Combined measurements of anomalous charged trilinear gauge-boson couplings from diboson production in collisions at TeV
We present measurements of the anomalous and trilinear gauge couplings from a combination of four diboson production and decay channels using data collected by the D0 detector at the Fermilab Tevatron Collider. These results represent the first high statistics combination of limits across different diboson production processes at the Tevatron and use data corresponding to an integrated luminosity of approximately 1 fb. When respecting symmetry, we measure central values and 68% C.L. allowed intervals of , and . We present the most stringent measurements to date for the boson magnetic dipole and electromagnetic quadrupole moments of and , respectively.
pacs:14.70.Fm, 13.40.Em, 13.85.Rm, 14.70.Hp
The gauge theory of electroweak interactions contains a striking feature. In quantum electrodynamics, the photons carry no electric charge and thus lack photon-to-photon couplings and do not self-interact. In contrast, the weak vector bosons carry weak charge and do interact amongst themselves through trilinear and quartic gauge boson vertices.
The most general and interactions can be described lagrangian (); HWZ () using a Lorentz invariant effective Lagrangian that contains fourteen dimensionless couplings, seven each for and . Assuming electromagnetic gauge invariance and conservation reduces the number of independent couplings to five (electromagnetic gauge invariance requires ), and the Lagrangian takes the form:
where denotes the boson field, , , or , and is the mass of the boson. The global coupling parameters are and , as in the standard model (SM) in which and are the magnitude of the electron charge and the weak mixing angle, respectively. In the SM and . For convenience, anomalous trilinear gauge couplings (anomalous TGCs) and are defined as and , respectively.
The boson magnetic dipole and electric quadrupole moments may be expressed in terms of the coupling parameters as
As mentioned above, .
If the coupling parameters have non-SM values then the amplitudes for gauge boson pair production grow with energy, eventually violating tree-level unitarity. The unitarity violation can be controlled by parametrizing the anomalous couplings as dipole form factors with a cutoff scale, . The anomalous couplings then take a form in which is the center-of-mass energy of the colliding partons and is the coupling value in the limit newref (). The quantity is physically interpreted as the mass scale where the new phenomenon responsible for the anomalous couplings is directly observable. The cutoff is conservatively set at the limit of sensitivity, close to the collision center-of-mass energy. We use TeV; coupling limits depend only weakly on for TeV in hadronic collisions at Tevatron energies.
We measure the electroweak coupling parameters through the study of gauge boson pairs. Several processes contribute to SM boson pair production. Fig. 1(a) shows -channel production of dibosons in which are , , or . The -channel production shown in Fig. 1(b) involves boson self-interactions through a trilinear gauge vertex. Final states () produced via the coupling are or . Final states produced through the coupling are or . The typical effect of anomalous TGCs is to increase the cross section especially at high boson transverse momentum (). We thus analyze corresponding observables to measure such effects.
Previously published limits on anomalous TGCs from a combination of channels come from the D0 Collaboration in the 1992-1996 Tevatron run with integrated luminosity () of 100 pb run1prd (), the CDF Collaboration with the current Tevatron run ( pb) cdfresult (), and LEP2 experiments LEP (). The best previously published boson magnetic dipole moment result is from a combination of measurements by the DELPHI Collaboration delphi ().
In this Letter, we investigate the and trilinear vertices through diboson production. We set limits on the non-SM or anomalous TGC parameters , , and . These limits are derived from a combination of previously published measurements involving four final states: wgamprl (), wwpaper (), wzpaper (), and wwwzpaper (), in which is an electron or muon, is a neutrino, and is a jet. Each measurement used data collected by the D0 detector dzeronim () from collisions at TeV delivered by the Fermilab Tevatron Collider.
The process is sensitive only to the coupling. The process was studied with data corresponding to 0.7 fb wgamprl (). The main requirements were an electron with transverse energy 25 GeV or a muon with transverse momentum 20 GeV, a photon with 9 GeV, missing transverse energy 25 (20) GeV for the electron (muon) channel, and separation between the photon and lepton in measures () space of . Furthermore, to suppress final state radiation the three-body transverse mass mt3 () of the lepton, photon, and was required to exceed 120 (110) GeV for the electron (muon) channel. In total 180 (83) candidate events were observed. After subtracting backgrounds, the signal was events, consistent with the SM prediction of events for the channel. The photon spectra of the candidates in the data and those estimated for the backgrounds are input into the combination. For production in the presence of TGCs, spectra were simulated using the Baur Monte Carlo (MC) baurwgamlo (); baurwgamnlo () with a fine grid in space.
The measurement wwpaper () used data corresponding to an integrated luminosity of 1 fb. The data were divided into three channels defined by the flavor of the leptons from the boson decays: , , and . For all channels, the leading lepton had 25 GeV and the trailing lepton had 15 GeV. The leptons were required to have opposite charge. In the data 22 (), 64 () and 14 () candidate events were observed, consistent with the sum of SM and backgrounds of (), () and () events. Two-dimensional histograms of leading and trailing lepton were produced for the data and backgrounds and used as inputs in the combination. Distributions for SM and anomalous TGC values were generated using the event generator from Hagiwara, Zeppenfeld, and Woodside (HZW) HWZ ().
The measurement wzpaper () selected the four final states , , , and . The data corresponded to an integrated luminosity of 1 fb. All three charged leptons were required to have GeV. boson candidates consisted of like-flavor lepton pairs with mass GeV or GeV. For the and channels, the oppositely charged lepton pair with mass closest to the pole mass was chosen as the boson candidate. To select boson candidates, the must have exceeded 20 GeV. To reduce background events from to a negligible level, the magnitude of the vector sum of the charged lepton transverse momenta and the was required to be less than 50 GeV. The sum over all channels yielded 13 candidate events in the data consistent with a SM estimate of events and background events. The of the boson is sensitive to anomalous TGCs and is used in the combination. The HZW MC is used to estimate the SM spectrum as well as spectra from anomalous TGCs.
Finally, the measurement wwwzpaper () selected events in which one boson decays leptonically and the other boson decays hadronically. The data corresponded to an integrated luminosity of fb. The main requirements were an electron or muon with 20 GeV, 20 GeV, and at least two jets with 20 GeV with the leading jet satisfying 30 GeV. In total 12,473 (14,392) candidate events in the channel were observed, consistent with the SM prediction of 12,460550 (14,370620) events lnujjcaveat (). An observable sensitive to anomalous TGCs is the of the dijet system. The data and background spectra for this variable are used as inputs for the combination. Spectra with anomalous TGCs were generated with the HZW MC.
Distributions of the sensitive observables mentioned above for each final state are generated for signal with the corresponding Monte Carlos and for backgrounds using simulations or data. The signal distributions vary as a function of the TGC parameters under study both in spectral shape and event yield. In addition to allowing variation in the TGC parameters themselves, nuisance parameters are used to allow systematic offsets to vary within their uncertainties. A simultaneous fit to the data distributions is performed in order to determine the anomalous TGC limits. The function used in this fit is wadeLim ():
in which the variables and index the number of histogram bins () and the number of systematic uncertainties () respectively. In this function is the Poisson probability for events with a mean of events; is the Gaussian probability for the value in a distribution with a mean value of and a variance ; (in vector form as ) is a dimensionless parameter describing departures in nuisance parameters in units of the associated systematic uncertainty ; is the number of data events in bin ; and is the number of predicted events in bin . The number of bins used in the fit is the sum of the number of bins in each kinematic distribution for each channel.
In total 49 sources of systematic uncertainty are considered. As implied in Eq. 1, systematic uncertainties are treated as Gaussian priors on the expected number(s) of events. Systematic uncertainties on the luminosity, lepton identification, and theoretical uncertainties on the cross sections for the backgrounds estimated from MC are correlated across all observables. Uncertainties on background estimates based on data are correlated across specific final states within a diboson production channel as appropriate. The uncertainties with the largest impact on the result are those related to background cross sections and the luminosity. The effect of incorporating systematic uncertainties into the fit is to degrade the resulting limits by 30%.
Four two-dimensional surfaces in TGC space are examined: (a) each of the three pairings of the three free parameters (, , ) while respecting symmetry by using the constraints lepscen () and (b) the plane for the equal-couplings scenario HWZ () in which , . The two-dimensional 68% and 95% C.L. contours are shown in Figs. 2 and 3. The two-dimensional contours for boson magnetic dipole and electric quadrupole moments are shown in Fig. 4. The one-dimensional 68% and 95% C.L. limits for each coupling parameter, with the other couplings parameters fixed at their SM values, are shown in Table 1.
|Results respecting symmetry|
|Parameter||Minimum||68% C.L.||95% C.L.|
|Results for equal-couplings|
|Parameter||Minimum||68% C.L.||95% C.L.|
These results provide the most stringent limits on anomalous values of and TGCs measured from hadronic collisions to date. The 95% C.L. limits in both scenarios represent an improvement relative to the previous D0 run1prd () and CDF cdfresult () results of about a factor of 3. When respecting symmetry, our measurements with 68% C.L. allowed intervals of , and are only factors of approximately 2 – 3 times less sensitive than the combined results from the four LEP2 experiments: , and , also at 68% C.L. LEP (). Furthermore, with only 1 fb of data our sensitivity is comparable to that of an individual LEP2 experiment aleph (); opal (); l3 (); delphi ().
We also extract measurements of the boson magnetic dipole and electric quadrupole moments. When respecting symmetry with we measure 68% C.L. intervals (one-dimensional with the other parameter held at its SM value) of and , respectively. The most stringent previously published result is and from the DELPHI Collaboration delphi ().
In summary, we presented measurements of anomalous and trilinear gauge couplings and related boson magnetic dipole and electric quadrupole moments based on the combination of four diboson production and decay channels using fb of data collected with the D0 detector at the Fermilab Tevatron Collider. While many of the measurements considered in this combination are limited by statistics, projections indicate that a combination of CDF and D0 data with 5 fb each will improve the sensitivity to levels comparable or better than the combined LEP2 limits.
We thank the staffs at Fermilab and collaborating institutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); STFC and the Royal Society (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); CAS and CNSF (China); and the Alexander von Humboldt Foundation (Germany).
- (a) Visitor from Augustana College, Sioux Falls, SD, USA.
- (b) Visitor from Rutgers University, Piscataway, NJ, USA.
- (c) Visitor from The University of Liverpool, Liverpool, UK.
- (d) Visitor from Centro de Investigacion en Computacion - IPN, Mexico City, Mexico.
- (e) Visitor from ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico.
- (f) Visitor from Universität Bern, Bern, Switzerland.
- (g) Visitor from Universität Zürich, Zürich, Switzerland.
- (8) K. Hagiwara, R. D. Peccei, and D. Zeppenfeld, Nucl. Phys. B282, 253 (1987).
- (9) K. Hagiwara, J. Woodside, and D. Zeppenfeld, Phys. Rev. D 41, 2113 (1990).
- (10) Limits on anomalous couplings presented in this Letter are given as the low energy limits of the couplings.
- (11) B. Abbott et al. (D0 Collaboration), Phys. Rev. D 60, 072002 (1999).
- (12) T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 76, 111103(R) (2007).
- (13) C. Amsler et al. (Particle Data Group), Phys. Lett. B 667, 1 (2008); P. Bambade et al. (LEP Collaborations), arXiv:hep-ex/0307056 (2003); J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C 54, 345 (2008).
- (14) P. Abreu et al. (DELPHI Collaboration), Phys. Lett. B 502, 9 (2001).
- (15) V. M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 100, 241805 (2008).
- (16) V. M. Abazov et al. (D0 Collaboration), arXiv:0904.0673 [hep-ex] (2009), submitted to Phys. Rev. Lett.
- (17) V. M. Abazov et al. (D0 Collaboration), Phys. Rev. D 76, 111104(R) (2007).
- (18) V.M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 102, 161801 (2009); V. M. Abazov et al. (D0 Collaboration), arXiv:0907.4398 [hep-ex] (2009), submitted to Phys. Rev. D.
- (19) V. M. Abazov et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res. A 565, 463 (2006).
- (20) D0 uses a cylindrical coordinate system with the axis running along the beam axis. Angles and are the polar and azimuthal angles, respectively. Pseudorapidity is defined as in which is measured with respect to the primary vertex. In the massless limit, is equivalent to the rapidity . is the pseudorapidity measured with respect to the center of the detector.
- (21) U. Baur, S. Errede and G. Landsberg, Phys. Rev. D 50, 1917 (1994).
- (22) U. Baur and E. L. Berger, Phys. Rev. D 41, 1476 (1990).
- (23) U. Baur, T. Han, and J. Ohnemus, Phys. Rev. D 48, 5140 (1993).
- (24) Note that the backgrounds for the measurement, +jets, +jets, and single top, were all modeled with Monte Carlo simulations. The dominant +jets background was scaled to match the data, while all other backgrounds were normalized using SM next-to-leading order or next-to-next-to-leading-order predictions for cross sections.
- (25) W. Fisher, FERMILAB-TM-2386-E (2007).
- (26) M. Bilenky, J. L. Kneur, F. M. Renard and D. Schildknecht, Nucl. Phys. B 409, 22 (1993); Nucl. Phys. B 419, 240 (1994).
- (27) S. Schael et al. (ALEPH Collaboration), Phys. Lett. B 614, 7 (2005).
- (28) G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 33, 463 (2004).
- (29) P. Achard et al. (L3 Collaboration), Phys. Lett. B 586, 151 (2004).