Phenomenological study on the wino radiative decay in anomalous Uð1Þ0 models

Francesco Fucito,1 Andrea Lionetto,1 Antonio Racioppi,2 and Daniel Ricci Pacifici1

1Dipartimento di Fisica dell’Universita di Roma, ‘‘Tor Vergata’’and INFN Sezione di Roma ‘‘Tor Vergata,’’ Via della Ricerca Scientifica, 1 – 00133 Roma, Italy

2National Institute of Chemical Physics and Biophysics, Ravala 10, Tallinn 10143, Estonia(Received 22 September 2010; published 2 December 2010)

An extension of the standard model by at least one extra Uð1Þ gauge symmetry has been investigated

by many authors. In this paper we explore the possibility that this extra Uð1Þ is anomalous. One possible

signature of this model could be given by the photons produced in the decays of the next to lightest

supersymmetric particle into the lightest supersymmetric particle.

DOI: 10.1103/PhysRevD.82.115004 PACS numbers: 12.60.Jv, 11.25.-w

I. INTRODUCTION

The start of the LHC has greatly motivated detailedphenomenological studies of scenarios which involvephysics beyond the standard model (SM). Among themD-brane constructions in string theory are one of the mostpromising frameworks in which the SM can be embeddedand extended. Such brane constructions naturally lead toextra anomalousUð1Þ’s in the four-dimensional low energytheory and, in turn, to the presence of possible heavy Z0particles 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 theoreticalmodels of the unification of forces (see [1] for a recentreview). In [2] we have considered a minimal extension ofthe minimal supersymmetric standard model (MSSM) witha single extra Uð1Þ0 gauge symmetry in a string-inspiredsetup. We believe that our model encodes the key featuresof the low-energy sector of some of those brane construc-tions. In the framework in [3] the radiative decay of thenext to lightest supersymmetric particle (NLSP) into thelightest supersymmetric particle (LSP). This kind of pro-cess is very interesting since it might be the first one wherethe LSP could be observed at LHC [4,5] and at the upcom-ing International eþe� Linear Collider [6,7].

II. PRELIMINARIES AND LAGRANGIAN

Under suitable assumptions the LSP in our model turnsout to be an axino [8], the fermion component of theStuckelberg supermultiplet related to the anomaly cancel-lation mechanism (see for details [2,3,8]). Without loss ofgenerality we assume a wino-like NLSP. In the followingwe just give the interaction term which involves the axinoand the wino relevant for our analysis. The interactionterm, written in terms of four component Majorana

spinors,1 is given by iL ¼ ffiffiffi2

psin�W

g0Að2ÞMZ0

�g22

32�2��2�5½��; ���ð@�A�Þc S, where �2 is the neutral

wino, c S is the axino, A� is the photon, �W the Weinberg

angle, g0 and g2, respectively, the Uð1Þ0 and SUð2Þ cou-pling constants, Að2Þ the Uð1Þ0 � SUð2Þ � SUð2Þ anom-aly factor, and MZ0 the Z0 mass. The rate of the radiativedecay (�2 ! �S�) is

�ð2Þ� ¼ g42sin

2�W

�g0Að2Þ

MZ0

�2 ð�MÞ3ð�Mþ 2MSÞ31024�5ð�MþMSÞ3

; (1)

where �M ¼ M2 �MS, while M2 and MS are, respec-tively, the wino and axino masses. As we showed in [3],the radiative decay is the most dominant wino decay modewith a branching ratio (BR) close to 1 (* 94%), so we canuse (1) to give an estimation of the wino mean life time

��2’ "

�ð2Þ�

(2)

III. LHC PHENOMENOLOGY

In order to fall into the WMAP range in the most experi-mentally attractive situation, we considered a light LSP(115 GeV & MS & 150 GeV) and a mass gap of order�M=MS ’ 20%, which implymore energetic and thereforeeasier to detect photons. This requirement is necessarybecause the detector resolution increases with energy, whileat low energy there is an obstruction for the detectionof photons due to bremsstrahlung, QCD background, andabsorption before the detection from the calorimeter [9].Moreover, we considered a universal squark mass M ~Q

for the first two squark generations (since under this as-sumption they are nearly degenerate) and we assumedflavor blindness [10]. The contribution from the thirdgeneration squarks is always negligible. In Fig. 1 wesummarize the results obtained in [3] by plotting thenumber of directly produced winos as a function of MS

and M ~Q having assumed 14 TeVof center-of-mass energy

and 100 fb�1 of integrated luminosity. Since the BR isalmost close to 1 this is also the number of photons inthe final state. The number of photons produced is of theorder of 105. In our analysis we follow [9,11–13], wherethe NLSP decay in the gauge mediated supersymmetry1The gamma matrices �� are in the Weyl representation.

PHYSICAL REVIEW D 82, 115004 (2010)

1550-7998=2010=82(11)=115004(5) 115004-1 � 2010 The American Physical Society

breaking (GMSB) framework is controlled by the parame-ter Cgrav. If the NLSP lifetime is not too long (Cgrav � 1)

photons originate close to the primary interaction vertex(‘‘prompt photons’’). In the case of large Cgrav and there-

fore long-lived neutralinos, the resulting photons arenonpointing. We repeat this type of analysis for our model.The comparison with the GMSB holds in the sense that wetake comparable lifetimes and branching ratios for theNLSP ! LSPþ �, while other details of the models areobviously different. From now on we fix the axino massMS ’ 124 GeV and the universal squark mass M ~Q ’3:5 TeV. In our framework the role of Cgrav is played by

the ratio g0Að2Þ=MZ0 . In the following we discuss twodifferent cases: a short-lived NLSP and a long-lived one.

A. Short life time

We compare the number of photons produced by radia-tive decay with the ones produced by the cascade decays ofall the other supersymmetric processes. We slightly modi-fied the Herwig code 6.5 [14] in order to take into accountthe new axino state in the neutral sector. It should bestressed that Herwig does not implement extra Z0 in asupersymmetric framework. This in turn implies that thetotal number of photons can be underestimated due tothe lack of sparticles interactions with the Z0. Howeverthis problem can be overcome by assuming a decoupledZ0 either because it is very heavy or because it is extra-weak coupled. We generated by Herwig 2-partons !2-sparticles events, using about 1 fb�1 of integrated lumi-nosity, but we have not considered the case of SM particlesproduced directly in the parton-parton interaction. A gooddiscriminant variable of the process is the PT of the pho-tons produced by radiative decay, in particular, in theregion of PT between 30–80 GeV=c. The correspondingdistribution is shown in Fig. 2. We denote in red (lightcurve) the number of �’s radiatively produced from thedecay of the wino, in blue (medium light curve) the numberof�’s from all the other processes, while in black (dark curve)the sum of the two. We assumed ��2

’ 1:29� 10�15 s,

which is obtainable with MZ0 ’ 1 TeV and g0Að2Þ ’ 0:2.We performed the same cut on the number of generatedphotons as in [13] with PT > 20 GeV and with pseudor-apidity j�j � 1:37, 1:52< j�j< 2:5, which provides agood way to further suppress the supersymmetry (SUSY)background.2 The result obtained by using Herwig in gen-erating 104 net events is given in Fig. 3. The most importantdifference between our case and the GMSB1 sample[9,11,12] is in the number of events with zero or twophotons in the final state. The latter, in particular, is only30 in our case. This behavior can be related to the squarkmasses we have considered. In our case they areabout 3.5 TeV, while in the GMSB1 they are lowerthan 1 TeV (�900 GeV). We choose the value of3.5 TeV for the squark masses since in this case the numberof directly produced winos essentially depends only onMS

(see Fig. 1). The number of produced squarks is low sincethey have a high mass. Hence, they give a lower contribu-tion to the NLSP production. If we consider lightersquarks, with masses less than 1 TeV, there is an increasein the number of events with 2 photons in the final state. Inany case the channel with one photon in the final state isalways the dominant one. We cite here the GMSB1 point,because the analysis of [9] is carried out in this case.Recent results from the Tevatron (Fig. 3 of [15]) seem toexclude this point, even though the model used is subject toan extra constraint with respect to GMSB1.The key point in the analysis is the SM background

discrimination. We considered the same SM backgroundas in [13]: events with QCD jets, single gauge bosons(W and Z) production, di-Boson, ��, and t�t production.In order to disentangle the SM background from the signal

Entries 1552960

Mean 0.002703± 0.6876

RMS 0.001911± 3.368

Underflow 0

Overflow 16

(GeV/c)TP

0 20 40 60 80 100 120 140 160 180 200

nu

mb

er o

f p

ho

ton

s/ 2

GeV

/c

1

10

210

310

410

510

610

Entries 1552960

Mean 0.002703± 0.6876

RMS 0.001911± 3.368

Underflow 0

Overflow 16

γ

Entries 6129

Mean 0.2901± 33.15

RMS 0.2051± 22.69

Underflow 0

Overflow 10

Entries 1546831

Mean 0.001827± 0.5592

RMS 0.001292± 2.272

Underflow 0

Overflow 6

2λ not from γTP

2λ from γTP

2λ and not from 2

λ from γT

and PγTP

γ

2λ from γ

2λ not from γ

γTP

FIG. 2 (color online). PT distribution of photons (in log scale)for 104 SUSY events.

115 120 125 130 135 140 145 150

1

2

3

4

MS GeV

MQ

TeV

Wino Production: M MS 20

2.0

4.0N 105

4.0

3.5

3.0

2.5

2.0

FIG. 1. Number of directly produced winos in function of theaxino mass MS and the universal squark mass M ~Q.

2After having employed the SUSY preselection cut which wedescribe later.

F. FUCITO et al. PHYSICAL REVIEW D 82, 115004 (2010)

115004-2

we require a standard preselection cut for SUSY-likesignatures:

(i) at least four jets must be present with pT > 50 GeV(pT > 100 GeV for the leading jet);

(ii) missing transverse energy EmissT > 60 GeV.

After having applied these preselection cuts we are able toreconstruct photons with pT > 20 GeV and j�j � 1:37,1:52< j�j< 2:5. The jet-finder algorithm used in ouranalysis is the Durham-type KT clustering package [16].The cut on the Emiss

T requires some care. In hadron col-liders, the initial momentum of the colliding partons alongthe beam axis is not known since the energy of each hadronis distributed and constantly exchanged between thepartons. Hence the total amount of missing energycannot be determined in a straightforward way. However,the 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 ith not-detected particle ineach generated event, we considered the following proce-dure: take a transverse direction (perpendicular to the z

axis) and define the vector ð ~EmissT Þi ¼ Eið ~PT=j ~PjÞi whose

direction is given by its momentum. Then EmissT ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

½ðEmissT ÞTOTx �2 þ ½ðEmiss

T ÞTOTy �2q

where ð ~EmissT ÞTOTx ¼P

iðð ~EmissT ÞxÞi and analogously for the y component. The

result is shown in Fig. 4. In this plot the number of photonsfrom the NLSP decay is that generated by Herwig whilethe number of background photons is the reconstructed one[13]. We note that in the channels with N� � 1 the signal

can be easily disentangled by the SM background.

B. Long life time

In the case in which the wino is a long-lived particle thereconstruction of the emitted photon after its decaying

plays an important role. If the NLSP has a significant decaylength, a photon will not ‘‘point back’’ to the primaryinteraction point (O in Fig. 5) but towards a kind of‘‘virtual’’ point (O0). The relevant discriminant variable isz�, the distance between O and O0. Using simple trigono-

metric relations we have z� ¼ dz � dxy cot� with cot� ¼P�Z=P

�T , the ratio between the photon momentum along the

beam direction (z axis) and the transverse momentum.By fitting the vertex resolution along z as a function of

the photon energy for j�j< 0:5 (see plot in section‘‘Electrons and Photons’’ in [9]) we derive the functionaldependence of the standard deviation for the Gaussiandistribution associated with z� on the energy in GeVof all

the photons as

mm’ 0:7

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE=GeV

p þ 65ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE=GeV

p : (3)

ic1

γN

0 1 2

to

t]4

Nu

mb

er o

f ev

ents

[10

0

1000

2000

3000

4000

5000

6000

7000

ic1

GMSB1

ic2GMSB1

our model

| < 2.5η| < 1.37, 1.52 < |η > 20 GeV/c and |T

Number of generated photons with P

FIG. 3 (color online). Number of generated photons before thepreselection cuts.

γN

0 1 2

]-1

Nu

mb

er o

f ev

ents

[1

fb

1

10

210

310

410

γN

0 1 2

]-1

Nu

mb

er o

f ev

ents

[1

fb

1

10

210

310

410

our modelGMSB1di-Boson

γW/ZWZtt

jet

FIG. 4 (color online). Number of generated photons per eventfor our model and for GMSB1 and number of reconstructedphotons for the SM background, after having applied the cutsdescribed in the main text.

FIG. 5 (color online). Schematic diagram of a nonpointingphoton. d�2

is the distance traveled by �2 before its radiative

decay. z� is the value of the displaced vertex.

PHENOMENOLOGICAL STUDY ON THE WINO . . . PHYSICAL REVIEW D 82, 115004 (2010)

115004-3

To each z� we can associate a random number sampled

from a Gaussian distribution centered on that specificvalue of z� and with given by the relation in (3). We

considered a wino mean life time ��2� 3:463� 10�10 s,

so that the distance travelled by this particle before itsradiative decay is always within the ATLAS trackerradius (� 115 cm). In Fig. 6 we show the results ofthe analysis for photons of E> 50 GeV and with j�j<0:5 (photons with great angle to the beam direction,because these are more easily detected than the onesalong the z direction), for an integrated luminosity of10 fb�1. By considering the value of their energy and thecontribution of the tail of the associated Gaussian distri-bution, we observe a consequent enlargement of thedistribution of �’s not coming from �2, which otherwisewould be a spike centered on the origin of the x axis inFig. 6. The red line (light curve) stands for photonsproduced by radiative wino decay, while the black one(dark curve) from the others SUSY processes. We cansee that in the region jz�j> 3 cm the photons from

the radiative decay are well distinguished from the back-ground ones. Since we have assumed �M=MS ¼ 20%,MS ’ 124 GeV, and ��2

� 3:463� 10�10 s, we get

from (2)

g0Að2Þ

MZ0’ 3:9� 10�4

TeV: (4)

To satisfy (4) we need either a superheavy Z0 [MZ0 ’385 TeV if g0Að2Þ ’ 0:15] or an extra-weakly coupled

[g0Að2Þ ’ 0:00039 if MZ0 ’ 1 TeV] one. This decou-pling makes our simulation more consistent since in itwe have neglected the Z0 contribution. Cases of extra-weak Z0 were already studied in the past [1,17].

IV. 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� is centered in zero

while the half-width is a function of the NLSP decay lengthd�2

. This means that the radiative photons which are pro-

duced are preferably emitted along the NLSP direction ormore generally at a very small angle. Thus the signal can bedisentangled from the background by applying a suitablecut in a region jz�j & 5 cm, as shown in Fig. 6. Our result,

with the caveat exposed just before at the beginning ofSec. III, can be compared with [9] in which the NLSP is along-lived wino-like particle in the particular gauge medi-ated model dubbed GMSB3. The main difference is in themass gap. In our model we considered a mass gap of 20%and an LSP of 124 GeV, while in the GMSB3 case the massgap is much higher: the gravitino (the LSP) is almostmassless (m ~G ¼ 1:08� 10�8 GeV) and the NLSP has amass m~1

¼ 118:8 GeV. In this case the energy distribu-

tion for the photons produced by the NLSP decay is peakedon the value of the NLSP mass E ’ m~1

¼ 118:8 GeV

while in our case the peak is around 20 GeV. Moreover,in the GMSB3 c�~1

’ 3:2 m and so the NLSP long-lived

particles tend to escape the detector before their decay.This implies a sizable reduction in the number of photonsdetected (see Fig. 7).

ACKNOWLEDGMENTS

The authors gratefully acknowledge the ATLAS groupof Tor Vergata, in particular, Professor A. Di Ciaccio, G.Cattani, and R. Di Nardo for many stimulating discussionsand help. A. R. would like to thank Professor M. Raidal andDr. K. Kannike for discussions and the ESF JD164 contractfor financial support.

ic2Entries 2109Mean -0.01286RMS 1.409

(cm)γz

-20 -15 -10 -5 0 5 10 15 20

] / 0

.4 c

m-1

Nu

mb

er o

f p

ho

ton

s [1

0 fb

0

20

40

60

80

100

120

140

160

180

200

ic2Entries 2109Mean -0.01286RMS 1.4092

λ not from γ

ic1

Mass gap: 20 %Mass gap: 20 %

2λ not from γ

2λ from γ

> 50 GeVγ

|< 0.5 and EηDisplaced vertex: |

FIG. 6 (color online). Displaced vertex z� for photons of E>50 GeV and j�j< 0:5: the red line (light curve) stands forphotons produced by wino decay, the black one (dark curve)for photons from the other SUSY processes.

(cm)γz

-100 -80 -60 -40 -20 0 20 40 60 80 100

] /2

.3 c

m-1

Nu

mb

er o

f p

ho

ton

s [1

0 fb

0

50

100

150

200

250

300

350

400

450

>50 GeVγ

|<0.5 and EηDisplaced vertex for |

GMSB3

Our model

FIG. 7 (color online). Displaced vertex z� for photons pro-duced by NLSP decay with E > 50 GeV and j�j< 0:5: the redline (lower curve) stands for our model case, the blue one(peaked curve) for the GMSB3 scenario.

F. FUCITO et al. PHYSICAL REVIEW D 82, 115004 (2010)

115004-4

[1] P. Langacker, Rev. Mod. Phys. 81, 1199(2009).

[2] P. Anastasopoulos, F. Fucito, A. Lionetto, G. Pradisi, A.Racioppi, and Y. S. Stanev, Phys. Rev. D 78, 085014(2008).

[3] A. Lionetto and A. Racioppi, Nucl. Phys. B831, 329(2010).

[4] H. Baer and T. Krupovnickas, J. High Energy Phys. 09(2002) 038.

[5] H. Baer, A. Mustafayev, E. K. Park, and X. Tata, J. HighEnergy Phys. 05 (2008) 058.

[6] H. K. Dreiner, O. Kittel, and U. Langenfeld, Phys. Rev. D74, 115010 (2006).

[7] R. Basu, P. N. Pandita, and C. Sharma, Phys. Rev. D 77,115009 (2008).

[8] F. Fucito, A. Lionetto, A. Mammarella, and A. Racioppi,Eur. Phys. J. C 69, 455 (2010).

[9] G. Aad et al. (The ATLAS Collaboration),arXiv:0901.0512.

[10] H. Baer and X. Tata, Weak Scale Supersymmetry: FromSuperfields to Scattering Events (University Press,Cambridge, England, 2006), p. 537.

[11] D. Prieur, arXiv:hep-ph/0507083.[12] M. Terwort (ATLAS Collaboration and CMS

Collaboration), arXiv:0805.2524.[13] M. Terwort, Ph.D. thesis, Universitat Hamburg, 2009,

http://www-atlas.desy.de/theses.html.[14] G. Corcella et al., J. High Energy Phys. 01 (2001) 010.[15] T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett.

104, 011801 (2010).[16] S. Catani, Y. L. Dokshitzer, M.H. Seymour, and B. R.

Webber, Nucl. Phys. B406, 187 (1993).[17] D. Feldman, Z. Liu, and P. Nath, Phys. Rev. D 75, 115001

(2007).

PHENOMENOLOGICAL STUDY ON THE WINO . . . PHYSICAL REVIEW D 82, 115004 (2010)

115004-5