Neutrino Non-Standard Interactions via Light Scalar Garv Chauhan - PowerPoint PPT Presentation

Neutrino Non-Standard Interactions via Light Scalar Garv Chauhan Washington University in St. Louis, USA Based on arXiv: 1912.13488 In Collaboration with K.S. Babu (OSU) and Bhupal Dev (WUSTL) Contact: garv.chauhan@wustl.edu Phenomenology 2020 Symposium May 4, 2020

Motivation • The global neutrino oscillation program is now entering a new era, measurements being done with an ever-increasing accuracy. • Sub-dominant efgects in oscillation data are sensitive to • Neutrino physics beyond the SM oħten comes with additional non-standard interactions (NSI). 1 the currently unknown parameters, namely the θ CP , sign of ∆ m 2 atm and the octant of θ 23 .

Scalar NSI lagrangian term as: mass matrix. • In a medium, this appears as a correction to the neutrino ff m 2 2 • For low-momentum transfer, we can write the efgective • Consider the interaction of fermions f , ν with a light scalar ϕ , where Yukawa terms are of the form: ν α ϕν β − y f ¯ L Yukawa ( ϕ, f ) = − y αβ ¯ f ϕ f L efg ∝ − y f y αβ ν α ν β ¯ ¯ φ

Field theoretic origin 1 d 3 p 1 • The efgect of matter on self-energy of a fermion can be where, 3 calculated with the help of finite temperature Greens function for a free Dirac field. [ ] S f ( p ) = ( / p + m ) p 2 − m 2 + i ϵ + i Γ( p ) Γ( p ) = 2 πδ ( p 2 − m 2 )[ n f ( p )Θ( p 0 ) + n ¯ f ( p )Θ( − p 0 )] , ∫ f ) = e ( | p . u |± µ ) / T + 1 , N f = 2 ( 2 π ) 3 n f ( p ) n f (¯

Field theoretic origin • The relevant diagrams for mass correction to neutrino : Figure 1: Neutrino self-energy corrections • The mass correction at finite temperature and density evaluates to: m 2 d 3 p E p 4 n f ( p ) + n ¯ f ( p ) ∫ αβ = 2 m f y αβ y f ∆ M ν ( 2 π ) 3 φ

Field theoretic origin m 2 scalar coupling only to electron ( y e ) and Dirac neutrinos • In this talk, we discuss constraints in the scenario with • The result for Earth/Sun matches Ge and Parke, PRL ’19 3 6 m 2 3 2 m f • The form of sNSI expression for various domains : m 2 5  y f y αβ for Earth, Sun ( µ, T < m f )   φ N f     ( 3 N f ) 2  y αβ y f ฀M ν for Supernova ( µ > m f > T ) αβ : π φ  ] 2  [ π 2 ( N f + N ¯ f )   y αβ y f m f for Early Universe ( µ < m f < T )   3 ζ ( 3 )  φ ( y ν ).

Finite Medium Efgects • A light scalar coupling to fermions can lead to long-range forces. • Even when the neutrino propagates outside of the medium, such long-range forces can afgect its 1 Wise, Zhang JHEP 06 (2018) 2 Smirnov, Xu JHEP 12 (2019) 6 propagation 1 , 2 .

Finite Medium Efgects r f k 2 dk 0 m f where, • Our work presents generalized analytical results for finite 7 0 medium efgects extending to relativistic cases. ( ∫ r y f y ν x ⟨ ¯ e − m φ r ∆ m ν,αβ ( r ) = ff ⟩ sinh ( m φ x ) dx m φ r ∫ ∞ ) x ⟨ ¯ ff ⟩ e − m φ x dx + sinh ( m φ r ) ∫ ∞ √ [ ] ⟨ ¯ ff ⟩ = m f 0 − m 2 n f ( k 0 ) + n ¯ f ( k 0 ) . π

Finite Medium Efgects 3 where • For a relativistic medium with constant electron 8 background, { ( r ≤ R ) , ( 3 N f ( 0 ) ) 2 F < ∆ m ν,αβ ( r ) = y ν y f m f × π ( r > R ) , 2 m φ r F > F < = 1 − m φ R + 1 e − m φ R sinh ( m φ r ) , m φ r F > = e − m φ r m φ r [ m φ R cosh ( m φ R ) − sinh ( m φ R )] .

7 , which is eff • If they decoupled earlier say at QCD phase transition BBN. 9 Constraints on y ν • If at time of nucleosynthesis ( T ≃ 1 MeV), ν and ϕ are still in equilibrium then they contribute ∆ N eff = 3 + 4 in tension with allowed ∆ N BBN ≃ 0 . 5. temperature ( ∼ 200 MeV), it contributes less to ∆ N eff at • This yields a strong limit of y ν < 2 . 6 × 10 − 10 .

Experimental Constraints on y e the electron anomalous magnetic moment : e 0 dx long range force appears as a violation of equivalence principle in experiments. 10 • ( g − 2 ) e : A scalar coupling to electron will contribute to ∫ 1 ( 1 − x ) 2 ( 1 + x ) ∆ a e = y 2 ( 1 − x ) 2 + x ( m φ / m e ) 2 8 π 2 • Fiħth Forces : A light scalar coupling to matter leading to a

Experimental Constraints on y e 11 10 - 4 ( g - 2 ) e 10 - 8 10 - 12 10 - 16 II I I I I V 10 - 20 VII Torsional Balances IV VI y e 10 - 24 10 - 28 10 - 32 y ν = 2.6 x 10 - 10 Dirac ν 10 - 36 10 - 18 10 - 14 10 - 10 10 - 6 10 - 2 10 2 10 6 m ϕ ( eV )

Experimental Constraints on y e • Red Giants, HB Stars & SN1987A : The production of the for energy loss leading to rapid cooling. • These processes in red giants can delay their onset of helium ignition. • It can change the helium-burning lifetime of the horizontal branch stars. 12 light scalar ϕ in stellar bodies can lead to a new channel

Experimental Constraints on y e • The mediator thermalizes and decreases the deuterium abundance if scalar mediators. 13 • BBN : In early universe, the scalar mediator ϕ can be in thermal equilibrium with the SM through ( e + e − → γϕ ) and ( e − γ → e − ϕ ). ⟨ σ v ⟩ > H ( T ) at T = 1 MeV • This yields an upper bound of y e = 5 × 10 − 10 for ultra-light

Experimental Constraints on y n m 2 m 2 m 2 m 2 14 decay of a charged Kaon and is constrained from the • Meson Decays : The scalar ϕ can be produced through measurement of K + → π + + Missing Energy • The production cross section for K + → π + + ϕ is : Br ( K + → π + ϕ ) = ( 3 y u G F f π f K B ) 2 32 π m K + Γ K + | V ud V us | 2 λ 1 / 2 ( 1 , φ π + , m 2 ) K + K + where, B = π m u + m d λ ( a , b , c ) = a 2 + b 2 + c 2 − 2 ab − 2 bc − 2 ac • Using nucleon scalar charges, y n ≃ 18 . 8 y u

principle of quantum mechanics sets a lower limit on the minimum q 2 . • Recoil momentum of the electron is subject to the uncertainty relation. Its position is not precisely known inside the atom, so we have 15 Quantum Mechanical Bound on m φ • Consider ν α − e elastic scattering, the uncertainty ∆ p ∆ x ∼ ℏ • Using ∆ x = 140 × 10 − 8 cm, the radius of 26 Fe – most of Earth’s matter, one obtains for the uncertainty in q 2 to be q 2 ≈ ( 14 . 14 eV ) 2

Experimental Limit on Max. Scalar NSI production will be afgected, in direct conflict with 3 Ge and Parke, PRL 122 (2019) 4 Smirnov, Xu JHEP 12 (2019) 16 • Sun : The χ 2 -analysis of the Borexino data sets a 3σ upper bound on the scalar NSI in Sun 3 : ∆ m Sun = 7 . 4 × 10 − 3 eV • Supernova : If ∆ m SN becomes too large, then neutrino observations from SN1987A 4 . For typical core temperature around T = 30 MeV , we constrain : ∆ m SN < 5 MeV

Scalar NSI : Electron 17 10 - 4 ( g - 2 ) e Δ m Earth = 10 - 10 eV 10 - 8 SN1987A BBN 10 - 12 RG / HB Stars 10 - 16 II I I I I V 10 - 20 VII Torsional Balances IV VI y e 10 - 24 Δ m SN = 1 eV Δ m SN = 10 - 2 eV Δ m Sun > 7.4 meV Δ m SN > 5 MeV Δ m Sun = 10 - 5 eV 10 - 28 10 - 32 y ν = 2.6 x 10 - 10 Dirac ν 10 - 36 10 - 18 10 - 14 10 - 10 10 - 6 10 - 2 10 2 10 6 m ϕ ( eV )

Scalar NSI : Nucleon 18 10 - 4 K + → π + + ϕ Δ m Earth = 10 - 22 eV 10 - 8 BBN SN1987A RG / HB Stars 10 - 12 10 - 16 II I I I I V 10 - 20 VII Torsional Balances IV y N VI 10 - 24 Δ m Sun > 7.4 meV Δ m SN = 1 eV Δ m SN = 10 - 2 eV 10 - 28 Δ m Sun = 10 - 6 eV Δ m SN > 5 MeV 10 - 32 y ν = 2.6 x 10 - 10 Dirac ν 10 - 36 10 - 18 10 - 14 10 - 10 10 - 6 10 - 2 10 2 10 6 m ϕ ( eV )

Conclusion • Neutrino NSI with matter mediated by a light scalar induces medium-dependent neutrino masses. • A general field-theoretic derivation of the scalar NSI is presented, which is valid at arbitrary temperature and density environments. • We extended the analysis of long-range force efgects for all background media, including both relativistic and non-relativistic limits. • Observable scalar NSI efgects, although precluded in terrestrial experiments, are still possible in future solar and supernovae neutrino data. 19

Thank you ! Questions ? Email: garv.chauhan@wustl.edu 20