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Inclusive Higgs boson production at LHC within the kT-factorization approach
M.A. Malyshev in collaboration with A.V. Lipatov N.P. Zotov
M.V. Lomonosov Moscow State University D.V. Skobeltsyn Institute of Nuclear Physics

Phys. Lett. B735 (2014) 79

M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Outline
1. Introduction 2. kT-factorization approach - unintegrated parton distributions - off-shell matrix elements 3. Parameters 4. Numerical results 5. Conclusion

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Introduction
The recent discovery of Higgs boson is a triumph of the Glashow-Salam-Weinberg theory of electroweak interactions and simultaneously marks the commencement of a new era in high-energy physics. The subprocess of gluongluon fusion, gg H, is the basic mechanism of inclusive Higgs boson production in protonproton collisions at the LHC energy. Dominant contribution to the respective cross section comes from diagrams that involve a triangle loop of heavy (primarily t) quarks. In the conventional collinear QCD approach good description of the Higgs boson production is only achieved if higher orders diagrams are taken into account.
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M.A. Malyshev

Samara, June, 29, 2015

Introduction
Higgs boson production in the kT-factorization approach has been intensively studied in the last decade: 2005: the process was investigated in [Lipatov, Zotov, Eur.Phys.J. C44, 559], pT-distributions were presented. Good description is achieved in the lowest perturbative order! 2006: finite mt-mass was correctly introduced in [Pasechnik, Teryaev, Szczurek, Eur.Phys.J. C47, 429]. 2011: the kT-factorization formula for Higgs production was rigorously proven ([Sun, Xiao, Yan, Phys. Rev. D84, 094005 (2011)], see also a review by Boer, arxiv:1502.00899 [hep-ph] and references therein)
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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Introduction
Recently the ATLAS Collaboration has reported first measurements of the Higgs boson differential cross sections in the diphoton decay mode. In particular, the distributions with respect to the diphoton transverse momentum pT, rapidity y and helicity angle |cos *| have been presented. Here we for the first time in the kT-factorization approach describe those experimental data.

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

kT-factorization approach
1. Unintegrated (or TMD) parton distributions 2. Matrix elements which depend on the transverse momenta of incoming gluons.

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Off-shell matrix element g*g*H

Effective vertices (t-quark loops, mt; for diphoton production -- also W-loops)

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Effective vertices
The effective lagrangian for the gluon fusion subpocess gg H in the limit mt takes the form:

The effective vertex:

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Effective vertices
For the decay H one has:

where

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Cross section

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Unintegrated parton distributions
1. KMR approach(Kimber, Martin, Ryskin) [M.A. Kimber, A.D. Martin, M.G. Ryskin, 2001; G. Watt, A.D. Martin, M.G. Ryskin, 2003]. The TMD distributions are obtained from the conventional collinear ones. 2. CCFM unintegrated distributions [H. Jung, 2004; M. Deak, H. Jung, K. Kutak, 2008]. Numerical solutions of CCFM equation. The starting distribution is chosen to satisfy proton structure function F2(x, 2). Two sets of parameters describe F2(x, 2) equally well. We use just one of them (so called A0 set).
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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Parameters

Theoretical uncertainties are connected with the choice of the factorization and renormalization scales. We took R = F = = mH. We varied the scale parameter between 1/2 and 2 about the default value = 1. We set mH=126.8 GeV and H=4.3 MeV For completeness, we use LO formula for the strong coupling constant s(2) with nf = 4 active quark flavors at QCD = 200 MeV. Also we use running QED coupling constant (2).

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Numerical results
1. The differential cross section of the Higgs boson production in pp collisions at the LHC as a function of diphoton transverse momentum. Dashed histograms on the left panel show the scale variations of CCFM A0-based calculations

1. The differential cross section of the Higgs boson production in pp collisions at the LHC as a function of diphoton transverse momentum. Left panel: the solid and dash-dotted histograms correspond to the CCFM A0 and KMR predictions, respectively; and the upper and lower dashed histograms correspond to the scale variations in the CCFM-based calculations. Right panel: the solid histogram corresponds to the CCFM A0 predictions, and the hatched histogram represent the NNLO + NNLL predictions obtained in the collinear QCD factorization (taken from the ATLAS paper). The experimental data are from ATLAS.
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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Numerical results
2. The differential cross section of the Higgs boson production in pp collisions at the LHC as a function of diphoton rapidity. Dashed histograms on the left panel show the scale variations of CCFM A0-based calculations

2. The differential cross section of the Higgs boson production in pp collisions at the LHC as a function of diphoton rapidity. Left panel: the solid and dash-dotted histograms correspond to the CCFM A0 and KMR predictions, respectively; and the upper and lower dashed histograms correspond to the scale variations in the CCFM-based calculations. Right panel: the solid histogram corresponds to the CCFM A0 predictions, and the hatched histogram represent the NNLO + NNLL predictions obtained in the collinear QCD factorization (taken from the ATLAS paper). The experimental data are from ATLAS.
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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Numerical results
3. The differential cross section of the Higgs boson production in pp collisions at the LHC as a function of the helicity angle. Dashed histograms on the left panel show the scale variations of CCFM A0-based calculations

3. The differential cross section of the Higgs boson production in pp collisions at the LHC as a function of the helicity angle. Left panel: the solid and dash-dotted histograms correspond to the CCFM A0 and KMR predictions, respectively; and the upper and lower dashed histograms correspond to the scale variations in the CCFM-based calculations. Right panel: the solid histogram corresponds to the CCFM A0 predictions, and the hatched histogram represent the NNLO + NNLL predictions obtained in the collinear QCD factorization (taken from the ATLAS paper). The experimental data are from ATLAS.
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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Conclusion
In the presented work process of the inclusive Higgs boson production with its subsequent decay to diphoton pair in the kT-factorization QCD approach at LHC energies has been studied for the first time. The off-shell matrix element for g*g*H subprocess has been evaluated. Reasonably good description of ATLAS data for the inclusive production of Higgs boson, decaying to diphoton pair, at LHC has been obtained. The CCFM A0 results give the upper limit of NNLO+NNLL predictions, which shows the effective including of higher orders corrections in the kT-factorization approach. We have demonstrated that the kT-factorization approach can be used to study processes incorporating Higgs bosons decays and that the experimental data give limitations on the TMDs. Future experimental analyses are necessary in order to discriminate between NNLO+NNLL and kT-factorization predictions.

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Back up

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M.A. Malyshev

QFTHEP'15, Samara, June, 29, 2015

Unintegrated parton distributions
In the KMR approach the distribution functions start to depend on the transverse momenta of the partons, and fa(x,kT2)=const, if kT2<02~1 GeV2, otherwise they take the form:

As the input we use MSTW2008 set.
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