News from the Precision Frontier at the LHC

Doreen Wackeroth

Colloquium @ McMaster University Hamilton, Ontario, January 25, 2017

HEPCOS@UB is a member of the LHC CMS collaboration and gratefully acknowledges funding by the U.S. National Science Foundation The Standard Model in a nutshell

The physical world at the very fundamental level follows a symmetry principle: the strong and electroweak interactions of matter particles (leptons and quarks) are prescribed by gauge symmetries, i. e. the Lagrangian L = LQCD + LEW is form-invariant, L → L, under SU(3)color and SU(2)I =isospin × U(1)Y =hypercharge transformations of the matter and gauge ﬁelds.

1 a µν,a LQCD = − 4 Gµν G

Pf j µ a λa j + j=1 q¯ (x)iγ (∂µ + igs Gµ(x) 2 )q (x)

P ¯ µ Yf b b LEW = f ΨL,f γ (i∂µ − g1 2 Bµ + g2I Wµ )ΨL,f

P µ (±1+yf ) + f a¯R,f γ (i∂µ + g1 2 Bµ)aR,f

1 µν 1 b µν,b − 4 Bµν B − 4 Wµν W

Glashow (1961)

b Bµ : U(1) gauge ﬁeld, Wµ, b = 1, 2, 3 : SU(2) gauge ﬁelds

ΨL,f (aR,f ): SU(2) doublet(singlet) for left(right)-handed fermions Electroweak symmetry breaking in the Standard Model

The mediators of the weak interaction, the W and Z bosons, are massive, but 2 b µ,b naively introducing mass terms in L such as M Wµ W breaks the electroweak symmetry of LEW . The mechanism of spontaneous symmetry breaking allows for simultaneously generating W and Z boson masses and preserving the gauge symmetry of LEW . This is achieved by the interaction of the W and Z bosons with a neutral, spin–0 (scalar) field (Higgs field), whose potential has been chosen in such a way that the vacuum state of the Higgs field is no longer invariant under SU(2)I , but still invariant under U(1)em (the photon remains massless).

Goldstone (1961); Higgs (1964,1966); Brout and Englert (1964); Guralnik, Hagen and Kibble (1964); Kibble (1967), Weinberg (1967); Salam (1968) Spontaneous electroweak symmetry breaking

Introduce two complex scalar ﬁelds, Φ = (Φ+, Φ0), with gauge-invariant interactions among themselves and with SM fermions (Yukawa) and bosons † LH =( DµΦ) (DµΦ) − V (Φ) + LYukawa ~τ ~ yi with Dµ = ∂µ − ig2 2 Wµ − ig1 2 Bµ. Arrange self-interactions, so that spontaneous symmetry breaking can occur: V (Φ) = −µ2Φ†Φ + λ(Φ†Φ)2 (λ > 0) 2 2 2 2 µ v SSB:µ > 0: V (Φ) is minimized by |hΦi0| = = 6= 0 2λ 2

Orientation of Φ in the Choose Φ = (0, √v ) 0 0 2 SU(2) space is not ﬁxed: invariant under U(1)em i ~τ ~χ(x) v Φ = e 2 (0, √ ) but not under SU(2) 0 2 I

W ± and Z bosons and fermions acquire mass: ve ve vgf MW = MZ = mf = √ 2 sin θw 2 sin θw cos θw 2 √ √ −1/2 with e = g2 sin θW = g1 cos θW (e = 4πα) and v = ( 2GF ) = 246 GeV. One physical,√ neutral,√ scalar particle emerges, the Higgs boson, with mass v MH = λ 2 = λ · 123 GeV. The Standard Model in a nutshell

LSM = LQCD + LEW + LH

X ¯ µ ¯ µ LEW + LH = (Ψf (iγ ∂µ − mf )Ψf − eQf Ψf γ Ψf Aµ)+ f g X i µ i + i µ i − g2 X µ 3 2 3 + √ (¯a γ b W + b¯ γ a W ) + Ψ¯ γ (I − 2s Q − I γ5)Ψ Zµ+ L L µ L L µ 2c f f w f f f 2 i w f

1 − + + − 2 1 + + − |∂µAν − ∂ν Aµ − ie(W W − W W )| − |∂µW − ∂ν W + 4 µ ν µ ν 2 ν µ + + + + 2 −ie(Wµ Aν − Wν Aµ) + ig1cw (Wµ Zν − Wν Zµ)| +

1 − + + − 2 − |∂µZν − ∂ν Zµ + ig1cw (W W − W W )| + 4 µ ν µ ν 2 02 2 1 2 2 g2MH 3 g MH 4 + g2 + 2 − MH H − H − H + |MW Wµ + HWµ | + 2 8MW 32MW 2 1 ig2 2 X g2 mf + |∂µH + iM Zµ + HZµ| − Ψ¯ Ψ H 2 Z 2c 2 M f f w f W During the past 40+ years the Standard Model has been thoroughly scrutinized with high precision at the quantum level. This needs precision theory and experiments! Testing the Standard model

Precision Theory: the SM as a renormalizable Quantum Field Theory is predictive beyond the Born approximation, and Precision Experiments: experiments have been made available with high collision energies ECM and large number of particle collisions (=luminosity L) such as LEP/SLC (e+e−), HERA (ep), and Tevatron (pp¯):

number of events ∝ Lint σ(ECM )

The LHC now explores a new energy (ECM ) and precision frontier (Lint ). This allows us to look for rare processes, e.g., searches for the Higgs boson are extremely challenging: small signal and large background −10 −3 LHC: σH ≈ 10 σpp and σH ≈ 10 σW /Z for heavy new particles,

to measure masses MW , mtop, MH and couplings, and probe the SM with extremely high precision and in new kinematic regimes. Precision Tests of the Standard Model: Past Experiments

CERN LEP and SLAC SLC e+e− colliders: 91 GeV (LEP I, SLC) and 209 GeV (LEP II) Shutdown in 2000 (LEP II), 1998 (SLC)

Precision tests of the electroweak sector; MW measurement Higgs mass prediction and lower bound from direct search

DESY HERA ep collider: 27.5 GeV electron and 920 GeV proton (shutdown in 2007) Structure of the proton (Parton Distribution functions!)

Fermilab Tevatron pp¯ collider at 1960 GeV (shutdown in 2011): Discovery of the top quark Precision tests of the electroweak and QCD sector Improved bounds on Higgs mass (LEP,Tevatron,EWPO):

114.4 GeV < MH < 156 GeV(95%C.L.) The LHC era - a new energy and precision frontier

The CERN Large Hadron Collider (LHC) in Geneva, Switzerland, protons are accelerated to 99.9999991% of c (7 TeV) and the ’debris’ of their collisions are observed in detectors: CMS detector ATLAS detector The LHC era - a new energy and precision frontier

An unprecedented high number of collisions at an unprecedented high energy! 2012: Announcement of the discovery of a new boson at the LHC

The ATLAS Collaboration, Phys. Lett. B 716 (2012)

The CMS Collaboration, Phys. Lett. B 716 (2012) Francois Englert and Peter Higgs Nobel Prize 2013 Is it the SM Higgs boson?

The new boson has properties (mass, spin, CP, couplings) consistent with the SM Higgs boson:

MH = 125.09 ± 0.21(stat) ± 0.11(syst) GeV ATLAS and CMS, Phys. Rev, Lett. 114, 191803 (2015) This is consistent with the expectation from indirect bounds on MH : 2 Gµ πα(0)MZ √ = 2 2 2 [1 + ∆r(α(0), MZ , MW , mt , MH ,...)] 2 2(MZ − MW )MW

11 / 29 Is it the SM Higgs boson?

Data strongly prefers scalar (SM: 0+) to pseudoscalar (0−), i.e. O− is excluded at 97.8 % (99.5%) CL at ATLAS (CMS) Production and decay rates agree with SM expectation:

https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsHIG https://twiki.cern.ch/twiki/bin/view/AtlasPublic/HiggsPublicResults

12 / 29 New physics?

With the discovery of the Higgs boson the Standard Model is now complete! No direct or indirect signals of new physics have been found yet at collider experiments. All tests of electroweak and strong interactions among SM particles have been proven to be consistent with the SM expectation (possible exception: anomalous muon magnetic moment gµ − 2 = aµ). We know that the SM cannot be the final theory. It not only leaves too many questions unanswered but has some inherent unattractive features, e.g.,no gauge coupling unification and fine-tuning. Couplings are not constant but change with energy (running couplings), e.g., the strong coupling decreases with increasing energy (asymptotic freedom of QCD):

13 / 29 New physics?

Running gauge couplings in the SM and the Minimal Supersymmetric SM (MSSM):

PDG 2016; Dimopoulos, Raby, Wilczek, Physics Today, October 1991 2 The Higgs mass receives large radiative corrections δMH at a higher energy scale, and ﬁne-tuning is needed to obtain 125 GeV at the electroweak scale: 2 2 2 2 2 MH (Q ) = MH (µ ) + δMH

14 / 29 A new era of precision physics at the LHC

New physics could be hiding in a number of places: We are just at the beginning of probing Higgs couplings, the reconstruction of the Higgs potential at a satisfying level of precision may even be only possibly at future colliders, the self-interactions of the W and Z bosons, especially the quartic interactions still need to be probed with high precision, new resonances may be revealed due to higher precision in new kinematic regimes, some SM processes will be accessible for the ﬁrst time (triple EW gauge boson production, vector boson fusion, Higgs production in association with top quarks)

15 / 29 A new era of precision physics at the LHC

We need improved calculations, since the potential for discovery or constraining new physics models relies on superb theoretical control of all aspects of predictions for LHC cross sections: higher-order contributions in perturbation theory: NNLO (NNNLO) QCD and NLO electroweak (EW), mixed QCD/EW, resummation (QCD, QED, EW Sudakovs), implementation in (improved) parton shower Monte Carlo programs for realistic simulation of data, (5) non-perturbative eﬀects (∆αhad , PDF, ...), parametric uncertainties due to uncertainties in the measurement of the input parameters: MW , MH , mt , αs ,....

16 / 29 Precision tests of the Standard Model: Theory

Precision calculations of observables, such as scattering cross sections dσ, can be performed as a perturbative expansion of the probability amplitude A in the interaction strengths: 2 2 α(MZ ) = e /(4π) = 0.008, αs (MZ ) = gs /(4π) = 0.118

− + 2 Example: pp → γ, Z → µ µ up to O(ααs ) 2 0 0 2 1 1 2 2 2 A(egs ) = e gs A + e gs A + e gs A +

2 3 3 2 4 4 +e gs A + e gs A + ...

2 2 0 2 2 h 1 2 2 † 0 0 † 2i dσ ∝ |A| = α |A | +α αs |A | + (A ) A + (A ) A + ... | {z } LO | {z } NLO Precision tests of the Standard Model: Theory

General structure of a diﬀerential cross section for A + B → N particles scattering with A, B being p, p or p, p¯:

R P dσ(ECM ) = ij dx1dx2fi/A(x1, µf )fj/B (x2, µf )dσˆij (ˆskl , µr , µf ) × PS O

fi/A(x1, µf ): Parton Distribution Function (PDF); PS: Parton shower with matching procedure

O deﬁnes the observable (cuts, jet function) 18 / 29 The theory community has been busy ...

Gavin Salam at LHCP 2016 19 / 29 Higgs production at N3LO in QCD at the LHC

Anastasiou et al., PRL 114 (2015)

LHC 50 pp→h+X gluon fusion MSTW08 68cl LO NLO NNLO NNNLO μ=μR=μF ∈[m H /4,mH ] Central scale:μ=m H /2

30 σ/pb

0 0.3

0.2

0.1

0.0

-0.1

-0.2 2 4 6 8 10 12 14

S/TeV 20 / 29 Production cross sections of SM particles at ATLAS

21 / 29 Production cross sections of SM particles at CMS

July 2016 CMS Preliminary

CMS measurements 7 TeV CMS measurement (stat,stat+sys) vs. NNLO (NLO) theory 8 TeV CMS measurement (stat,stat+sys) 13 TeV CMS measurement (stat,stat+sys) γγ 1.06 ± 0.01 ± 0.12 5.0 fb-1 Wγ, (NLO th.) 1.16 ± 0.03 ± 0.13 5.0 fb-1 Zγ, (NLO th.) 0.98 ± 0.01 ± 0.05 5.0 fb-1 Zγ, (NLO th.) 0.98 ± 0.01 ± 0.05 19.5 fb-1 WW+WZ 1.01 ± 0.13 ± 0.14 4.9 fb-1 WW 1.07 ± 0.04 ± 0.09 4.9 fb-1 WW 1.00 ± 0.02 ± 0.08 19.4 fb-1 WW 0.96 ± 0.05 ± 0.08 2.3 fb-1 WZ 1.08 ± 0.07 ± 0.06 4.9 fb-1 WZ 1.04 ± 0.03 ± 0.07 19.6 fb-1 WZ 0.80 ± 0.06 ± 0.07 2.3 fb-1 ZZ 0.97 ± 0.13 ± 0.07 4.9 fb-1 ZZ 0.97 ± 0.06 ± 0.08 19.6 fb-1 ZZ 0.90 ± 0.11 ± 0.04 2.6 fb-1

0.5 1 1.5 2 All results at: Production Cross Section Ratio: σ / σ http://cern.ch/go/pNj7 exp theo

22 / 29 WW production at the LHC: new physics or missing h.o. corrections?

Josh Kunkle (CMS), LHCC-EP seminar (2016)

23 / 29 Search for new resonances in muon-pair production

Di-muon invariant mass in pp → γ, Z → µ+µ− measured by ATLAS and the impact of NLO EW+QCD corrections in percent of the LO prediction (J.Campbell et al, Phys.Rev. D94 (2016) ):

30 scale uncert. δ add 20 δ prod

0 [%] δ

-10

-20

-30 1000 2000 3000 4000 5000 6000 7000 8000 M(l+l-) [GeV]

24 / 29 The role of MW , MH , and mt in precision tests of the SM

MW , MH , mt play important roles both as input parameters and electroweak precision observables (EWPO). They have been measured with impressive high precision (from PDG 2016):

MW = 80385 ± 15 MeV ; mt = 173.21 ± 0.51 ± 0.71 GeV ; MH = 125.09 ± 0.21 ± 0.11 GeV Further improved measurements will allow for: Decreased parametric uncertainties in precision observables. Precise SM predictions for Higgs boson properties, e.g., the Higgs width directly depends on MH ! More and more stringent consistency checks of the SM: measurement vs SM prediction of MW , MH , mt . Increased sensitivity to loop-induced new physics eﬀects and for discriminating between SM and new physics, or even between diﬀerent new physics scenarios. Precise prediction for the Higgs quartic coupling at high energy scales (EW vacuum stability).

25 / 29 First measurement of MW at the LHC

± ± MW extracted from the measured transverse mass (or pT (l)) of the lν pair in pp → W → l ν production: q l ν MT (lνl ) = pT pT (1 − cos(Φl − Φν )) (ATLAS-CONF-2016-113 (2016)) and the impact of NLO EW corrections in percent of LO predictions (DY report, Phys.Rev. D94 (2016), 093009 ):

26 / 29 First measurement of MW at the LHC

ATLAS-CONF-2016-113 (2016)

27 / 29 MW (∆r) in the MSSM and NMSSM

From O.Stal, G.Weiglein, L.Zeune et al, arXiv:1506.07465 [hep-ph].

MSSM, NMSSM tan β = 3(left); 5.5(right), µ = 200 GeV; points allowed by HiggsBounds; Mh1 = 125.09 ± 3.04 GeV for M2 < 725 GeV from NMSSMTools. r.h.s. plot: the MSSM and NMSSM Higgs sectors are chosen to be similar.

28 / 29 Final remarks

The Higgs discovery and a wealth of measurements of electroweak and strong processes at very high precision (per mil/percent level) and in new kinematic regimes are all in agreement with the SM. Many new physics scenarios have been probed at new energy regimes, and no signal of new physics has been detected (yet). As impressive the progress is in both experiment and theory, this is just the beginning. Ideas for new physics models, new and improved experimental analysis techniques, and improved calculational approaches and predictions, all are needed to fully exploit the potential of the LHC for discovery.

This is a special and exciting time for high-energy physics: the next discovery is going to be truly unexpected and will be a harbinger for what lies beyond the Standard Model.

29 / 29