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Probing heavy neutrino oscillation and associated CP violation at future hadron colliders Yongchao Zhang ( [ ) Washington University in St. Louis July 26, 2019 Flasy 2019, Hefei based on P. S. B. Dev, R. N. Mohapatra & YCZ,

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Probing heavy neutrino oscillation and associated CP violation at future hadron colliders

Yongchao Zhang («[‡)

Washington University in St. Louis July 26, 2019 Flasy 2019, Hefei

based on

  • P. S. B. Dev, R. N. Mohapatra & YCZ, 1904.04787
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Seesaw mechanism

Minkowski, ’77; Mohapatra & Senjanovic, ’80; Yanagida, ’79; Gell-Mann, Ramond & Slansky, ’79; Glashow, ’80

mν ≃ −mDM−1

N mT D

At least two heavy right-handed neutrinos (RHNs) to generate the tiny neutrino masses. (“fair-play rule”)

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 2 / 24

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Seesaw scenarios

In pure type-I seesaw and U(1)B−L gauge extension of SM, RHN mixing and associated CP violation signatures depend on heavy-light neutrino mixing. Thanks to the discussions with Shun Zhou [Chao, Si, Zheng, Zhou ’09] In the left-right model based on the gauge group SU(2)L × SU(2)R × U(1)B−L:

[Pati & Salam, ’74; Mohapatra & Pati, ’75; Senjonavi´ c & Mohapatra, ’75]

QL = uL dL

  • ∈
  • 2, 1, 1

3

  • P

← → QR = uR dR

  • ∈
  • 1, 2, 1

3

  • ΨL =
  • νL

eL

  • ∈ (2, 1, −1)

P

← → ΨR =

  • NR

eR

  • ∈ (1, 2, −1)

The RHN mixing and CP violation can be measured at colliders. This can be used to directly test TeV-scale leptogenesis at future hadron colliders!

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 3 / 24

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Flavor dependence of same-sign dilepton signals

W −

R

ℓ−

α

ℓ−

β

¯ q′ q N1, 2 WR

The “smoking-gun” signal of WR and N! [Keung & Senjanovi´

c, ’83]

With only one RHN, or the production and decays of RHNs not interfering coherently: Γ(N → ℓ+jj) = Γ(N → ℓ−jj) = ⇒ N(ℓ±ℓ±) = N(ℓ+ℓ−) If we have more than one RHNs, and there are mixing and CPV in the RHN sector [Dev & Mohapatra, ’15; Gluza, Jelinski & Szafron, ’16; Anamiati, Hirsch & Nardi,

’16; Antusch, Cazzato & Fischer, ’17; Das, Dev & Mohapatra, ’17]

Γ(Nα → ℓ+

β jj) = Γ(Nα → ℓ− β jj) ,

but N(ℓ±

α ℓ± β ) = N(ℓ+ αℓ− β ) ,

N(ℓ+

αℓ+ β ) = N(ℓ− α ℓ− β ) (CP-induced effects)

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 4 / 24

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RHN mixing and CP violation

Some assumptions Only two RHNs Ne, µ mixing with each other; the third one Nτ does not mix with Ne, µ:

  • Ne

Nµ

  • =
  • cos θR

sin θRe−iδR − sin θReiδR cos θR N1 N2

  • ,

The mass relation M1, 2 < MWR (and M3 > MWR):

  • n-shell production of RHNs from WR decay: W ±

R → ℓ± α Nα

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 5 / 24

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Same-sign charge asymmetry (SSCA)

Define the same-sign charge asymmetry (SSCA) Aαβ ≡ N(ℓ+

αℓ+ β ) − N(ℓ− α ℓ− β )

N(ℓ+

αℓ+ β ) + N(ℓ− α ℓ− β )

= σ(pp → W +

R )R(ℓ+ αℓ+ β ) − σ(pp → W − R )R(ℓ− α ℓ− β )

σ(pp → W +

R )R(ℓ+ αℓ+ β ) + σ(pp → W − R )R(ℓ− α ℓ− β )

Combing both the three-body decays of Nα through the gauge couplings to WR boson (1 − BRy) and two-body decays of Nα through the Yukawa couplings via heavy-light neutrino mixing (BRy) R(ℓ±

α ℓ± β ) ≃ (1 − BRy)R(ℓ± α ℓ± β )

  • 3-body decay ctrb.

+ 1 4BRyBαβ

  • 2-body decay ctrb.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 6 / 24

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3-body and 2-body decay contributions

Three-body decays Nα → ℓ±

β jj, in the limit of Γ1 = Γ2, with x ≡ ∆EN/Γavg

[normalization condition

α,β=e,µ R(ℓ± α ℓ± β ) = 1]

R(e±µ±) = R(µ±e±) ≃ 1 4 sin2 2θR

  • 1 − cos 2δR ± xsin 2δR

1 + x2

  • ,

R(e±e±) ≃ R(µ±µ±) ≃ 1 2 − R(e±µ±) , Two-body decays Nα → ℓ±

β W ∓ (α = e, µ, β = e, µ, τ)

N(ℓ±

α ℓ± β ) ∝

  • R(e±e±) + R(e±µ±)
  • Beβ = 1

2Beβ Bαβ = Γ(Nα → ℓ±

β W ∓)/Γ(Nα →

  • β

ℓ±

β W ∓)

In most of the parameter space of interest, the dependence of SSCAs on θR and δR is negligible.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 7 / 24

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Some comments

Aee, µµ depend both on θR and δR, while Aeµ depends only on δR. We expect the relation, in the limit of (1 − BRy) ≫ BRy, Aeµ(δR) = Aee, µµ

  • θR = π

4 , δR + π 2

  • .

Aee, µµ, eµ can be used to determine the RHN mixing angle θR and CP phase δR at future colliders. If the two-body decay dominates, the CP-induced SSCAs will be suppressed. If the three-body decay dominates, the TeV-scale leptogenesis efficiency will be suppressed.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 8 / 24

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Dominant (reducible) backgrounds

Figure: From ATLAS, 1809.11105, with L = 36.1 fb−1. [See also CMS, 1803.11116; Mitra, Ruiz, Scott & Spannowsky, ’16; Nemevsek, Nesti & Popara, ’18]

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 9 / 24

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Production cross sections

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 0.001 0.010 0.100 1

WR mass [TeV] σ(pp → WR

± → ℓ±ℓ±jj)

s = 14 TeV WR

+

WR

  • Figure: Using a conservative k-factor of 1.1. Mitra, Ruiz, Scott & Spannowsky, ’16

Even if there is no CPV in the RHN sector, we can still expect non-zero SSCAs: σ(pp → W +

R ) > σ(pp → W − R )

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 10 / 24

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The proton PDF uncertainties are more important...

5.0 5.2 5.4 5.6 5.8 6.0

  • 0.4
  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

WR mass [TeV] αβ LHC14 (BRy = 0)

current LHC limit w/o CPV [ee, μμ & eμ] w/ CPV [ee, μμ] w / C P V [ e μ ] 5.0 5.2 5.4 5.6 5.8 6.0

  • 0.4
  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

WR mass [TeV] αβ LHC14 (BRy = 1/2)

current LHC limit w/o CPV [ee, μμ & eμ] w/ CPV [ee] w / C P V [ μ μ ] w/ CPV [eμ]

Figure: Using NNPDF3.1 and θR = δR = π/4. Left: BRy = 0 and Right: BRy = 1/2.

The proton parton energy fraction x1x2 = ˆ s s ≃ M2

WR

s 0.1 for MWR 5 TeV We need a higher-energy collider!

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 11 / 24

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Prospects @ HE-LHC √s = 27 TeV

5.0 5.5 6.0 6.5 7.0 7.5 8.0

  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

WR mass [TeV] αβ HE-LHC (BRy = 0)

current LHC limit w/o CPV [ee, μμ & eμ] w/ CPV [ee, μμ] w / C P V [ e μ ] 5.0 5.5 6.0 6.5 7.0 7.5 8.0

  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

WR mass [TeV] αβ HE-LHC (BRy = 1/2)

current LHC limit w/o CPV [ee, μμ & eμ] w / C P V [ e e ] w/ CPV [μμ] w/ CPV [eμ]

Figure: Left: BRy = 0 and Right: BRy = 1/2.

One could measure the RHN mixing and CPV at future high energy colliders by using the SSCA signals. The maximal CPV case (θR = δR = π/4) can be measured at √s = 27 TeV, for a WR mass up to 7.2 TeV. We need only O(100 fb−1) of data to have at least 100 events of both ℓ+ℓ+ and ℓ−ℓ− at HE-LHC for a WR mass of 5 TeV.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 12 / 24

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Prospects @ FCC-hh/SPPC √s = 100 TeV

5 10 15 20 25 30

  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

WR mass [TeV] αβ FCC-hh (BRy = 0)

current LHC limit w /

  • C

P V [ e e , μ μ & e μ ] w / C P V [ e e , μ μ ] w/ CPV [eμ] 5 10 15 20 25 30

  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

WR mass [TeV] αβ FCC-hh (BRy = 1/2)

current LHC limit w /

  • C

P V [ e e , μ μ & e μ ] w/ CPV [ee] w / C P V [ μ μ ] w / C P V [ e μ ]

Figure: Left: BRy = 0 and Right: BRy = 1/2.

One could measure the RHN mixing and CPV at future high energy colliders by using the SSCA signals. The maximal CPV case (θR = δR = π/4) can be measured at √s = 100 TeV, for a WR mass up to 26 TeV. We need only O(100 fb−1) of data to have at least 100 events of both ℓ+ℓ+ and ℓ−ℓ− at FCC-hh/SPPC for a WR mass of 10 TeV.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 13 / 24

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Expected SSCAs: benchmark points

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

δR/π αβ

ee μμ eμ w/o CPV

θR = π/4 HL-LHC [WR = 5 TeV] 0.0 0.2 0.4 0.6 0.8 1.0

  • 0.2

0.0 0.2 0.4 0.6 0.8 1.0

δR/π αβ

ee μμ eμ w/o CPV

θR = π/4 FCC-hh [WR = 15 TeV]

The Aeµ does not depend on θR, thus one can use Aeµ to first determine the phase δR, up to a twofold ambiguity. Then one can use Aee, µµ to determine the mixing angle θR (and potentially remove the ambiguity of δR). By comparing the Aee and Aµµ data, we can get information on the BRs of 3- and 2-body decays of RHNs.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 14 / 24

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Expected SSCAs: benchmark points

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

θR/(π/2) δR/π ee @ FCC-hh

0.8 0.6 0.4 0.2 MWR = 15 TeV, BRy = 1/2 leptogenesis leptogenesis 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

θR/(π/2) δR/π ee @ FCC-hh

0.75 0.5 0.25 MWR = 20 TeV, BRy = 1/4 leptogenesis leptogenesis

With only Aee (or Aµµ), one can limit θR and δR to a circle (band). Then one can use Aeµ to determine θR and δR (to a limited range).

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 15 / 24

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Casas-Ibarra parameterization

Casas & Ibarra, ’01; Nemevˇ sek, Senjanovi´ c, Tello, ’12 PRL

For simplicity, we “decouple” Nτ, with one of the active neutrinos being massless. Casas-Ibarra parameterization of the MD matrix (equiv. to Nemevˇ sek-Senjanovi´ c-Tello form in the LRSM) MD = iVPMNS m1/2

ν

OM1/2

N

The arbitrary matrix O =   cos ζ sin ζ − sin ζ cos ζ   , OOT = 12×2

  • for NH ,

O =   cos ζ sin ζ − sin ζ cos ζ   , OOT = 12×2

  • for IH .

ζ could be complex, enhancing largely the couplings y = MD/vEW.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 16 / 24

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Leptogenesis

The lepton asymmetry generated from RHN decay, with K eff

α

the washout factor [Dev, Lee & Mohapatra, ’14] η∆L

i

≃ 3 2zcK eff

α

  • α

εiαdi, The dilution factor due to the right-handed gauge interactions of RHNs, di = γNi

Lφ/

  • γNi

Lφ + γNi Lqq + γNi WR

  • The flavor-dependent CP asymmetry contains the information of RHN mixing

and CPV, with i = j, εiα ≃ (M2

i − M2 j )Im[y ∗ αiyαj]Re[(y †y)ij]

4π[4(Mi − Mj)2 + Γ2

j ](y †y)ii

× BRy(Ni)

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 17 / 24

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Complex ζ

Frer` e, Hambye & Vertongen, ’08; Dev, Lee & Mohapatra, ’14; Dhuria, Hati, Rangarajan & Sarkar, ’15

Without any significant cancellation or fine-tuning in the MD matrix, |y| ∼

  • |mνMN| ∼ 10−6 ≪ gR

This sets a lower bound on the WR boson mass MWR 50 TeV = ⇒ no CPV prospect @ 100 TeV collider The WR mass could be significantly smaller, if | sin ζ|, | cos ζ| ≫ 1 ⇒ y ≫ 10−6 However, Imζ can not be too large

◮ The ∆L = 0 processes Lφ ↔ Lφ, ∆L = 2 process Lφ ↔ ¯

Lφ† and/or the inverse decay Lφ → Ni induce significant dilution/washout effects.

◮ It is potentially constrained by high-precision low-energy constraints, such as

µ → eγ, 0νββ and electron EDM (almost no limit in our case).

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 18 / 24

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Imζ ranges

not excluded by 0νββ excluded by 0νββ 2 4 6 8 10 10-11 10-9 10-7 10-5

Im ζ |ηΔL|

NH

not excluded by 0νββ excluded by 0νββ 2 4 6 8 10 10-11 10-9 10-7 10-5

Im ζ |ηΔL|

IH

Ranges of parameters, with RHN mass splitting ε = Γavg/2 to have the maximal lepton asymmetry: δν ∈ [0, 2π] , α ∈ [0, 2π] , ζ ∈ [0, 10]i , MN ∈ [0.15, 10] TeV , MWR ∈ [3, 50] TeV , θR ∈ [0, 2π] , δR ∈ [0, 2π] . The limits from LFV decay µ → eγ and electron EDM can not provide any limits in our case.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 19 / 24

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Imζ ranges and Yukawa couplings

The ranges of Imζ we found:

  • 1.3 Imζ 7.8 ,

for NH , 0.8 Imζ 7.7 , for NH , and the resultant magnitudes of Yukawa couplings y = MD/vEW:

  • 1.3 × 10−6 |y|max 7.2 × 10−4 ,

for NH , 1.0 × 10−6 |y|max 8.6 × 10−4 , for IH .

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 20 / 24

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Absolute WR mass limits

0.5 1 5 10 5 10 20 50

MN [TeV] MWR limit [TeV]

NH IH

MWR > 9.38 (8.87) TeV for NH (IH) at MN ≃ 500 GeV Leptogenesis lmits on WR mass depend on RHN masses as well as active neutrino data and other parameters.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 21 / 24

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Leptogenesis limits on θR & δR

MWR = 15 TeV, BRy = 1/2 MWR = 20 TeV, BRy = 1/4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

θR/(π/2) δR/π

The neutrino data within their 2σ ranges, and MN = 1 TeV ∆MN = Γavg/2 to maximize the CP asymmetry.

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 22 / 24

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Testing leptogenesis @ colliders

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

θR/(π/2) δR/π ee @ FCC-hh

0.8 0.6 0.4 0.2 MWR = 15 TeV, BRy = 1/2 leptogenesis leptogenesis 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

θR/(π/2) δR/π ee @ FCC-hh

0.75 0.5 0.25 MWR = 20 TeV, BRy = 1/4 leptogenesis leptogenesis

Other methods to measure RHN CPV and test leptogenesis at colliders:

◮ Model-independent analysis of LNV signals pp → ℓ±ℓ±jj [Deppisch, Harz, Hirsch, ’13] ◮ LNV decays of right-handed doubly-charged scalar [Vasquez, ’14] ◮ The decays N → ℓ±H∓ (H± being charged mesons) [Caputo, Hernandez, Kekic, Lopez-Pavon & Salvado, ’16] ◮ Heavy-light neutrino mixing at future lepton colliders [Antusch, Cazzato, Drewes, Fischer, Garbrecht, Gueter, Klaric, ’17]

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 23 / 24

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Conclusion

The mixing and CP violation in the RHN sector of TeV-scale left-right models can be directly probed at future high-energy hadron colliders, by measuring the same-sign charge asymmetries (SSCAs). In the case with only Ne, µ, the e±µ± channel can be used to measure the CP phase δR, which is independent of the RHN mixing angle; using the channels e±e±, µ±µ±, one can then determine the mixing angle θR. The future 100 (27) TeV collider could probe the RHN mixing and CPV, for WR mass up to 26 (7.2) TeV. TeV-scale resonant leptogenesis can be directly tested at future hadron colliders by measuring the SSCAs. There is an absolute lower bound around 9 TeV on the WR boson mass to make leptogenesis work in the case with effectively only two RHNs.

Thank you very much!

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 24 / 24

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backup slides

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Absolute WR mass limit

In the large MN limit, the dependence is respectively (for the 2-body decays we have taken into account also the dependence MD ∝ M1/2

N )

Γ(N → ℓq¯ q′) ∝ M5

N/M4 WR ,

Γ(N → Lφ) ∝ M2

N .

When MN gets larger, the 3-body width grows faster than the 2-body decays, therefore the WR mass has to be larger to make leptogenesis work. When RHN masses get smaller ↓ ( 500 GeV), Keff ↑, di ↓, εiα ↑ ⇒ MWR limits ↑

Yongchao Zhang (Wustl) RHN mixing & CPV July 26, 2019 26 / 24