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E6 Exotic quark production in ep collisions
Volume 196, number 2
PHYSICS LETTERS B
1 October 1987
E6 E X O T I C Q U A R K P R O D U C T I O N I N ep C O L L I S I O N S JoAnne L. H E W E T T Centerfor Particle Theory, Universityof Texas, Austin, TX 78712, USA Received 22 June 1987
We examine the possibility of producing exotic quarks from E 6 theories via flavor changing couplings in high energy ep collisions at HERA and the proposed LEP X LHC. We find that the rate is rather small and very mixing angle dependent. Assuming maximal mixing, the production rates are -~ 10-30 events per year at HERA (for masses up to 100 GeV) and -~200 events per year at LEP×LHC (for masses up to 300 GeV).
The low-energy limit o f superstring-motivated E 6 grand unified theories [ 1 ] contains new phenomenology [ 2 ] which can be tested in the next generation of accelerators. This new phenomenology includes an extension o f the low-energy electroweak gauge group by (at least) one extra U(1 ) factor beyond that o f the standard model (SM), and the existence of new fermions which complete the 27 representation o f E 6. The additional U (1) factor implies the existence o f a new neutral gauge boson, Z2, which could be as light as Mz2 --- 140 GeV [ 3 ]. In addition to the usual fermions of the SM, the 27 o f E 6 contains 11 new fields, including a color triplet, iso-singlet, charge - 1/3 fermion, D. In principle D may be light and its mass is constrained by PEP and P E T R A data ~i to lie above 23 GeV. The most general Yukawa interactions o f the D fermion allowed by the E 6 superpotential are rather ambiguous [ 5 ], allowing for several different possible baryon and lepton number assignments for the D. In one scenario which has been popular in the literature [6] and which we shall consider here, the baryon (B) and lepton (L) numbers of the D are that of a SM quark, i.e., B = 1/3 and L = 0 . This leads to a breakdown o f the Glashow-Weinberg-Paschos [ 7 ] naturalness conditions implying the existence of fla1 Permanent address: Ames Laboratory and Department of Physics, Iowa State University, Ames, IA 50011, USA. ~t For a recent review on the present limits for new quark masses see ref. [ 4].
vor changing neutral currents ( F C N C ) and mixing between the SM and E 6 exotic fermions [ 6 ]. In this paper we explore the possibility o f producing these exotic D quarks in ep collisions via the above off-diagonal couplings and FCNC. Clearly, if the D quarks have masses less than ~ 46 GeV they should be copiously produced at the SLC of LEP. I f the D is heavier it could be pair-produced at the TEVATRON, but may be lost in the hadronic background. The ep machines that we shall discuss here •are H E R A at DESY with x/~ = 314 GeV and the proposed L E P × L H C at C E R N with x/s___ 1.5 TeV. The quark-parton sub-processes which are responsible for single D quark production in ep collisions are shown in fig. 1. The F e y n m a n diagram in fig. l a represents the charged current reaction eu--,Dve and diagram lb shows the neutral current production e d ~ D e . In our analysis we have omitted the process e d - , D e as it yields a very small cross section as compared to the above. The double differential cross section for these processes is given by d20 .
dxdy-
:4 G 2FM~: 4~z s Z Cij{ce°Fl(q(z)+cl(Z))
ij
+floF2(q(z) - #(z)) }.
(1)
For the neutral current interaction M x = M z , ; q(z) = d ( z ) , the d quark distribution function; and the sum extends over the two gauge bosons, ZI and Z2. In the charged current case we replace M x by Mw/x/~, q(z) = u(z), and the sum reduces to a single
0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
223
Volume 196, number 2
PHYSICS LETTERSB
1 October 1987
12-x~Y<~l.
(5)
The coefficients C, a, and fl in eq. (1) are defined by Co = [(Q2 +M~)(Q2 + M 2) + ( F , M , ) ( F j M j ) ] u
X {[(Q2 +M~)2 + (V,Mi) 2]
D (o)
X [(Q2 +M2)2 + (FjMj)2] } - , ,
Ol0 = ( ViVj--kaiaj)e( PiPjq- aiaj)qD , flo = ( viaj + aivj)e( viaj + aivj)qD ,
(6)
where M i ( F i ) is the mass (width) of the ith gauge boson, and O2=sxy. The couplings are defined via the lagrangian
d
D
(b) Fig. 1. Feynman diagrams at the parton level for single D quark production in ep collisions via (a) charged current, (b) neutral current interactions.
L=g~--g {I7)Y/t(UiqD--aiqDYs)dq-6~v(Uie--a~ws)e}Z~ ~Cw
+ 2-~2{D7~ (vqo - aqDy 5) u + ~7~(Ve -- a w s) e}W ~ v
(7) term since only the W boson contributes. The functions F~.2 are F, =2_(l_y) +x(1 - y + ½y2), Y
F2=xy(1-½y),
(2)
where it is defined as
2=M2/s.
(3)
Here, x//s is the center of mass energy of the ep collision, x and y are the usual deep inelastic scattering variables, and z is the fraction of the proton's momentum that is carried by the struck quark. For a massive quark in the final state z is given by [ 8]
z = x + it/y .
(4)
The scaling variables are constrained to lie within the following ranges
O<~x <~1-2/y<~ 1 - 2 , 224
The fermion couplings to the second Z can be obtained from our earlier work [9], in which we studied several different E6 models which contained a low energy electroweak gauge group of the form SU(2)L × U(1 ) y × U ( 1 )x. In the following we assume that Fz2/Mz2 = 0.01 as we allow Mz2 to vary. We found that our results are insensitive to the exact value of F z J M z 2 . We take Mz, = 9 3 GeV, M w = 8 2 GeV, Fz, = F w = 2 . 8 GeV, and we use the parton distribution functions q(z) of both Duke and Owens, and EHLQ [ 10] for A =200 MeV, For simplicity we also assume that the mixing between d and D is the same for both left- and righthanded fields. In presenting our results for the production cross section the factor associated with d - D mixing has been neglected. Estimates [6 ] show that the d - D mixing angle ¢, is constrained by sin2¢d_D<0.01. Thus the final results need to be scaled by the appropriate mixing factor. In fig. 2 we present our results for the total cross section for e p - ~ v D + X via charged current interactions. These curves were obtained by using the EHLQ
PHYSICS LETTERS B
Volume 196, number 2 102
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MD(GeV) Fig. 2. The total cross section in picobarns as a function of MD for the charged current process ep-,vD+X in the absence of mixing angle suppression. quark distribution functions; the distribution functions o f Duke and Owens did not yield significantly different results. It is clear from the figure that at H E R A energies the total cross section is reasonably small and falls off quickly as MD increases. For an integrated luminosity o f 2 x 10 38 c m - 2 S-1 at H E R A this yields approximately 3000 events/yr for MD = 50 GeV and 300 events/yr for Mo= 150 GeV, neglecting d - D mixing factors. When the mixing factors are included the n u m b e r o f events are drastically reduced. Even if the mixing is as large as possible (i.e., sin z edDg0.01) the n u m b e r o f events/yr is reduced to 30 (3) for M D = 5 0 (150) GeV, respectively. At higher energies at the LEP × L H C collider at C E R N the cross section is significantly increased, especially for larger values MD. For Mo= 300 GeV we find a = 2 0 pb which yields (neglecting mixing) 2 × 10 4 events/yr (assuming an integrated luminosity o f 1039 cm -2 s-~ for L E P × L H C ) . Mixing effects
1
0
50
-
4 ~ I00 15O MD(GeV)
200
250
Fig. 3. Same as fig. 2 but for the neutral current process ep-~eD+X with Mz2 = 300 GeV. will lower the event rate, but m a y still leave a sizable n u m b e r o f events if sin 2 edD is not far below its upper bound. The total cross section for the neutral current process e p - - , e D + X is presented is fig. 3. In this figure we take Mz2 = 300 GeV; we have found that the cross section did not change by more than 15% as we varied Mz2 from 150 GeV to 500 GeV. The shaded area between the curves for x//~ = 314 G e V represents the range of values obtained for a set o f four E 6 models A - D [9] and the two sets of parton distribution functions. The curve labeled v / s = 1.5 TeV is for the case of E6 model B with E H L Q distribution functions and is representative of all the above E 6 models. It is clear from the figure that the cross sections from the neutral current process are at least an order of magnitude smaller than those in the charged current case. At H E R A energies the cross section is above 1 pb only for M D ~ 50 GeV which translates to 200 or less events/yr neglecting mixing. For the proposed 225
Volume 196, number 2
PHYSICS LETTERS B
LEP × LHC the total cross section is only a few picobarns for all values of MD a n d hence is disappointingly small. Thus the neutral current process e p - , e D + X will not be a good p r o d u c t i o n mechan i s m for D quarks. The D quark has a distinct experimental signature [ 11]. Due to the existence of F C N C in E 6 theories the decay D--,dZI (Z1 real or virtual depending on MD) is allowed. IfZ~ then decays by Z l ~ + £ - , then a signal for D production is jet + £ + £ - . There is no SM process which possesses this signature. To compute the event rate for this clean signal we need to know the following branching ratios: F(D~dZI)/F (D~all) and F(ZI-~+9~-)/F (Z,-~ all). F r o m the work ofrefs. [ 11,12] we estimate that for M D = 5 0 , 150 300 GeV the branching ratio for D-~d~+~ - is ---6.6%, 2.3%, 2.7%, respectively (assuming all E 6exotics are heavier t h a n - 4 6 GeV). Thus for the charged current process we obtain, assuming m a x i m a l mixing, 2 (0.07) events/year at H E R A for MD = 50 (150) GeV, a n d 5.4 events/year at LEP X LHC for MD = 300 GeV. Clearly, if the d - D mixing is any smaller, ep collisions will not be a good place to look for D quarks. A signal might also be extracted from the decay D - ~ u W and consequently W ~ 9 . However, production of new heavy quarks, such as SM fourth generation quarks, would have this same signature. I n conclusion, we have calculated the production cross sections for the processes ep -~ ~D + X ( ~ = e, v). We f o u n d that the production rate for D quarks at H E R A a n d LEP X LHC for the neutral current process is very small. The event rate for the charged current process is more promising, depending on the value of d - D mixing. If the mixing is large enough we could search for D quarks up to - 1 0 0 GeV at H E R A a n d ~ 300 GeV at LEP X LHC.
The author would like to t h a n k T. Rizzo for his comments, a n d the Center for Particle Theory for their hospitality. This work was supported in part by the US Department of Energy, Contract No. W-7405ENG-82, Office of Basic Science (KA-01-01 ), Division of High Energy Physics a n d Nuclear Physics,
226
1 October 1987
a n d in part by the Center for Particle Theory, DOE grant n u m b e r DE-FG05-84ER40200.
References [ 1] E. Witten, Nucl. Phys. B 258 (1985) 75; P. Candelas, G.T. Horowitz, A. Stominger and E. Witten, Nucl. Phys. B 258 (1985) 46; M. Dine, R. Rohm, N. Seibergand E. Witten, Phys. Lett. B 150 (1985) 55; M.B. Green and J.H. Schwarz, Phys. Lett. B 149 (1984) 117. [2] M. Dine et al., Nucl. Phys. B 259 (1985) 549; B. Cecotti et al., Phys. Lett. B 156 (1985) 318; E. Cohen et al., Phys. Lett. B 161 (1985) 85; B'165 (1985) 76; S.M. Barr, Phys. Rev. Lett. 55 (1985) 2778; P. Bindtury et al., Nucl. Phys. B 273 (1986) 501; P.K. Mohapatra et al., Phys. Rev. D 33 (1986) 3010; J. Breit et al., Phys. Lett. B 158 (1985 ) 33; R. Holman and D. Reiss, Phys. Lett. B 166 (1986) 305. [3] L.S. Durkin andP. Langacker,Phys. Lett. B 166 (1986) 436; V. Barger, N.G. Deshpande and K. Whisnant, Phys. Rev. Lett. 56 (1986) 30; D. London, G. Brlanger and J.N. Ng, Triumf Report TRIPP-86-78 (1986). [4] G. Altarelli, talk 23rd Intern. Conf. on High energyphysics, Berkeley, CA (July (1986). [5 ] J. Ellis,K. Enqvist,D.V. Nanopoulosand F. Zwirner,CERN report CERN-TH 4323/85; V. Barger et al., Proc. 1986 Summer Study on the Design and utilization of the superconducting super collider (Snowmass, CO). [6] V. Barger el al., Phys. Rev. D 33 (1986) 1912; R.W. Robinett, Phys. Rev. D 33 (1986) 1908; D. London and J.L. Rosner, Phys. Rev. D 34 (1986) 1530; J. Rosner, Comm. Nucl. Part. Phys. 15 (1986) 1985; T.G. Rizzo, Phys. Rev. D 33 (1986) 3329; D 34 (1986) 892, 2160, 2163, 2076. [7 ] S. Glashowand S. Weinberg,Phys. Rev. D 15 (1977) 1958; E.A. Paschos, Phys. Rev. D 15 (1977) 1966. [8] R.M. Barnett, Phys. Rev. D 14 (1976) 70. [ 9 ] J.L. Hewett et al., Phys. Rev. D 33 (1986) 1476;D 34 (1986) 2179. [ 10] E. Eichten et al., Rev. Mod. Phys. 56 (1984) 579; D. Duke and J. Owens, Phys. Rev. D 30 (1984) 49. [11] T.G. Rizzo, Phys. Lett. B 181 (1986) 185. [12] T.G. Rizzo, Phys. Rev. D 34 (1986) 1438.
PHYSICS LETTERS B
1 October 1987
E6 E X O T I C Q U A R K P R O D U C T I O N I N ep C O L L I S I O N S JoAnne L. H E W E T T Centerfor Particle Theory, Universityof Texas, Austin, TX 78712, USA Received 22 June 1987
We examine the possibility of producing exotic quarks from E 6 theories via flavor changing couplings in high energy ep collisions at HERA and the proposed LEP X LHC. We find that the rate is rather small and very mixing angle dependent. Assuming maximal mixing, the production rates are -~ 10-30 events per year at HERA (for masses up to 100 GeV) and -~200 events per year at LEP×LHC (for masses up to 300 GeV).
The low-energy limit o f superstring-motivated E 6 grand unified theories [ 1 ] contains new phenomenology [ 2 ] which can be tested in the next generation of accelerators. This new phenomenology includes an extension o f the low-energy electroweak gauge group by (at least) one extra U(1 ) factor beyond that o f the standard model (SM), and the existence of new fermions which complete the 27 representation o f E 6. The additional U (1) factor implies the existence o f a new neutral gauge boson, Z2, which could be as light as Mz2 --- 140 GeV [ 3 ]. In addition to the usual fermions of the SM, the 27 o f E 6 contains 11 new fields, including a color triplet, iso-singlet, charge - 1/3 fermion, D. In principle D may be light and its mass is constrained by PEP and P E T R A data ~i to lie above 23 GeV. The most general Yukawa interactions o f the D fermion allowed by the E 6 superpotential are rather ambiguous [ 5 ], allowing for several different possible baryon and lepton number assignments for the D. In one scenario which has been popular in the literature [6] and which we shall consider here, the baryon (B) and lepton (L) numbers of the D are that of a SM quark, i.e., B = 1/3 and L = 0 . This leads to a breakdown o f the Glashow-Weinberg-Paschos [ 7 ] naturalness conditions implying the existence of fla1 Permanent address: Ames Laboratory and Department of Physics, Iowa State University, Ames, IA 50011, USA. ~t For a recent review on the present limits for new quark masses see ref. [ 4].
vor changing neutral currents ( F C N C ) and mixing between the SM and E 6 exotic fermions [ 6 ]. In this paper we explore the possibility o f producing these exotic D quarks in ep collisions via the above off-diagonal couplings and FCNC. Clearly, if the D quarks have masses less than ~ 46 GeV they should be copiously produced at the SLC of LEP. I f the D is heavier it could be pair-produced at the TEVATRON, but may be lost in the hadronic background. The ep machines that we shall discuss here •are H E R A at DESY with x/~ = 314 GeV and the proposed L E P × L H C at C E R N with x/s___ 1.5 TeV. The quark-parton sub-processes which are responsible for single D quark production in ep collisions are shown in fig. 1. The F e y n m a n diagram in fig. l a represents the charged current reaction eu--,Dve and diagram lb shows the neutral current production e d ~ D e . In our analysis we have omitted the process e d - , D e as it yields a very small cross section as compared to the above. The double differential cross section for these processes is given by d20 .
dxdy-
:4 G 2FM~: 4~z s Z Cij{ce°Fl(q(z)+cl(Z))
ij
+floF2(q(z) - #(z)) }.
(1)
For the neutral current interaction M x = M z , ; q(z) = d ( z ) , the d quark distribution function; and the sum extends over the two gauge bosons, ZI and Z2. In the charged current case we replace M x by Mw/x/~, q(z) = u(z), and the sum reduces to a single
0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
223
Volume 196, number 2
PHYSICS LETTERSB
1 October 1987
12-x~Y<~l.
(5)
The coefficients C, a, and fl in eq. (1) are defined by Co = [(Q2 +M~)(Q2 + M 2) + ( F , M , ) ( F j M j ) ] u
X {[(Q2 +M~)2 + (V,Mi) 2]
D (o)
X [(Q2 +M2)2 + (FjMj)2] } - , ,
Ol0 = ( ViVj--kaiaj)e( PiPjq- aiaj)qD , flo = ( viaj + aivj)e( viaj + aivj)qD ,
(6)
where M i ( F i ) is the mass (width) of the ith gauge boson, and O2=sxy. The couplings are defined via the lagrangian
d
D
(b) Fig. 1. Feynman diagrams at the parton level for single D quark production in ep collisions via (a) charged current, (b) neutral current interactions.
L=g~--g {I7)Y/t(UiqD--aiqDYs)dq-6~v(Uie--a~ws)e}Z~ ~Cw
+ 2-~2{D7~ (vqo - aqDy 5) u + ~7~(Ve -- a w s) e}W ~ v
(7) term since only the W boson contributes. The functions F~.2 are F, =2_(l_y) +x(1 - y + ½y2), Y
F2=xy(1-½y),
(2)
where it is defined as
2=M2/s.
(3)
Here, x//s is the center of mass energy of the ep collision, x and y are the usual deep inelastic scattering variables, and z is the fraction of the proton's momentum that is carried by the struck quark. For a massive quark in the final state z is given by [ 8]
z = x + it/y .
(4)
The scaling variables are constrained to lie within the following ranges
O<~x <~1-2/y<~ 1 - 2 , 224
The fermion couplings to the second Z can be obtained from our earlier work [9], in which we studied several different E6 models which contained a low energy electroweak gauge group of the form SU(2)L × U(1 ) y × U ( 1 )x. In the following we assume that Fz2/Mz2 = 0.01 as we allow Mz2 to vary. We found that our results are insensitive to the exact value of F z J M z 2 . We take Mz, = 9 3 GeV, M w = 8 2 GeV, Fz, = F w = 2 . 8 GeV, and we use the parton distribution functions q(z) of both Duke and Owens, and EHLQ [ 10] for A =200 MeV, For simplicity we also assume that the mixing between d and D is the same for both left- and righthanded fields. In presenting our results for the production cross section the factor associated with d - D mixing has been neglected. Estimates [6 ] show that the d - D mixing angle ¢, is constrained by sin2¢d_D<0.01. Thus the final results need to be scaled by the appropriate mixing factor. In fig. 2 we present our results for the total cross section for e p - ~ v D + X via charged current interactions. These curves were obtained by using the EHLQ
PHYSICS LETTERS B
Volume 196, number 2 102
,
,
,
i
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vS- --I. 5 T e V
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1 October 1987 i
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v'Y--- 514 GeV _Q
,/Y- =514 GeV
£Z
b
b i0 -I
ep~eD+X
ep ~ u D +X
10-3
10-2
10-3
f
i 5O
K
I
I
I00
I
150
I
I
200
I
k
250
MD(GeV) Fig. 2. The total cross section in picobarns as a function of MD for the charged current process ep-,vD+X in the absence of mixing angle suppression. quark distribution functions; the distribution functions o f Duke and Owens did not yield significantly different results. It is clear from the figure that at H E R A energies the total cross section is reasonably small and falls off quickly as MD increases. For an integrated luminosity o f 2 x 10 38 c m - 2 S-1 at H E R A this yields approximately 3000 events/yr for MD = 50 GeV and 300 events/yr for Mo= 150 GeV, neglecting d - D mixing factors. When the mixing factors are included the n u m b e r o f events are drastically reduced. Even if the mixing is as large as possible (i.e., sin z edDg0.01) the n u m b e r o f events/yr is reduced to 30 (3) for M D = 5 0 (150) GeV, respectively. At higher energies at the LEP × L H C collider at C E R N the cross section is significantly increased, especially for larger values MD. For Mo= 300 GeV we find a = 2 0 pb which yields (neglecting mixing) 2 × 10 4 events/yr (assuming an integrated luminosity o f 1039 cm -2 s-~ for L E P × L H C ) . Mixing effects
1
0
50
-
4 ~ I00 15O MD(GeV)
200
250
Fig. 3. Same as fig. 2 but for the neutral current process ep-~eD+X with Mz2 = 300 GeV. will lower the event rate, but m a y still leave a sizable n u m b e r o f events if sin 2 edD is not far below its upper bound. The total cross section for the neutral current process e p - - , e D + X is presented is fig. 3. In this figure we take Mz2 = 300 GeV; we have found that the cross section did not change by more than 15% as we varied Mz2 from 150 GeV to 500 GeV. The shaded area between the curves for x//~ = 314 G e V represents the range of values obtained for a set o f four E 6 models A - D [9] and the two sets of parton distribution functions. The curve labeled v / s = 1.5 TeV is for the case of E6 model B with E H L Q distribution functions and is representative of all the above E 6 models. It is clear from the figure that the cross sections from the neutral current process are at least an order of magnitude smaller than those in the charged current case. At H E R A energies the cross section is above 1 pb only for M D ~ 50 GeV which translates to 200 or less events/yr neglecting mixing. For the proposed 225
Volume 196, number 2
PHYSICS LETTERS B
LEP × LHC the total cross section is only a few picobarns for all values of MD a n d hence is disappointingly small. Thus the neutral current process e p - , e D + X will not be a good p r o d u c t i o n mechan i s m for D quarks. The D quark has a distinct experimental signature [ 11]. Due to the existence of F C N C in E 6 theories the decay D--,dZI (Z1 real or virtual depending on MD) is allowed. IfZ~ then decays by Z l ~ + £ - , then a signal for D production is jet + £ + £ - . There is no SM process which possesses this signature. To compute the event rate for this clean signal we need to know the following branching ratios: F(D~dZI)/F (D~all) and F(ZI-~+9~-)/F (Z,-~ all). F r o m the work ofrefs. [ 11,12] we estimate that for M D = 5 0 , 150 300 GeV the branching ratio for D-~d~+~ - is ---6.6%, 2.3%, 2.7%, respectively (assuming all E 6exotics are heavier t h a n - 4 6 GeV). Thus for the charged current process we obtain, assuming m a x i m a l mixing, 2 (0.07) events/year at H E R A for MD = 50 (150) GeV, a n d 5.4 events/year at LEP X LHC for MD = 300 GeV. Clearly, if the d - D mixing is any smaller, ep collisions will not be a good place to look for D quarks. A signal might also be extracted from the decay D - ~ u W and consequently W ~ 9 . However, production of new heavy quarks, such as SM fourth generation quarks, would have this same signature. I n conclusion, we have calculated the production cross sections for the processes ep -~ ~D + X ( ~ = e, v). We f o u n d that the production rate for D quarks at H E R A a n d LEP X LHC for the neutral current process is very small. The event rate for the charged current process is more promising, depending on the value of d - D mixing. If the mixing is large enough we could search for D quarks up to - 1 0 0 GeV at H E R A a n d ~ 300 GeV at LEP X LHC.
The author would like to t h a n k T. Rizzo for his comments, a n d the Center for Particle Theory for their hospitality. This work was supported in part by the US Department of Energy, Contract No. W-7405ENG-82, Office of Basic Science (KA-01-01 ), Division of High Energy Physics a n d Nuclear Physics,
226
1 October 1987
a n d in part by the Center for Particle Theory, DOE grant n u m b e r DE-FG05-84ER40200.
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