1. Double Higgs Production
S. Dawson
CMS HH Workshop
January 18, 2016
S. Dawson

2. Outline Why measure the Higgs-self couplings? What do we expect?
Standard Model
Issues with the top mass dependence
Beyond the Standard Model
Resonances
Effective Field Theory
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3. Higgs self-couplings a prediction
hhh and hhhh couplings predictions of theory
They are perturbative:
In general:
Corrections to relationship between l3 and l4 of O(1/L2)
* This is NOT true in models with new light particles
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4. Production of hh h h h
Sensitive to heavy colored particles (eg stops or top partners) h h h h
Sensitive to anomalous top-Higgs couplings h h
Sensitive to anomalous VVhh couplings h h h
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5. Small Rates for hh Only gluon fusion likely to be relevant
sNLO(fb)
sNLO(fb)
dl3
√S (TeV)
Only gluon fusion likely to be relevant
Large increase in hh rate at high energy
* Light bands, LO, Solid bands NLO
[Frederix et al, ]
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6. Two Higgs Production at LHC
Cross section has spin-0 and spin-2 contributions
mt2>>s, pT2 (low energy theorem)
(hhh coupling/hhhSM)
For large s, dependence on dl3 suppressed
More sensitivity to negative dl3
Exact cancellation in SM at threshold
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7. Double Higgs Production
Cancellation in large mt limit between box and triangle diagrams
QCD corrections computed in mt infinity limit and weighted by exact LO
Greatly restricted by single Higgs production h h h
[Dawson, Dittmaier, Spira, hep-ph/ ]
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8. Progress in SM Calculations
Dominant process is gg  hh
Threshold resummation at NNLL matched to NNLO
Scale uncertainty reduced at NNLL
Good convergence
These calculations are in mt ∞ limit
Fixed Order
Resummed
*MSTW2008 PDFs
[De Florian, Mazzitelli, ]
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9. Using newest NNLO PDFs
NEW: PDF uncertainty significantly reduced from MSTW PDFs
[De Florian, Mazzitelli, ; Contribution to LHC Higgs Cross Section Working Group]
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10. Choosing the Scale
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11. Radiative corrections in large mt limit?
Large mt limit known to poorly reproduce distributions at LO
Exact LO
ds/dMhh (fb/GeV)
ds/dpTj (fb/GeV)
mt∞
Mhh (GeV)
pTj (GeV)
Adding extra powers of 1/mt2 doesn’t help distributions
[Dawson, Furlan, and Lewis, arXiv: ;Dolan, Englert, and Spannowsky, arXiv: ]
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12. Towards including mt effects at NLO, NNLO
HOW BIG ARE 1/mt2 CORRECTIONS?
Compute NLO with virtual corrections in mt∞ limit and real corrections with exact mt dependence (improved HEFT)
Compute 1/mt2n corrections to NNLO and normalize to exact LO
Different results from 2 approaches
Arbitrarily assign ±10% uncertainty from mt dependence
[1/mt2 corrections: Grigo,Hoff, Melnikov, Steinhauser, arXiv: ; Grigo, Melnikov, Steinhauser, arXiv: ; Grigo, Hoff, Steinhauser, arXiv: ;
HEFT: Maltoni, Vryonidou, Zaro, arXiv: ; Frederix et al, arXiv: ]
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13. Compute NLO corrections to hh production
O(s3) contributions
Compute as expansion in small external momentum
Can keep as many terms in expansion as desired
Need 2 loop box integrals with mt, Mh
Known
Easy
New
[Borowka, Di VitaGreiner, Heinrich, Jones, Kerner, Luisoni, Mastrolia, Schlenk, Schubert, Zirke]
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14. Gudrun’s plot
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15. Andrea’s Plot
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16. What is contributing to hh?
Do we know it’s a top quark?
Could it be a stop? Or other colored scalar?
Parameters restricted by requirement that ggh has SM value
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17. Colored scalar in loop? Could we replace the top with a scalar?
Physical mass (m0=0 all mass from EWSB)
Color octet: SM 1h rate predicts highly suppressed 2h rate
s/sSM
Color triplet: SM 1h rate obtained for k=±3.7 k
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[Dawson, Ismail, Low, arXIv: ]

18. What about adding a scalar?
At high invariant mass, distributions different in presence of color triplet scalar
13 TeV
100 TeV
ds/dMhh (fb/GeV)
ds/dMhh (fb/GeV)
Mhh (GeV)
Mhh (GeV)
[Dawson, Ismail, Low, arXiv: ]
[See also, Batell, McCullough, Stolarski, Verhaaren, arXiv: ]
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19. Need a resonance to increase rate!
Simplest example: Add a scalar singlet, S
Before EWSB, singlet only couples to Higgs doublet
After EWSB, singlet mixes with SM Higgs boson
For simplicity, impose Z2 symmetry:
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20. Singlet Model Very predictive: Physical fields: Physical parameters:
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21. Z2 symmetric singlet model
Very simple model:
If kinematically allowed, H  hh SM
h,H
Coupling to light Higgs ~ cos q
Coupling to heavy Higgs ~ sin q SM

22. Branching ratio can be significant
Large tan b gives problems with perturbative unitarity of hhhh
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23. Limits on singlet model
Limits from MW, Higgs coupling measurements, direct searches for heavy Higgs bosons
|sin q (mqx) |
MH (GeV)
[Bojarski, Chalons, Lopex-Val, Robens, arXiv: ]
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24. Resonant production of hh
Large resonant effects when MH~2Mh
NWA approximation accurate for MH < 400 GeV
Can get factor of 20 enhancements
*Similar effects in MSSM, NMSSM models
[Dawson, Lewis, arXiv: ]
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25. Large resonance/interference effects
[Dawson, Lewis, arXiv: ]
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26. NLO corrections to singlet model
Computed in mt∞limit
K factor ~ 2 (as in SM)
[Dawson, Lewis, arXiv: ]
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27. Higgs singlet model without Z2
Models without Z2 symmetry motived by desire to explain electroweak baryogenesis
(They typically prefer negative a1, b3 and heavier H)
[Profumo, Ramsey-Musolf, Wainwright, Winslow, arXiv: ; Curtin, Meade, Yu, ]

28. Enhanced hh in singlet model without Z2
MH(GeV)
s(pphh)/sSM
ssinglet/sSM
* Allowed in singlet model
BR(Hhh)
MH(GeV)
Enhancements of hh by factors if MH < 400 GeV
Easy to arrange in many models…. Major constraint is gg h needs to have observed rate
Minimum of potential must give v=246 GeV
[Chen, Dawson, Lewis, arXiv: ]

29. No resonance: Use EFT Very simple EFT:
gg h rate within d of SM prediction
*Neglecting some derivative operators
1+ct
Would be excluded by 20% measurement of tth cg

30. hh production breaks EFT degeneracy
Single Higgs:
If Higgs arises from a doublet, only (F+F) combination:
Double Higgs rate not proportional to ct+cg
c2h
cgg cg ct
dl3 ct
[Chen, Dawson, Lewis, arXiv: ]
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31. Fits to EFT Coefficients
Many fits in literature
Use kinematics of signal to improve fits (Correlations!)
c2h, dl3 only probed in hh production
300, 3000 fb-1, bbgg
14 TeV, 600 fb-1, bbtt
dl3
p values
cgg
1s contours ct
c2h
[Azatov, Contino, Panico, Son, Arxiv: ; Goertz, Papaefstathiou, Yang, Zurita, arXiv: ]
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32. How big do you expect EFT coefficients to be?
Singlet model only generates dl3
Top partner model
Colored scalar triplet
*Z2 symmetry assumed
These estimated coefficients are much smaller than projected sensitivities
[Dawson, Lewis, Zeng, arXiv: ; Chen, Dawson, Lewis, arXiv: ]
[See also, Brehmer, Freitas, Lopez-Val, Plehn, arXiv: ]
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33. Conclusions
Measuring hh production required to understand Higgs potential
Difficult to make hh rate much different from SM rate without resonant enhancement because of constraints from single Higgs production and electroweak measurements
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