THE TENSOR AND THE SCALAR CHARGES OF THE NUCLEON FROM HADRON PHENOMENOLOGY AURORE COURTOY Instituto de Física, UNAM, Mexico
How can hadronic physics help BSM search? Hadronic observables extraction Impact on β -decay observables partially based on Phys.Rev.Lett. 115 (2015) 162001 OUTLINE
� � � � � � � Direct search Large-x PDF α s Indirect search Parity Violating DIS HERE Beyond V-A interactions ... QCD FOR BSM
N ( p n ) − → P ( p p ) e − ( p e )¯ ν e ( p ν ) can be sketched as h i u Γ d | N i ] ” Γ ‟ � ! u e − ( p e )¯ ν e ( p ν ) ⇥ [ h P | ¯ d Electroweak: Proton structure: V-A g V & g A Β ETA DECAY IN SM
� � � � [Jackson et al., PR106] Neutron decay rate parameterized: [Lee & Yang, PR104] G 2 F | V ud | 2 1 p e E e ( E 0 − E e ) 2 d E e d Ω e d Ω ν d 3 Γ = (2 π ) 5 2 � 1 + a p e · p ν � �� + bm e A p e + B p ν × ξ + s n + . . . E e E ν E e E e E ν Effective Hamiltonian for β -decay Lorentz low energy constants C S,P,V,A,T ➡ SM 1param λ =-C A /C V ➡ a( λ ), A ( λ ), B ( λ ) ➡ b=0 in SM sensitivity of neutron beta decay to new physics ➡ B ⊂ b ν =0 in SM BETA DECAY OBSERVABLES
� � � [Jackson et al., PR106] Neutron decay rate parameterized: [Lee & Yang, PR104] G 2 F | V ud | 2 1 p e E e ( E 0 − E e ) 2 d E e d Ω e d Ω ν d 3 Γ = (2 π ) 5 2 � 1 + a p e · p ν � �� + bm e A p e + B p ν × ξ + s n + . . . E e E ν E e E e E ν b=0 in SM sensitivity of neutron beta decay to new physics ➡ B ⊂ b ν =0 in SM √ � C S � C T 1 − α 2 � � �� b = 2 + 3 λ 2 Re Re 1 + 3 λ 2 C V C A this point, we already have a reasonably strong constraint b sensitive to scalar and tensor LEC ➡ same for b ν ➡ BETA DECAY OBSERVABLES
� Extract LEC C V = C SM + δ C V NEW PHYSICS IN δ V C ′ + δ C ′ V = C SM V V C A = C SM + δ C A A SM C ′ + δ C ′ C = g V A = C SM V A A λ → pretty well known SM C A = − g A C S = δ C S C ′ S = δ C ′ S Best constraints so far C T = δ C T C ′ T = δ C ′ T . C S / C V = 0 . 0014 ( 13 ) @1 σ � from various processes [Hardy et al., PRC91] � decay rate for super allowed 0 + → 0 + − 0 . 0026 < C T / C A < 0 . 0024 @95%CL � decay rate for beta decay (total, angular correlation in unpolarized & polarized parts) [Pattie et al., PRC88] � radiative pion decay SCALAR & TENSOR INTERACTIONS
� � New particles hints New particles produced directly • in loops • mediators of interaction • ... Low energy High energy Effective field theories for low energy New (heavy) dof integrated out ➡ Consider all Dirac bilinears for EW interactions 1, γ 5 , γ μ (1+ γ 5 ), σ μν ➡ Define ``Wilson coe ffi cient" for new interaction ➡ NEW FUNDAMENTAL INTERACTIONS
d j → u i l − ¯ u EFT AT THE QUARK LEVEL ν l d 1 (eff) = L SM + X L O i Λ 2 4-fermion interaction i i ¯ → ν ℓ = − g 2 � ¯ u L γ µ d j R γ µ d j u i L + [ v R ] ℓℓ ij ¯ u i �� 1 + [ v L ] ℓℓ ij ℓ L γ µ ν ℓ L ¯ ℓ L γ µ ν ℓ L ¯ L d j → u i ℓ − ¯ V ij R 2 m 2 W right R d j L d j + [ s L ] ℓℓ ij ¯ u i L + [ s R ] ℓℓ ij ¯ u i ℓ R ν ℓ L ¯ ℓ R ν ℓ L ¯ R R σ µ ν d j + [ t L ] ℓℓ ij ¯ u i � ℓ R σ µ ν ν ℓ L ¯ + h.c. , d L Scalars SM Tensor ε S ≣ s L +s R ε T ≣ t L BETA DECAY IN EFT [Bhattarchaya et al., PRD85] [Cirigliano et al., NPB 830]
[Bhattarchaya et al., PRD85] [Cirigliano et al., NPB 830] h i Γ ‟ ” � ! u e − ( p e )¯ ν e ( p ν ) ⇥ [ h P | ¯ u Γ d | N i ] d C SM = G F | g S ✏ S | = 0 . 0014 ± 0 . 0013 STANDARD MODEL @1 σ 2 V ud ( g V − g A ) √ | g T ✏ T | < 6 · 10 − 4 @95%CL C S = G F } 2 V ud g S ✏ S √ NEW BSM S & T INTERACTIONS C T = G F 2 V ud 4 g T ✏ T √ Precision with which the NEW COUPLINGS can be measured depend on the knowledge of hadronic charges New LEC factorized into hadronic contribution & new EW interaction LEC IN TERMS OF HADRONIC × NEW INT.
⇓ h P ( p p , S p ) | ¯ u Γ d | N ( p n , S n ) i Proton Neutron FORM FACTORS p Isovector vector FF h P ( p p , S p ) | ¯ u γ µ d | N ( p n , S n ) i = g V ( t ) ¯ u P γ µ u N + O ( t/M ) Exist in hadronic physics t, Q 2 � � Isovector tensor FF h P ( p p , S p ) | ¯ u σ µ ν d | N ( p n , S n ) i = g T u P σ µ ν u N ¯ When t → 0, g(0) ≡ charge t=(p n -p p ) 2 Q 2 RGE scale MATCHING AT HADRONIC LEVEL
� � Nonlocal matrix element for proton structure Parton Distribution Functions built from Lorentz symmetry from vectors at hand - defined in Bjorken scaling - nonperturbative objects - 1st principle related to ``charges" - Fundamental charges for γ μ & γ μ γ 5 only Structural charges for the others Scalar & tensor charge accessible through sum rules of Parton Distributions HADRONIC STRUCTURE
Lorentz structure Kinematics of the Bjorken scaling Q 2 → ∞ Discrete symmetries Z 1 p.q → ∞ Vectors at hand... Q 2 /2p.q ≡ x=finite dx h u V − d V ( x ) = g T 1 To leading twist: − 1 f q g q h q 1 ( x ) , 1 ( x ) , 1 ( x ) PDFs ⇒ Vector Axial-vector Tensor Dirac operator ⇒ - - g V , g A, g T Charges ⇒ PDF AT LEADING TWIST
π , ... di- π , ... Semi-inclusive processes Inclusive processes σ→ PDF × d σ × Fragmentation Function σ→ PDF × d σ π , ... DEFINITION AND FACTORIZATION Exclusive processes σ→ |Generalized PDF × H × Meson Amplitude| 2 ACCESS TO DISTRIBUTION FUNCTIONS
TRIPTIC OF TARGET SPIN ASYMMETRY SIDIS PRODUCTION OF PION PAIRS @ COMPASS & HERMES 〉 θ 0.05 0.05 0.05 sin 2002-4 Deuteron Data 0 0 0 RS φ UT,d sin -0.05 A -0.05 -0.05 〈 -0.1 -0.1 -0.1 -0.15 -0.15 -0.15 〉 -2 -1 0.2 0.4 0.6 0.8 0.5 1 1.5 2 10 10 1 θ 0.05 0.05 0.05 sin 0 0 0 RS φ UT,p sin A -0.05 -0.05 -0.05 〈 -0.1 -0.1 -0.1 2007 Proton Data -0.15 -0.15 -0.15 -2 -1 0.2 0.4 0.6 0.8 0.5 1 1.5 2 10 10 1 2 x z M [GeV/ c ] hh x-dependence only from (z, M h )-dpdence determined Transversity by DiFF from Belle [A.C., et al, PRL 2012, JHEP 2013, 2015] [A.C., Bacchetta, Radici, Bianconi, Phys.Rev. D85] EXAMPLE OF DATA & EXTRACTION
� � � � u v x h 1 0.6 Torino 2013 @2.4 GeV 2 0.4 0.2 Kang et al central value 0.0 - 0.2 - 0.4 0.01 0.03 0.1 0.3 1 1 σ error band from replicas @2.4 GeV 2 PAVIA x [Radici et al., JHEP 2015] Semi-inclusive processes eN → e π X Torino et al eN → e ( ππ ) X Pavia et al Exclusive: eP → e π 0 P GGL TRANSVERSITY PDF [Goldstein et al, PRD 2015]
ROLE OF FUNCTIONAL u V (x)-x h 1 d V (x)/4 x h 1 FORM FOR FIT fit data HERMES 0.4 data COMPASS flexible functional form 0.2 0.0 0.01 0.10 0 1 x u V (x)-x h 1 d V (x)/4 x h 1 fit data HERMES rigid functional form 0.4 data COMPASS 0.2 0.0 0.01 0.10 0 1 x UNCERTAINTY & DATA RANGE
CLAS12 projection on proton target SoLID projection on neutron target 0 0.15 0.125 -0.02 sin φ R A UT 0.1 ? -0.04 0.007 < x < 0.53 0.075 -0.06 sin φ R 0.05 A UT -0.08 0.025 -0.1 0 0.2 0.2 1 0.25 0.5 1 0.25 0.5 M h x M h x MORE DATA + MONTE CARLO LIKE FITTING x h u − u ( x ) m H x,z,P hT , Q 2 L , proton target 1 3 p - X x \ ~ 0.15 2 X Q 2 \ ~ 2.9 GeV 2 0.27 < z < 0.30 0.38 < z < 0.48 1 0.0 0.4 0.8 SOLUTIONS P hT x Pavia 15 procedure repeated 100 times JHEP1505 (2015) 123 (until reproduce mean and std. deviation of original data)
ge g T = δ u v − δ d v . d u -d d H Q 2 = 4 GeV 2 L WITH MONTE CARLO - LIKE FITTING 1.2 - - ¯ Ï - - - - - Ê Ù - 1.0 - ‡ - - Ú - 0.8 ‡ 0.6 0.4 Various Lattice QCD results - 0 1 2 3 4 5 6 7 In Fig. 11, the at Q 2 = 4 GeV 2 for g T = 0 . 81 ± 0 . 44 We compare it wi % confidence level. Pavia flexible 0.125 LATTICE RESULTS PRESENT TINY ERRORS W.R.T. HADRONIC EXTRACTIONS HERE TESTING GROUND FOR LATTICE QCD CALCULATIONS ISOVECTOR TENSOR CHARGE
� � � � * p � � o p' x Bj = 0.2, Q 2 = 1.5 GeV 2 � u = 0.91 ! 0.08, � d = -0.12 0.1 � u = 0.6, � d = -0.12 � u = 1.4, � d = -0.12 -0 UTsin ��� s GGL depends on new JLab data A -0.1 Courtoy et al, PRL 115 -0.2 Pavia depends on new JLab data -0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Torino depends on TMD evolution +new JLab data -t (GeV 2 ) Ye et al.,1609.02449 u v � x �� h 1 u v � x � ∆ h 1 extra-flex 2.0 1.5 1.0 0.5 u v � x �� h 1 u v � x � ∆ h 1 0.0 1.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x 1.0 u v � x �� h 1 u v � x � ∆ h 1 0.5 2.0 flex 0.0 0.2 0.4 0.6 0.8 1.0 1.5 x 1.0 FUTURE 0.5 rigid 0.0 0.0 0.2 0.4 0.6 0.8 1.0 x
PNDME LHPC NOW WITH g T ± σ gT RQCD AND | g T ✏ T | < 6 · 10 − 4 Single hadron FF Dihadron FF DVMP we find.... g T New PNDME: g T =0.987(51)(20) [PRD94] NME compatible results [1611.07452 ] Ye et al.: g T =0.64±0.021 (Q 2 =2.4GeV 2 ) TENSOR INTERACTION AS OF NOW
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