σ µν q ν k µ g g t t J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Protos : Monte Carlo with anomalous couplings General features ★ Matrix elements calculated with HELAS ★ Top and W off-shell (Breit-Wigner resonances) ★ Spin information kept in decay chain ★ Integration done with VEGAS ★ Many numerical outputs (checks) provided: W helicity fractions, angular asymmetries, t ¯ t spin correlations . . . ★ Implemented in ATLAS framework (full simulation samples available) J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Protos for Wtb anomalous couplings The generator includes: single top in all channels, with double counting removal top pair production . . . but why is this necessary? Event samples with Wtb anomalous couplings necessary for several LHC analyses W helicity measurements with templates Limits on anomalous Wtb couplings from single top J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Generating templates for W helicities m t = 175 GeV Parameters 0.10 Set L Set 0 W L : V L ≃ − 0 . 4917 V R = 0 0.08 Set R g L ≃ 0 g R ≃ − 1 . 069 σ (normalised) 0.06 W 0 : V L ≃ 1 . 513 V R = 0 0.04 g L ≃ − 0 . 0191 g R ≃ 0 . 6956 0.02 W R : V L = 0 V R ≃ 0 . 4917 g L ≃ 1 . 069 g R ≃ 0 0 0 -1 -0.75 -0.5 -0.25 0.25 0.5 0.75 1 * cos θ l distributions for detector fit F L , F R , F 0 ➙ ➙ pure W L , W R , W 0 simulation with real data J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Generating templates for W helicities Top and W boson invariant mass keep Breit-Wigner shape in all cases 0.40 0.40 Set L Set L 0.35 0.35 Set 0 Set 0 Set R Set R 0.30 0.30 σ (normalised) σ (normalised) 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0 0 150 155 160 165 170 175 180 185 190 195 200 60 65 70 75 80 85 90 95 100 2 ] (GeV) 2 ] (GeV) sqrt [p t sqrt [p W This can only be done consistently with Wtb anomalous couplings J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Testing efficiency variations with anomalous couplings When limits on Wtb anomalous couplings are extracted from total cross sections the efficiency variations must be taken into account σ µν couplings affect kinematics ➙ affect efficiency This can be done by extracting limits assuming SM efficiency and testing the variations within the limits obtained [JAAS NPB ’08] ☞ Samples required with anomalous couplings J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Testing efficiency dependence on anomalous couplings Final state 1 ( tj ) Fast simulation + typical cuts SM Set A Set B 2 . 02 ± 0 . 02 2 . 08 ± 0 . 02 2 . 07 ± 0 . 02 tj t ¯ 1 . 44 ± 0 . 02 1 . 40 ± 0 . 02 1 . 46 ± 0 . 02 bj Parameters t ¯ 0 . 76 ± 0 . 01 0 . 73 ± 0 . 01 0 . 74 ± 0 . 01 b tW − 0 . 173 ± 0 . 008 0 . 161 ± 0 . 007 0 . 173 ± 0 . 008 SM: V L = 1 tW − ¯ 0 . 146 ± 0 . 004 0 . 150 ± 0 . 004 0 . 151 ± 0 . 004 b rest zero Final state 2 ( t ¯ b ) SM Set A Set B + typical limits from global fit tj 0 . 102 ± 0 . 005 0 . 103 ± 0 . 005 0 . 104 ± 0 . 005 t ¯ [JAAS NPB ’08] bj 0 . 328 ± 0 . 009 0 . 315 ± 0 . 009 0 . 328 ± 0 . 009 t ¯ b 2 . 70 ± 0 . 03 2 . 75 ± 0 . 03 2 . 70 ± 0 . 03 tW − 0 . 073 ± 0 . 005 0 . 082 ± 0 . 005 0 . 065 ± 0 . 005 tW − ¯ V L = 1 b 0 . 071 ± 0 . 003 0 . 071 ± 0 . 003 0 . 071 ± 0 . 003 V R = 0 . 3 Set A: Final state 3 ( tjj ) g L = 0 . 15 SM Set A Set B tj 0 . 146 ± 0 . 006 0 . 158 ± 0 . 006 0 . 132 ± 0 . 006 t ¯ bj 0 . 294 ± 0 . 008 0 . 313 ± 0 . 009 0 . 292 ± 0 . 008 Set B: V L = 1 t ¯ b 0 . 33 ± 0 . 10 0 . 38 ± 0 . 10 0 . 32 ± 0 . 10 tW − g R = 0 . 024 2 . 38 ± 0 . 03 2 . 47 ± 0 . 03 2 . 39 ± 0 . 03 tW − ¯ b 2 . 37 ± 0 . 02 2 . 38 ± 0 . 02 2 . 36 ± 0 . 02 J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Single top and t ¯ t generators are LO but ... ★ t ¯ bj kinematics similar to NLO [Campbell et al. JHEP ’09] ★ For t ¯ b too [Sullivan PRD ’04] ➙ ★ QCD corrections to decay effective g R coupling effect 1 / 3 smaller than ATLAS sensitivity [JAAS et al. EPJC ’08] ★ Hard extra jets do not affect top decay kinematics (but may affect reconstruction) ★ t ¯ t + 1 j does not change spin correlations (checked with Alpgen) J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses Protos for top FCNC processes The generator includes: single top: pp → Zt /γ t / t / Ht top pair production with t → Zq /γ q / gq / Hq more to come . . . Simulated event samples for these processes absolutely necessary to compare with real data and extract limits on top FCN interactions J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (I) ★ Fermion trilinear interactions arising from dim 6 gauge-invariant effective operators are simpler than expected γ µ , σ µν q ν terms for gauge bosons scalar and pseudo-scalar for the Higgs ★ This is the minimal structure: if more operators are found redundant it will not be simplified further ★ Dropping one operator or another is a matter of taste, but our choice seems simpler for top phenomenology J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (II) The (other) preparation for data J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (II) The (other) preparation for data ➀ ✔ Establish the Lagrangian, minimal but general (that is, to know which the anomalous couplings are) J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (II) The (other) preparation for data ➀ ✔ Establish the Lagrangian, minimal but general (that is, to know which the anomalous couplings are) ➁ ✔ Identify the observables, look for improvements Use accurate theoretical expressions for them J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (II) The (other) preparation for data ➀ ✔ Establish the Lagrangian, minimal but general (that is, to know which the anomalous couplings are) ➁ ✔ Identify the observables, look for improvements Use accurate theoretical expressions for them ➂ ✔ A program to fit the data TopFit http://www-ftae.ugr.es/topfit/ J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (II) The (other) preparation for data ➀ ✔ Establish the Lagrangian, minimal but general (that is, to know which the anomalous couplings are) ➁ ✔ Identify the observables, look for improvements Use accurate theoretical expressions for them ➂ ✔ A program to fit the data TopFit http://www-ftae.ugr.es/topfit/ ➃ ✔ Generators involving top anomalous couplings Protos http://www-ftae.ugr.es/protos/ J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
Operator contributions to top vertices Comparison between Tevatron and LHC Conclusion (II) The (other) preparation for data ➀ ✔ Establish the Lagrangian, minimal but general (that is, to know which the anomalous couplings are) ➁ ✔ Identify the observables, look for improvements Use accurate theoretical expressions for them ➂ ✔ A program to fit the data TopFit http://www-ftae.ugr.es/topfit/ ➃ ✔ Generators involving top anomalous couplings Protos http://www-ftae.ugr.es/protos/ ➄ Ready and waiting for the data at 7 TeV! J. A. Aguilar-Saavedra Acoplamientos anómalos del quark top ...
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