Vector vs. Scalar NSIs, Light Mediators, and other considerations - PowerPoint PPT Presentation

Vector vs. Scalar NSI’s, Light Mediators, and other considerations Tatsu Takeuchi, Virginia Tech April 27, 2019 Amherst Center for Fundamental Interactions “Neutrino-Electron Scattering at Low Energies”

Collaborators v Sofiane M. Boucenna (INFN, Italy) v David Vanegas Forero (U. of Campinas, Brazil) v Patrick Huber (Virginia Tech) v Ian Shoemaker (Virginia Tech) v Chen Sun (Brown)

Non-Standard Interactions: v Effects of new physics at low energies can be expressed via dimension-six four-fermion operators v There are five types: v Operators relevant for neutrino-electron scattering are those in which two of the operators are neutrinos and the other two operators are electrons

Fierz Identities

Fierz Identities for Chiral Fields v LL, RR cases v LR, RL cases

Fierz Transformation Example: v neutrino-electron interaction from W exchange : v neutrino-electron interaction from Z exchange :

New Physics: v Vector exchange: v Scalar exchange:

Fierz Transformed New Physics: v Charged vector exchange: v Charged scalar exchange:

Vector and Scalar NSI: v Vector NSI’s : v See talk by Chen Sun from yesterday v Scalar NSI’s : v Shao-Feng Ge and Stephen J. Parke, arXiv:1812.08376

Effect of Scalar NSI to Neutrino Propagation: v Shao-Feng Ge and Stephen J. Parke, arXiv:1812.08376 v In matter: v Mass matrix is shifted:

Bounds from Borexino: v Shao-Feng Ge and Stephen J. Parke, arXiv:1812.08376 v electron-neutrino survival probability: Scalar NSI’s Vector NSI’s

Further points to consider: v The Ge-Parke analysis assumes Dirac masses v If neutrino masses are Majorana v There is also a matter potential effect:

Can we generate large NSI’s? v Generating large NSI’s from heavy mediators is very difficult v Can light mediators help us?

Interactions must be SU(2) x U(1) invariant: v Case 1: () < 10 -. Constrained by ! → #$$ : % &' v Case 2: () < 10 -2 Constrained by µ → $0 ( 0 ' , ! → $0 ( 0 & , ! → #0 ( 0 ( : % &'

Farzan-Shoemaker Model v Y. Farzan and I. M. Shoemaker, “Lepton Flavor Violating Non- Standard Interactions via Light Mediators,” JHEP07(2016)033, arXiv:1512.09147 ε qC µ τ ∼ 0 . 005 ε µ τ ∼ 0 . 06 → v Is the model truely viable?

Farzan-Shoemaker Model : Fermion Content v SU(3) C × SU(2) L × U(1) Y × U(1)’ gauge theory v Quarks:  u Li � ✓ ◆ ✓ ◆ ✓ ◆ 3 , 2 , +1 3 , 1 , +2 3 , 1 , − 1 Q i = 6 , 1 , u Ri ∼ 3 , 1 , d Ri ∼ 3 , 1 ∼ d Li v Leptons:  ⌫ L 0 � ✓ ◆ 1 , 2 , − 1 L 0 = 2 , 0 ` R 0 ∼ (1 , 1 , − 1 , 0) , , ∼ ` L 0  ⌫ L + � ✓ 1 , 2 , − 1 ◆ L + = 2 , + ⇣ ` R + ∼ (1 , 1 , − 1 , + ⇣ ) , , ∼ ` L +  ⌫ L − � ✓ 1 , 2 , − 1 ◆ L − = ` R − ∼ (1 , 1 , − 1 , − ⇣ ) , 2 , − ⇣ , ∼ ` L − v Extra (heavy) fermions for anomaly cancellation (?)

Farzan-Shoemaker Model : Scalar Content v Higgses:  H + � ✓ ◆ 1 , 2 , +1 H = 2 , 0 , ∼ H 0 H +  � ✓ ◆ 1 , 2 , +1 ++ H ++ = 2 , +2 ζ , ∼ H 0 ++ H +  � ✓ ◆ 1 , 2 , +1 H −− = 2 , − 2 ζ . −− ∼ H 0 −− v Yukawa couplings: ⇣ ⌘ 3 3 X X � ij u Ri e � ij d Ri H † Q j + ˜ H † Q j + h.c. i =1 j =1 X � � f j ` Rj H † L j + h.c. + j =0 , + , − ⇣ ⌘ c − ` R + H † −− L − + c + ` R − H † ++ L + + h.c. +

Farzan-Shoemaker Model : Symmetry Breaking v Higgs VEV’s: v ++ i = v + −− i = v − h H 0 i = h H 0 h H 0 p p p 2 , 2 , 2 , w v Assume (no Z-Z’ or ! -Z’ mixing at tree-level) v + = v − = √ 2 v Gauge boson masses: p g 2 1 + g 2 M W = g 2 p p v 2 + w 2 , v 2 + w 2 , 2 M Z 0 = 2 ζ g 0 w M Z = 2 2

Farzan-Shoemaker Model : Z’ Mass & Coupling v The mass of the Z’ is chosen to be: 135 MeV < M Z 0 < 200 MeV so that the decays π 0 → γ + Z 0 , Z 0 → µ + + µ � cannot occur v Range of the Z’-exchange force comparable to that of strong interactions → Z’ interactions between quarks can be sizable but still be masked by the strong force (?) v Z’ coupling to the leptons are strongly constrained by: τ → µ + Z 0

Farzan-Shoemaker Model : Problems v U(1) charges are ill defined in models with multiple U(1)’ s → They necessarily mix under renormalization group running (See W. A. Loinaz and T. Takeuchi, Phys.Rev. D60 (1999) 115008) v Constraint on ! g’ does not allow the generation of Z’ mass in the 135 ∼ 200 MeV range without making the Higgs VEV w too large for the W and Z masses → Need to introduce a SM-singlet scalar v Full MNS neutrino mixing matrix cannot be generated. The U(1)’ singlet lepton cannot mix with the non-singlet leptons. → Need to introduce a more scalars v Not clear whether the fermions necessary for anomaly cancelation can be made heavy → Even more scalars?

Constraints on the Z’ couplings revisited: v Z’-quark coupling v Z’-lepton coupling v Semi-Empirical Mass Formula of Nuclei: Z 2 ( A − 2 Z ) 2 E B = a V A − a S A 2 / 3 − a C ± δ ( A, Z ) A 1 / 3 − a A A v Coulomb term: Q 2 ( eZ ) 2 Z 2 E C = 3 = 3 ( r 0 A 1 / 3 ) = (0 . 691 MeV)(1 . 25 fm) A 1 / 3 5 R 5 r 0

Z’ potential energy: v Z’ potential energy term: Q 0 2 (3 g 0 A ) 2 3 R f ( mR ) = 3 ( r 0 A 1 / 3 ) f ( mr 0 A 1 / 3 ) E Z 0 = 5 5 ◆ 2 (0 . 691 MeV)(1 . 25 fm) ✓ 3 g 0 A 5 / 3 f ( mr 0 A 1 / 3 ) = r 0 e where " # 1 − x 2 + 2 x 3 15 − (1 + x ) 2 e − 2 x f ( x ) ≡ 4 x 5 3 1.0 6 + 3 x 2 − x 3 1 − 5 x 0.8 = 6 + · · · 7 0.6 0.4 0.2 10 x 0 2 4 6 8

Result of Fit: v Our result from fit to stable nuclei (90% C.L. left) compared to Figure from Farzan-Shoemaker paper (JHEP07(2016)033 right) 10 0 10 -1 Excluded 10 -2 10 -3 g ' 10 -4 r 0 =1.2 fm r 0 =1.22 fm 10 -5 r 0 =1.25 fm r 0 =1.3 fm 10 -6 1 10 100 m Z ' [MeV]

Result of Fit: 200 150 M Z ′ / MeV 100 r 0 = 1.30 fm 50 r 0 = 1.22 fm 0 - 2.0 - 1.5 - 1.0 - 0.5 0.0 Log 10 ( g ′ )

Coupling to the electron from photon-Z’ mixing: v Recall that ! → #$$ is strongly bounded: %(! ' → # ' $ ' $ ( ) < 1.8 × 10 ', v At tree level the Z’ does not couple to electrons v But Z’ and the photon can mix!

Optical Theorem:

photon-photon and photon-Z’ correlations:

Separation of Isovector and Isoscalar parts: Dolinsky Isoscalar + BW resonance 1000 Total R ratio 100 R 10 1 0.1 0.5 1.0 1.5 2.0 s / GeV

Running of the effective coupling to electrons:

Resulting bounds:

Does this bound apply? v For the Z’ decay into an electron-positron decay to be observable, the Z’ must decay inside the detector v Belle central drift chamber: Z’ must decay within 0.88 m to 1.7 m

Two-body decay bound: v Argus (1995) v Belle has 2000 times more statistics and is expected to improve the bound to 1×10 $% (Yoshinobu and Hayasaka, Nucl. Part. Phys. Proc. 287-288 (2017) 218-220)

Conclusion : v Both g’ and g’ ! are more tightly bound than originally assumed v Constructing viable models that predict sizable neutrino NSI’s is not easy!