Adam Falkowski (LPT Orsay) Model Independent Constraints on Physics Beyond the Standard Model Florence, 17 September 2015 Based on my 1505.00046, 1503.07872 with Aielet Efrati and Yotam Soreq, 1411.0669 with Francesco Riva, and 1508.00581 with Martín Gonzalez-Alonso, Admir Greljo, and David Marzocca Thursday, September 17, 15 1
Plan Effective field theory approach to physics beyond the standard model Current precision constraints: - from LEP-1 pole observables - from LHC Higgs data and LEP-2 WW production - from LEP-2 ee->ll scattering (preview) Thursday, September 17, 15 2
Effective Field Theory approach to BSM physics Thursday, September 17, 15 3
Premise SM is probably a correct theory the weak scale, at least as the lowest order term in an effective theory expansion If new particles are heavy, their effects can be parametrized by higher-dimensional operators added to the SM Lagrangian EFT framework offers a systematic expansion around the SM organized in terms of operator dimensions, with higher dimensional operator suppressed by the mass scale Λ of new physics Thursday, September 17, 15 4
Effective Theory Approach to BSM Basic assumptions New physics scale Λ separated from EW scale v, Λ >> v Linearly realized SU(3)xSU(2)xU(1) local symmetry spontaneously broken by VEV of Higgs doublet field EFT Lagrangian beyond the SM expanded in operator dimension D Alternatively, non-linear Lagrangians with derivative expansion Thursday, September 17, 15 5
Effective Theory Approach to BSM Basic assumptions New physics scale Λ separated from EW scale v, Λ >> v Linearly realized SU(3)xSU(2)xU(1) local symmetry spontaneously broken by VEV of Higgs doublet field EFT Lagrangian beyond the SM expanded in operator dimension D X X X By assumption, subleading Lepton number violating, to D=6 hence too small to probe at LHC Thursday, September 17, 15 6
EFT approach to BSM First attempts to classify dimension-6 Buchmuller,Wyler operators back in 1986 pre-arxiv (1986) First complete and non-redundant set of Grz ą dkowski et al. operators explicitly written down only in 2010 1008.4884 Operators can be traded for other operators using integration by parts, field redefinition, equations of motion, Fierz transformation, etc Because of that, one can choose many see e.g. Grz ą dkowski et al. 1008.4884 different bases == non-redundant sets of Giudice et al hep-ph/0703164 Contino et al 1303.3876 operators Thursday, September 17, 15 7
For D=6 Lagrangian several D=6 Basis complete non-redundant set of operators Giudice et al hep-ph/0703164 SILH (so-called basis) Contino et al 1303.3876 basis proposed in the literature HISZ h Hagiwara et al (1993) basis LHCHXSWG-INT-2015-001 basis Warsaw Grz ą dkowski et al. 1008.4884 Primary Basis Gupta et al 1405.0181 basis All bases are equivalent, but some may be more equivalent convenient for specific applications Physics description (EWPT, Higgs, RG running) in any of these bases contains the same information, provided all operators contributing to that process are taken into account Thursday, September 17, 15 8
Example: Warsaw Basis Grz ą dkowski et al. H 4 D 2 and H 6 f 2 H 3 V 3 D 3 1008.4884 ⇥ ⇤ 2 − ( H † H − v 2 @ µ ( H † H ) eH † ` g 3 s f abc G a µ ⌫ G b ⌫⇢ G c O H O e 2 )¯ O 3 G ⇢ µ ⇣ ⌘ 2 59 different H † ← → s f abc e − ( H † H − v 2 u e H † q g 3 G a µ ⌫ G b ⌫⇢ G c 2 )¯ O T D µ H O u O f ⇢ µ 3 G − ( H † H − v 2 2 ) ¯ µ ⌫ W j dH † q g 3 ✏ ijk W i ⌫⇢ W k kinds of operators, ( H † H ) 3 O d O 3 W O 6 H ⇢ µ g 3 ✏ ijk f µ ⌫ W j W i ⌫⇢ W k O g of which 17 are complex ⇢ µ 3 W V 2 H 2 f 2 H 2 D f 2 V HD 2499 distinct operators, `� µ ` H † ← → g 2 i ¯ g ¯ 4 H † H G a µ ⌫ G a `� µ ⌫ e � i HW i O GG O H ` D µ H O eW s µ ⌫ µ ⌫ `� i � µ ` H † � i ← → g 2 i ¯ g 0 ¯ 4 H † H e G a µ ⌫ G a including flavor structure O 0 `� µ ⌫ eHB µ ⌫ O g D µ H O eB s µ ⌫ H ` GG eH † ← → g 2 q � µ ⌫ T a u e 4 H † H W i µ ⌫ W i H G a O WW O He i ¯ e � µ ¯ D µ H O uG g s ¯ and CP conjugates µ ⌫ µ ⌫ q � µ qH † ← → g 2 q � µ ⌫ u � i e 4 H † H f W i µ ⌫ W i H W i O ] O Hq i ¯ D µ H O uW g ¯ µ ⌫ µ ⌫ WW Alonso et al 1312.2014 q � i � µ qH † � i ← → g 0 2 q � µ ⌫ u e 4 H † H B µ ⌫ B µ ⌫ O 0 i ¯ g 0 ¯ O BB D µ H O uB H B µ ⌫ Hq u � µ uH † ← → g 0 2 4 H † H e q � µ ⌫ T a dH G a i ¯ g s ¯ O g B µ ⌫ B µ ⌫ O Hu D µ H O dG µ ⌫ BB d � µ dH † ← → i ¯ gg 0 H † � i H W i q � µ ⌫ d � i H W i O WB µ ⌫ B µ ⌫ O Hd D µ H O dW g ¯ µ ⌫ gg 0 H † � i H f u � µ d ˜ W i H † D µ H g 0 ¯ O g µ ⌫ B µ ⌫ O Hud i ¯ O dB q � µ ⌫ dH B µ ⌫ WB (¯ LL )(¯ LL ) and (¯ LR )(¯ ( ¯ RR )( ¯ (¯ LL )( ¯ LR ) RR ) RR ) (¯ `� µ ` )(¯ (¯ `� µ ` ) (¯ e � µ e )(¯ e � µ e ) `� µ ` )(¯ e � µ e ) O `` O ee O ` e (¯ O qq (¯ q � µ q )(¯ q � µ q ) O uu (¯ u � µ u )(¯ u � µ u ) O ` u `� µ ` )(¯ u � µ u ) ( ¯ d � µ d )( ¯ (¯ `� µ ` )( ¯ q � µ � i q )(¯ q � µ � i q ) O 0 (¯ d � µ d ) d � µ d ) O dd O ` d qq (¯ `� µ ` )(¯ q � µ q ) (¯ e � µ e )(¯ u � µ u ) (¯ q � µ q )(¯ e � µ e ) O ` q O eu O qe (¯ e � µ e )( ¯ `� µ � i ` )(¯ q � µ � i q ) O 0 (¯ d � µ d ) (¯ q � µ q )(¯ u � µ u ) O ed O qu ` q u � µ u )( ¯ q j u ) ✏ jk (¯ q k d ) q � µ T a q )(¯ u � µ T a u ) O 0 O quqd (¯ O ud (¯ d � µ d ) (¯ qu u � µ T a u )( ¯ q � µ q )( ¯ q j T a u ) ✏ jk (¯ q k T a d ) d � µ T a d ) O 0 O 0 (¯ (¯ O qd (¯ d � µ d ) quqd ud (¯ q � µ T a q )( ¯ ` j e ) ✏ jk (¯ q k u ) d � µ T a d ) O 0 (¯ O ` equ qd (¯ ` j � µ ⌫ e ) ✏ jk (¯ q k � µ ⌫ u ) O 0 ` equ (¯ ` j e )( ¯ dq j ) O ` edq Thursday, September 17, 15 9
LHCHXSWG-INT-2015-001 Similar “EFT Primaries” of Gupta et al 1405.0181 h-basis Connection between operators and observables a bit obscured in Warsaw or SILH basis. Also, in Warsaw basis EW precision constraints look complicated h-basis proposed by LHCHXSWG2 to separate combinations of Wilson coefficients strongly constrained by EWPT from those relevant for LHC Higgs studies Rotation of any other D=6 basis such that one isolates linear combinations affecting Higgs observables and not constrained severely by precision tests Very constrained parameters Relevant Linear for LHC Higgs transformation Irrelevant for LHC Higgs 2499 dimensional 2499 parameters vector of 2499x2499 dimensional defining Higgs Basis Wilson coefficients transformation matrix Thursday, September 17, 15 10
h-basis Lagrangian LHCHXSWG-INT-2015-001 h-basis is defined via effective Lagrangian of mass eigenstates after electroweak symmetry breaking (photon,W,Z,Higgs boson, top). SU(3)xSU(2)xU(1) is not manifest but hidden in relations between different couplings Feature #1: In the tree-level Lagrangian, all kinetic terms are canonically normalized, and there’ s no kinetic mixing between mass eigenstates. In particular, all oblique corrections from new physics are zero, except for a correction to the W boson mass Feature #2: Tree-level relation between the couplings in the Lagrangian and SM input observables is the same as in the SM. In particular, photon and gluon couple as in SM, and there’ s no correction to Z mass term Features #1 and #2 can always be obtained without any loss of generality, via integration by parts, fields and couplings redefinition Thursday, September 17, 15 11
h-Basis: Z and W couplings to fermions By construction, photon and gluon couplings as in the SM. Only W and Z couplings are affected Effects of dimension-6 operators are parametrized by a set of vertex corrections Dependent Couplings: Relations enforced by linearly realized SU(3)xSU(2)xU(1) symmetry at the level of dimension-6 operators Thursday, September 17, 15 12
h-Basis: Higgs couplings to matter In HB, Higgs couplings to gauge bosons described by 6 CP even and 4 CP odd parameters that are unconstrained by LEP-1 D=6 EFT with linearly realized SU(3)xSU(2)xU(1) enforces relations between Higgs couplings to gauge bosons (otherwise, more parameters) Corrections to Higgs Yukawa relative correction to W mass couplings to fermions are also unconstrained by EWPT Apart from δ m and δ g, additional 6+3x3x3 CP-even and 4+3x3x3 CP-odd parameters to parametrize LHCHXSWG-INT-2015-001 LHC Higgs physics Thursday, September 17, 15 13
h-basis: Triple Gauge Couplings SM predicts TGCs in terms of gauge couplings as consequence of SM gauge symmetry and renormalizability: In EFT with D=6 operators, new “anomalous”contributions to TGCs arise These depend on previously introduced h-basis parameters describing Higgs couplings to electroweak gauge bosons, and on 2 new parameters Thursday, September 17, 15 14
For more details and the rest of the Lagrangian, see LHCHXSWG-INT-2015-001 In the rest of the talk I will discuss constraints on the parameters in the h-basis Thursday, September 17, 15 15
Model-independent precision constraints on dimension 6 operators Thursday, September 17, 15 16
Recommend
More recommend
