Adam Falkowski Constraints on new physics from nuclear beta - PowerPoint PPT Presentation

Adam Falkowski Constraints on new physics 
 from nuclear beta transitions Torino, October 16, 2020 based on work to appear with Martin Gonzalez-Alonso and Oscar Naviliat-Cuncic

Properties of new particles 10 TeV or 10 EeV ? beyond the Standard Model can be related to parameters ? of the e ff ective Lagrangian describing low-energy interactions Standard 
 between nucleons, electrons, and neutrinos Model 100 GeV Quarks 2 GeV E ff ective weak interactions for nucleons p γ μ n ( C + p γ μ γ 5 n ( C + e γ μ ν R ) − ¯ e γ μ ν R ) e γ μ ν L + C − e γ μ ν L − C − ℒ ⊃ − ¯ V ¯ V ¯ A ¯ A ¯ Hadrons p σ μν n ( C + e ν R ) − 1 e σ μν ν R ) pn ( C + e ν L + C − e σ μν ν L + C − 1 GeV − ¯ S ¯ S ¯ 2 ¯ T ¯ T ¯ All these parameters can be precisely measured Nuclei in nuclear beta transitions 1 MeV

Part of larger precision program Nuclear Mesons New Physics Heavy Electro Flavor weak Higgs

Language for 
 nuclear beta transitions

Language • Nuclear beta decays probe di ff erent aspects of how first generation quarks and leptons interact with each other • Possible to perform model-dependent studies using popular benchmark models with heavy particles (SUSY, composite Higgs, extra dimensions) or light particles (axions, dark photons) • E ffi cient and model-independent description can be developed under assumption that no non-SM degrees of freedom are produced on-shell in a given experiment. This leads to the universal language of e ff ective field theories

EFT Ladder “Fundamental” BSM model Connecting high-energy physics to nuclear physics 10 TeV? via a series of e ff ective theories EFT for SM particles 100 GeV EFT for Light Quarks 2 GeV EFT for Nucleons 1 GeV E ff ective description of nuclear observables 1 MeV

“Fundamental” models “Fundamental” BSM model In the SM beta decay is mediated by the W boson 10 TeV? ν e d W EFT for u SM particles e 100 GeV Several high-energy e ff ects may contribute to beta decay ν e d EFT for W’ Light Quarks u 2 GeV e EFT for d ν e Leptoquark Nucleons 1 GeV u e E ff ective description of nuclear observables ν e d W W-W’ mixing 1 MeV u e

EFT at electroweak scale “Fundamental” BSM model At the electroweak scale, these e ff ects can be 
 approximated by gauge invariant operators describing contact 4-fermion interactions or 10 TeV? modified W boson couplings to quarks and leptons u ν e d ν e W W EFT for SM particles u e e 100 GeV d EFT for ℒ EFT ⊃ c HQ H † σ a D μ H ( ¯ Q σ a γ μ Q ) + c HL H † σ a D μ H (¯ L σ a γ μ L ) Light Quarks 2 GeV + c Hud H T D μ H ( ¯ c Hud H T D μ H (¯ u R γ μ d R ) + ˜ ν R γ μ e R ) + c LQ ( ¯ Q σ a γ μ Q )(¯ L σ a γ μ L ) + c ′ � LeQu (¯ e R σ μν L )( ¯ u R σ μν Q ) EFT for u R Q ) + c LedQ (¯ Le R )( ¯ + c LeQu (¯ e R L )( ¯ d R Q ) Nucleons 1 GeV c L ν Qu (¯ + ˜ L ν R )( ¯ u R Q ) + … E ff ective description For any “fundamental” model, the Wilson coe ffi cients c i 
 of nuclear observables can be calculated in terms of masses and couplings 
 of new particles at the high-scale 1 MeV c i = c i ( M , g * ) ∼ g 2 * / M 2

EFT below electroweak scale “Fundamental” BSM model Below the electroweak scale, there is no W, 
 thus all leading e ff ects relevant for beta decays 10 TeV? are described contact 4-fermion interactions, whether in SM or beyond the SM v 2 { ( 1+ ϵ L ) ¯ ℒ EFT ⊃ − V ud u γ μ (1 − γ 5 ) d u γ μ (1 − γ 5 ) d e γ μ ν L ⋅ ¯ + ˜ ϵ L ¯ e γ μ ν R ⋅ ¯ EFT for SM particles u γ μ (1 + γ 5 ) d u γ μ (1 + γ 5 ) d + ϵ R ¯ e γ μ ν L ⋅ ¯ + ˜ ϵ R ¯ e γ μ ν R ⋅ ¯ 1 1 100 GeV u σ μν (1 − γ 5 ) d u σ μν (1 + γ 5 ) d e σ μν ν L ⋅ ¯ e σ μν ν R ⋅ ¯ + ϵ T 4 ¯ + ˜ ϵ T 4 ¯ e ν L ⋅ ¯ e (1 + γ 5 ) ν R ⋅ ¯ + ϵ S ¯ ud + ˜ ϵ S ¯ ud u γ 5 d } + hc EFT for − ϵ P ¯ e ν L ⋅ ¯ u γ 5 d − ˜ ϵ P ¯ e ν R ⋅ ¯ Light Quarks 2 GeV Much simplified description, only 10 (in principle complex) parameters 
 EFT for Nucleons at leading order 1 GeV E ff ective description of nuclear observables 1 MeV

Translation from low-to-high energy EFT Assuming lack of right-handed neutrinos, the EFT below the weak scale (WEFT) 
 can be matched to the EFT above the weak scale (SMEFT) v 2 { ( 1+ ϵ L ) ¯ ℒ WEFT ⊃ − V ud u γ μ (1 − γ 5 ) d e γ μ ν L ⋅ ¯ ℒ SMEFT ⊃ c HQ H † σ a D μ H ( ¯ Q σ a γ μ Q ) + c HL H † σ a D μ H (¯ L σ a γ μ L ) u γ μ (1 + γ 5 ) d + c Hud H T D μ H ( ¯ + ϵ R ¯ e γ μ ν L ⋅ ¯ u R γ μ d R ) 1 LQ ( ¯ + c (3) Q σ a γ μ Q )(¯ L σ a γ μ L ) + c (3) u σ μν (1 − γ 5 ) d e σ μν ν L ⋅ ¯ LeQu (¯ e R σ μν L )( ¯ u R σ μν Q ) + ϵ T 4 ¯ e ν L ⋅ ¯ + ϵ S ¯ ud Le R )( ¯ u R Q ) + c LedQ (¯ + c LeQu (¯ e R L )( ¯ d R Q ) } − ϵ P ¯ e ν L ⋅ ¯ u γ 5 d At the scale m Z , WEFT parameters ε X map to dimension-6 operators in the SMEFT LQ − 2 δ m W + 1 ϵ L /v 2 = − c (3) δ g Wq 1 + δ g We L L V ud 1 ϵ R /v 2 = c Hud 2 V ud Known RG running equations can 1 translate it to Wilson coe ffi cients ε X 
 ϵ S /v 2 = − 2 V ud ( V ud c * LedQ ) LeQu + c * at a low scale μ ~ 2 GeV ϵ T /v 2 = − 2 c (3)* LeQu 1 ϵ P /v 2 = − 2 V ud ( V ud c * LedQ ) LeQu − c * More generally, the low-energy theory can be matched to RSMEFT

Quark level effective Lagrangian E ff ective Lagrangian defined at a low scale μ ~ 2 GeV Left-handed Right-handed neutrino neutrino CKM element v 2 { ( 1+ ϵ L ) ¯ ℒ ⊃ − V ud u γ μ (1 − γ 5 ) d u γ μ (1 − γ 5 ) d V-A e γ μ ν L ⋅ ¯ e γ μ ν R ⋅ ¯ + ˜ ϵ L ¯ u γ μ (1 + γ 5 ) d u γ μ (1 + γ 5 ) d V+A + ϵ R ¯ e γ μ ν L ⋅ ¯ + ˜ ϵ R ¯ e γ μ ν R ⋅ ¯ Normalization scale, 
 set by Fermi constant 1 1 Tensor u σ μν (1 − γ 5 ) d u σ μν (1 + γ 5 ) d e σ μν ν L ⋅ ¯ e σ μν ν R ⋅ ¯ + ϵ T 4 ¯ + ˜ ϵ T 4 ¯ 1 v = ≈ 246 GeV 2 G F Scalar + ϵ S ¯ e ν L ⋅ ¯ ud + ˜ ϵ S ¯ e (1 + γ 5 ) ν R ⋅ ¯ ud u γ 5 d } + h . c . Pseudo- − ϵ P ¯ e ν L ⋅ ¯ − ˜ ϵ P ¯ e ν R ⋅ ¯ u γ 5 d scalar The Wilson coe ffi cients of this EFT can be connected, to the Wilson coe ffi cients above the electroweak scale, and consequently to masses and couplings of new heavy particles at the scale M : v 2 ϵ X ∼ v 2 c i ∼ g 2 ϵ X , ˜ * M 2

EFT for nucleons “Fundamental” BSM model Below the QCD scale there is no quarks. 
 The relevant degrees of freedom are instead nucleons 10 TeV? Leading order EFT described by the Lee-Yang Lagrangian p γ μ n ( C + + C − e γ μ ν R ) ℒ EFT ⊃ − ¯ V ¯ e γ μ ν L V ¯ EFT for SM particles − C − p γ μ γ 5 n ( C + e γ μ ν R ) − ¯ A ¯ e γ μ ν L A ¯ 100 GeV pn ( C + + C − e ν R ) − ¯ S ¯ e ν L S ¯ − 1 p σ μν n ( C + + C − e σ μν ν R ) 2 ¯ T ¯ e σ μν ν L T ¯ EFT for Light Quarks p γ 5 n ( C + − C − e ν R ) +hc 2 GeV + ¯ P ¯ e ν L P ¯ T.D. Lee and C.N. Yang (1956) EFT for Nucleons Again, 10 (in principle complex) parameters 
 1 GeV at leading order to describe physics of beta decays E ff ective description Nuclear physics experiments 
 of nuclear observables measure the Wilson coe ffi cients C X+/- 1 MeV

Translation from nuclear to particle physics V = V ud V = V ud R ( 1 + ϵ L + ϵ R ) C − R ( ˜ ϵ R ) C + 1 + Δ V 1 + Δ V v 2 g V v 2 g V ϵ L + ˜ Non-zero in the SM A = − V ud A = V ud C + 1 + Δ A R ( 1 + ϵ L − ϵ R ) C − 1 + Δ A R ( ˜ ϵ R ) ϵ L − ˜ v 2 g A v 2 g A T = V ud T = V ud C − C + v 2 g T ϵ T v 2 g T ˜ ϵ T S = V ud S = V ud C − C + v 2 g S ˜ v 2 g S ϵ S ϵ S P = V ud P = − V ud C + C − v 2 g P ϵ P v 2 g P ˜ ϵ P v 2 { ( 1+ ϵ L ) ¯ p γ μ n ( C + + C − e γ μ ν R ) ℒ EFT ⊃ − ¯ V ¯ e γ μ ν L V ¯ ℒ EFT ⊃ − V ud u γ μ (1 − γ 5 ) d u γ μ (1 − γ 5 ) d e γ μ ν L ⋅ ¯ e γ μ ν R ⋅ ¯ + ˜ ϵ L ¯ p γ μ γ 5 n ( C + − C − e γ μ ν R ) − ¯ A ¯ e γ μ ν L A ¯ u γ μ (1 + γ 5 ) d u γ μ (1 + γ 5 ) d e γ μ ν L ⋅ ¯ e γ μ ν R ⋅ ¯ + ϵ R ¯ + ˜ ϵ R ¯ pn ( C + + C − e ν R ) − ¯ S ¯ e ν L S ¯ 1 1 u σ μν (1 − γ 5 ) d u σ μν (1 + γ 5 ) d e σ μν ν L ⋅ ¯ e σ μν ν R ⋅ ¯ + ϵ T 4 ¯ + ˜ ϵ T 4 ¯ − 1 + C − e ν L ⋅ ¯ e (1 + γ 5 ) ν R ⋅ ¯ p σ μν n ( C + e σ μν ν R ) + ϵ S ¯ ud + ˜ ϵ S ¯ ud 2 ¯ T ¯ e σ μν ν L T ¯ u γ 5 d } + hc − ϵ P ¯ e ν L ⋅ ¯ u γ 5 d − ˜ ϵ P ¯ e ν R ⋅ ¯ p γ 5 n ( C + − C − e ν R ) +hc + ¯ P ¯ e ν L P ¯