Neutrino Trident Production

Transcription

1 Neutrino Trident Production Takashi Shimomura (Miyazaki U.) in collaborations with Yuya Kaneta (Niigata U.)

2 Review of Neutrino Trident Production

3 What is Neutrino Trident Production (NTP) Processes? Charged lepton pair production by the scattering of a neutrino off the Coulomb field of a nucleus/nucleon µ + N! µ + µ + µ + N N: Nucleus/Nucleon neutrino beam µ weak int. L = G F p 2 l µ (C V C A 5 )l µ (1 5) µ µ Coulomb field µ target Nucleus/Nucleon Nucleus/Nucleon

4 Brief History of the NTP s Back in the early days, 1934 Four Fermi interaction (Fermi) 1956,7 Parity Violation discovered (Lee and Yang, Wu) µ + N! µ + W + + N! e/µ + µ + N! + µ + µ + N 1957 the V-A theory (Feynman, Gell-mann) 1964 Trident Production to examine the V-A theory (Czyz, Sheppey, Walecka) 1967 Weinberg-Salam theory 1971 Momentum and angular distribution of the NTP (Lovseth and Radomiski, Koike et al, Fujikawa) 1972 Trident production to examine the WS theory (Brown, Hobbs, Smith and Stanko) 1974 Neutral current (CERN) 1983 W and Z boson discovered 1990 CHARM-II 1991 CCFR 1995 NuTeV consistent with the SM prediction revival 2014 Trident production to constrain new physics (Altmannshofer, Gori, Pospelov, Yavin)

5 Types of the NTPs and kinematical threshold Mono-flavour µ + N! µ + µ + + µ + N (W/Z) µ + N! µ + e + + e + N (Z) µ + N! µ N (Z) Minimum neutrino energy: E,thresh =2m l (l=e,μ,τ) Multi-flavour µ + N! e + e + + µ + N etc Minimum neutrino energy: E,thresh = m l + m l 0 (W) (l,l =e,μ,τ) The same processes exist for other flavours, and also exist for anti-neutrinos if CP is conserved.

6 The NTPs with atomic electrons In principle, the NTPs can occur with bound electrons. But these are negligible due to the high threshold and small cross sec. µ + e! µ + µ + + µ + e E,thresh = 2m µ m e m µ ' 43 GeV µ + e! e + e + + µ + e E,thresh = m µ 2m e m µ ' 11 GeV These do not occur for low energy neutrino beam. The following process always occurs e + e! e + e + + e + e E,thresh =4m e ' 2MeV The cross sec. of this process is much small and will be important for lower energy neutrino beams.

7 The NTP cross sections Czyz et al (1964), Lovseth et al (1971), Brown et al (1972) The cross section can be divided into two parts Z = Z 2 2 G 2 F dlips M µ J µ 1 q 4 where J µ = hn 0 J µ NihN J N 0 i (Z : atomic number) J μ : nuclear electromagnetic current particle physics GF e l l 0 Nucleus/Nucleon Ze nuclear physics Nucleus/Nucleon

8 Nuclear Electromagnetic Current The nuclear electromagnetic current can be expressed in terms of form factors, F. spin-0 particle ( 12 C, 56 Fe, 208 Pb, etc) hn 0 J µ Ni =(Q + Q 0 ) µ F (q 2 ) (q = Q 0 Q) where F (0) = 1 spin-1/2 particle (p, n) hn 0 J µ Ni =ū(q 0 ) where M is the proton mass, and apple µ F 1 (q 2 )+i apple µ q 2M F 2(q 2 ) u(q) F 1 (0) = 1, F 2 (0) = 1, apple =1.79 for proton F 1 (0) = 0, F 2 (0) = 1, apple = 1.91 for neutron

9 Nuclear Form Factor The form factors in the literature are the dipole fit F (q 2 )= 1 q 2 R or q2 M 2 p 2 the exponential fit F (q 2 )=exp q 2 R Mp: proton mass where R 0 =1.21A 1/3 fm the Fermi fit (more realistic) Z F (q 2 )= (r)e iq r dr/q (r) =(1+exp(r R)/b) 1 where R =1.07A 1/3 fm and b =0.57 fm

10 q 2 dependence of the form factors The main contribution to the NTP comes from small q 2. Iron nucleus B : R 0 =1.21A 1/3 fm A dipole C :R 0 =1.3A 1/3 fm B exponential 0 10 Fermi D C lo I Brown et al, PRD(1972) (q~l in (GeV/c)~

11 q 2 dependence of the form factors The main contribution to the NTP comes from small q 2. Iron nucleus B : R 0 =1.21A 1/3 fm A dipole The dipole fit overestimates the cross sec. as much as 50% C :R 0 =1.3A 1/3 fm B exponential 0 10 Fermi D C lo I Brown et al, PRD(1972) (q~l in (GeV/c)~ These form factors are almost the same for small q 2

12 The NTP cross sections (in the V-A theory) 1. NTP by the coherent scattering off a nucleus nucleus(µµ) Z 2 2 G 2 F nucleus(ee) Z 2 2 G 2 F E R 0 log E R 0 m 2 µ E R 0 log (E R 0 ) R0: nuclear radius

13 The NTP cross sections (in the V-A theory) 1. NTP by the coherent scattering off a nucleus nucleus(µµ) Z 2 2 G 2 F nucleus(ee) Z 2 2 G 2 F E R 0 log E R 0 m 2 µ E R 0 log (E R 0 ) R0: nuclear radius 2. NTP by the incoherent scattering off a nucleon nucleon 2 G 2 E M p F E M p log (0.5Z +0.1N) m 2 µ

14 The NTP cross sections (in the V-A theory) 1. NTP by the coherent scattering off a nucleus nucleus(µµ) Z 2 2 G 2 F nucleus(ee) Z 2 2 G 2 F E R 0 log E R 0 m 2 µ E R 0 log (E R 0 ) R0: nuclear radius 2. NTP by the incoherent scattering off a nucleon nucleon 2 G 2 E M p F E M p log (0.5Z +0.1N) m 2 µ 3. NTP by the incoherent scattering off an atomic electron electron 2 G 2 F E m e log 2 E m e

15 The NTP cross sections (in the SM) The neutrino trident production in the SM occurs via µ W contrib. (V-A) µ Z contrib. µ µ W µ µ + + Z µ µ + Nucleus/Nucleon Nucleus/Nucleon

16 The NTP cross sections (in the SM) The neutrino trident production in the SM occurs via µ W contrib. (V-A) µ Z contrib. µ µ W µ µ + + Z µ µ + Nucleus/Nucleon Nucleus/Nucleon The Z boson contributes to the NTP cross section destructively, where L = G F 2 µ (1 5) l µ (C V C A 5 )l C V = sin2 W (+1),C A = 1 2 (+1) Then, the cross section is given by SM ' (C 2 V + C 2 A) V A ' 0.6 V A (CV=CA=1 in V-A)

17 The NTP cross sections (in the SM) lo-~~ ee trident I I I I I Io-4o μμ trident µ + N! µ + µ + µ + N IO 40 e + N! e + e + e + N IO-4 I V-A E c3 I0-4 I SM b SM NC I0-42 µ + N! µ + e + e + N 4p V-A SM I045 I I l I I l IOO I EI in GeV IO IOO l20 I40 EI in GeV The νe NTP is one order larger than the νμ NTP

18 Experimental Results of the NTP CHARM-II (CERN) PLB 245 (1990) The first observation of the NTP using beam energy : he i = 23.8 GeV ( µ ) he i = 19.3 GeV ( µ ) Fiducial target mass : 547 t glass plates, hz 2 i = 97.6 Results (per nucleus) exp =[3.0 ± 0.9(stat.) ± 0.5(sys.)] cm 2 The result is consistent wit the SM prediction, theo =[1.9 ± 0.4] cm 2 which is consistent with the experimental results. Theoretical uncertainty comes from 1.the uncertainty of the form factor 2.the estimation of diffractive contributions

19 Experimental Results of the NTP CCFR (FNAL) PRL 66 (1991) The first observation of the destructive interference between W and Z using beam energy : Fiducial target mass : he i = 160 GeV ( µ, µ ) 324 t iron plates, Z = 26 Results N exp = 37.0 ± 12.4 exp =[7.5 ± 2.6] cm 2 The expected numbers of events in the V-A and in the SM are N V A = 78.1 ± 3.9 N SM = 45.3 ± 2.3 The experimental result rules out the V-A theory at 99% C.L.

20 Short Summary of the NTP 1. The neutrino trident production processes have been studied since 60 s. 2. Nuclear form factors are necessary to compute the cross sections. 3. The NTP cross section is much smaller than the charged current one. Typically below cm The latest results are more than 20 years ago, with large errors. 5. The experimental results are consistent with the SM so far within the error.

21 Neutrino Trident Production in a gauged L μ -L τ model

22 Light Gauge Boson as New Physics resonant absorption of cosmic ν cos C B M Z 0 Z 0 ' p 2E m ' O(10) MeV cos C B Eν = 1 PeV, mν = 0.1 ev JN 09 (e + e -based) 301 ± 65 DHMZ 10 (τ-based) 197 ± 54 DHMZ 10 (e + e ) 289 ± 49 HLMNT 11 (e + e ) 263 ± 49 BNL-E821 (world average) 0 ± 63 BNL-E IPCC (relative unit) exp 10 a µ a 11 µ a µ new int. with muon Z 0 µ µ For mz mμ and g =10-4 a µ ' g ' O(10 9 ) m 0 c 2 =15.6 MeV m 0 c 2 =16.6 MeV m 0 c 2 =17.6 MeV Θ (deg.) m Z 0 Seto san s talk decay into e + e - Be best fit Z 0 e e + Be = MeV

23 Light Gauge Boson as New Physics These anomalies/tensions can be explained by m Z 0 ' O(10 100) MeV g The origin of the mass = The spontaneous breaking of a symmetry v = m Z 0 g 0 O( )GeV

24 Gauged U(1)Lμ-Lτ model Minimal extension of the SM Anomaly free Large neutrino mixing Choubey, Rodejohann, Eur.Phys.J, (2005) Ota, Rodejohann, Phys.Lett. (2006) R. Foot, Mod.Phys.Lett. (1991), He, Joshi, Lew, Volkas, PRD (1991) l e e R l µ µ R l R L µ L The Lagrangian without the kinetic mixing, L = 1 4 Z0 µ Z 0 µ + m2 Z 0 2 Z0 µ Z0 µ +g 0 Z 0 µ ( µ µ µ + µ µ µ µ µ ) new interactions for μ and ν The IceCube gap can be explained by O(10) MeV Z with g 10-4 The muon (g-2) also can explain by the same mass and the coupling Araki, Kaneko, Ota, Sato, T.S, PRD93 (2016)

25 Z contribution to the NTP the SM µ /µ µ µ NP µ Z/W µ/ µ Z 0 µ µ µ Nucleus Nucleus Nucleus Nucleus G F = g2 2 m 2 Z ONLY weak int. g 0 2 q 2 m 2 Z 0

26 Z contribution to the NTP the SM µ /µ µ µ NP µ Z/W µ/ µ Z 0 µ µ µ Nucleus Nucleus Nucleus Nucleus G F = g2 2 m 2 Z ONLY weak int. g 0 2 q 2 m 2 Z 0 g 02 m 2 Z GeV 2 g 0 10 mz =10 MeV sensitive to small g & mz

27 Allowed parameter region Altmannshofer, et al, PRL. 113 (2014) CHARM II/ SM =1.58 ± 0.57 at E 20 GeV CCFR/ SM =0.82 ± 0.28 at E 160 GeV (1990) (1991)

28 Allowed parameter region Altmannshofer, et al, PRL. 113 (2014) CHARM II/ SM =1.58 ± 0.57 at E 20 GeV CCFR/ SM =0.82 ± 0.28 at E 160 GeV (1990) (1991)

29 Allowed parameter region g 0 m Z 0 (MeV) CHARM II/ SM =1.58 ± 0.57 at E 20 GeV CCFR/ SM =0.82 ± 0.28 at E 160 GeV (1990) (1991)

30 Allowed parameter region g 0 m Z 0 (MeV) CHARM II/ SM =1.58 ± 0.57 at E 20 GeV CCFR/ SM =0.82 ± 0.28 at E 160 GeV (1990) (1991)

31 Energy dependence of the cross section / SM g 0 = g 0 = g 0 = g 0 = SM solid : 10 MeV dashed: 100 MeV SM CHARM-II solid : 10 MeV dashed: 100 MeV CHARM-II The cross section SM / G 2 F 2 E E log R 0 R 0 m 2 µ int / G F g 02 log 2 E R 0 m 2 µ = SM + int + Z 0 int SM / log E E NP is enhanced at low E

32 Sensitivity to g and mz in a gauged Lμ-Lτ model Preliminary Eν=1.5 GeV CCFR BaBar (g-2)μ 2σ (g-2)μ 3σ g' 10-3 CHARM II SM+NP SM m Z' (GeV) CHARM II/ SM =1.58 ± 0.57 at E 20 GeV CCFR/ SM =0.82 ± 0.28 at E 160 GeV (1990) (1991)

33 Gauged U(1)Lμ-Lτ model with kinetic mixing In general, there are no reasons to forbid the kinetic mixing, L kin = Bµ B µ 4 Z0 µ Z 0 µ + 2 Bµ Z 0 µ The kinetic mixing induces new interactions with Z and fermions, f Z 0 e (c W = cos W ) c W L int = Z 0 µ [ "ec W ē µ e +(g 0 "ec W ) µ µ µ +( g 0 "ec W ) µ +g 0 ( µ µ µ µ )] f B : field strength of U(1)Y The muon coupling can be negative. The neutrino coupling is the same.

34 NTP Cross Section with kinetic mixing constructive 2 / SM R MeV g 0 = 10 4 / MeV 300 MeV ε destructive The ratio >1 or <1 is also important information.

35 Summary 1. The new physics above the EW scale can appear as a light gauge boson. 2. The NTP is a powerful tool to search such a light gauge boson, especially a gauged Lμ-Lτ model. 3. Lower energy neutrino beams have better sensitivity to new physics search. Future works (under progress) 1. Backgrounds to the NTP come from leptonic decays of mesons (pi, K, rho, ). µ + N! µ + X + N X! µ + + µ + 2. Momentum and angular distributions of the charged leptons are important to discriminate the signals from the backgrounds.

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39 Z contribution to the NTP the SM Z/W µ /µ µ µ NP µ 1 2 +sin2 W 1 4 µ/ µ Z 0 +g 0 +g 0 µ µ µ Nucleus Nucleus Nucleus Nucleus G F = g2 2 m 2 Z g 0 2 q 2 m 2 Z 0 Only weak int. sensitive to small g & mz The Z contribution to this process is proportional to (+g ) 2 always constructive

40 IceCube gap and muon g-2 400TeV - 1PeV is resonantly scattered by cosmic ν background The resonant energy of comic ν is cos E res ' m2 Z 0 m For mz = 10 MeV, C B g 0 g 0 Z 0 E res ' 1 PeV The scattering cross section is = 2 g0 2 M 2 Z 0 1 E res E From numerical analysis, g E ν 2 Φ [10-8 GeV cm -2 s -1 sr -1 ] Araki, Kaneko, Ota, Sato, T.S, PRD93 (2016) E ν [GeV] s ν =2.5 s ν =2.3 s ν =2.1 IceCube

41 IceCube gap and muon g-2 Z contribution to (g-2)μ a µ = g0 2 8 Z 1 0 2m 2 µ x(1 x)2 dx xm 2 Z +(1 x) 2 m 2 0 µ µ Z 0 µ For mz =10 MeV and g =4 10-4, a µ ' g ' O(10 9 ) Araki, Kaneko, Ota, Sato, T.S, PRD93 (2016) IceCube and (g-2)μ can be explained g 0 m Z 0 (MeV)

42 Energy dependence of Neutrino Trident Prod. Cross Section Cross Section [pb] Cross Section ε=3x10-3,g =2x10-3,M Z =300MeV ε=1.3x10-3,g =1.3x10-3,M Z =100MeV ε=7x10-4,g =6x10-4,M Z =50MeV ε=6x10-5,g =4x10-4,M Z =10MeV SM Ratio E ν [GeV] Ratio σsm+np/σsm ε=3x10-3,g =2x10-3,M Z =300MeV ε=1.3x10-3,g =1.3x10-3,M Z =100MeV ε=7x10-4,g =6x10-4,M Z =50MeV ε=6x10-5,g =4x10-4,M Z =10MeV SM E ν [GeV] The lower energy of neutrinos has smaller cross sections The lower energy of neutrinos is more sensitive to NP. cf CC/E cm 2 GeV 1