PDF Understanding electroweak physics in the Standard Model and beyond

(1)

Nuclear Physics B Proceedings Supplement 00 (2014) 1–8

Supplement

Understanding electroweak physics in the Standard Model and beyond

A. Freitas^a

aPittsburgh Particle physics, Astrophysics&Cosmology Center (PITT-PACC), Department of Physics&Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA

Abstract

This contribution discusses the current status of tests of the electroweak theory and some of their essential theoretical ingredients. At medium and low energies, electroweak precision measurements are sensitive to high-scale physics through virtual loop corrections. At the energy frontier, on the other hand, the electroweak theory is tested through anomalous gauge boson couplings. It is discussed how effective field theories can be used to describe these couplings in a model-independent and theoretically well-defined way, and to correlate them to other observables. Finally, focus- ing on the example ofW⁺W⁻production, it is demonstrated that the precise measurement of anomalous gauge boson couplings at the LHC requires good control of higher-order radiative corrections.

1. Electroweak precision measurements

Electroweak precision observables (EWPOs) are quantities that are measured at relatively low energies with very high precision. Due to the small experimental uncertainty, they provide indirect sensitivity to the effects of top quarks, Higgs bosons, and potential heavy new particles beyond the Standard Model (SM). These very massive particles contribute to the EWPOs through the virtual quantum corrections, which need to be taken into account in theoretical predictions beyond the leading order in perturbation theory.

Broadly speaking, EWPOs can be divided into two categories. The first comprises measurements of theZ- boson resonance at LEP and SLC:(i)its massMZ, width ΓZ and total peak cross-sectionσ⁰, which are obtained from the line-shape ofσ[e⁺e⁻ → ff¯] for values of the center-of-mass energy √

snearMZ; (ii)the branching ratios for different ff¯final states; and(iii)the effective weak mixing angles

sin²θ_e^f_ff= 1 2|Q_f|Re

( gê_R^ff gê_R^ff−gê_L^ff

)

, (1)

Email address:[email protected](A. Freitas)

which depend on the effective couplingsg^e_L,R^ff of theZ- boson to left- and right-handed fermions, and which are determined from measuring the forward-backward asymmetry of the final state fermion f (A_FB^f ) or the left- right beam polarization asymmetry (ALR). More details aboutZ-resonance quantities can be founde.g.in Ref. [1].

The second category comprises observables at low energies: (i) the muon decay constant, which is used for an indirect prediction of the W-boson mass, MW; (ii) polarized electron-electron [2], electron-proton [3]

and electron-deuteron [4] scattering, neutrino-nucleon scattering [5], and atomic parity violation [6, 7], all of which are sensitive to the running of the MS weak mixing angle sin²θ(µ) at di¯ fferent scalesµ[8].

Global electroweak fits combine a large number of precision observables (typically about 20 or more) to- gether with direct measurements of masses of the W- boson (MW), top quark (mt) and Higgs masses (MW), and compare the measured values with the SM predictions (for recent examples see Refs. [8, 9, 10]). Over- all, the agreement between experiment and SM theory is very good, with a global p-value of about 20% [10].

This is illustrated in Fig. 1 in themt–MWplane. How- ever, there are some notable discrepancies: the determination of the leptonic weak mixing angle sin²θ_e^`_ff from

(2)

[GeV]

mt

140 150 160 170 180 190

[GeV]WM

80.25 80.3 80.35 80.4 80.45 80.5

68% and 95% CL contours measurements and mt

fit w/o MW

measurements and MH

, mt

fit w/o MW

measurements and mt

direct MW

σ

± 1 world comb.

MW Phys. Rev. D 88 052018 (2013)

σ

± 1 world comb.

mt arXiv:1403.4427

= 125.7 GeV MH = 50 GeV

MH = 300 GeV

MH = 600 GeV

MH GfitterSM

Jun '14

Figure 1: Comparison of direct determinations (green) ofm_tandM_W with the indirect determination from electroweak precision data before (gray) and after (blue) the Higgs discovery. From Ref. [10].

the measurement ofA_LR at SLC and ofA^b_FBat LEP de- viate by about 2.0 and 2.5 standard deviations from the SM prediction, respectively [8, 9, 10].

Most of the quantities used in the global electroweak fits have been measured with a uncertainty of less than 1%. To match this precision, radiative corrections at the two-loop level and leading three-loop corrections need to be included. However, these calculations are highly non-trivial, since they involve many different Feynman diagram topologies and renormalization terms. Fur- thermore, two- and higher-loop integrals with several masses and external momenta can in general not be solved analytically. One approach uses asymptotic expansions in a suitable small parameter, such asM_Z²/m²_t [11]. Alternatively, the integration is performed numer- ically after recasting the integrals such that they are free of singularities.

Using a combination of these techniques, results for the prediction ofMW and theZ-resonance observables are now available with either complete or fermionic two-loop corrections [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] and approximate three- and four-loop corrections in the limit of largemt[23, 24, 25, 26, 27, 28].

Here “fermionic” refers to electroweak corrections from diagrams involving closed fermion loops, which are dominant due to the large fermion multiplicity in the SM and the fact that some terms are enhanced by the large top-quark mass. In fact, where explicit results for the remaining, “bosonic”, two-loop corrections are available [13, 14, 18, 19], they are found to be about one order of magnitude smaller than the fermionic ones.

Most of the available higher-order corrections have been implemented in public codes, such as ZF[29, 30]

and GF[31]. The current theory uncertainty from missing higher order corrections is shown in Tab. 1 for

Currentexp.error ILCexp.error Currentth.error Projectedth.error Parametricerror

M_W[MeV] 15 2.5–5 4 1 2.6

ΓZ[MeV] 2.3 ∼1 0.5 0.2 0.5

sin²θ^`_e_ff [10⁻⁵] 16 1.3 4.5 1.5 2

Table 1: Current and projected future experimental and theory errors for a few typical electroweak precision observables [32]. See text for details about the future projections.

a few representative quantities, and it can be seen that it is safely below the current experimental uncertainty.

Due to the high precision of the experimental results and the theoretical calculations, and the good agreement between the two, EWPOs can be used to put strong limits on physics beyond the SM. In particular, they are sensitive to modified couplings of the Higgs boson, as they can occur in the Two-Higgs-Doublet Model [33]

or in models with TeV-scale strong interactions [9]. Al- ternatively, one can also derive bounds on the “oblique”

parametersS,TandU, which describe modifications to the gauge-boson self-energies in a model-independent way [8, 9, 10].

Future collider data can put improved constraints on the EWPOs. At the full-luminosity 14-TeV run of the LHC, the experimental error on M_Wis expected to be reduced to 5–8 MeV [34]. Furthermore, it can provide an independent determination of sin²θ^`_e_fffrom the measurement of pp → Z → `⁺`⁻with a competitive precision of 2.9×10⁻⁴ [35]. This may help to resolve the discrepancy between the values of sin²θ^`_e_ffderived from ALRandA^b_FB(see above).

However,`⁺`⁻production at the LHC receives large QCD and sizable electroweak corrections, which must be controlled to make such a measurement possible.

QCD corrections are known up to next-to-next-leading order (NNLO) for the total cross-section [36, 37] and next-to-next-leading logarithmic order (NNLL) for the pTdistribution [38]. Moreover, the complete NLO electroweak corrections [39, 40] and approximate higher- order photon emission contributions [41] are also available. Non-factorizable mixed QCD-electroweak corrections of O(αα_s) may also be non-negligible and work on these contributions is in progress [42]. In addition, a significant reduction of the uncertainty of quark and antiquark parton distribution functions (PDFs) will be

(3)

necessary.

It should be noted that recent results from DØ [43]

and the projected ultimate sensitivity of CDF [44] are already less than a factor of two away from the LHC target precision, thus showing that precision measurements at hadron colliders are possible.

A significant reduction of the experimental error for weak-scale EWPOs can be expected from a future high- luminositye⁺e⁻ collider running on theZ-pole (√

s ≈ MZ) and at theW-pair threshold (√

s≈2MW). This op- tion is currently considered for the planned ILC [45, 34]

and TLEP [46, 34] colliders. For concreteness, the fol- lowing discussion will focus on the ILC case. The expected experimental precision for a few representative EWPOs is shown in Tab. 1. As evident from the table, the theory errors from currently unknown higher-order corrections will dominate over the experimental uncertainty at least for some observables. To improve on this situation, one will need to include three-loop corrections beyond the leading contributions for large values ofmt. In Ref. [32] it has been estimated that the calculation of theO(α²α²_s) corrections and electroweak corrections with at least two closed fermions loop will be sufficient to reduce the theoretical error below the ILC experimental error for most observables. One exception is the effective weak mixing angle, sin²θ^`_e_ff, whose experimental precision can be improved by more than an order of magnitude at the ILC with polarized beams, which will be a challenge to match from the theory side.

2. Anomalous gauge boson couplings

The form of the triple-gauge boson couplings (TGCs) γWW andZWW may be modified by physics beyond the SM. Assuming CP conservation, they are usually written in terms of the interaction Lagrangian [47]

L=−ie

g^γ₁(W_µν⁺W^−µ−W_µν⁻W⁺^µ)A^ν+κγW_µ⁺W_ν⁻A^µν +_M^λ^γ2

W

W_µ⁺^νW_ν⁻^ρA_ρ^µ

−igc

g^Z₁(W_µν⁺W^−µ−W_µν⁻W⁺^µ)Z^ν +κ_ZW_µ⁺W_ν⁻Z^µν+_M^λ^Z2

W

W_µ⁺^νW_ν⁻^ρZρµ

, (2)

wherec≡cosθW,s ≡sinθW andgⁱ₁,κiandλiare the anomalous gauge coupling constants. Electromagnetic gauge invariance demandsg^γ₁ = 1. However, all individual terms in (2) also break weak SU(2) gauge invariance. Moreover, there is no power counting prescription that allows us to rank the terms in (2) according to their expected numerical magnitude and that tells us why other possible terms with extra derivatives, such as W_µ⁺W_ν⁻∂ρ∂^ρA^µν, are not included.

Λ+[TeV] Λ−[Te V]

(ci= +1) (ci=−1) O⁽⁶⁾_W 0.44 0.35 O⁽⁶⁾_B 0.19 0.17 O⁽⁶⁾_WWW 0.49 0.34

Table 2: Limits on the scale of the operators in (4) derived by trans- lating experimental bounds for the couplings in (2) according to (5).

These shortcomings are avoided by describing the anomalous gauge boson couplings through an extension of the SM by higher-dimensional operators

L=L_SM+

∞

X

d=5

1 Λ^d−4

X

i

ciO^(d)_i , (3) whereΛis the mass scale of unresolved heavy particles that mediate the interaction(s). This effective field theory (EFT) description is valid for energiesE Λ. By construction, all operatorsO^(d)_i must respect SM gauge invariance, and they can be ranked by the power ofΛ with which they are suppressed. The leading contribution to CP-even TGCs stems from the threed=6 operators [48]

O⁽⁶⁾_WWW=Tr[WµνW^νρWρµ], O⁽⁶⁾

W =(DµΦ)^†W^µν(DνΦ), (4) O⁽⁶⁾_B =(D_µΦ)^†B^µν(D_νΦ).

Thus there are only three independent parameters (cWWW,cW,cB) in this formalism. Eq. (2), which con- tains five independent coefficients, can be reproduced when replacingΦin (4) with its vev (0,v)^> and using the relations

g^Z₁ =1+cW

M²_Z 2Λ², κ_γ=1+(cW+cB)M_W²

2Λ², κZ=1+(cW−cBs²

c²)M_W² 2Λ², λ_γ=λ_Z=c_WWW3g²M²_W

2Λ² .

(5)

Conversely, one can use (5) to translate the published bounds on anomalous gauge couplings from ATLAS [49, 50], CMS [51, 52], DØ [53] and LEP [54] into limits on the scale of the operators in (4), see Tab. 2¹.

1This translation ignores correlations between the measurements of the individual anomalous gauge couplings and the potential im- provement from combining different channels.

(4)

The EFT description breaks down for energiesE &

Λ, when the heavy mediators may be produced directly.

In general, this poses a difficulty for LHC analysis, since the current bounds on c_i/Λare of the order of a few 100 GeV, but the tails of kinematical distributions can reachO(TeV) momenta or energies. For measurements of processes with a sufficiently high overall event yield, this is usually not a problem since the kinematical tails have low statistics and thus do not contribute signifi- cantly in the analysis. An exception to this statement oc- curs for very weakly coupled new physics, withci1.

In this case,Λcan by relatively small, so that the EFT description is not valid for the majority of the observed kinematical range. Instead, such a scenario may be best probed by searching for direct production of new reso- nances withO(Λ) masses.

Another concern is that the EFT is not renormaliz- able and thus will violate perturbative unitary at high energies. However, given the current limits on thed=6 operators in Tab. 2, the unitarity bound is only reached in the multi-TeV regime, safely beyond the reach of the LHC [55].

The operatorsOWWW andOW also generate quartic gauge boson couplings (QGCs), of the form γγWW, ZZWW andWWWW. This means that the contributions fromd=6 operators to triple and quartic gauge boson couplings are connected by gauge invariance. As- suming that these operators are dominant compared to operators withd>6, the current limits on TGCs imply bounds on QGCs that are stronger than the direct limits.

However, measurements of QGCs also probe a number ofd=8 operators that do not contribute to TGCs [56].

These are most strongly constrained by data from Teva- tron [57] and LHC [58, 59], but the experimental collaborations use a simplified set of operators, which cannot be matched to the full list in App. A of Ref. [56].

Neutral triple gauge boson couplings (γγZ,γZZand ZZZ) do not exist at tree-level in the SM, but they may be generated by loop corrections within the SM and from new physics. Assuming CP conservation, the anomalous vertices can be written in the form [47]

iΓ^αβγ_ZZV(q1,q2,p)= p²−M_V²

M_Z² f₅^V^µαβρ(q1−q2)ρ, iΓ^αβγ_ZγV(q₁,q₂,p)= p²−M_V²

M_Z²

h^V₃^µαβρq_2ρ (6) + h^V₄

M_Z²p^α^µβρσp_ρq_2σ ,

where V = γ,Z and q_1,2 are restricted to be on-shell, whilepmust be off-shell. In the EFT formalism, neutral

TGCs are generated first at dimension d=8. The only relevant CP-conserving operator is [60, 61]:

O⁽⁸⁾

eBW= Φ^†eBµνW^µρ{Dρ,D^ν}Φ. (7) Thus the six independent couplings in (6) can all be expressed in terms of the single gauge-invariant coefficient c_e_BW:

f₅^γ=h^Z₃ =g

eBW

v²M_Z² 4scΛ⁴, f₅^Z=h^γ₃ =h^γ₄=h^Z₄ =0.

(8)

Let us note in passing that there are similar sets of CP-oddoperators for the charged TGC [48, 55],

O⁽⁶⁾

WWWe =Tr[WeµνW^νρWρµ], O⁽⁶⁾

We =(D_µΦ)^†We^µν(D_νΦ), (9) and for the neutral TGC [61],

O⁽⁸⁾_BB= Φ^†B_µνB^µρ{D_ρ,D^ν}Φ,

O⁽⁸⁾_BW= Φ^†BµνW^µρ{Dρ,D^ν}Φ, (10) O⁽⁸⁾_WW= Φ^†W_µνW^µρ{D_ρ,D^ν}Φ,

in terms of which the CP-odd anomalous triple couplings can be expressed.

It is worth pointing out that the EFT formalism can also be used to describe new physics contributions to EWPOs, in a way that is model-independent but more general than the “oblique”S,T,Uparameters. The most important operators in this context, at the leading di- mensiond=6, are

O⁽⁶⁾_φ1 =(DµΦ)^†ΦΦ^†(D^µΦ), (11) O⁽⁶⁾_BW= Φ^†B_µνW^µνΦ, (12) which modify the gauge-boson self-energies at tree- level, and

O⁽⁶⁾

Φψ1 =i[Φ^†(DµΦ)−(DµΦ)^†Φ]( ¯ψγ^µψ), (13) O⁽⁶⁾_Φ_ψ3 =i[Φ^†σ^a(DµΦ)−(DµΦ)^†σ^aΦ]( ¯ψγ^µσaψ), (14) which modify the gauge-boson–fermion vertices at tree- level. The limits from EWPOs on the scaleΛof these operators are very strong, of the order O(10 TeV) for ci = O(1) [9]. For illustration, the constraints onO⁽⁶⁾_φ1 andO⁽⁶⁾

BWare shown in Fig. 2.

In addition, the EFT can be a useful tool for describing deviations of the Higgs boson couplings in Higgs production and decay, where some of the same operators as in anomalous gauge boson couplings and in EW- POs occur, seee.g.Ref. [63] for a review.

(5)

-0.4 -0.2 0.0 0.2 0.4 -0.10

-0.05 0.00 0.05 0.10

fBW L²

HTeV^-2L fΦ1 L2HTeV-2L

Figure 2: Constraints on the coefficients of the operatorsO⁽⁶⁾_φ1andO⁽⁶⁾_BW from EWPOs, assuming that no other higher-dimensional operators contribute. From Ref. [62].

3. High-energyW-pair production

Anomalous triple-gauge boson couplings can be probed at the LHC by analyzing gauge-boson pair production. In particular, qq¯⁰ → W⁺W⁻ is sensitive to γWW andZWW couplings. In general,W +W⁻ production also receives contributions from photon collisions, γγ → W +W⁻, which become especially important at large transverse momenta of the W bosons [64]. The photon-induced process depends on different, quartic anomalous couplings, so that it is desirable to separate it from the quark-inducedW⁺W⁻ production in the experimental analysis. Such a separation is possible in the quasi-elastic limit, where the incident protons remain intact and can be tagged [58], but the extrapo- lation from this limit to the total cross-section at high energies is subject to substantial PDF uncertainties.

In addition, the qq¯ channel itself is subject to theoretical uncertainties from radiative corrections. QCD corrections have been computed to NLO+NNLL order [65], and they can modify the Born cross-section by up to 50%. Very recently, a full NNLO calculation of the total cross-section, without resummation of threshold logarithms, has become available [66]. Despite the magnitude of the QCD corrections, the remaining error from missing higher-order contributions is estimated to be small, at the level of few percent, which will be sufficient for most purposes.

Electroweak corrections become particularly important for large transverseW momenta, due to the pres- ence of electroweak Sudakov logarithms of the form L ≡αlog²_M^ˆ^s2

W

. Here ˆs = (pW⁺+pW−)² is theW⁺W⁻ invariant mass. For large values of ˆsthe factor L can

δQCDδgg/10 δγγ

δEW

pT,W⁻(GeV) δ(%)

200 180 160 140 120 100 80 60 20 10 0

−10

−20

−30

−40 σ_LO^gg

σ^γγ_LO σ^q_LO^q^¯

Tevatron

pT,W⁻(GeV) dσ/dp_T,W⁻(pb/GeV)

200 180 160 140 120 100 80 60 1 0.1 0.01 0.001 0.0001

10⁻⁵ 10⁻⁶ 10⁻⁷

δQCDδgg/10 δγγ

δEW

pT,W⁻(GeV) δ(%)

400 350 300 250 200 150 100 50 20 10 0

−10

−20

−30

−40 σ^gg_LO

σ_LO^γγ σ_LO^q¯^q

LHC at 8 TeV

pT,W⁻(GeV) dσ/dpT,W⁻(pb/GeV)

400 350 300 250 200 150 100 50 1 0.1 0.01 0.001 0.0001

10⁻⁵ 10⁻⁶ 10⁻⁷

δQCD/10 δgg

δγγ

δEW

pT,W⁻(GeV) δ(%)

800 700 600 500 400 300 200 100 20 10 0

−10

−20

−30

−40 σ^gg_LO

σ^γγ_LO σ^q¯_LO^q

LHC at 14 TeV

pT,W⁻(GeV) dσ/dpT,W⁻(pb/GeV)

800 700 600 500 400 300 200 100 1 0.1 0.01 0.001 0.0001

10⁻⁵ 10⁻⁶ 10⁻⁷

Figure 3: Radiative corrections toW⁺W⁻production at LHC (√ s= 14 TeV) from different sources. δggandδγγ refer to the gluon- and photon-induced subprocesses, respectively. From Ref. [64].

become of orderO(1) so that higher ordersLⁿ, αLⁿ, ...

need to be resummed to all orders inn. This has been carried out up to NNLL, i.e.including terms of order Lⁿ, αLⁿ andα²Lⁿ[67, 68, 69]. Beyond the logarithmi- cally enhanced contributions, the complete NLO electroweak corrections are also known [64]. The relative impact of the different contributions to the totalW⁺W⁻ cross-section is shown in Fig. 3.

Due to the magnitude of the QCD and electroweak corrections, it is important to include all available results in the experimental analyses and carefully account for theoretical uncertainties from missing higher orders.

For instance, the measurement of the W⁺W⁻ cross- section by ATLAS and CMS [50, 52, 70, 71] differs by 2σ from the SM prediction evaluated by the program MCFM, which includes fixed-order NLO QCD corrections [72, 73]. This discrepancy can be interpreted as an indication for new physics within the context of the Minimal Supersymmetric Standard Model (MSSM) [74, 75, 76]. However, the effect of higher-order QCD corrections and SM electroweak corrections may be significant and should be included before drawing any conclusions. Furthermore, the experimental collaborations applied a jet veto for background suppression, which gives rise to large logarithms ∝log^p^veto^T_s_ˆ that may need to be resummed [77, 78].

4. Conclusions

In exploring the TeV scale of elementary particle physics, electroweak precision observables (EWPOs)

(6)

and direct multi-gauge boson production are both relevant and complement each other. For both groups of observables, the inclusion of higher-order QCD and electroweak corrections is mandatory to prevent the theory uncertainties from dominating the overall error. Much progress has been made in the calculation of these corrections, culminating in complete results for two-loop electroweak corrections to EWPOs and two-loop QCD corrections to LHC production processes. In addition, the resummation of large logarithms that occur in the high-energy and threshold limits, as well as when jet veto cuts are applied, is well understood and has been driven to the next-to-next-to-leading logarithmic level.

The data from LHC and lower-energy precision ex- periments leads to strong constraints on new physics.

These limits can be studied either by considering con- crete models or by working in a model-independent effective field theory (EFT) framework. The EFT has the advantage of being theoretically well-defined, respect- ing all SM symmetries, and providing a prescription for ranking the possible new-physics terms according to the power of a new mass scale by which they are suppressed. On the downside, the EFT is not applicable if the measured momenta or energy are comparable in magnitude to the hypothetical new scale. The EFT setup can be applied to EWPOs, high-energy multi-gauge boson production, and Higgs physics, with each sector providing complementary information on the EFT parameters.

However, the search for new physics in electroweak processes and the setting of limits requires careful control of theoretical uncertainties in the SM predictions.

Currently, not all available theoretical calculations have been incorporated into the experimental analyses, and there is no general prescription for defining theory errors from missing higher-order corrections. This may play a role in explaining the observed discrepancy between the measured and predictedW⁺W⁻cross-section at the LHC.

New physics constraints from EWPOs can be signifi- cantly improved with data from a future high-luminosity e⁺e⁻ collider running on theZ-boson pole and theW- pair threshold, such as ILC or TLEP. To fully capital- ize on the potential of these machines, the precision of the SM theory calculations for the EWPOs will need to be increased substantially. This will require the inclusion of exact three-loop electroweak and mixed QCD- electroweak corrections, a goal that is currently out of reach but may soon become feasible if innovation in this field keeps progressing at a steady pace.

References

[1] S. Schael, et al., Precision electroweak measurements on the Z resonance, Phys.Rept. 427 (2006) 257–454. arXiv:hep- ex/0509008, doi:10.1016/j.physrep.2005.12.006.

[2] P. Anthony, et al., Precision measurement of the weak mixing angle in Moller scattering, Phys.Rev.Lett. 95 (2005) 081601.

arXiv:hep-ex/0504049, doi:10.1103/PhysRevLett.95.081601.

[3] D. Androic, et al., First Determination of the Weak Charge of the Proton, Phys.Rev.Lett. 111 (2013) 141803. arXiv:1307.5275, doi:10.1103/PhysRevLett.111.141803.

[4] A. Camsonne, et al., JLab Measurement of the ⁴He Charge Form Factor at Large Momentum Transfers, Phys.Rev.Lett. 112 (2014) 132503. arXiv:1309.5297, doi:10.1103/PhysRevLett.112.132503.

[5] G. Zeller, et al., A Precise determination of electroweak parameters in neutrino nucleon scattering, Phys.Rev.Lett. 88 (2002) 091802. arXiv:hep-ex/0110059, doi:10.1103/PhysRevLett.88.091802.

[6] C. Wood, et al., Measurement of parity nonconservation and an anapole moment in cesium, Science 275 (1997) 1759–1763.

doi:10.1126/science.275.5307.1759.

[7] J. Guena, M. Lintz, M. Bouchiat, Measurement of the parity vi- olating 6S-7S transition amplitude in cesium achieved within 2 x 10(-13) atomic-unit accuracy by stimulated-emission detec- tion, Phys.Rev. A71 (2005) 042108. arXiv:physics/0412017, doi:10.1103/PhysRevA.71.042108.

[8] K. Olive, et al., Review of particle physics, Chin.Phys. C38 (2014) 090001, chapt. 10. doi:10.1088/1674-1137/38/9/090001.

[9] M. Ciuchini, E. Franco, S. Mishima, L. Silvestrini, Electroweak Precision Observables, New Physics and the Nature of a 126 GeV Higgs Boson, JHEP 1308 (2013) 106. arXiv:1306.4644, doi:10.1007/JHEP08(2013)106.

[10] M. Baak, et al., The global electroweak fit at NNLO and prospects for the LHC and ILC, arXiv:1407.3792.

[11] V. A. Smirnov, Applied asymptotic expansions in momenta and masses, Springer Tracts Mod.Phys. 177 (2002) 1–262.

[12] A. Freitas, W. Hollik, W. Walter, G. Weiglein, Complete fermionic two loop results for the M(W) - M(Z) interde- pendence, Phys.Lett. B495 (2000) 338–346. arXiv:hep- ph/0007091, doi:10.1016/S0370-2693(00)01263-6.

[13] M. Awramik, M. Czakon, Complete two loop bosonic contributions to the muon lifetime in the standard model, Phys.Rev.Lett. 89 (2002) 241801. arXiv:hep-ph/0208113, doi:10.1103/PhysRevLett.89.241801.

[14] A. Onishchenko, O. Veretin, Two loop bosonic electroweak corrections to the muon lifetime and M(Z) - M(W) inter- dependence, Phys.Lett. B551 (2003) 111–114. arXiv:hep- ph/0209010, doi:10.1016/S0370-2693(02)03004-6.

[15] M. Awramik, M. Czakon, A. Freitas, G. Weiglein, Pre- cise prediction for the W boson mass in the standard model, Phys.Rev. D69 (2004) 053006. arXiv:hep-ph/0311148, doi:10.1103/PhysRevD.69.053006.

[16] M. Awramik, M. Czakon, A. Freitas, G. Weiglein, Complete two-loop electroweak fermionic corrections to sin²θ^lept_eff and indirect determination of the Higgs boson mass, Phys.Rev.Lett. 93 (2004) 201805. arXiv:hep-ph/0407317, doi:10.1103/PhysRevLett.93.201805.

[17] W. Hollik, U. Meier, S. Uccirati, The effective electroweak mixing angle sin²θeff with two-loop fermionic contributions, Nucl.Phys. B731 (2005) 213–224. arXiv:hep-ph/0507158, doi:10.1016/j.nuclphysb.2005.10.015.

[18] M. Awramik, M. Czakon, A. Freitas, Electroweak two- loop corrections to the effective weak mixing angle, JHEP

(7)

0611 (2006) 048. arXiv:hep-ph/0608099, doi:10.1088/1126- 6708/2006/11/048.

[19] W. Hollik, U. Meier, S. Uccirati, The Effective electroweak mixing angle sin²θeff with two-loop bosonic contributions, Nucl.Phys. B765 (2007) 154–165. arXiv:hep-ph/0610312, doi:10.1016/j.nuclphysb.2006.12.001.

[20] M. Awramik, M. Czakon, A. Freitas, B. Kniehl, Two- loop electroweak fermionic corrections to sin²θ^b_e_ff^¯^b, Nucl.Phys. B813 (2009) 174–187. arXiv:0811.1364, doi:10.1016/j.nuclphysb.2008.12.031.

[21] A. Freitas, Two-loop fermionic electroweak corrections to the Z-boson width and production rate, Phys.Lett. B730 (2014) 50–

52. arXiv:1310.2256, doi:10.1016/j.physletb.2014.01.017.

[22] A. Freitas, Higher-order electroweak corrections to the partial widths and branching ratios of the Z boson, JHEP 1404 (2014) 070. arXiv:1401.2447, doi:10.1007/JHEP04(2014)070.

[23] K. Chetyrkin, J. Kuhn, M. Steinhauser, Corrections of order O(GFM²_tα²_s) to theρparameter, Phys.Lett. B351 (1995) 331–

338. arXiv:hep-ph/9502291, doi:10.1016/0370-2693(95)00380- 4.

[24] M. Faisst, J. Kuhn, T. Seidensticker, O. Veretin, Three loop top quark contributions to the rho parameter, Nucl.Phys. B665 (2003) 649–662. arXiv:hep-ph/0302275, doi:10.1016/S0550- 3213(03)00450-4.

[25] R. Boughezal, J. Tausk, J. van der Bij, Three-loop electroweak corrections to the W-boson mass and sin²θ^lept_{e f f} in the large Higgs mass limit, Nucl.Phys. B725 (2005) 3–14. arXiv:hep- ph/0504092, doi:10.1016/j.nuclphysb.2005.07.013.

[26] Y. Schroder, M. Steinhauser, Four-loop singlet contribution to the rho parameter, Phys.Lett. B622 (2005) 124–130. arXiv:hep- ph/0504055, doi:10.1016/j.physletb.2005.06.085.

[27] K. Chetyrkin, M. Faisst, J. H. Kuhn, P. Maierhofer, C. Sturm, Four-Loop QCD Corrections to the Rho Parame- ter, Phys.Rev.Lett. 97 (2006) 102003. arXiv:hep-ph/0605201, doi:10.1103/PhysRevLett.97.102003.

[28] R. Boughezal, M. Czakon, Single scale tadpoles and O(GFm²_tα³_s) corrections to the rho parameter, Nucl.Phys. B755 (2006) 221–238. arXiv:hep-ph/0606232, doi:10.1016/j.nuclphysb.2006.08.007.

[29] D. Y. Bardin, et al., ZFITTER v.6.21: A Semianalytical program for fermion pair production in e+ e- annihilation, Comput.Phys.Commun. 133 (2001) 229–395. arXiv:hep- ph/9908433, doi:10.1016/S0010-4655(00)00152-1.

[30] A. Arbuzov, et al., ZFITTER: A Semi-analytical program for fermion pair production in e+e- annihilation, from version 6.21 to version 6.42, Comput.Phys.Commun. 174 (2006) 728–758.

arXiv:hep-ph/0507146, doi:10.1016/j.cpc.2005.12.009.

URLhttp://zfitter.desy.de/

[31] H. Flacher, et al., Revisiting the Global Electroweak Fit of the Standard Model and Beyond with Gfitter, Eur.Phys.J. C60 (2009) 543–583. arXiv:0811.0009, doi:10.1140/epjc/s10052- 009-0966-6, 10.1140/epjc/s10052-011-1718-y.

URLhttp://gfitter.desy.de/Software/

[32] A. Freitas, et al., Exploring Quantum Physics at the ILC, arXiv:1307.3962.

[33] O. Eberhardt, U. Nierste, M. Wiebusch, Status of the two- Higgs-doublet model of type II, JHEP 1307 (2013) 118.

arXiv:1305.1649, doi:10.1007/JHEP07(2013)118.

[34] M. Baak, et al., Working Group Report: Precision Study of Elec- troweak Interactions, arXiv:1310.6708.

[35] G. Aad, et al., Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics, arXiv:0901.0512.

[36] K. Melnikov, F. Petriello, Electroweak gauge boson production at hadron colliders through O(α²_s), Phys.Rev. D74 (2006) 114017. arXiv:hep-ph/0609070,

doi:10.1103/PhysRevD.74.114017.

[37] S. Catani, L. Cieri, G. Ferrera, D. de Florian, M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys.Rev.Lett. 103 (2009) 082001.

arXiv:0903.2120, doi:10.1103/PhysRevLett.103.082001.

[38] G. Bozzi, S. Catani, G. Ferrera, D. de Florian, M. Grazz- ini, Production of Drell-Yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to- leading logarithmic accuracy, Phys.Lett. B696 (2011) 207–213.

arXiv:1007.2351, doi:10.1016/j.physletb.2010.12.024.

[39] U. Baur, O. Brein, W. Hollik, C. Schappacher, D. Wackeroth, Electroweak radiative corrections to neutral current Drell-Yan processes at hadron colliders, Phys.Rev. D65 (2002) 033007.

arXiv:hep-ph/0108274, doi:10.1103/PhysRevD.65.033007.

[40] C. Carloni Calame, G. Montagna, O. Nicrosini, A. Vicini, Precision electroweak calculation of the production of a high transverse-momentum lepton pair at hadron colliders, JHEP 0710 (2007) 109. arXiv:0710.1722, doi:10.1088/1126- 6708/2007/10/109.

[41] S. Jadach, B. Ward, Z. Was, KK MC 4.22: Coherent exclusive exponentiation of electroweak corrections forff¯→ f⁰f¯⁰ at the LHC and muon colliders, Phys.Rev. D88 (2013) 114022.

arXiv:1307.4037, doi:10.1103/PhysRevD.88.114022.

[42] S. Dittmaier, A. Huss, C. Schwinn,O(αsα) corrections to Drell- Yan processes in the resonance region, PoS LL2014 (2014) 045.

arXiv:1405.6897.

[43] V. M. Abazov, et al., Measurement of the effective weak mixing angle inpp¯→Z/γ^∗→e⁺e⁻events, arXiv:1408.5016.

[44] A. Bodek, A measurement of the electro-weak mixing angle and an indirect measurement of the W mass at CDF, contribution to this conference.

URLindico.ific.uv.es/indico/contributionDisplay .py?contribId=909&confId=2025

[45] R. Hawkings, K. Monig, Electroweak and CP violation physics at a linear colliderZfactory, Eur.Phys.J.direct C1 (1999) 8.

arXiv:hep-ex/9910022.

[46] M. Bicer, et al., First Look at the Physics Case of TLEP, JHEP 1401 (2014) 164. arXiv:1308.6176, doi:10.1007/JHEP01(2014)164.

[47] K. Hagiwara, R. Peccei, D. Zeppenfeld, K. Hikasa, Probing the Weak Boson Sector in e+e- —¿ W+W-, Nucl.Phys. B282 (1987) 253. doi:10.1016/0550-3213(87)90685-7.

[48] K. Hagiwara, S. Ishihara, R. Szalapski, D. Zeppen- feld, Low-energy effects of new interactions in the electroweak boson sector, Phys.Rev. D48 (1993) 2182–2203.

doi:10.1103/PhysRevD.48.2182.

[49] G. Aad, et al., Measurement ofWZproduction in proton-proton collisions at√

s=7 TeV with the ATLAS detector, Eur.Phys.J.

C72 (2012) 2173. arXiv:1208.1390, doi:10.1140/epjc/s10052- 012-2173-0.

[50] G. Aad, et al., Measurement ofW⁺W⁻production in pp collisions at √

s=7 TeV with the ATLAS detector and limits on anomalous WWZ and WWγcouplings, Phys.Rev. D87 (2013) 112001. arXiv:1210.2979, doi:10.1103/PhysRevD.87.112001, 10.1103/PhysRevD.88.079906.

[51] S. Chatrchyan, et al., Measurement of the sum of WW andWZ production with W+dijet events in ppcollisions at

√s=7 TeV, Eur.Phys.J. C73 (2013) 2283. arXiv:1210.7544, doi:10.1140/epjc/s10052-013-2283-3.

[52] S. Chatrchyan, et al., Measurement of theW⁺W⁻Cross section inppCollisions at √

s= 7 TeV and Limits on Anoma- lousWWγandWWZcouplings, Eur.Phys.J. C73 (2013) 2610.

arXiv:1306.1126, doi:10.1140/epjc/s10052-013-2610-8.

[53] V. M. Abazov, et al., Limits on anomalous trilinear gauge boson couplings fromWW,WZ andWγproduction inpp¯ col-

(8)

lisions at √

s = 1.96 TeV, Phys.Lett. B718 (2012) 451–459.

arXiv:1208.5458, doi:10.1016/j.physletb.2012.10.062.

[54] S. Schael, et al., Electroweak Measurements in Electron- Positron Collisions at W-Boson-Pair Energies at LEP, Phys.Rept. 532 (2013) 119–244. arXiv:1302.3415, doi:10.1016/j.physrep.2013.07.004.

[55] C. Degrande, N. Greiner, W. Kilian, O. Mattelaer, H. Mebane, et al., Effective Field Theory: A Modern Approach to Anomalous Couplings, Annals Phys. 335 (2013) 21–32.

arXiv:1205.4231, doi:10.1016/j.aop.2013.04.016.

[56] O. Eboli, M. Gonzalez-Garcia, J. Mizukoshi,pp→ j je^±µ^±νν and j je^±µ^∓νν at O(α⁶_em) and O(α⁴_emα²_s) for the study of the quartic electroweak gauge boson vertex at CERN LHC, Phys.Rev. D74 (2006) 073005. arXiv:hep-ph/0606118, doi:10.1103/PhysRevD.74.073005.

[57] V. M. Abazov, et al., Search for anomalous quarticWWγγ couplings in dielectron and missing energy final states in pp¯ collisions at √

s=1.96 TeV, Phys.Rev. D88 (2013) 012005.

[58] S. Chatrchyan, et al., Study of exclusive two-photon production ofW⁺W⁻inppcollisions at √

s=7 TeV and constraints on anomalous quartic gauge couplings, JHEP 1307 (2013) 116.

arXiv:1305.5596, doi:10.1007/JHEP07(2013)116.

[59] S. Chatrchyan, et al., A search for WW gamma and WZ gamma production and constraints on anomalous quartic gauge couplings in pp collisions at sqrt(s)=8 TeV, Phys.Rev. D90 (2014) 032008. arXiv:1404.4619, doi:10.1103/PhysRevD.90.032008.

[60] G. Gounaris, J. Layssac, F. Renard, Off-shell struc- ture of the anomalous Z and γ selfcouplings, Phys.Rev. D62 (2000) 073012. arXiv:hep-ph/0005269, doi:10.1103/PhysRevD.62.073012.

[61] C. Degrande, A basis of dimension-eight operators for anomalous neutral triple gauge boson interactions, JHEP 1402 (2014) 101. arXiv:1308.6323, doi:10.1007/JHEP02(2014)101.

[62] C.-Y. Chen, S. Dawson, C. Zhang, Electroweak Effective Op- erators and Higgs Physics, Phys.Rev. D89 (2014) 015016.

[63] C. Englert, A. Freitas, M. Muhlleitner, T. Plehn, M. Rauch, et al., Precision Measurements of Higgs Couplings: Impli- cations for New Physics Scales, J.Phys. G41 (2014) 113001.

arXiv:1403.7191, doi:10.1088/0954-3899/41/11/113001.

[64] A. Bierweiler, T. Kasprzik, J. H. Khn, S. Uccirati, Electroweak corrections to W-boson pair production at the LHC, JHEP 1211 (2012) 093. arXiv:1208.3147, doi:10.1007/JHEP11(2012)093.

[65] S. Dawson, I. M. Lewis, M. Zeng, Threshold resummed and approximate next-to-next-to-leading order results for W⁺W⁻ pair production at the LHC, Phys.Rev. D88 (2013) 054028.

[66] T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhfer, A. von Manteuffel, et al., W⁺W⁻ production at hadron colliders in NNLO QCD, arXiv:1408.5243.

[67] V. S. Fadin, L. Lipatov, A. D. Martin, M. Melles, Resum- mation of double logarithms in electroweak high-energy processes, Phys.Rev. D61 (2000) 094002. arXiv:hep-ph/9910338, doi:10.1103/PhysRevD.61.094002.

[68] E. Accomando, A. Denner, A. Kaiser, Logarithmic electroweak corrections to gauge-boson pair production at the LHC, Nucl.Phys. B706 (2005) 325–371. arXiv:hep-ph/0409247, doi:10.1016/j.nuclphysb.2004.11.019.

[69] J. Kuhn, F. Metzler, A. Penin, S. Uccirati, Next-to- Next-to-Leading Electroweak Logarithms for W-Pair Produc- tion at LHC, JHEP 1106 (2011) 143. arXiv:1101.2563, doi:10.1007/JHEP06(2011)143.

[70] CMS Collaboration, Measurement of WW production rate, CMS-PAS-SMP-12-013.

[71] J. Berryhill, Electroweak Physics: highlights of experimental results from hadron colliders, contribution to this conference.

URLindico.ific.uv.es/indico/contributionDisplay .py?contribId=83&confId=2025

[72] J. M. Campbell, R. K. Ellis, An Update on vector boson pair production at hadron colliders, Phys.Rev. D60 (1999) 113006.

arXiv:hep-ph/9905386, doi:10.1103/PhysRevD.60.113006.

[73] J. M. Campbell, R. K. Ellis, C. Williams, Gluon-Gluon Contributions to W+ W- Production and Higgs Interfer- ence Effects, JHEP 1110 (2011) 005. arXiv:1107.5569, doi:10.1007/JHEP10(2011)005.

[74] D. Curtin, P. Jaiswal, P. Meade, Charginos Hiding In Plain Sight, Phys.Rev. D87 (2013) 031701. arXiv:1206.6888, doi:10.1103/PhysRevD.87.031701.

[75] K. Rolbiecki, K. Sakurai, Light stops emerging in WW cross section measurements?, JHEP 1309 (2013) 004.

arXiv:1303.5696, doi:10.1007/JHEP09(2013)004.

[76] D. Curtin, P. Jaiswal, P. Meade, P.-J. Tien, Casting Light on BSM Physics with SM Standard Candles, JHEP 1308 (2013) 068. arXiv:1304.7011, doi:10.1007/JHEP08(2013)068.

[77] P. Meade, H. Ramani, M. Zeng, Transverse momentum resummation effects inW⁺W⁻measurements, arXiv:1407.4481.

[78] P. Jaiswal, T. Okui, An Explanation of the WW Excess at the LHC by Jet-Veto Resummation, arXiv:1407.4537.