LHC 750 GeV Diphoton excess in a radiative seesaw model · Figure 2: p-value for the background-only hypothesis p 0 as a function of the mass mX of a probed NWA resonance signal

LHC 750 GeV Diphoton excess ina radiative seesaw model

Kenji Nishiwaki (KIAS)

based on collaboration with

Shinya Kanemura (Univ. of Toyama),Hiroshi Okada (NCTS),

Yuta Orikasa (KIAS, Seoul National Univ.),Seong Chan Park (Yonsei Univ.),Ryoutaro Watanabe (CTPU-IBS)

[arXiv:1512.09048]

talk @ Overview on the recent di-photon excess at the LHC Run 2,IBS-CTPU (8th January 2016) -/7

Intro: 750 GeV diphoton excess awakens!! [GeV]Xm

200 400 600 800 1000 1200 1400 1600 1800Lo

cal p

-val

ue5−10

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3−10

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ATLAS Preliminary-1 = 13 TeV, 3.2 fbs

Observed

σ0

σ1

σ2

σ3

σ4

Figure 2: p-value for the background-only hypothesis p0 as a function of the mass mX of a probed NWA resonancesignal.

[GeV]Xm200 400 600 800 1000 1200 1400 1600 1800

BR

[fb]

× fidσ

95%

CL

Uppe

r Lim

it on

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310ATLAS Preliminary

-1 = 13 TeV, 3.2 fbs

ObservedExpected

σ 1 ±σ 2 ±

Figure 3: Expected and observed upper limits on �fiducial ⇥BR(X ! ��) expressed at 95% CL, as a function of theassumed value of the narrow-width scalar resonance mass.

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Figure 6: Expected and observed 95% C.L. exclusion limits for different signal hypotheses. Therange 500 GeV < mG < 4.5 TeV is shown for k = 0.01, 0.1, 0.2 on the top-left, top-right, bottomrespectively.

icance is expected to reduce further after accounting for the fact that several k hypotheses havebeen searched for.

[ATLAS-CONF-2015-081] [CMS-PAS-EXO-15-004]

m�� ' 750GeV m�� ' 760GeV

Kenji Nishiwaki (KIAS) 1/7

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LHC,” arXiv:1512.05751 [hep-ph].[31] D. Curtin and C. B. Verhaaren, “Quirky Explanations for the Diphoton Excess,”

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Promising Interpretation of Diphoton Resonance at 750 GeV,” arXiv:1512.08497[hep-ph].

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[121] S. K. Kang and J. Song, “Top-phobic heavy Higgs boson as the 750 GeV diphoton

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resonance,” arXiv:1512.08963 [hep-ph].[122] Y. Hamada, T. Noumi, S. Sun, and G. Shiu, “An O(750) GeV Resonance and Inflation,”

arXiv:1512.08984 [hep-ph].[123] X.-J. Huang, W.-H. Zhang, and Y.-F. Zhou, “A 750 GeV dark matter messenger at the

Galactic Center,” arXiv:1512.08992 [hep-ph].[124] S. Kanemura, K. Nishiwaki, H. Okada, Y. Orikasa, S. C. Park, and R. Watanabe, “LHC

750 GeV Diphoton excess in a radiative seesaw model,” arXiv:1512.09048 [hep-ph].[125] S. Kanemura, N. Machida, S. Odori, and T. Shindou, “Diphoton excess at 750 GeV in an

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arXiv:1512.09159 [hep-ph].[130] A. Dasgupta, M. Mitra, and D. Borah, “Minimal Left-Right Symmetry Confronted with

the 750 GeV Di-photon Excess at LHC,” arXiv:1512.09202 [hep-ph].[131] D. Palle, “On the possible new 750 GeV heavy boson resonance at the LHC,”

arXiv:1601.00618 [physics.gen-ph].[132] S. Jung, J. Song, and Y. W. Yoon, “How Resonance-Continuum Interference Changes 750

GeV Diphoton Excess: Signal Enhancement and Peak Shift,” arXiv:1601.00006[hep-ph].

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[134] E. Palti, “Vector-Like Exotics in F-Theory and 750 GeV Diphotons,” arXiv:1601.00285[hep-ph].

[135] T. Nomura and H. Okada, “Four-loop Neutrino Model Inspired by Diphoton Excess at 750GeV,” arXiv:1601.00386 [hep-ph].

[136] X.-F. Han, L. Wang, L. Wu, J. M. Yang, and M. Zhang, “Explaining 750 GeV diphotonexcess from top/bottom partner cascade decay in two-Higgs-doublet model extension,”arXiv:1601.00534 [hep-ph].

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[142] T. Modak, S. Sadhukhan, and R. Srivastava, “750 GeV Diphoton excess from Gauged

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B � L Symmetry,” arXiv:1601.00836 [hep-ph].[143] B. Dutta, Y. Gao, T. Ghosh, I. Gogoladze, T. Li, Q. Shafi, and J. W. Walker, “Diphoton

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Intro: 750 GeV diphoton excess awakens!!

Toward explanation of LHC 750GeV excess in terms ofGlobal U(1) radiative neutrino model (with multiple

charged scalars)

Kenji Nishiwaki * †

School of Physics, Korea Institute for Advanced Study

Ver. 6 January 2016, (20h 07min in Korean ST)

In this writeup, I summarize relevant references on the recently observed LHC 750GeVexcess in the ATLAS and the CMS experiments.

The relevant references are [1–146].

References

[1] K. Harigaya and Y. Nomura, “Composite Models for the 750 GeV Diphoton Excess,”arXiv:1512.04850 [hep-ph].

[2] Y. Mambrini, G. Arcadi, and A. Djouadi, “The LHC diphoton resonance and darkmatter,” arXiv:1512.04913 [hep-ph].

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*e-mail: [email protected]†Based on discussions with S. Kanemura, H. Okada, Y. Orikasa, S. C. Park, R. Watanabe.

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[13] J. Ellis, S. A. R. Ellis, J. Quevillon, V. Sanz, and T. You, “On the Interpretation of aPossible ⇠ 750 GeV Particle Decaying into ��,” arXiv:1512.05327 [hep-ph].

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[17] C. Petersson and R. Torre, “The 750 GeV diphoton excess from the goldstinosuperpartner,” arXiv:1512.05333 [hep-ph].

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[19] A. Falkowski, O. Slone, and T. Volansky, “Phenomenology of a 750 GeV Singlet,”arXiv:1512.05777 [hep-ph].

[20] B. Dutta, Y. Gao, T. Ghosh, I. Gogoladze, and T. Li, “Interpretation of the diphotonexcess at CMS and ATLAS,” arXiv:1512.05439 [hep-ph].

[21] Q.-H. Cao, Y. Liu, K.-P. Xie, B. Yan, and D.-M. Zhang, “A Boost Test of AnomalousDiphoton Resonance at the LHC,” arXiv:1512.05542 [hep-ph].

[22] S. Matsuzaki and K. Yamawaki, “750 GeV Diphoton Signal from One-Family WalkingTechnipion,” arXiv:1512.05564 [hep-ph].

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750 GeV Diphoton Excess May Not Imply a 750 GeV Resonance,” arXiv:1512.06824[hep-ph].

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by a Resonant Sneutrino in R-parity Violating Supersymmetry,” arXiv:1512.07645[hep-ph].

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[97] J. A. Casas, J. R. Espinosa, and J. M. Moreno, “The 750 GeV Diphoton Excess as a FirstLight on Supersymmetry Breaking,” arXiv:1512.07895 [hep-ph].

[98] L. J. Hall, K. Harigaya, and Y. Nomura, “750 GeV Diphotons: Implications for

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Supersymmetric Unification,” arXiv:1512.07904 [hep-ph].[99] H. Han, S. Wang, and S. Zheng, “Dark Matter Theories in the Light of Diphoton Excess,”

arXiv:1512.07992 [hep-ph].[100] J.-C. Park and S. C. Park, “Indirect signature of dark matter with the diphoton resonance

at 750 GeV,” arXiv:1512.08117 [hep-ph].[101] A. Salvio and A. Mazumdar, “Higgs Stability and the 750 GeV Diphoton Excess,”

arXiv:1512.08184 [hep-ph].[102] D. Chway, R. Dermısek, T. H. Jung, and H. D. Kim, “Glue to light signal of a new

particle,” arXiv:1512.08221 [hep-ph].[103] G. Li, Y.-n. Mao, Y.-L. Tang, C. Zhang, Y. Zhou, and S.-h. Zhu, “A Loop-philic

Pseudoscalar,” arXiv:1512.08255 [hep-ph].[104] M. Son and A. Urbano, “A new scalar resonance at 750 GeV: Towards a proof of concept

in favor of strongly interacting theories,” arXiv:1512.08307 [hep-ph].[105] Y.-L. Tang and S.-h. Zhu, “NMSSM extended with vector-like particles and the diphoton

excess on the LHC,” arXiv:1512.08323 [hep-ph].[106] H. An, C. Cheung, and Y. Zhang, “Broad Diphotons from Narrow States,”

arXiv:1512.08378 [hep-ph].[107] J. Cao, F. Wang, and Y. Zhang, “Interpreting The 750 GeV Diphton Excess Within

TopFlavor Seesaw Model,” arXiv:1512.08392 [hep-ph].[108] F. Wang, W. Wang, L. Wu, J. M. Yang, and M. Zhang, “Interpreting 750 GeV Diphoton

Resonance in the NMSSM with Vector-like Particles,” arXiv:1512.08434 [hep-ph].[109] C. Cai, Z.-H. Yu, and H.-H. Zhang, “The 750 GeV diphoton resonance as a singlet scalar in

an extra dimensional model,” arXiv:1512.08440 [hep-ph].[110] Q.-H. Cao, Y. Liu, K.-P. Xie, B. Yan, and D.-M. Zhang, “The Diphoton Excess, Low

Energy Theorem and the 331 Model,” arXiv:1512.08441 [hep-ph].[111] J. E. Kim, “Is an axizilla possible for di-photon resonance?,” arXiv:1512.08467 [hep-ph].[112] J. Gao, H. Zhang, and H. X. Zhu, “Diphoton excess at 750 GeV: gluon-gluon fusion or

quark-antiquark annihilation?,” arXiv:1512.08478 [hep-ph].[113] W. Chao, “Neutrino Catalyzed Diphoton Excess,” arXiv:1512.08484 [hep-ph].[114] X.-J. Bi, R. Ding, Y. Fan, L. Huang, C. Li, T. Li, S. Raza, X.-C. Wang, and B. Zhu, “A

Promising Interpretation of Diphoton Resonance at 750 GeV,” arXiv:1512.08497[hep-ph].

[115] F. Goertz, J. F. Kamenik, A. Katz, and M. Nardecchia, “Indirect Constraints on the ScalarDi-Photon Resonance at the LHC,” arXiv:1512.08500 [hep-ph].

[116] L. A. Anchordoqui, I. Antoniadis, H. Goldberg, X. Huang, D. Lust, and T. R. Taylor, “750GeV diphotons from closed string states,” arXiv:1512.08502 [hep-ph].

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[119] L. E. Ibanez and V. Martin-Lozano, “A Megaxion at 750 GeV as a First Hint of Low ScaleString Theory,” arXiv:1512.08777 [hep-ph].

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[121] S. K. Kang and J. Song, “Top-phobic heavy Higgs boson as the 750 GeV diphoton

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resonance,” arXiv:1512.08963 [hep-ph].[122] Y. Hamada, T. Noumi, S. Sun, and G. Shiu, “An O(750) GeV Resonance and Inflation,”

arXiv:1512.08984 [hep-ph].[123] X.-J. Huang, W.-H. Zhang, and Y.-F. Zhou, “A 750 GeV dark matter messenger at the

Galactic Center,” arXiv:1512.08992 [hep-ph].[124] S. Kanemura, K. Nishiwaki, H. Okada, Y. Orikasa, S. C. Park, and R. Watanabe, “LHC

750 GeV Diphoton excess in a radiative seesaw model,” arXiv:1512.09048 [hep-ph].[125] S. Kanemura, N. Machida, S. Odori, and T. Shindou, “Diphoton excess at 750 GeV in an

extended scalar sector,” arXiv:1512.09053 [hep-ph].[126] A. E. C. Hernandez, “The 750 GeV diphoton resonance can cause the SM fermion mass

and mixing pattern,” arXiv:1512.09092 [hep-ph].[127] Y. Jiang, Y.-Y. Li, and T. Liu, “750 GeV Resonance in the Gauged U(1)0-Extended

MSSM,” arXiv:1512.09127 [hep-ph].[128] K. Kaneta, S. Kang, and H.-S. Lee, “Diphoton excess at the LHC Run 2 and its

implications for a new heavy gauge boson,” arXiv:1512.09129 [hep-ph].[129] E. Ma, “Diphoton Revelation of the Utilitarian Supersymmetric Standard Model,”

arXiv:1512.09159 [hep-ph].[130] A. Dasgupta, M. Mitra, and D. Borah, “Minimal Left-Right Symmetry Confronted with

the 750 GeV Di-photon Excess at LHC,” arXiv:1512.09202 [hep-ph].[131] D. Palle, “On the possible new 750 GeV heavy boson resonance at the LHC,”

arXiv:1601.00618 [physics.gen-ph].[132] S. Jung, J. Song, and Y. W. Yoon, “How Resonance-Continuum Interference Changes 750

GeV Diphoton Excess: Signal Enhancement and Peak Shift,” arXiv:1601.00006[hep-ph].

[133] C. T. Potter, “Pseudoscalar Gluinonia to Diphotons at the LHC,” arXiv:1601.00240[hep-ph].

[134] E. Palti, “Vector-Like Exotics in F-Theory and 750 GeV Diphotons,” arXiv:1601.00285[hep-ph].

[135] T. Nomura and H. Okada, “Four-loop Neutrino Model Inspired by Diphoton Excess at 750GeV,” arXiv:1601.00386 [hep-ph].

[136] X.-F. Han, L. Wang, L. Wu, J. M. Yang, and M. Zhang, “Explaining 750 GeV diphotonexcess from top/bottom partner cascade decay in two-Higgs-doublet model extension,”arXiv:1601.00534 [hep-ph].

[137] P. Ko, Y. Omura, and C. Yu, “Diphoton Excess at 750 GeV in leptophobic U(1)0 modelinspired by E6 GUT,” arXiv:1601.00586 [hep-ph].

[138] K. Ghorbani and H. Ghorbani, “The 750 GeV Diphoton Excess from a Pseudoscalar inFermionic Dark Matter Scenario,” arXiv:1601.00602 [hep-ph].

[139] U. Danielsson, R. Enberg, G. Ingelman, and T. Mandal, “The force awakens - the 750 GeVdiphoton excess at the LHC from a varying electromagnetic coupling,” arXiv:1601.00624[hep-ph].

[140] W. Chao, “The Diphoton Excess from an Exceptional Supersymmetric Standard Model,”arXiv:1601.00633 [hep-ph].

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[142] T. Modak, S. Sadhukhan, and R. Srivastava, “750 GeV Diphoton excess from Gauged

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B � L Symmetry,” arXiv:1601.00836 [hep-ph].[143] B. Dutta, Y. Gao, T. Ghosh, I. Gogoladze, T. Li, Q. Shafi, and J. W. Walker, “Diphoton

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Toward explanation of LHC 750GeV excess in terms ofGlobal U(1) radiative neutrino model (with multiple

charged scalars)

Kenji Nishiwaki * †

School of Physics, Korea Institute for Advanced Study

Ver. 6 January 2016, (20h 07min in Korean ST)

In this writeup, I summarize relevant references on the recently observed LHC 750GeVexcess in the ATLAS and the CMS experiments.

The relevant references are [1–146].

References

[1] K. Harigaya and Y. Nomura, “Composite Models for the 750 GeV Diphoton Excess,”arXiv:1512.04850 [hep-ph].

[2] Y. Mambrini, G. Arcadi, and A. Djouadi, “The LHC diphoton resonance and darkmatter,” arXiv:1512.04913 [hep-ph].

[3] M. Backovic, A. Mariotti, and D. Redigolo, “Di-photon excess illuminates Dark Matter,”arXiv:1512.04917 [hep-ph].

[4] A. Angelescu, A. Djouadi, and G. Moreau, “Scenarii for interpretations of the LHCdiphoton excess: two Higgs doublets and vector-like quarks and leptons,”arXiv:1512.04921 [hep-ph].

[5] Y. Nakai, R. Sato, and K. Tobioka, “Footprints of New Strong Dynamics via Anomaly,”arXiv:1512.04924 [hep-ph].

[6] S. Knapen, T. Melia, M. Papucci, and K. Zurek, “Rays of light from the LHC,”arXiv:1512.04928 [hep-ph].

[7] D. Buttazzo, A. Greljo, and D. Marzocca, “Knocking on New Physics’ door with a ScalarResonance,” arXiv:1512.04929 [hep-ph].

[8] A. Pilaftsis, “Diphoton Signatures from Heavy Axion Decays at LHC,” arXiv:1512.04931[hep-ph].

[9] R. Franceschini, G. F. Giudice, J. F. Kamenik, M. McCullough, A. Pomarol, R. Rattazzi,M. Redi, F. Riva, A. Strumia, and R. Torre, “What is the gamma gamma resonance at 750GeV?,” arXiv:1512.04933 [hep-ph].

[10] S. Di Chiara, L. Marzola, and M. Raidal, “First interpretation of the 750 GeV di-photonresonance at the LHC,” arXiv:1512.04939 [hep-ph].

[11] T. Higaki, K. S. Jeong, N. Kitajima, and F. Takahashi, “The QCD Axion from AlignedAxions and Diphoton Excess,” arXiv:1512.05295 [hep-ph].

[12] S. D. McDermott, P. Meade, and H. Ramani, “Singlet Scalar Resonances and the DiphotonExcess,” arXiv:1512.05326 [hep-ph].

*e-mail: [email protected]†Based on discussions with S. Kanemura, H. Okada, Y. Orikasa, S. C. Park, R. Watanabe.

1

~150 papers already arose.

Intro: misc. on the excess

Both of ATLAS and CMS reported the bump around 750GeV.

The diphoton channel would look clean, then reliable(!?).

In terms of signal strength:

1 Introduction

Very recently, both of the ATLAS and CMS experiments announced the observation of a newresonance around 750GeV as a bump in the diphoton invariant mass spectrum from the run-II datain

ps = 13TeV [1, 2]. Their results are based on the accumulated data of 3.2 fb�1 (ATLAS) and

2.6 fb�1 (CMS), and local/global significances are 3.9�/2.3� (ATLAS) and 2.6�/ . 1.2� (CMS),respectively. The best-fit values of the invariant mass are 750GeV by ATLAS and 760GeV byCMS, where the ATLAS also reported the best-fit value of the total width as 45GeV. After theadvent of the announcement, various ways for explaining the 750GeV excess have been proposedin Refs. [3–120]. An interpretation of the excess in terms of the signal strength of a scalar (or apseudoscalar) resonance S, pp ! S + X ! �� + X, was done in Ref. [9] based on the expectedand observed exclusion limits. The authors claimed,

µATLAS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (6.2+2.4�2.0) fb, (1.1)

µCMS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (5.6± 2.4) fb, (1.2)

with a Poissonian likelihood function (for the ATLAS measurement) and the Gaussian approxi-mation (for the CMS measurement), respectively.

On the other hand, both of the ATLAS and CMS groups reported that no significant excessover the standard model (SM) background was observed in their analyses based on the run-I dataat

ps = 8TeV [121, 122], while a mild upward bump was found in their data around 750GeV. In

Ref. [9], the signal strengths atps = 8TeV were extracted by use of the corresponding expected

and observed exclusion limits given by the experiments, in the Gaussian approximation, as

µATLAS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.46± 0.85) fb, (1.3)

µCMS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.63± 0.25) fb. (1.4)

It is mentioned that when we upgrade the collider energy from 8TeV to 13TeV, a factor 4.7enhancement is expected [9, 123], when the resonant particle is produced via gluon fusion, andthen the data at

ps = 8TeV and 13TeV are compatible at around 2� confidence level (C.L.).

These observations would give us a stimulating hint for surveying the structure of physics beyondthe SM above the electroweak scale even though the accumulated amount of the data would notbe enough for detailed discussions and the errors are large at the present stage.

A key point to understand the resonance is the fact that no bump around 750GeV has beenfound in the other final states in both of the 8TeV and 13TeV data. If B(S ! ��) is the same asthe 750GeV Higgs one, B(h ! ��)|

750GeVSM

= 1.79⇥10�7 [124], we can immediately recognize thatsuch a possibility is inconsistent with the observed results, e.g., in ZZ final state, at

ps = 8TeV,

where the experimental 95% C.L. limits on the ZZ channel are 22 fb by ATLAS [125], 27 fb byCMS [126], and the branching ratio B(h ! ZZ)|

750GeVSM

= 0.290 [124]. In general, the processS ! �� should be loop induced since S has zero electromagnetic charge and then the value ofB(S ! ��) tends to be suppressed because tree level decay branches generate primary componentsof the total width of S. Then, a reasonable setup for explaining the resonance consistently is thatall of the decay channels of S are one loop induced, where S would be a gauge singlet underSU(3)C and SU(2)L since a non-singlet gauge assignment leads to a tree level gauge interaction.

An example of this direction is that S is a singlet scalar and it couples to vector-like quarks,which contribute to both of pp ! S + X and S ! �� via gluon fusion and photon fusion,respectively. In such a possibility, a typical digit of B(S ! ��) is ⇠ 1%. On the other hand,when B(S ! ��) is O(10)%, another direction for generating S at the one loop level opens up

1

1 Introduction




µATLAS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (6.2+2.4�2.0) fb, (1.1)

µCMS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (5.6± 2.4) fb, (1.2)






µATLAS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.46± 0.85) fb, (1.3)

µCMS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.63± 0.25) fb. (1.4)





750GeVSM


ps = 8TeV,


750GeVSM



1

[ATLAS-CONF-2015-081, CMS-PAS-EXO-15-004]

[CERN-PH-EP-2015-043, CMS-PAS-HIG-14-006]

[Buttazzo,Greljo,Marzocca, arXiv:1512.04929]

looks compatibleat around 2σ


Both of ATLAS and CMS reported the bump around 750GeV.

The diphoton channel would look clean, then reliable(!?).

In terms of signal strength:

1 Introduction




µATLAS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (6.2+2.4�2.0) fb, (1.1)

µCMS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (5.6± 2.4) fb, (1.2)






µATLAS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.46± 0.85) fb, (1.3)

µCMS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.63± 0.25) fb. (1.4)





750GeVSM


ps = 8TeV,


750GeVSM



1

1 Introduction




µATLAS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (6.2+2.4�2.0) fb, (1.1)

µCMS

13TeV

= �(pp ! S +X)13TeV

⇥ B(S ! ��) = (5.6± 2.4) fb, (1.2)






µATLAS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.46± 0.85) fb, (1.3)

µCMS

8TeV

= �(pp ! S +X)8TeV

⇥ B(S ! ��) = (0.63± 0.25) fb. (1.4)





750GeVSM


ps = 8TeV,


750GeVSM



1

[ATLAS-CONF-2015-081, CMS-PAS-EXO-15-004]

[CERN-PH-EP-2015-043, CMS-PAS-HIG-14-006]

looks compatibleat around 2σ

No excess is found in the other channels (ZZ, Zγ, ll, jj, ...)

ATLAS best-fit value of ΓS = 45GeV (ΓS /mS ≈ 6%)

Via 8TeV LHC bounds, they should not be so large

sizable

!?!?!?looks very exotic...

Kenji Nishiwaki (KIAS) 2/7Small ΓS would be OK at the current stage.

[Buttazzo,Greljo,Marzocca, arXiv:1512.04929]

[GeV]γγm200 400 600 800 1000 1200 1400 1600

Even

ts /

40 G

eV

1−10

1

10

210

310

410ATLAS Preliminary

-1 = 13 TeV, 3.2 fbs

Data

Background-only fit

[GeV]γγm200 400 600 800 1000 1200 1400 1600

Dat

a - f

itted

bac

kgro

und

15−10−

5−05

1015

Figure 1: Invariant mass distribution of the selected diphoton events. Residual number of events with respect to thefit result are shown in the bottom pane. The first two bins in the lower pane are outside the vertical plot range.

The events in this region are scrutinized. No detector or reconstruction e�ect that could explain the largerrate is found, nor any indication of anomalous background contamination. The kinematic properties ofthese events are studied with respect to those of events populating the invariant mass regions above andbelow the excess, and no significant di�erence is observed.

The Run-1 analysis presented in Ref. [13] is extended to invariant masses larger than 600 GeV by using thenew background modeling techniques presented in this note (cf. Section 7). The compatibility betweenthe results obtained with the 8 TeV and 13 TeV datasets is estimated under the NWA hypothesis andassuming a large-width resonance with ↵ = 6%, using the best fit value of the ratio of cross sections. Foran s-channel gluon-initiated process, the parton-luminosity ratio is expected to be 4.7 [43]. Under thoseassumptions, the results obtained with the two datasets are found to be compatible within 2.2 and 1.4standard deviations for the two width hypotheses respectively.

The 95% CL expected and observed upper limits on �fiducial⇥BR(X ! ��), corresponding to the fiducialvolume defined in Section 6, are computed using the CLs technique [39, 44] for a scalar resonance withnarrow width as a function of the mass hypothesis mX , and are presented in Figure 3. The larger diphotonrate in the mass region around 750 GeV is translated to a higher-than-expected cross section limit at the

13

Intro: misc. on the excess

Intro: basic setups for explanation[an ordinary type]

production: gluon fusion (decay: photon fusion)

p

p

g

g

S S

�

�New particles fly in the loops

for enhancement(e.g., vector-like quark)

[McDermott,Meade,Ramani, arXiv:1512.05326], many others


singlet scalar

[an ordinary type]

[another type: (when B(S→γγ) = O(10)%)]

production: gluon fusion (decay: photon fusion)

p

p

g

g

S S

�

�New particles fly in the loops

for enhancement(e.g., vector-like quark)

production: photon fusion (decay: photon fusion)

p

p

S S

�

�new charged particles

for enhancement

�

�

Statement: radiative seesaw model isa reasonable setup to realize this scenario.Kenji Nishiwaki (KIAS) 3/7

Colored new particle

is not required.

p

p

We considerthe elastic scattering only

(cleaner than inelastic ones)

singlet scalar

[McDermott,Meade,Ramani, arXiv:1512.05326], many others

[Fichet,von Gersdorff,Royon, arXiv:1512.05751][Csaki,Hubisz,Terning, arXiv:1512.05776][Csaki,Hubisz,Lombardo,Terning, arXiv:1601.00638]

Intro: basic setups for explanation

Kenji Nishiwaki (KIAS)

Contents

0. Introduction (finished)

1. Prospects in radiative seesaw model

Summary & Discussion

-/7

Model Setup

via photon fusion discussed in Refs. [32, 38]. When a model contains SU(2)L singlet particleswith large U(1)Y hypercharges, the magnitude of the photon fusions in the production and decaysequences is enhanced and we can accommodate the 750GeV excess.

In this paper, we focus on the radiative seesaw models [127–131], especially where neutrinomasses are generated at the three loop level [132–149]. In such type of scenarios, multiple chargedscalars are introduced for realizing three-loop origin of the neutrino mass, (distinctively fromthe models with one or two loops). We show that when these charged scalars couple to thesinglet S strongly enough, we can achieve a reasonable amount of the production cross sectionin pp ! S + X ! �� + X through photon fusion. Concretely, we start from the three loopmodel [146], and extend the model with additional charged scalars to explain the data.

This paper is organized as follows. In Sec. 2, we introduce our model based on the model forthree-loop induced neutrino masses. In Sec. 3, we show detail of analysis and numerical results.In Sec. 4, we are devoted to summary and discussions.

2 Model

Multiple (doubly) charged particles would induce a large radiative coupling with a singlet scalarS with �� via one-loop diagrams. We may find the source from multi-Higgs models or extradimensions [150–167] but here we focus on a model for radiative neutrino masses recently suggestedby some of the authors [146] as a benchmark model, which can be extended with a singlet scalarS for the 750 GeV resonance.

2.1 Review: A model for three-loop induced neutrino mass

Our strategy is based on the three loop induced radiative neutrino model with a U(1) globalsymmetry [146], where we introduce three Majorana fermions NR

1,2,3 and new bosons; one gauge-singlet neutral boson ⌃

0

, two singly charged singlet scalars (h±1

, h±2

), and one gauge-singlet doublycharged boson k±± to the SM. The particle contents and their charges are shown in Table 1.

Lepton Fields Scalar Fields New Scalar FieldsCharacters LLi eRi NRi � ⌃

0

h+

1

h+

2

k++ j++

a SSU(3)C 1 1 1 1 1 1 1 1 1 1SU(2)L 2 1 1 2 1 1 1 1 1 1U(1)Y �1/2 �1 0 1/2 0 1 1 2 2 0U(1) 0 0 �x 0 2x 0 x 2x 2x 0

Table 1: Contents of lepton and scalar fields and their charge assignment under SU(3)C⇥SU(2)L⇥U(1)Y ⇥U(1), where U(1) is an additional global symmetry and x 6= 0. The subscripts found in thelepton fields i (= 1, 2, 3) indicate generations of the fields. The bold letters emphasize that thesenumbers correspond to representations of the Lie groups of the NonAbelian gauge interactions.The scalar particles shown in the right category (New Scalar Fields) are added to the originalmodel proposed in Ref. [146] to explain the 750GeV excess.

We assume that only the SM-like Higgs � and the additional neutral scalar ⌃0

have VEVs,which are symbolized as h�i ⌘ v/

p2 and h⌃

0

i ⌘ v0/p2, respectively. x ( 6= 0) is an arbitrary

number of the charge of the hidden U(1) symmetry, and under the assignments, neutrino massmatrix is generated at the three loop level, where a schematic picture is shown in Fig. 1. Note

2

SM leptons

SMHiggs

global U(1)flavor sym.

negative parityremains after U(1) breaking

(lightest one → DM)

origin ofbreakdown of global U(1)

(including pseudo NG boson)

that a remnant Z2

symmetry remains after the hidden U(1) symmetry breaking and the particlesNR

1,2,3 and h±2

have negative parities. Then, when a Majorana neutrino is the lightest among them,it becomes a dark matter (DM) candidate and the stability is accidentally ensured.

⌫L ⌫L`L `LeR eRNR NR

h+2 h+

2

k++h+1 h+

1

h⌃0i

(, j++a )

Figure 1: A schematic description for the radiative generation of neutrino masses.

In the original model, the Lagrangian of Yukawa sector LY and scalar potential V , allowedunder the gauge and global symmetries, are given as

�LY = (y`)ijLLi�eRj +1

2(yL)ijL

cLiLLjh

+

1

+ (yR)ijNRiecRjh�2

+1

2(yN)ij⌃0

N cRiNRj + h.c., (2.1)

V = m2

�

|�|2 +m2

⌃

|⌃0

|2 +m2

h1

|h+

1

|2 +m2

h2

|h+

2

|2 +m2

k|k++|2

+h

�11

⌃⇤0

h�1

h�1

k++ + µ22

h+

2

h+

2

k�� + h.c.i

+ ��

|�|4 + ��⌃

|�|2|⌃0

|2 + ��h

1

|�|2|h+

1

|2

+ ��h

2

|�|2|h+

2

|2 + ��k|�|2|k++|2 + �

⌃

|⌃0

|4 + �⌃h

1

|⌃0

|2|h+

1

|2 + �⌃h

2

|⌃0

|2|h+

2

|2+ �

⌃k|⌃0

|2|k++|2 + �h1

|h+

1

|4+�h1

h2

|h+

1

|2|h+

2

|2 + �h1

k|h+

1

|2|k++|2+ �h

2

|h+

2

|4 + �h2

k|h2

|2|k++|2 + �k|k++|4, (2.2)

where the indices i, j indicate matter generations and the superscript “c” means charge conjugation(with the SU(2)L rotation by i�

2

for SU(2)L doublets). We assume that yN is diagonal, wherethe right-handed neutrino masses are calculated as MNi = v0p

2

(yN)ii with the assumed ordering

MN1

(= DM mass) < MN2

< MN3

. The neutral scalar fields are shown in the Unitary gauge as

� =

0v+�p

2

�

, ⌃0

=v0 + �p

2eiG/v0 , (2.3)

with v ' 246GeV and an associated Nambu-Goldstone (NG) boson G via the global U(1) breakingdue to the occurrence of nonzero v0. Requiring the tadpole conditions, @V/@�|�=v = @V/@�|�=v0 =0, the resultant mass matrix squared of the CP even components (�, �) is given by

m2(�, �) =

2��

v2 ��⌃

vv0

��⌃

vv0 2�⌃

v02

�

=

cos↵ sin↵� sin↵ cos↵

�

m2

h 00 m2

H

�

cos↵ � sin↵sin↵ cos↵

�

, (2.4)

where h is the SM-like Higgs (mh = 125GeV) and H is an additional CP even Higgs masseigenstate. The mixing angle ↵ is determined as

sin 2↵ =2�

�⌃

vv0

m2

H �m2

h

. (2.5)

3

doubly-charged scalarsfor enhancing loop effect

candidate for750GeV excess

[Kanemura,KN,Okada,Orikasa,Park,Watanabe, arXiv:1512.09048], [KN,Okada,Orikasa, arXiv:1507.02412]

[3-loop ν mass]

ν mass: naturally explained

DM is found. Relic is explained.

k±± has no direct coupling to leptons: - less lepton flavor violation, - can be light as ~300GeV

S

k++, j++a

k��, j��a

These trilinear couplingscontribute to S ⇔ γγ.

[note: a huge trilinearcoupling leads to

violation of tree-levelunitarity.]


DM

S Production through Photon Fusion

The two functions f(z) and g(z) (z ⌘ x�1 or y�1) are formulated as

f(z) = arcsin2

pz for z 1, (3.6)

g(z) =pz�1 � 1 arcsin

pz for z 1, (3.7)

where the situation mS 2mk±± , mZ 2mk±± corresponds to z 1. For simplicity, we assumethe relation

µSk = µSja , (3.8)

for all a.For the production of S corresponding to the 750GeV resonance, we consider the photon

fusion process, as recently discussed in Refs. [32, 38]. In the following part, the general formulationdiscussed in Ref. [38] is introduced. The resonant parton-level cross section of the process A+B !S ! C +D is generally formulated as

�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)

where the factors (2J+1) show spin multiplicities of the initial and the resonant states. The factortakes 2 (1) for the initial photons (the scalar resonance), respectively. By adopting the narrowwidth approximation (NWA) and e↵ective photon approximation, the cross section is given withthe convolution with the photon parton distribution function (PDF) f�

s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)

with the two parton fractions x1,2 with s = x

1

x2

s at the first line. At the second line, we integratedthe delta function originating from NWA. x

min

and xmax

represent the lower and upper values ofthe range of the integral.

Besides, we adopt the equivalent photon (or Weizsacker–Williams) approximation [174, 175]which gives the dominant contribution to the photon PDF in the diphoton production process forsmall x as [176, 177]

f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)

where mp (= 938.272MeV) is the proton mass [178], and q⇤ ⇠ O(100) MeV shows the inverse ofthe minimum impact parameter for elastic scattering, naively it being the radius of the proton.We take q⇤ = (130� 170)MeV in our numerical analysis below. Now, we can exactly execute theintegration over x and obtain the result,

�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)

with r⇤ ⌘ q⇤/mp and rm ⌘ mS/ps. For a scalar resonance (JS = 0) with mS = 750GeV and

q⇤ = (130� 170)MeV, we obtain the following values

�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6

[general formula]


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6

spin of S

proton mass(minimum) impact parameter (uncertainty contained)


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6[branching ratio of S]

can contribute to the three-loop induced neutrino masses shown in Fig. 1. The trilinear termsin the square brackets are required for evading the stability of j±±

a . Here for brevity, we simplyignore the possible terms allowed by the symmetries, such as |j++

a |2|�|2, |j++

a |2|⌃0

|2, S|�|2, S|⌃0

|2in Eq. (2.8). A large VEV of S generates large e↵ective trilinear couplings µSk and µSja throughthe original terms S2|k++| and S2|j++

a |, respectively even when the dimensionless coe�cients �Sk

and �Sja are not so large.

3 Analysis

3.1 Formulation of p(�)p(�) ! S +X ! �� +X

Note that under the assumption that additional interactions are only ones shown in Eq. (2.9),possible decay branches of S up to the one-loop level is to ��, Z�, ZZ and k++k�� or j++

a j��a .

We assume that mk±± and mj±±a

are greater than mS/2 (= 375GeV), where the last two decaychannels at the tree level are closed kinematically. In the present case that no tree-level decaybranch is open and only SU(2)L singlet charged scalars describe the loop-induced partial widths,the relative strengths among �S!��, �S!Z�, �S!ZZ and �S!W+W� are governed by quantumnumbers at the one-loop level1 as

�S!�� : �S!Z� : �S!ZZ : �S!W+W� ⇡ 1 : 2

✓

s2Wc2W

◆

:

✓

s4Wc4W

◆

: 0. (3.1)

In the following, we calculate �S!ZZ in a simplified way of �S!ZZ ⇡ s2W/(2c2W )�S!Z� ' 0.15�S!Z�.Here, we represent a major part of partial decay widths of S with our notation for loop functions

with the help of Refs. [169–173]. In the following part, for simplicity, we set all the masses of thedoubly charged scalars mj±±

aas the same as mk±± , while we ignore the contributions from the two

singly charged scalars h±1,2 since they should be heavy as at least around 3TeV and decoupled as

mentioned in Appendix. The concrete form of �S!�� and �S!Z� are given as

�S!�� =↵2

EM

m3

S

256⇡3

�

�

�

�

1

2

v

m2

k±±Q2

kCSkkA��0

(⌧k)

�

�

�

�

2

, (3.2)

�S!Z� =↵2

EM

m3

S

512⇡3

✓

1� m2

Z

m2

S

◆

3

�

�

�

�

� v

m2

k±±(2QkgZkk)CSkkA

Z�0

(⌧k,�k)

�

�

�

�

2

, (3.3)

with

CSkk =

✓

1

v

◆

2

4µSk +

NjX

a=1

µSja

3

5 , gZkk = �Qk

✓

sWcW

◆

, ⌧k =4m2

k±±

m2

S

, �k =4m2

k±±

m2

Z

. (3.4)

Qk (= 2) is the electric charge of the doubly charged scalars in unit of the positron’s one. cW andsW are the cosine and the sine of the Weinberg angle ✓W , respectively. ↵

EM

is the electromagneticfine structure constant. In the following calculation, we use s2W = 0.23120 and ↵

EM

= 1/127.916.The loop factors take the following forms,

A��0

(x) = �x2

⇥

x�1 � f(x�1)⇤

,

AZ�0

(x, y) =xy

2(x� y)+

x2y2

2(x� y)2⇥

f(x�1)� f(y�1)⇤

+x2y

(x� y)2⇥

g(x�1)� g(y�1)⇤

, (3.5)

1The branching fractions are easily understood in an e↵ective theory with the standard model gauge symmetries.See e.g. [168] with s2 = 0 in the paper.

5

3.2 Results

Under our assumptions, the relevant parameters are (mk±± , µSk, Nj): the universal physical massof the doubly charged scalars, the universal e↵ective scalar trilinear coupling, and the number ofthe additional doubly charged singlet scalars. We observe the unique relation among the branchingratios of S irrespective of mk±± and µSk, which is suggest by Eq. (3.1), as

B(S ! ��) ' 0.591, B(S ! �Z) ' 0.355, B(S ! ZZ) ' 0.0535. (3.14)

In Fig. 2, situations in our model are summarized. The blue and red curves show the pointsof {mk±± , µSk} predicting �S = 45GeV and �S = 5.3GeV, respectively. The value 45GeV isthe best-fit value of �S reported from the ATLAS experiment [1], while the value 5.3GeV is theexperimental resolution ��

E used in the analysis of [14]. Six cases with di↵erent numbers of doublycharged scalars are considered with Nj = 0, 1, 10, 100, 500 and 1000.

As pointed out in Eq. (3.14), the value of B(S ! ��) is uniquely fixed as ' 60% in thepresent model. From the values in Eqs. (1.1) and (1.2), we set our target cross section �(pp !S +X ! �� +X) at the

ps = 13TeV LHC as 2 ⇠ 10 fb within a 2� confidence level from the

central value ' 6 fb. The green regions in Fig. 2 indicate the areas where we obtain the centralvalue (6 fb) at

ps = 13TeV in the production cross section of p(�)p(�) ! S +X ! �� +X with

varying the parameter q⇤ from 130MeV to 170MeV, which is related to the two choices of thefactorization scale of the photon PDF [defined in Eq. (3.11)] discussed in Ref. [38]. The upper andlower boundaries correspond to the cases of q⇤ = 130MeV and q⇤ = 170MeV, respectively. On theother hand, the yellow regions, on which the green regions are superimposed, show the area wherewe obtain the 0.6 fb cross section at

ps = 8TeV.

Also, we report that when we consider the case with q⇤ = 170MeV, the total width �S shouldbe within [1.59GeV, 7.95GeV] to realize the cross section within 2 ⇠ 10 fb from Eq. (3.13). On theother hand in q⇤ = 130MeV, the favored range of �S is [3.53GeV, 17.6GeV] from Eq. (3.13) if thecross section is within 2 ⇠ 10 fb. We find a tension with the ATLAS best fit value �S = 45GeV inour scenario, which is apparently suggested from panels in Fig. 2.2 From now on, our target valuein �S is set as 5.3GeV.

2When �S = 45GeV, from Eq. (3.13), the target value of B(S ! �� +X) to realize �(p(�)p(�) ! S +X !�� +X) = 6 fb becomes 0.192 (when q⇤ = 170MeV) and 0.287 (when q⇤ = 130MeV).

7

Quantum numbers determine the ratios.(They are universal, not sensitive to

number of Ja±±, S ⇔ Ja±± trilinear couplings)

dominant! subdominant.8TeV LHC constraint is no problem.

[ATLAS, arXiv:1407.8150]


sizable σ when B(S→γγ), ΓS arereasonably large.

[Csaki,Hubisz,Terning, arXiv:1512.05776]

S Production through Photon Fusion


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6

[general formula]


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6

spin of S

proton mass(minimum) impact parameter (uncertainty contained)


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6


f(z) = arcsin2

pz for z 1, (3.6)


pz for z 1, (3.7)


µSk = µSja , (3.8)



�(s) = 32⇡2JS + 1

(2JA + 1)(2JB + 1)

�AB�CD

(s�m2

S)2 +m2

S�2

S

, (3.9)


s (x) at s = E2

CM

as

�(p(�)p(�) ! S +X ! �� +X) =

Z

dx1

dx2

f�s (x1

)f�s (x2

)�(x1

x2

s)

=8⇡2�S

smS

B2(S ! ��)(2JS + 1)

Z xmax

xmin

dx

xf�s (x)f

�s

✓

m2

S

xs

◆

,

(3.10)


1

x2


min

and xmax



f�s (x) =

1

x

2↵EW

⇡log

q⇤mp

1

x

�

, (3.11)


�(p(�)p(�) ! S +X ! �� +X) =128↵2

EW

�S

3m3

S

B2(S ! ��)(2JS + 1) log3

r⇤rm

�

, (3.12)



�(pp ! S +X ! �� +X) =

✓

�S

45GeV

◆

⇥ B2(S ! ��)⇥(

(6.5� 31)fb ,ps = 8 TeV,

(73� 162)fb ,ps = 13 TeV.

(3.13)

6[branching ratio of S]

can contribute to the three-loop induced neutrino masses shown in Fig. 1. The trilinear termsin the square brackets are required for evading the stability of j±±

a . Here for brevity, we simplyignore the possible terms allowed by the symmetries, such as |j++

a |2|�|2, |j++

a |2|⌃0

|2, S|�|2, S|⌃0

|2in Eq. (2.8). A large VEV of S generates large e↵ective trilinear couplings µSk and µSja throughthe original terms S2|k++| and S2|j++

a |, respectively even when the dimensionless coe�cients �Sk

and �Sja are not so large.

3 Analysis

3.1 Formulation of p(�)p(�) ! S +X ! �� +X

Note that under the assumption that additional interactions are only ones shown in Eq. (2.9),possible decay branches of S up to the one-loop level is to ��, Z�, ZZ and k++k�� or j++

a j��a .

We assume that mk±± and mj±±a

are greater than mS/2 (= 375GeV), where the last two decaychannels at the tree level are closed kinematically. In the present case that no tree-level decaybranch is open and only SU(2)L singlet charged scalars describe the loop-induced partial widths,the relative strengths among �S!��, �S!Z�, �S!ZZ and �S!W+W� are governed by quantumnumbers at the one-loop level1 as

�S!�� : �S!Z� : �S!ZZ : �S!W+W� ⇡ 1 : 2

✓

s2Wc2W

◆

:

✓

s4Wc4W

◆

: 0. (3.1)

In the following, we calculate �S!ZZ in a simplified way of �S!ZZ ⇡ s2W/(2c2W )�S!Z� ' 0.15�S!Z�.Here, we represent a major part of partial decay widths of S with our notation for loop functions

with the help of Refs. [169–173]. In the following part, for simplicity, we set all the masses of thedoubly charged scalars mj±±

aas the same as mk±± , while we ignore the contributions from the two

singly charged scalars h±1,2 since they should be heavy as at least around 3TeV and decoupled as

mentioned in Appendix. The concrete form of �S!�� and �S!Z� are given as

�S!�� =↵2

EM

m3

S

256⇡3

�

�

�

�

1

2

v

m2

k±±Q2

kCSkkA��0

(⌧k)

�

�

�

�

2

, (3.2)

�S!Z� =↵2

EM

m3

S

512⇡3

✓

1� m2

Z

m2

S

◆

3

�

�

�

�

� v

m2

k±±(2QkgZkk)CSkkA

Z�0

(⌧k,�k)

�

�

�

�

2

, (3.3)

with

CSkk =

✓

1

v

◆

2

4µSk +

NjX

a=1

µSja

3

5 , gZkk = �Qk

✓

sWcW

◆

, ⌧k =4m2

k±±

m2

S

, �k =4m2

k±±

m2

Z

. (3.4)

Qk (= 2) is the electric charge of the doubly charged scalars in unit of the positron’s one. cW andsW are the cosine and the sine of the Weinberg angle ✓W , respectively. ↵

EM

is the electromagneticfine structure constant. In the following calculation, we use s2W = 0.23120 and ↵

EM

= 1/127.916.The loop factors take the following forms,

A��0

(x) = �x2

⇥

x�1 � f(x�1)⇤

,

AZ�0

(x, y) =xy

2(x� y)+

x2y2

2(x� y)2⇥

f(x�1)� f(y�1)⇤

+x2y

(x� y)2⇥

g(x�1)� g(y�1)⇤

, (3.5)

1The branching fractions are easily understood in an e↵ective theory with the standard model gauge symmetries.See e.g. [168] with s2 = 0 in the paper.

5

3.2 Results

Under our assumptions, the relevant parameters are (mk±± , µSk, Nj): the universal physical massof the doubly charged scalars, the universal e↵ective scalar trilinear coupling, and the number ofthe additional doubly charged singlet scalars. We observe the unique relation among the branchingratios of S irrespective of mk±± and µSk, which is suggest by Eq. (3.1), as

B(S ! ��) ' 0.591, B(S ! �Z) ' 0.355, B(S ! ZZ) ' 0.0535. (3.14)

In Fig. 2, situations in our model are summarized. The blue and red curves show the pointsof {mk±± , µSk} predicting �S = 45GeV and �S = 5.3GeV, respectively. The value 45GeV isthe best-fit value of �S reported from the ATLAS experiment [1], while the value 5.3GeV is theexperimental resolution ��

E used in the analysis of [14]. Six cases with di↵erent numbers of doublycharged scalars are considered with Nj = 0, 1, 10, 100, 500 and 1000.

As pointed out in Eq. (3.14), the value of B(S ! ��) is uniquely fixed as ' 60% in thepresent model. From the values in Eqs. (1.1) and (1.2), we set our target cross section �(pp !S +X ! �� +X) at the

ps = 13TeV LHC as 2 ⇠ 10 fb within a 2� confidence level from the

central value ' 6 fb. The green regions in Fig. 2 indicate the areas where we obtain the centralvalue (6 fb) at

ps = 13TeV in the production cross section of p(�)p(�) ! S +X ! �� +X with

varying the parameter q⇤ from 130MeV to 170MeV, which is related to the two choices of thefactorization scale of the photon PDF [defined in Eq. (3.11)] discussed in Ref. [38]. The upper andlower boundaries correspond to the cases of q⇤ = 130MeV and q⇤ = 170MeV, respectively. On theother hand, the yellow regions, on which the green regions are superimposed, show the area wherewe obtain the 0.6 fb cross section at

ps = 8TeV.

Also, we report that when we consider the case with q⇤ = 170MeV, the total width �S shouldbe within [1.59GeV, 7.95GeV] to realize the cross section within 2 ⇠ 10 fb from Eq. (3.13). On theother hand in q⇤ = 130MeV, the favored range of �S is [3.53GeV, 17.6GeV] from Eq. (3.13) if thecross section is within 2 ⇠ 10 fb. We find a tension with the ATLAS best fit value �S = 45GeV inour scenario, which is apparently suggested from panels in Fig. 2.2 From now on, our target valuein �S is set as 5.3GeV.

2When �S = 45GeV, from Eq. (3.13), the target value of B(S ! �� +X) to realize �(p(�)p(�) ! S +X !�� +X) = 6 fb becomes 0.192 (when q⇤ = 170MeV) and 0.287 (when q⇤ = 130MeV).

7

Quantum numbers determine the ratios.(They are universal, not sensitive to

number of Ja±±, S ⇔ Ja±± trilinear couplings)

dominant! subdominant.8TeV LHC constraint is no problem.

fixedCross section and ΓS are

directly correlated.



[Csaki,Hubisz,Terning, arXiv:1512.05776]

Result!

S"

45

GeV

!S"

5.3

GeV

13 T

eV,

6 fb

8 TeV

, 0.

6 fb

400 500 600 700 800 900 10000

200

400

600

800

1000

mk!! !GeV"

"S

k!T

eV"

Nj # 0

400 500 600 700 800 900 10000

200

400

600

800

1000

mk!! !GeV"

"S

k!T

eV"

Nj # 1

400 500 600 700 800 900 10000

100

200

300

400

500

mk!! !GeV"

"S

k!T

eV"

Nj # 10

500 1000 1500 20000

10

20

30

40

50

mk!! !GeV"

"S

k!T

eV"

Nj # 100

500 1000 1500 20000

2

4

6

8

10

mk!! !GeV"

"S

k!T

eV"

Nj # 500

500 1000 1500 20000

1

2

3

4

5

mk!! !GeV"

"S

k!T

eV"

Nj # 1000

Figure 2: The blue and red curves show the points of {mk±± , µSk} predicting �S = 45GeV and �S =5.3GeV, respectively. Six cases with di↵erent numbers of doubly charged scalars are consideredwith Nj = 0, 1, 10, 100, 500 and 1000. The green (yellow) regions indicate the areas where weobtain 6 fb (0.6 fb) in the production cross section of p(�)p(�) ! S +X ! �� +X with varyingthe parameter q⇤ from 130MeV (upper boundaries) to 170MeV (lower boundaries) evaluated byEq. (3.12). The gray shaded region mk±± 438GeV in Nj = 0 shows the excluded parts in 95%C.L. via the ATLAS 8TeV data with the assumption of B(k±± ! µ±µ±) = 100% [179]. Thevertical black dotted lines represent corresponding bounds on the universal physical mass mk±±

when we assume B(j±±a ! µ±µ±) = 100% for all j±±

a .

8

!S"

45

GeV

!S"

5.3

GeV

13 T

eV,

6 fb

8 TeV

, 0.

6 fb

400 500 600 700 800 900 10000

200

400

600

800

1000

mk!! !GeV"

"S

k!T

eV"

Nj # 0

400 500 600 700 800 900 10000

200

400

600

800

1000

mk!! !GeV"

"S

k!T

eV"

Nj # 1

400 500 600 700 800 900 10000

100

200

300

400

500

mk!! !GeV"

"S

k!T

eV"

Nj # 10

500 1000 1500 20000

10

20

30

40

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mk!! !GeV"

"S

k!T

eV"

Nj # 100

500 1000 1500 20000

2

4

6

8

10

mk!! !GeV"

"S

k!T

eV"

Nj # 500

500 1000 1500 20000

1

2

3

4

5

mk!! !GeV"

"S

k!T

eV"

Nj # 1000

Figure 2: The blue and red curves show the points of {mk±± , µSk} predicting �S = 45GeV and �S =5.3GeV, respectively. Six cases with di↵erent numbers of doubly charged scalars are consideredwith Nj = 0, 1, 10, 100, 500 and 1000. The green (yellow) regions indicate the areas where weobtain 6 fb (0.6 fb) in the production cross section of p(�)p(�) ! S +X ! �� +X with varyingthe parameter q⇤ from 130MeV (upper boundaries) to 170MeV (lower boundaries) evaluated byEq. (3.12). The gray shaded region mk±± 438GeV in Nj = 0 shows the excluded parts in 95%C.L. via the ATLAS 8TeV data with the assumption of B(k±± ! µ±µ±) = 100% [179]. Thevertical black dotted lines represent corresponding bounds on the universal physical mass mk±±

when we assume B(j±±a ! µ±µ±) = 100% for all j±±

a .

8

excluded by

ATLAS 8TeV data

k++ k++

(h+1 )

⇤

(h+1 )

⇤µ+

µ+

µ+

µ+

h+2

h+2

NR2

NR2

j++a j++

a

⌫e,⌧⌫e,⌧

Figure 3: A schematic description for the decay patterns of k++ or j++

a with two anti-muons inthe final state. Here, h+

1

’s in the left diagram are o↵-shell particles.

We comment on the bound from the 8TeV LHC results. As mentioned in [14], the bound�(pp ! S +X ! Z� +X)|

8TeV

= 5.75 fb from [180] with B(Z ! ``) = 0.06. From Eqs. (1.3)and (1.4), we consider �(pp ! S)|

8TeV

as 0.6 fb. From Eq. (3.14), we evaluate �(pp ! S +X !Z� +X)|

8TeV

' 0.21 fb and conclude that the 8TeV bound is not harmful for our case.Here, we should mention an important issue. As indicated in Fig. 2, when Nj is zero, more

than 100TeV is required in the e↵ective trilinear coupling µSk. Such a large trilinear couplingimmediately leads to the violation of tree level unitarity in the scattering amplitudes includingµSk, e.g., k++k�� ! k++k�� or SS ! k++k�� at around the energy 1TeV, where the physicswith our interest is spread. Also, the vacuum is possibly threatened by the destabilization viathe large trilinear coupling, which calls charge breaking minima. To evade the problems, naivelyspeaking, the value of µSk is less than 1 ⇠ 10TeV.3 As shown in Fig. 2, when we introduceadditional charged scalars, we can realize �S = 5.3GeV with a smaller value of the commone↵ective trilinear coupling µSk. But, we should consider the bound on the doubly charged singletscalars from the LHC 8TeV data. Note that the production channel of a SU(2)L singlet doublycharged scalar k±± is the following pair creation, pp ! �⇤/Z +X ! k++k�� +X.

Lower bounds at 95% C.L. on mk±± via the 8TeV LHC data were provided by the ATLASgroup in Ref. [179] as 374GeV, 402GeV, 438GeV when assuming a 100% branching ratio to e±e±,e±µ±, µ±µ± pairs, respectively. In our model, the doubly charged scalars can decay through theprocesses as shown in Fig. 3, where h+

1

’s are o↵ shell since it should be heavy at least 3TeV. In thecase of k++ in Nj = 0, when the values of µ

11

and µ22

are the same or similar, from Eq. (2.2), therelative branching ratios between k++ ! µ+µ+⌫i⌫j and k++ ! µ+µ+ are roughly proportional to(yL)2i(yL)2j and ((yR)22)2. As concluded in our previous work [146], the absolute value of (yR)22should be large as around 8 ⇠ 9 to generate the observed neutrino properties, while a typicalmagnitude of (yL)2i is 0.5 ⇠ 1. Then, the decay branch k++ ! µ+µ+ is probably dominant as⇠ 100% and we need to consider the 8TeV bound seriously. A simplest attitude would be to avoidto examine the shaded regions in Fig. 2, which indicate the excluded parts in 95% C.L. via theATLAS 8TeV data with the assumption of B(k±± ! µ±µ±) = 100% [179].

When one more doubly charged scalar j++

1

(Nj = 1) exists, a detailed analysis is needed forprecise bounds on k±± and j±±

1

. Benchmark values are given in Fig. 2 by the vertical blackdotted lines, which represent corresponding bounds on the universal physical mass mk±± whenwe assume B(j±±

a ! µ±µ±) = 100% for all j±±a . We obtain the 95% C.L. lower bounds on

the universal mass value mk±± as ⇠ 500GeV (Nj = 1), ⇠ 660GeV (Nj = 10), ⇠ 900GeV (Nj =

3In the case of MSSM with a light t1 (100GeV), A = At = Ab, tan� � 1, mA � MZ , |µ| ⌧ MQ and Mb, thebound on the trilinear coupling |A| . 5TeV was reported in Ref. [181].

9

less significantfinal state

significantfinal state

excluded by

ATLAS 8TeV data

when B(ja±±→μ

±μ± )=100%

excluded by

ATLAS 8TeV data

when B(ja±±→μ

±μ± )=100%

ΓS=45GeV is not achievable in this scenario.

ΓS=5.3GeV (experimental resolution) is OK.

After considering (i) tree-level unitarity: μSk ≤ 1~10 TeV, (ii) ATLAS 8TeV bound,

~100 additional ja±± are required.

(N2 enhancement in ΓS→γγ, only N enhancement in signal of pp→doubly charged scalars)



(ATLAS bound is)

B(k±±→μ±μ±)≈100%in the original model



Radiative seesaw model with various doubly-charged scalars is interesting:


DM is found. Relic is OK.

+

LHC 750 diphoton excess is also explained through photon fusion.

less ambiguous than gluon fusion

Issues on photon-fusion production:

collider-rich in doubly-charged scalar pair productions

inelastic scattering

detailed collider analysis

how to discriminate it from gluon-fusion production

[Fichet,von Gersdorff,Royon, arXiv:1512.05751][Csaki,Hubisz,Lombardo,Terning, arXiv:1601.00638]

4-loop extension: multiple k±±s also help ν physics. [Nomura,Okada, arXiv:1601.00386]

Other motivations are there.


Radiative seesaw model with various doubly-charged scalars is interesting:


DM is found. Relic is OK.

+

LHC 750 diphoton excess is also explained through photon fusion.

less ambiguous than gluon fusion

Issues on photon-fusion production:

collider-rich in doubly-charged scalar pair productions

inelastic scattering

detailed collider analysis

how to discriminate it from gluon-fusion production

[Fichet,von Gersdorff,Royon, arXiv:1512.05751][Csaki,Hubisz,Lombardo,Terning, arXiv:1601.00638]

4-loop extension: multiple k±±s also help ν physics.

Other motivations are there.

[Nomura,Okada, arXiv:1601.00386]

thank you:-)


Documents

LHC 750 GeV Diphoton excess in a radiative seesaw model · Figure 2: p-value for the background-only hypothesis p 0 as a function of the mass mX of a probed NWA resonance signal