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ELECTROWEAK HIGGS BOSON PRODUCTION IN ASSOCIATION WITH THREE JETS
(A.K.A. VBF + 1 JET) AT NLO QCD
IN COLLABORATION WITH S. PLATZER, F. CAMPANERIO, AND M. SJODAHL
!
PRL 111, 211802, (2013), ARXIV:1311.5455 !Dr. Terrance Figy
NAFUM Research Associate The University of Manchester
!April 21, 2014
WSU Physics Seminar !!
OUTLINE
• Introduction
• Details of calculation
• Results
• Outlook
A. Salam S. Weinberg S. Glashow
D. Gross F. Wilczek D. Politzer
):
The Standard Model
SU(2)L ⇥ U(1)Y :
SU(3)c:
Standard Electroweak(EW) gauge theory
Quantum Chromo Dynamics (QCD)
How is mass generated?
30 December 2013 Physics Today www.physicstoday.org
Higgs boson
Goldstone boson. Superconductors also exhibit thefamous Meissner effect, the expulsion of externalmagnetic fields that makes possible magnetic levi-tation. Anderson started with the simple Londontheory of the Meissner effect, rewrote the equationsin a relativistic form more palatable to particlephysicists, and showed that they describe what is,in effect, a massive photon; he called it a plasmon.Being a massive spin-1 boson, the plasmon has anextra longitudinal polarization compared with apropagating photon, which also is a spin-1 bosonbut with only two transverse polarizations. Wheredid the extra degree of freedom come from? It’s theGoldstone mode! Anderson concluded that “thesetwo types of bosons [the massless Goldstone bosonand the massless gauge boson] seem capable of ‘can-celling each other out’ and leaving finite mass bosonsonly.” Anderson’s work made it clear that gauge the-ories and symmetry breaking have a special rela-tionship; what remained was to understand it.
In his first paper of 1964, Peter Higgs pointed outa loophole in the Goldstone, Salam, and Weinbergtheorem: The proof assumes explicit Lorentz invari-ance in relating broken symmetries to particles.6
Due to the necessity of fixing a gauge, that assump-tion is violated when electromagnetism or any othergauge theory is quantized.
Gauge symmetries, in fact, are not symmetriesin the usual sense of relating seemingly distinctphysical processes or configurations. Instead, gaugesymmetry is a redundancy; you can formulate thequantum theory in a way that is manifestly Lorentzinvariant and manifestly gauge invariant, but thatformulation actually represents an infinite numberof copies of the same physical system. In quantizingthe theory, you need to choose arbitrarily one of theequivalent quantum descriptions of the physics;that’s what is meant by fixing a gauge. The Lorentz
and gauge symmetries that are built into the classi-cal theory still control the quantum physics, butthey do so through a delicate choreography. Justhow gauge fixing invalidates the Goldstone, Salam,and Weinberg theorem was shown in a paper byGerald Guralnik, Carl Hagen, and Tom Kibble,7
published shortly after the Higgs loophole paper.
Mass effectsEven with the theorem by Goldstone and companyevaded, the question remains as to how a masslessgauge boson can obtain mass. To answer the ques-tion, in his second paper of 1964, Higgs reconsid-ered Goldstone’s Mexican-hat model and added aphoton.8 Once the boson field, also called the Higgsfield, acquires a vacuum expectation value (particlephysicists refer to “turning on the Higgs field”) andthe theory is quantized, the gauge symmetry of elec-tromagnetism imposes two new interactions notpresent in ordinary electrodynamics. One of thoseis a mass term for the photon; the other is a couplingof the photon to the would-be Goldstone boson (seePHYSICS TODAY, September 2012, page 14).
Early in 1964 Robert Brout and François Englertshowed that those two interactions work together toallow a gauge invariant quantum theory with a mas-sive gauge boson.9 The gauge invariance, already ex-plicitly broken by gauge fixing in quantization andseemingly again by the new mass term, is restoredin the quantum theory by the coupling between thephoton and the Goldstone boson. For one particularchoice of gauge fixing called the Coulomb gauge, thephysical degrees of freedom are manifest and thetwo interactions show that the would-be Goldstoneboson becomes the longitudinal polarization neededto turn a massless gauge boson into a massive one.It has become customary to say that the masslessGoldstone boson is “eaten” to give the gauge boson
Figure 1. Yoichiro Nambu, Jeffrey Goldstone, and Philip Anderson penned important early chapters in thestory of the Higgs boson. Beginning in 1960, particle physicists Nambu (left) and Goldstone (center) adaptedideas from condensed-matter physics to explore the relationship of symmetry breaking to the generation ofmassive particles. Two years later, condensed-matter physicist Anderson (right) argued that two types of troubling massless particles—Goldstone bosons and gauge bosons—could together yield a massive particle.(Nambu photo courtesy of the AIP Emilio Segrè Visual Archives, Marshak Collection. Goldstone and Andersonphotos courtesy of the AIP Emilio Segrè Visual Archives, PHYSICS TODAY Collection.)
This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:97.94.124.63 On: Sat, 30 Nov 2013 21:29:53
Condensed Matter Physics
Yoichiro Nambu, Jeffrey Goldstone, and Philip Anderson
The 1964 Physical Review Letters
Kibble GuralnikHagen
Englert
Brout Higgs
2010 J.J. Sakurai Prize
Overview H0 production via VBF Results Concluding Remarks
SM Higgs bosonSpontaneous Symmetry Breaking: SU(2)L × U(1)Y → U(1)em
SM Higgs Doublet
Φ = U(x)1√2
!
0v + H
"
The remormalizable Lagrangian
L = |DµΦ|2 + µ2Φ†Φ− λ(Φ†Φ)2
leads to the vacuum expectiation value v =#
µ2
λfor the Higgs
field H.
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
SM Higgs bosonHiggs couplings to gauge bosons
Kinetic energy term of the Higgs doublet field:
(DµΦ)† (DµΦ) =1
2∂µH∂µH +
!
"gv
2
#2W µ+W−
µ
+1
2
(g2 + g ′2)v2
4ZµZµ
$%
1 +H
v
&2
W ,Z mass generation: m2W =
'
gv2
(2,m2
Z =(g2+g ′2)v2
4
WWH and ZZH couplings are generated:couplingstrength = 2m2
V/v ≈ g 2v within SM
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
SM Higgs bosonHiggs couplings to fermions
Fermion masses arise from Yukawa couplings via
Φ† →!
0, v+H√2
"
.
LYukawa = −#
f
mf f f
$
1 +H
v
%
Test SM prediction: f fH Higgs coupling strength = mf /v
Observation of Hf f Yukawa coupling is no proof that av.e.v exists
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Happy Higgsdependence Day!”I think we have it” -Rolf-Dieter Heuer, 4 July 2012
ATLAS-CONF-2012-170
CMS-PAS-HIG-12-045
T. Figy H0 production via VBF
The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2013 to François Englert and Peter W. Higgs “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider”.
FURTHER READING! More information on the Nobel Prize in Physics 2013: http://kva.se/nobelprizephysics2013 and http://nobelprize.org REVIEW ARTICLES: Rose, J. (2013) I mörkret bortom Higgs, Forskning & Framsteg, nr 6 (Swedish). Llewellyn-Smith, C. (2000) The Large Hadron Collider, Scientific American, July. Weinberg, S. (1999) A Unified Physics by 2050?, Scientific American, December. BOOKS: Randall, L. (2013) Higgs Discovery: The Power of Empty Space, Bodley Head. Sample, I. (2013) Massive: The Higgs Boson and the Greatest Hunt in Science, Virgin Books. Carroll, S. (2012) The Particle at the End of the Universe, Dutton. Close, F. (2011) The Infinity Puzzle, Oxford University Press. Wilczek, F. (2008) The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books. LINKS: Link TV (2012) CERN Scientists Announce Higgs Boson: The Moment: http://www.youtube.com/watch?v=0CugLD9HF94 CERN (2010) CERN LHC Brochure: http://cds.cern.ch/record/1278169?In=en Cham, J. (2012) The Higgs Boson Explained. (animation): http://www.phdcomics.com/comics/archive.php?comicid=1489 Higgs, Peter W. (2010) My Life as a Boson. (transcribed speech): http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf More references can be found in the Scientific Background: http: //kva.se/nobelprizephysics2013
The Nobel Prize 2013 in Physics
Editors: Lars Bergström, Lars Brink and Olga Botner, The Nobel Committee for Physics, The Royal Swedish Academy of Sciences; Sara Strandberg and Oscar Stål, Stockholm University; Joanna Rose, Science Writer; Victoria Henriksson, Editor and Linnéa Wallgren, Nobel Assistant, The Royal Swedish Academy of Sciences. Graphic design: Ritator Illustrations: Johan Jarnestad/ Swedish Graphics Print: Åtta45
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© The Royal Swedish Academy of SciencesBox 50005, SE-104 05 Stockholm, SwedenPhone: +46 8 673 95 00e-mail: [email protected], http://kva.sePosters may be ordered free of charge at http://kva.se/posters or by phone.
Nob
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obel
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Here, at last! François Englert and Peter W. Higgs are jointly awarded the Nobel Prize in Physics 2013 for the theory of how particles acquire mass. In 1964, they proposed the theory independently of each other (Englert did so together with his now-deceased colleague Robert Brout). In 2012, their ideas were confirmed by the discovery of a so-called Higgs particle, at the CERN laboratory outside Geneva in Switzerland.
The awarded mechanism is a central part of the Standard Model of particle physics that describes how the world is constructed. According to the Standard Model, everything – from flowers and people to stars and planets – consists of just a few building blocks: matter particles which are governed by forces mediated by force particles. And the entire Standard Model also rests on the existence of a special kind of particle: the Higgs particle.
The Higgs particle is a vibration of an invisible field that fills up all space. Even when our universe seems empty, this field is there. Had it not been there, nothing of what we know
would exist because particles acquire mass only in contact with the Higgs field. Englert and Higgs proposed the existence of the field on purely mathematical grounds, and the only way to discover it was to find the Higgs particle.
The Nobel Laureates probably did not imagine that they would get to see the theory confirmed in their lifetimes. To do so required an enormous effort by physicists from all over the world. Almost half a century after the proposal was made, on July 4, 2012, the theoretical prediction could celebrate its biggest triumph, when the discovery of the Higgs particle was announced.
Broken Symmetry The Higgs mechanism relies on the concept of spontaneous symmetry breaking. Our universe was probably born symmetrical (1), with a zero value for the Higgs field in the lowest energy state – the vacuum. But less than one billionth of a second after the Big Bang, the symmetry was broken spontaneously as the lowest energy state moved away (2) from the symmetrical zero-point. Since then, the value of the Higgs field in the vacuum state has been non-zero (3).
The Field Matter particles acquire mass in contact with the invisible field that fills the whole universe. Particles that are not affected by the Higgs field do not acquire mass, those that interact weakly become light, and those that interact strongly become heavy. For example, electrons acquire mass from the field, and if it suddenly disappeared, all matter would collapse as the suddenly massless electrons dispersed at the speed of light. The weak force carriers, W and Z particles, get their masses directly through the Higgs mechanism, while the origin of the neutrino masses still remains unclear.
François Englert Belgian citizen. Born 1932 in Etterbeek, Belgium. Professor emeritus at Université Libre de Bruxelles, Brussels, Belgium.
Peter W. Higgs British citizen. Born 1929 in Newcastle upon Tyne, United Kingdom. Professor emeritus at University of Edinburgh, United Kingdom.
The Particle Collider LHCProtons – hydrogen nuclei – travel at almost the speed of light in opposite directions inside the circular tunnel, 27 kilometres long. The LHC (Large Hadron Collider) is the largest and most complex machine ever constructed by humans. In order to find a trace of the Higgs particle, two huge detectors, ATLAS and CMS, are capable of seeing the protons collide over and over again, 40 million times a second.
top quark
Heavier Lighter
bottom quark
tau
charm quark
muon
strange quark
down quark
up quark
electron
electron neutrino
muon neutrino
tau neutrino
The PuzzleThe Higgs particle (H) was the last missing piece in the Standard Model puzzle. But the Standard Model is not the final piece in the cosmic puzzle. One of the reasons for this is that the Standard Model only describes visible matter, accounting for one sixth of all matter in the universe. To find the rest – the mysterious so-called dark matter – is one of the reasons why scientists continue to chase unknown particles at CERN.
Potential energy of the Higgs field
CMS A short-lived Higgs particle is created in the collision and decays into four muons (tracks in red).
ATLAS In the collision, a short-lived Higgs particle is created, which decays into two muons (tracks in red) and two electrons (tracks in green).
1. 2. 3.
ATLAS
LHC
CMS
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Computing Scattering Cross sections
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Framework: QCD factorization
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Computing Scattering Cross sections
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Framework: QCD factorization Parton Distribution Functions
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Computing Scattering Cross sections
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Framework: QCD factorization Parton Distribution Functions
Partonic cross section
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Computing Scattering Cross sections
Hx1
x2
h2
h1
a
b X
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Framework: QCD factorization Parton Distribution Functions
Partonic cross sectionHx1
x2
h2
h1
a
b X
Precise predictions for depend on good knowledge of BOTH and
σ
σab fh,a(x, µ2
F )
σ(p1, p2;MH) =!a,b
" 1
0
dx1dx2 fh1,a(x1, µ2
F ) fh2,b(x2, µ2
F )×σab(x1p1, x2p2, αS(µ2
R);µ2
F )
Overview H0 production via VBF Results Concluding Remarks
Total SM Higgs cross sections at the LHC
H
H
H
W,Z
t
t
H
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Vector Boson Fusion
Event Characteristics
Energetic jets in the forward and backward directions(pT > 20 GeV)
Higgs decay products between tagging jets
Little gluon radiation in the central-rapidity region, due tocolorless W /Z exchange (central jet veto: no extra jetswith pT > 20 GeV and |η| < 2.5)
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Vector Boson FusionCentral Jet Veto
Example: Gluon fusion vs vector boson fusion
JHEP 05 (2004) 064
yrel = yvetoj − (y tag 1j + y
tag 2j )/2
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Hjjj via VBF at NLO (only t-channels)Total Cross section
µ0 = 40 GeV
ξ = 2∓1 scale variations:
LO: +26% to −19%
NLO: less than 5%
JHEP 0802 (2008) 076 [arXiv:0710.5621]
T. Figy H0 production via VBF
role of the polarization vector for the weak boson is taken by a current, hµ, which, for the
first two diagrams in Fig. 1, is given by
hµ(pbτb, p2τ2) = δτ2τb(−e)gHV V gV f2fb
τ2 DV [p2a13]DV [p2
b2]ψ(p2)γµPτ2ψ(pb) (2.4)
with pijk = pi − pj − pk and pij = pi − pj, while DV [q2] = 1/[q2 − M2V ] is the weak boson
propagator, which, in our calculation, only occurs with space-like momentum. In terms of
the Compton amplitude of Eq. (2.3) the A3 are then given by
A3(1q, 3g, aq; 2Q, bQ) = MB(p1, p3, pa13; ϵ3, h(pbτb, p2τ2)),
A3(2Q, 3g, bQ; 1q, aq) = MB(p2, p3, pb23; ϵ3, h(paτa, p1τ1)). (2.5)
The gQ → qqQH subprocess is obtained by crossing the initial state quark q(pa) with
the final state gluon in Eq. (2.2) and dropping the s-channel graphs which result from
crossing the diagrams in the second line of Fig. 1. The 3-parton matrix elements M3 have
been computed using the helicity amplitude method of Ref. [23].
The real emission corrections to VBF Hjjj production consist of four subprocess
classes with four final state partons. These classes are (a) qQ → qQggH, (b) qQ →
qQq′q′H, (c) gQ → qqQgH, and (d) gg → qqQQH. The generalization to the crossed
processes with q → q and/or Q → Q is straightforward.
Figure 2: The dominant virtual QCD corrections. The “blobs” correspond to the sum of all virtualcorrections to the basic Q → QgV Compton amplitude and are given more explicitly in Fig. 6. Thefirst diagram and the second pair of diagrams in each line form gauge invariant subsets.
The above subprocesses lead to soft and collinear singularities when integrated over
the phase space of the final state partons. We use the Catani-Seymour dipole subtraction
method to regulate these divergences [26] and to cancel them against those originating from
the virtual corrections. The virtual corrections can be divided into two classes of gauge
– 5 –
No pentagon or hexagon diagrams included.
Approximate as two DIS reactions.
COMMENTS ON VBF POWHEGBOX [ARXIV:0911.5299]
Overview H0 production via VBF Results Concluding Remarks
Hjjj via VBF at NLO
T. Figy H0 production via VBF
colored, are expected to radiate off more gluons.
For the analysis of the Higgs boson coupling to gauge bosons, Higgs boson + 2 jet
production via gluon fusion may also be treated as a background to VBF. When the two
jets are separated by a large rapidity interval, the scattering process is dominated by gluon
exchange in the t-channel. Therefore, like for the QCD backgrounds, the bremsstrahlung
radiation is expected to occur everywhere in rapidity. An analogous difference in the
gluon radiation pattern is expected in Z + 2 jet production via VBF fusion versus QCD
production [50]. In order to analyze this feature, in ref. [51] the distribution in rapidity
of the third jet was considered in Higgs + 3 jet production via VBF and via gluon fusion,
using cuts similar to the ones in eqs. (3.3) and (3.4). The analysis was done at the parton
level only. It showed that, in VBF, the third jet prefers to be emitted close to one of the
tagging jets, while, in gluon fusion, it is emitted anywhere in the rapidity region between
the tagging jets. Thus, at least with regard to the hard radiation of a third jet, the analysis
of refs. [51, 52, 53] confirmed the general expectations about the bremsstrahlung patterns
in Higgs production via VBF versus gluon fusion.
To study the distribution of the third hardest jet (the one with highest pT after the
two tagging jets), we plot in fig. 7 its rapidity and its rapidity with respect to the average
of the rapidities of the two tagging jets
yrelj3 = yj3 −yj1 + yj2
2. (3.6)
The distributions obtained using POWHEG interfaced to HERWIG and PYTHIA, are very similar
and turn out to be well modeled by the respective distributions of the NLO jet: the third
jet generally tends to be emitted in the vicinity of either of the tagging jets.
Figure 8: Jet-multiplicity distribution for jets that pass the cuts of eqs. (3.3) and (3.4) (leftpanel) and those that fall within the rapidity interval of the two tagging jets, min (yj1 , yj2) < yj <max (yj1 , yj2) (right panel).
In order to quantify the jet activity, we plot the jet-multiplicity distribution for jets
that pass the cuts of eqs. (3.3) and (3.4) in the left panel of fig. 8. Again, the first two
tagging jets and the third jet are well represented by the NLO cross section, that obviously
cannot contribute to events with more than three jets. From the 4th jet on, the showers
– 11 –
Figure 6: Transverse momentum (pj3T ) distribution of the third hardest jet (left panel) andazimuthal-distance distribution of the two tagging jets, ∆φjj (right panel).
where MV is the mass of the exchanged t-channel vector boson, and is dominated by
the contribution in the forward region, where the dot-products in the denominator are
small. Since the dependence of m2jj on ∆φjj is mild, we have the flat behavior depicted in
fig. 6. Good agreement is found in the two POWHEG results and both agree with the NLO
differential cross section.
Figure 7: Rapidity yj3 of the third hardest jet (the one with highest pT after the two tagging jets)on the left panel and rapidity of the same jet with respect to the average of the rapidities of thetwo tagging jets yrelj3
= yj3 − (yj1 + yj2) /2 on the right panel.
An additional feature characterizing VBF Higgs boson production is the fact that,
at leading order, no colored particle is exchanged in the t channel so that no t-channel
gluon exchange is possible at NLO, once we neglect, as stated in section 2.1, the small
contribution due to equal-flavour quark scattering with t ↔ u interference. The different
gluon radiation pattern expected for Higgs boson production via VBF compared to its
major backgrounds (tt production, QCD WW + 2 jet and QCD Z + 2 jet production) is
at the core of the central-jet veto proposal, both for light [8] and heavy [49] Higgs boson
searches. A veto of any additional jet activity in the central-rapidity region is expected
to suppress the backgrounds more than the signal, because the QCD backgrounds are
characterized by quark or gluon exchange in the t-channel. The exchanged partons, being
– 10 –
pS = 14 TeV mh = 120 GeV
HJETS++
• Our aim was to compute the missing pieces (s, t,and u-channel one-loop amplitudes) in H+3 Jets production where the Higgs boson is produced via the HVV coupling (a.k.a VBF+Jet).
• Virtuals: Hexagons, Pentagons, Boxes, and Triangles
• Reals: H+6 parton amplitudes (6 quark + H, 4 quark + 2 gluons +H) arX
iv:1
308.
2932
v2 [
hep-
ph]
12 S
ep 2
013
DESY 13-144, FTUV-13-1308, IFIC/13-55, LPN13-055, LU-TP 13-28, MAN/HEP/2013/17
Electroweak Higgs plus Three Jet Production at NLO QCD
Francisco Campanario,1 Terrance M. Figy,2 Simon Platzer,3 and Malin Sjodahl4
1Theory Division, IFIC, University of Valencia-CSIC, E-46100 Paterna, Valencia, Spain2School of Physics and Astronomy, University of Manchester
3Theory Group, DESY Hamburg4Dept. of Astronomy and Theoretical Physics, Lund University, Solvegatan 14A, 223 62 Lund, Sweden
We calculate next-to-leading order (NLO) QCD corrections to electroweak Higgs plus three jetproduction. Both vector boson fusion (VBF) and Higgs-strahlung type contributions are includedalong with all interferences. The calculation is implemented within the Matchbox NLO frameworkof the Herwig++ event generator.
PACS numbers: 12.38.Bx
I. INTRODUCTION
Higgs production via vector boson fusion (VBF) is anessential channel at the LHC for disentangling the Higgsboson’s coupling to fermions and gauge bosons. The ob-servation of two tagging jets is crucial to reduce the back-grounds. Furthermore, the possibility to identify Higgsproduction via VBF is enhanced by being able to increasethe signal to background ratio by vetoing additional softradiation in the central region [1–7], since this suppressesimportant QCD backgrounds, including Hjj via gluonfusion.
To exploit the central jet veto (CJV) strategy for Higgscoupling measurements, the reduction factor caused bythe CJV on the observable signal must be accuratelyknown. The fraction of VBF Higgs events with at leastone additional veto jet between the tagging jets providesthe relevant information, i.e., we need to know the ratioof Hjjj production to the inclusive cross section of Hjjproduction via VBF. Gluon fusion NLO QCD correctionsfor Hjjj within the top effective theory approximationhave been recently computed in [8], a validation of theeffective theory approximation at LO for this process canbe found in [9].
At present, the NLO QCD corrections of Hjjj viaVBF were calculated [10] with several approximationsand without the inclusion of five- and six-point functiondiagrams (Fig. 1, second row) and the corresponding realemission cuts, which were estimated to contribute at theper mille level. However, some studies [5] suggest thatthe contribution of the missing pieces can be larger. Dueto the importance of the process to Higgs measurements,a full calculation is necessary to ensure that integratedcross sections and kinematic distributions are not under-estimated.
In this letter, we present results for electroweak Higgsplus three jet production at NLO QCD. In Section II,we present technical details of our computation. In Sec-tion III, we present numerical results and the impactof the NLO QCD corrections on various differential dis-tributions. Finally, we summarize our findings in Sec-tion IV.
H H
H H
FIG. 1. Representative examples of diagrams of Hjjj pro-duction via vector boson fusion.
II. CALCULATIONAL DETAILS
For the calculation of the LO matrix elements for Higgsplus two (we have performed the Hjj calculation in par-allel within the same framework), three and four jets,we have used the builtin spinor helicity library of theMatchbox module [11] to build up the full amplitude fromhadronic currents. For the Born-virtual interference thehelicity amplitude methods described in [12] have beenemployed. Both methods resulted in two different im-plementations of the tree level amplitudes which havebeen validated against each other, including color cor-related matrix elements. The LO implementation hasfurther been cross checked against Sherpa [13, 14] andHawk [15, 16]. The dipole subtraction terms [17] havebeen generated automatically by the Matchbox mod-ule [11], which is also used for a diagram-based mul-tichannel phase space generation. For the virtual cor-rections, we have used in-house routines, extending thetechniques developed in [18]. The amplitudes have beencross checked against GoSam [19]. A representative setof topologies contributing are depicted in Fig. 1.For electroweak propagators, we have introduced finite
width effects following [20], using complex gauge bosonmasses and a derived complex value of the sine of theweak mixing angle. We used the OneLoop library [21]
page 1/6
Diagrams made by MadGraph5
u1
u3
g
d5
d~
u2 u 4
zh 7
zd~ 6
diagram 1 QCD=2, QED=3
u1
u3
g
d~6
d
u2 u 4
zh 7
zd 5
diagram 2 QCD=2, QED=3
u2 u 4
gd 5
d
u1
u3
z
h7
z
d~ 6
diagram 3 QCD=2, QED=3
u2 u 4
g d~ 6
d~
u1
u3
z
h7
z
d 5
diagram 4 QCD=2, QED=3
u1
u3
g
u4
u~
u2 d 5
w-h 7
w-d~ 6
diagram 5 QCD=2, QED=3
u1
u3
g
d~6
d
u2 d 5
w-h 7
w-u 4
diagram 6 QCD=2, QED=3
DIPOLE SUBTRACTION
Overview H0 production via VBF Results Concluding Remarks
Higgs Production via Vector Boson Fusion at NLODipole subtraction method
Catani and Seymour, hep-ph/9605323
NLO cross section:
σNLOab (p, p) = σNLO{4}
ab (p, p) + σNLO{3}ab (p, p)
+
! 1
0
dx [σNLO{3}ab (x , xp, p) + σNLO{3}
ab (x , p, xp)]
σNLO{3}ab (p, p) =
!
3
[dσVab(p, p) + dσB
ab(p, p)⊗ I]ϵ=0
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Higgs Production via Vector Boson Fusion at NLODipole subtraction method
Catani and Seymour, hep-ph/9605323
NLO cross section:
σNLOab (p, p) = σNLO{4}
ab (p, p) + σNLO{3}ab (p, p)
+
! 1
0
dx [σNLO{3}ab (x , xp, p) + σNLO{3}
ab (x , p, xp)]
σNLO{3}ab (p, p) =
!
3
[dσVab(p, p) + dσB
ab(p, p)⊗ I]ϵ=0
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Higgs Production via Vector Boson Fusion at NLODipole subtraction method
Catani and Seymour, hep-ph/9605323
NLO cross section:
σNLOab (p, p) = σNLO{4}
ab (p, p) + σNLO{3}ab (p, p)
+
! 1
0
dx [σNLO{3}ab (x , xp, p) + σNLO{3}
ab (x , p, xp)]
σNLO{3}ab (p, p) =
!
3
[dσVab(p, p) + dσB
ab(p, p)⊗ I]ϵ=0
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Higgs Production via Vector Boson Fusion at NLODipole subtraction method
Catani and Seymour, hep-ph/9605323
NLO cross section:
σNLOab (p, p) = σNLO{4}
ab (p, p) + σNLO{3}ab (p, p)
+
! 1
0
dx [σNLO{3}ab (x , xp, p) + σNLO{3}
ab (x , p, xp)]
! 1
0dx σNLO{3}
ab (x , xp, p) ="
a′
! 1
0dx
!
3{dσB
a′b(xp, p)
⊗ [P(x) +K(x)]aa′
}ϵ=0
T. Figy H0 production via VBF
Overview H0 production via VBF Results Concluding Remarks
Higgs Production via Vector Boson Fusion at NLODipole subtraction method
Catani and Seymour, hep-ph/9605323
NLO cross section:
σNLOab (p, p) = σNLO{4}
ab (p, p) + σNLO{3}ab (p, p)
+
! 1
0
dx [σNLO{3}ab (x , xp, p) + σNLO{3}
ab (x , p, xp)]
σNLO{4}ab (p, p) =
!
4
[dσRab(p, p)ϵ=0 − dσA
ab(p, p)ϵ=0]
T. Figy H0 production via VBF
For the H+2,3, and 4 jet amplitudes we use the in-house spinor library of Matchbox.
HJETS++
• Matchbox [S. Platzer and S. Gieseke, arXiv:1109.6256]
• Catani-Seymour Dipole subtraction [hep-ph/9605323]
• Subtractive and POWHEG style matching to parton shower
• ColorFull [M. Sjodahl, arXiv:1211.2099, http://home.thep.lu.se/~malin/ColorMath.htm#ColorMath, ColorFull will soon be public.]
• Tensorial Reduction [F. Capanario, arXiv:1105.0920]
• Scalar Loop Integrals: OneLOop [A. van Hameren arXiv:1007.4716 ]
THE RESULTS
• Input parameters and selection cuts.
• Scale variations for total cross section.
• Kinematic distributions.
INPUT PARAMETERS
• Ecm=14 TeV (proton - proton LHC)
• At least three anti-KT D=0.4 (E-scheme recombination) of 20 GeV and rapidity within -4.5 and 4.5 using FastJet [arXiv:0802.1189, arXiv:1111.6097]
• PDF choices: CT10 for NLO and CTEQ 6L1 for LO [arXiv:hep-ph/0201195, arXiv:1007.2241]
• Scales: W-boson mass (MW) and sum of transverse momentum of reconstructed jets (HT)
yi: rapidity�i: azimuthal angle
�yij = |yi � yj |: absolute rapidity di↵erence between i and j
��ij = |�i � �j |: absolute azimuthal angle di↵erence between i and j
mij =p(pi + pj)2: invariant mass of i and j
pi: four momentum vector of i
2
which supports complex masses to calculate the scalarintegrals. For the reduction of the tensor coefficients upto four-point functions, we apply the Passarino-Veltmanapproach [22], and for the numerical evaluation of the fiveand six point coefficients, we use the Denner-Dittmaierscheme [23], following the layout and notation of [18].To ensure the numerical stability of our code, we have
implemented a test based on Ward identities [18]. TheseWard identities are applied to each phase space point anddiagram, at the expense of a small additional computingtime and using a cache system. If the identities are notfulfilled, the amplitudes of gauge related topologies areset to zero. The occurrence of these instabilities are atthe per-mille level, and therefore well under control. Thismethod was also successfully applied in other two to fourprocesses [24, 25]. In the present work, it is applied forthe first time to a process which involves loop propagatorswith complex masses.The color algebra has been performed using ColorFull
[26] and double checked using ColorMath [27]. Withinthe same framework, we have implemented the corre-sponding calculation of electroweak Hjj production andperformed cross checks against Hawk [15, 16].
III. NUMERICAL RESULTS
In our calculation, we choose mZ = 91.188GeV,mW = 80.419002GeV, mH = 125GeV and GF =1.16637 × 10−5GeV−2 as electroweak input parametersand derive the weak mixing angle sin θW and αQED fromstandard model tree level relations. All fermion masses(except the top quark) are set to zero and effects fromgeneration mixing are neglected. The widths are calcu-lated to be ΓW = 2.0476 GeV and ΓZ = 2.4414 GeV.We use the CT10 [28] parton distribution functions withαs(MZ) = 0.118 at NLO, and the CTEQ6L1 set [29] withαs(MZ) = 0.130 at LO.We use the five-flavor scheme andthe center-of-mass energy is fixed to
√s = 14TeV.
To study the impact of the QCD corrections, we useminimal inclusive cuts. We cluster jets with the anti-kT algorithm [30] using FastJet [31] with D = 0.4, E-scheme recombination and require at least three jets withtransverse momentum pT,j ≥ 20 GeV and rapidity |yj | ≤4.5. Jets are ordered in decreasing transverse momenta.In Figure 2, we show the LO and NLO total cross-
sections for inclusive cuts for different values of the fac-torization and renormalization scale varied around thecentral scale, µ for two scale choices, MW /2, and thescalar sum of the jet transverse momenta, µR = µF =µ = HT /2 with HT =
!j pT,j . In general, we see a
somewhat increased cross section and - as expected - de-creased scale dependence in the NLO results. We alsonote that the central values for the various scale choicesare closer to each other at NLO. The uncertainties ob-tained by varying the central value a factor two up anddown are around 30% (24%) at LO and 2% (9%) at NLOusing HT /2 (MW /2) as scale choice. At µ = HT /2, we
1300
1400
1500
1600
1700
1800
1900
2000
2100
σ/fb
0.81
1.2
0.25 0.4 0.6 0.8 1.0
K
ξ
LO, µ = ξHT
LO, µ = ξMW
NLO, µ = ξHT
NLO, µ = ξMW
HJets++
FIG. 2. The Hjjj inclusive total cross section (in fb) at LO(cyan) and at NLO (blue) for the scale choices, µ = ξMW
(dashed) and µ = ξHT (solid). We also show the K-factor,K = σNLO/σLO for µ = ξMW (dashed) and µ = ξHT (solid).
obtained σLO = 1520(8)+208−171 fb σNLO = 1466(17)+1
−35
fb. Studying differential distributions, we find that thesegenerally vary less using the scalar transverse momentumsum choice, used from now on.In the following, we show some of the differential dis-
tributions which characterize the typical vector boson fu-sion selection cuts and central jet veto strategies as wellas the pT spectrum of the Higgs.For the leading jets (defined to be the two jets with
highest transverse momenta pT,1 and pT,2), we show therapidity difference in Fig. 3. Generally, we find smalldifferences in shape compared to the LO results.In Figure 4, the differential distribution for the pT of
the Higgs is shown. The NLO corrections are moderateover the whole spectrum and the scale uncertaities areclearly smaller.In Figure 5, the differential distribution of the third jet,
the vetoed jet for a CJV analysis, is presented. Here wefind large differences in the high energy tail of the trans-verse momentum distribution. Such high energy jets aresignificantly enhanced at NLO.We also study the normalized centralized rapidity dis-
tribution of the third jet w.r.t. the tagging jets, z∗3 =(y3 − 1
2(y1 + y2))/(y1 − y2). This variable beautifully
displays the VBF nature present in the process. Oneclearly sees how the third jet tends to accompany one of
µR = µF = HT /2 (MW /2):30% (24%) at LO and 2% (8%) at NLO
⇠ = µ/µ0
µ0 = HT (MW )
HT =P
j pT,j
K = �NLO/�LO
Scale Variations on Integrated Cross-sections
�LO = 1520(8)+208�171 fb �NLO = 1466(17)+1
�35 fb
JET DISTRIBUTIONS
z?3 = (y3 �1
2(y1 + y2))/(y1 � y2)
HJets++
LONLO
10−2
10−1
1
10 1
10 2
Transverse momentum of the third jet
dσ/dp⊥,3[fb/GeV
]
20 40 60 80 100 120 140 160 180 2000.5
1
1.5
2
2.5
3
3.5
p⊥,3 [GeV]
K
HJets++
LONLO
1
10 1
10 2
Rapidity of the third jet
dσ/dy3[fb]
-4 -2 0 2 4
0.6
0.8
1
1.2
1.4
y3
K
NLO QCD Corrections to EW H j j j Production at the LHC Terrance M. Figy
HJets++
LONLO
10−2
10−1
1
10 1
10 2
Transverse momentum of the third jet
dσ
/d
pT
,3[f
b/
GeV
]
20 40 60 80 100 120 140 160 180 2000.5
1
1.5
2
2.5
3
3.5
pT,3 [GeV]
K
HJets++
LONLO
10 2
10 3
Relative position of the third jet
dσ
/d
z∗ 3[f
b]
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0.6
0.8
1
1.2
1.4
z∗3
K
Figure 3: Differential cross section and K factor for the pT of the third hardest jet (left) and the normalizedcentralized rapidity distribution of the third jet w.r.t. the tagging jets (right). Cuts are described in the text.The bands correspond to varying µF = µR by factors 1/2 and 2 around the central value HT/2.
HJets++
LONLO
10−4
10−3
10−2
10−1
1
10 1
Transverse momentum of the third jet
dσ
/d
pT
,3[f
b/
GeV
]
20 40 60 80 100 120 140 160 180 200
0.6
0.8
1
1.2
1.4
pT,3 [GeV]
K
HJets++
LONLO
10−1
1
10 1
10 2
Relative position of third jet
dσ
/d
z∗ 3[f
b]
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0.6
0.8
1
1.2
1.4
z∗3
K
Figure 4: Differential cross section and K factor for the pT of the third hardest jet (left) and the normalizedcentralized rapidity distribution of the third jet w.r.t. the tagging jets (right) with µR = µF = HT . Beyondthe inclusive cuts described in the text, we include the set of VBF cuts: m12 =
!
(p1+ p2)2 > 600 GeV and|∆y12|= |y1− y2|> 4.0.
On the left-hand side of Figure 3, the differential distribution of the third jet, the vetoed jetfor a CJV analysis, is shown. Here we find large K factors in the high energy tail of the transversemomentum distribution. However, when VBF cuts 1 are included the K factor is almost flat forthe transverse momentum of the third jet (see the left-hand side of Figure 4). On the right-handside of Figure 3, we show the normalized centralized rapidity distribution of the third jet w.r.t. thetagging jets, z∗3 = (y3− 1
2(y1+ y2))/(y1− y2). This variable beautifully displays the VBF nature
1For the VBF cuts we have chosen to include the following cuts in addition to the inclusive cuts described in themain text : m12 =
!
(p1+ p2)2 > 600 GeV and |∆y12|= |y1−y2|> 4.0
5
HJets++
LONLO
1
10 1
10 2
Rapidity difference of first and second jet
dσ/d
∆y12
[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆y12
K
HJets++
LONLO
1
10 1
10 2
10 3Rapidity difference of first and third jet
dσ/d
∆y13
[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆y13
K
HJets++
LONLO
1
10 1
10 2
10 3Rapidity difference of second and third jet
dσ/d
∆y23
[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆y23
K
Rapidity separation
Higgs Boson Distributions
Transverse momentum Rapidity
HJets++
LONLO
10−3
10−2
10−1
1
10 1
10 2
Rapidity of the H
dσ/dyH[fb]
-4 -2 0 2 4
0.6
0.8
1
1.2
1.4
yH
K
HJets++
LO
NLO
10−1
1
10 1
Transverse momentum of the H
dσ/dp⊥,H
[fb/GeV
]
0 50 100 150 200 250 300 350 400
0.6
0.8
1
1.2
1.4
p⊥,H [GeV]
K
HJets++
LONLO
10 2
Azimuthal angle separation of H and third jet
dσ/d
∆φh3[fb]
-3 -2 -1 0 1 2 3
0.6
0.8
1
1.2
1.4
∆φh3
K
HJets++
LONLO
1
10 1
10 2
Rapidity separation of H and third jet
dσ/d
∆y h
3[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆yh3
K
Higgs Boson Distributions
Jet Masses
HJets++
LONLO
10−3
10−2
10−1
1
10 1
10 2
Mass of the second jet
dσ/dm
2[fb/GeV
]
0 20 40 60 80 100
0.6
0.8
1
1.2
1.4
m2
K
HJets++
LONLO
10−5
10−4
10−3
10−2
10−1
1
10 1
10 2
Mass of the first jet
dσ/dm
1[fb/GeV
]
0 20 40 60 80 100
0.6
0.8
1
1.2
1.4
m1
K
HJets++
LONLO
10−6
10−5
10−4
10−3
10−2
10−1
1
10 1
10 2
Mass of the third jet
dσ/dm
3[fb/GeV
]
0 20 40 60 80 100
0.6
0.8
1
1.2
1.4
m3
K
Here we see fat jets.
Distributions with VBF cutsLONLO
10−2
10−1
1
Mass of first and third jet
dσ/dm
13[fb/GeV
]
0 500 1000 1500 2000
0.6
0.8
1
1.2
1.4
m13 [GeV]
Ratio
LONLO
10−1
Mass of first and second jet
dσ/dm
12[fb/GeV
]
0 500 1000 1500 2000
0.6
0.8
1
1.2
1.4
m12 [GeV]
Ratio
LONLO
10−2
10−1
1
Mass of second and third jet
dσ/dm
23[fb/GeV
]
0 500 1000 1500 2000
0.6
0.8
1
1.2
1.4
m23 [GeV]
Ratio
• mj1j2 > 600 GeV
• �yj1j2 > 4.0
Distributions with VBF cutsLONLO
10−1
1
10 1
10 2
Rapidity difference of first and third jet
dσ/d
∆y13
[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆y13
Ratio
LONLO
10−1
1
10 1
10 2
Rapidity difference of first and second jet
dσ/d
∆y12
[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆y12
Ratio
LONLO
10−1
1
10 1
10 2
Rapidity difference of second and third jet
dσ/d
∆y23
[fb]
0 2 4 6 8 10
0.6
0.8
1
1.2
1.4
∆y23
Ratio
• mj1j2 > 600 GeV
• �yj1j2 > 4.0
Distributions with VBF cuts
LONLO
10−1
1
10 1
10 2
Relative position of third jetd
σ/dz∗ 3[fb]
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0.6
0.8
1
1.2
1.4
z∗
3
K
LONLO
10−4
10−3
10−2
10−1
1
10 1
Transverse momentum of the third jet
dσ/dp⊥,3[fb/GeV
]
20 40 60 80 100 120 140 160 180 200
0.6
0.8
1
1.2
1.4
p⊥,3 [GeV]
Ratio
LONLO
10−1
1
10 1
Rapidity of the third jet
dσ/dy3[fb]
-4 -2 0 2 4
0.6
0.8
1
1.2
1.4
y3
Ratio
• mj1j2 > 600 GeV
• �yj1j2 > 4.0
OUTLOOK
• NLO + Parton Shower matching
• Perform comprehensive phenomenology for Run 2
• Matching H+2 jets and H+3 jets to parton shower
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160 180 200d m
/d p
T,3 (
fb/G
eV)
pT,3(GeV)
VBF cuts
LO VBFNLOLO HJets++
-2
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160 180 200
d m
/d p
T,3 (
fb/G
eV)
pT,3(GeV)
VBF cuts
NLO VBFNLONLO HJets++
Comparison to VBFNLO