August 15, 2016

Looking for new physics …

…………………………. … why Higgs at high \(p_T\)?




Specifically:

  • Higgs crucial EWSB ingredient
  • Higgs mass UV-sensitivity

Look at Higgs sector: Higgs production, so at gluon fusion.

We did look at gluon fusion…


New physics is hiding behind inclusive production!

EFT used to search for new physics also describes SM behavior!

  • About 1% error for total inclusive cross-section (NNLO):
    • asymptotic expansions (Harlander, Ozeren '09; Pak, Rogal, Steinhauser '09)
    • exact high energy limit (Marzani, Ball, Del Duca, Forte, Vincini '08 '09; Harlander, Mantler, Marzani, Ozeren '10; Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld '03)

Need to break this degeneracy

\(-\kappa_t \frac{m_t}{v} H(\bar{t}_R t_L + \text{h.c.})\)   vs.   \(\kappa_g C_1 \frac{H}{v} G_{\mu\nu}^a G^{a,\mu\nu}\)

Higgs \(p_T\) distribution in effective field theory

\[ \mathcal{L}{\text{eff}} = \frac{\color{black}{C_{1}}}{\color{red}{\Lambda}} \mathcal{O}_1 + \frac{\color{black}{C_{2}}}{\color{red}{\Lambda^3}} \mathcal{O}_2 + \frac{\color{black}{C_{3}}}{\color{red}{\Lambda^3}} \mathcal{O}_3 + \frac{\color{black}{C_{4}}}{\color{red}{\Lambda^3}} \mathcal{O}_4 + \frac{\color{black}{C_{5}}}{\color{red}{\Lambda^3}} \mathcal{O}_5 \]

Normalization to corresponding part of cross-section: only shape matters here; coefficients \(C_i\) a priori unknown. (Harlander, TN '13)

High \(p_T\) Higgs!



High \(p_T\) Higgs at \(13\,\text{TeV}\)


Theory scale uncertanties:

  • \(\simeq 35\%\) at LO
  • \(\simeq 20\%\) at NLO
  • \(\simeq 8\%\) at NNLO

All of them in EFT.

What about a finite top-mass?

Higgs+jet at NLO

Asymptotic expansion in \(m_{\text{top}} \gg \Lambda\)

V. A. Smirnov 90's

\[ F(\Gamma) \to \sum_\gamma \mathcal{T} F(\gamma) \star F(\Gamma\backslash\gamma) \]

  • Two loop diagrams (\(\hat{s}, m_H^2, m_t^2\)) reduce to tadpole integrals with vanishing external momenta and massless integrals
  • Automatized setup exp/q2e (Harlander, Seidensticker, Steinhauser '98; Steinhauser '01)

Asymptotic expansion in \((\Lambda/m_t)^k\), where \(\Lambda\in\{m_H, \sqrt{\hat{s}}, p_T, \dots\}\)

Validity for exclusive production?

Our goal was to estimate effects and assess the validty of the HTL
(Harlander, TN, Ozeren, Wiesemann '12; TN, Wiesemann '14)

Beyond the asymptotic expansion

  • just asymptotic expansion in two loop virtual corrections

  • massive one loop real emission contributions exactly (H + 4 partons)

Three progressive approximations

  1. All parts in the asymptotic expansion: born, real and virtual pieces
  2. Just virtual corrections in the asymptotic expansion, born and real \(m_t\)-exact
  3. Everything but the two-loop integrals exact in \(m_t\):
    born piece of the virtual correction two-loop interference is \(m_t\)-exact

Approximation 2. has been used recently, rescaling the virtual piece by the \(m_t\)-exact born (Frederix, Frixione, Vryonidou, Wiesemann '16)

How well does rescaling the EFT really work, especially at high \(p_T\)?

Best NLO fixed order Higgs high \(p_T\) spectrum: NLO*

Rescaling the EFT: A successful approach

Higgs+jet @ NLO*

  • up to \(250-300\,\text{GeV}\) \(m_t\)-exact NLO prediction
  • assessed validity of using the born rescaling scheme
  • implemented in MCFM 7
    (almost ready to publish: cleanup, merge with MCFM 8)
  • check arXiv next week!

Backup

Virtual corrections: reweighting vs. NLO*

Higgs rapidity