A Phenomenological study on the wino radiative decay in anomalous U(1 ) ′ models
aa r X i v : . [ h e p - ph ] J u l A Phenomenological study on the wino radiative decay in anomalous U (1) ′ models Francesco Fucito a , Andrea Lionetto a , Antonio Racioppi b , Daniel Ricci Pacifici a a Dipartimento di Fisica dell’Universit`a di Roma ,“Tor Vergata” and I.N.F.N. - Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, 1 - 00133 Roma, ITALY b National Institute of Chemical Physics and Biophysics, Ravala 10, Tallinn 10143, Estonia
Abstract
An extension of the Standard Model by at least one extra U(1) gauge symmetry has been investigated by manyauthors. In this paper we explore the possibility that this extra U(1) is anomalous. One of the possible signatures ofthis model could be given by the photons produced in the decays of the NLSP into the LSP.
Keywords:
Beyond the SM; LHC; Anomalous U(1) Models; NLSP Radiative Decay
1. Introduction
The start of the LHC has greatly motivated detailedphenomenological studies of scenarios which involve physicsbeyond the Standard Model (SM). Among them D-braneconstructions in string theory are one of the most promis-ing framework in which the SM can be embedded and ex-tended. Such brane constructions naturally lead to extraanomalous U (1)’s in the four dimensional low energy the-ory and, in turn, to the presence of possible heavy Z ′ par-ticles in the spectrum. These particles should be amongthe early findings of LHC and besides for the above citedmodels they are also a prediction of many other theo-retical models of the unification of forces (see [1] for arecent review). In [2] we have considered a minimal ex-tension of the Minimal Supersymmetric Standard Model(MSSM) with a single extra U (1) ′ gauge symmetry in astring-inspired setup. We believe that our model encodesthe key features of the low-energy sector of some of thosebrane construction. In this framework we studied in [3]the radiative decay of the next to lightest supersymmetricparticle (NLSP) into the lightest supersymmetric parti-cle (LSP). This kind of process is very interesting since itmight be the first one where the LSP could be observedat LHC [4, 5] and at the upcoming ILC [6, 7].
2. Preliminaries and Lagrangian
Under suitable assumptions the LSP in our modelturns out to be an axino [8], the fermion component of theSt¨uckelberg supermultiplet related to the anomaly can-cellation mechanism (see for details [2, 3, 8]). Withoutloss of generality we assume a wino-like NLSP. In the fol-lowing we just give the interaction term which involve theaxino and the wino relevant for our analysis. The interac-tion term, written in terms of four components Majorana spinors , is given by i L = √ θ W g A (2) M Z ′ g π ¯ λ γ [ γ µ , γ ν ]( ∂ µ A ν ) ψ S (1)where λ is the neutral wino, ψ S is the axino, A ν is thephoton, θ W the Weinberg angle, g and g respectivelythe U (1) ′ and SU (2) coupling constants, A (2) the U (1) ′ − SU (2) − SU (2) anomaly factor and M Z ′ the Z ′ mass. Therate of the radiative decay ( λ → Ψ S γ ) isΓ (2) γ = g sin θ W (cid:18) g A (2) M Z ′ (cid:19) (∆ M ) (∆ M + 2 M S ) π (∆ M + M S ) (2)where ∆ M = M − M S , while M and M S are respec-tively the wino and axino masses. As we showed in [3], theradiative decay is the most dominant wino decay modewith a BR close to 1 ( & τ λ ≃ ℏ Γ (2) γ (3)
3. LHC Phenomenology
In order to fall into the WMAP range in the mostexperimentally attractive situation, we considered a lightLSP (115 GeV . M S .
150 GeV) and a mass gap of or-der ∆
M /M S ≃ M ˜ Q for The gamma matrices γ µ are in the Weyl representation. Preprint submitted to Elsevier December 6, 2018
15 120 125 130 135 140 145 1501234 M S H GeV L M Q Ž H T e V L Wino Production: D M (cid:144) M S = % < > H L Figure 1: Number of directly produced winos in function of theaxino mass M S and the universal squark mass M ˜ Q . the first two squark generations (since under this assump-tion they are nearly degenerate) and we assumed flavorblindness [10]. The contribution from the third genera-tion squarks is always negligible. In Fig. 1 we summa-rize the results obtained in [3] by plotting the numberof directly produced winos as a function of M S and M ˜ Q having assumed 14 TeV of center of mass energy and 100fb − of integrated luminosity. Since the BR is almostclose to one this is also the number of photons in thefinal state. The number of photons produced is of theorder of 10 . In our analysis we follow [9],[11]-[13], wherethe NLSP decay in the GMSB framework is controlledby the parameter C grav . If the NLSP lifetime is not toolong ( C grav ∼
1) photons originate close to the primaryinteraction vertex (“prompt photons”). In the case oflarge C grav and therefore long lived neutralinos the re-sulting photons are non-pointing. From now on we fixthe axino mass M S ≃
124 GeV and the universal squarkmass M ˜ Q ≃ . C grav is played by the ratio g A (2) /M Z ′ . In the following wediscuss two different cases: short lived NLSP and longlived one. We compare the number of photons produced by ra-diative decay with the ones produced by the cascadedecays of all the other supersymmetric processes. Weslightly modified the Herwig code 6.5 [14] in order to takeinto account the new axino state in the neutral sector.It should be stressed that Herwig does not implementextra Z ′ in a supersymmetric framework. This in turnimplies that the total number of photons can be underes-timated due to the lack of sparticles interactions with the Z ′ . However this problem can be overcome by assuminga decoupled Z ′ either because it is very heavy or be-cause it is extra-weak coupled. We generated by Herwig2-partons → f b − of in-tegrated luminosity but we have not considered the caseof SM particles produced directly in the parton-parton Entries 1552960Mean 0.002703 ± ± (GeV/c) T P0 20 40 60 80 100 120 140 160 180 200 nu m b e r o f pho t on s / G e V / c Entries 1552960Mean 0.002703 ± ± γ Entries 6129Mean 0.2901 ± ± ± ± λ not from γ T P λ from γ T P λ and not from λ from γ T and P γ T P γ λ from γ λ not from γ γ T P Figure 2: P T distribution of photons (in log scale) for 10 susyevents. ic1 Entries 10004Mean 1.675RMS 0.5259 γ N0 1 2 t o t] N u m b e r o f eve n t s [ ic1 Entries 10004Mean 1.675RMS 0.5259
GMSB1 ic2
Entries 10004Mean 0.3619RMS 0.4867
GMSB1 our model| < 2.5 η | < 1.37, 1.52 < | η > 20 GeV/c and | T Number of generated photons with P
Figure 3: Number of generated photons before the preselection cuts. interaction. A good discriminant variable of the processis the P T of the photons produced by radiative decay, inparticular in the region of P T between 30-80 GeV/c. Thecorresponding distribution is shown in Fig. 2. We denotein red the number of γ ’s radiatively produced from thedecay of the wino, in blue the number of γ ’s from all theother processes while in black the sum of the two. Weassumed τ λ ≃ . · − s , which is obtainable with M Z ′ ≃ g A (2) ≃ .
2. We performed thesame cut on the number of generated photons as in [13]with P T >
20 GeV and with pseudorapidity | η | ≤ . . < | η | < .
5, which provides a good way to furthersuppress the SUSY background . The result obtainedby using Herwig in generating 10 net events is given inFig. 3. The most important difference between our caseand the GMSB1 sample [9, 11, 12] is in the number ofevents with zero or two photons in the final state. Thelatter in particular is only 30 in our case. This behav-ior can be related to the squark masses we have consid-ered. In our case they are about 3.5 TeV, while in theGMSB1 they are lower than 1 TeV ( ∼
900 GeV). Wechoose the value of 3.5 TeV for the squark masses sincein this case the number of directly produced winos es-sentially depends only on M S (see Fig. 1). The numberof produced squarks is low since they have a high mass. After having employed the SUSY preselection cut which wedescribe later. γγ and t ¯ t production. Inorder to disentangle the SM background from the signalwe require a standard preselection cut for SUSY-like sig-natures:- at least four jets must be present with p T >
50 GeV( p T >
100 GeV for the leading jet);- missing transverse energy E missT >
60 GeV.After having applied these preselection cut we are able toreconstruct photons with p T >
20 GeV and | η | ≤ . . < | η | < .
5. The jet-finder algorithm used in ouranalysis is the Durham-type clustering KTCLUS [15].The cut on the E missT requires some care. In hadroncolliders, the initial momentum of the colliding partonsalong the beam axis is not known since the energy of eachhadron is distributed and constantly exchanged betweenthe partons. Hence the total amount of missing energycannot be determined in a straightforward way. Howeverthe initial energy of particles travelling transverse to thebeam axis is zero and thus any net momentum in thetransverse direction denotes missing transverse energy.To determine the latter for the i-th not-detected particlein each generated event, we considered the following pro-cedure: take a transverse direction (perpendicular to thez axis) and define the vector( −→ E missT ) i = E i −→ P T |−→ P | ! i whose direction is given by its momentum. Then E missT = q [( E missT ) T OTx ] + [( E missT ) T OTy ] where ( −→ E missT ) T OTx = P i (( −→ E missT ) x ) i and analogously for the y component.The result is shown in Fig. 4. In this plot the num-ber of photons from the NLSP decay is that generatedby Herwig while the number of background photons isthe reconstructed one [13]. We note that in the channelswith N γ ≥ In the case in which the wino is a long lived particlethe reconstruction of the emitted photon after its decay-ing plays an important role. If the NLSP has a significantdecay length, a photon will not “point back” to the pri-mary interaction point ( O in Fig. 5) but towards a kind γ N0 1 2 ] - N u m b e r o f eve n t s [ f b γ N0 1 2 ] - N u m b e r o f eve n t s [ f b our modelGMSB1di-Boson γ W/ZWZttjet
Figure 4: Number of generated photons per event for our modeland for GMSB1 and number of reconstructed photons for the SMbackground, after having applied the cuts described in the maintext.Figure 5: Schematic diagram of a non-pointing photon. d λ is thedistance traveled by λ before its radiative decay. z γ is the valueof the displaced vertex. of “virtual” point ( O ′ ). The relevant discriminant vari-able is z γ , the distance between O and O ′ . Using simpletrigonometric relations we have: z γ = d z − d xy cot θ (4)with cot θ = P γZ /P γT , the ratio between the photon mo-mentum along the beam direction (z-axis) and the trans-verse momentum.By fitting the vertex resolution along z as a functionof the photon energy for | η | < . σ for the Gaussiandistribution associated to z γ on the energy in GeV of allthe photons as σ mm ≃ . p E/ GeV + 65 p E/ GeV (5)To each z γ we can associate a random number sampledfrom a Gaussian distribution centered on that specificvalue of z γ and with σ given by the relation in (5). Weconsidered a wino mean life time τ λ ∼ . · − s, sothat the distance travelled by this particle before its ra-diative decay is always within the ATLAS tracker radius( ∼
115 cm). In Fig. 6 we show the results of the analysis3 c2 Entries 2109Mean -0.01286RMS 1.409 (cm) γ z-20 -15 -10 -5 0 5 10 15 20 ] / . c m - N u m b e r o f pho t on s [ f b ic2 Entries 2109Mean -0.01286RMS 1.409 λ not from γ ic1 Entries 2264Mean -0.03106RMS 4.768
Mass gap: 20 %Mass gap: 20 % λ not from γ λ from γ > 50 GeV γ |< 0.5 and E η Displaced vertex: |
Figure 6: Displaced vertex z γ for photons of E >
50 GeV and | η | < .
5: the red line stands for photons produced by wino decay,the black one for photons from the other susy processes. for photons of
E >
50 GeV and with | η | < . f b − . By consideringthe value of their energy and the contribution of the tailof the associated Gaussian distribution, we observe a con-sequent enlargement of the distribution of γ ’s not comingfrom λ , which otherwise would be a spike centered onthe origin of the x-axis in Fig. 6. The red line standsfor photons produced by radiative wino decay, while theblack one from the others SUSY processes. We can seethat in the region | z γ | > M/M S = 20%, M S ≃ τ λ ∼ . · − s, we get from (3) g A (2) M Z ′ ≃ . · − TeV (6)To satisfy (6) we need either a super-heavy Z ′ ( M Z ′ ≃
385 TeV if g A (2) ≃ .
15) or an extra-weakly coupled( g A (2) ≃ . M Z ′ ≃ Z ′ contribution. Cases of extra-weak Z ′ were already studied in the past [1, 16].
4. Conclusion
The most important result we get is shown in Fig. 6which gives a distinctive behavior of the photons comingfrom our model with respect to those coming from otherSUSY processes. The distribution of z γ is centered inzero while the half-width is a function of the NLSP de-cay length d λ . This means that the radiative producedphotons are preferably emitted along the NLSP directionor more generally at very small angle. Thus the signalcan be disentangled from the background by applying asuitable cut in a region | z γ | . m ˜ G = 1 . · − GeV) and the NLSP has a mass m ˜ χ = 118 . E ≃ m ˜ χ = 118 . cτ ˜ χ ≃ . Acknowledgments
The authors gratefully acknowledge the ATLAS group ofTor Vergata, in particular Prof. A. Di Ciaccio, G. Cattaniand R. Di Nardo for many stimulating discussions andhelp. A. R. would like to thank Prof. M. Raidal and Dr.K. Kannike for discussions and the ESF JD164 contractfor financial support.
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