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LSST/Rubin Dome Bridge Installation
Credit: Rubin Obs/NSF/AURA

Dr Farrukh Azfar

Lecturer

Research theme

  • Particle astrophysics & cosmology
  • Fundamental particles and interactions

Sub department

  • Particle Physics

Research groups

  • Accelerator Neutrinos
  • Rubin-LSST
Farrukh.Azfar@physics.ox.ac.uk
Telephone: 01865 (2)73327
Denys Wilkinson Building, room 669
  • About
  • Publications

Upsilon production and polarization in p p macro collisions at square root of s = 1.8 TeV.

Phys Rev Lett 88:16 (2002) 161802

Authors:

D Acosta, T Affolder, H Akimoto, MG Albrow, P Amaral, D Ambrose, D Amidei, K Anikeev, J Antos, G Apollinari, T Arisawa, A Artikov, T Asakawa, W Ashmanskas, F Azfar, P Azzi-Bacchetta, N Bacchetta, H Bachacou, S Bailey, P de Barbaro, A Barbaro-Galtieri, VE Barnes, BA Barnett, S Baroiant, M Barone, G Bauer, F Bedeschi, S Belforte, WH Bell, G Bellettini, J Bellinger, D Benjamin, J Bensinger, A Beretvas, JP Berge, J Berryhill, A Bhatti, M Binkley, D Bisello, M Bishai, RE Blair, C Blocker, K Bloom, B Blumenfeld, SR Blusk, A Bocci, A Bodek, G Bolla, Y Bonushkin, D Bortoletto, J Boudreau, A Brandl, S van den Brink, C Bromberg, M Brozovic, E Brubaker, N Bruner, E Buckley-Geer, J Budagov, HS Budd, K Burkett, G Busetto, A Byon-Wagner, KL Byrum, S Cabrera, P Calafiura, M Campbell, W Carithers, J Carlson, D Carlsmith, W Caskey, A Castro, D Cauz, A Cerri, AW Chan, PS Chang, PT Chang, J Chapman, C Chen, YC Chen, M-T Cheng, M Chertok, G Chiarelli, I Chirikov-Zorin, G Chlachidze, F Chlebana, L Christofek, ML Chu, JY Chung, YS Chung, CI Ciobanu, AG Clark, AP Colijn, A Connolly, M Convery, J Conway, M Cordelli, J Cranshaw, R Culbertson, D Dagenhart, S D'Auria, F DeJongh, S Dell'Agnello, M Dell'Orso, S Demers, L Demortier, M Deninno, PF Derwent, T Devlin, JR Dittmann, A Dominguez, S Donati, J Done, M D'Onofrio, T Dorigo, N Eddy, K Einsweiler, JE Elias, E Engels, R Erbacher, D Errede, S Errede, Q Fan, H-C Fang, RG Feild, JP Fernandez, C Ferretti, RD Field, I Fiori, B Flaugher, GW Foster, M Franklin, J Freeman, J Friedman, Y Fukui, I Furic, S Galeotti, A Gallas, M Gallinaro, T Gao, M Garcia-Sciveres, AF Garfinkel, P Gatti, C Gay, DW Gerdes, E Gerstein, P Giannetti, M Giordani, P Giromini, V Glagolev, D Glenzinski, M Gold, J Goldstein, I Gorelov, AT Goshaw, Y Gotra, K Goulianos, C Green, G Grim, P Gris, C Grosso-Pilcher, M Guenther, G Guillian, J Guimaraes da Costa, RM Haas, C Haber, SR Hahn, C Hall, T Handa, R Handler, W Hao, F Happacher, K Hara, AD Hardman, RM Harris, F Hartmann, K Hatakeyama, J Hauser, J Heinrich, A Heiss, M Herndon, C Hill, A Hocker, KD Hoffman, R Hollebeek, L Holloway, BT Huffman, R Hughes, J Huston, J Huth, H Ikeda, J Incandela, G Introzzi, A Ivanov, J Iwai, Y Iwata, E James, M Jones, U Joshi, H Kambara, T Kamon, T Kaneko, M Karagoz Unel, K Karr, S Kartal, H Kasha, Y Kato, TA Keaffaber, K Kelley, M Kelly, D Khazins, T Kikuchi, B Kilminster, BJ Kim, DH Kim, HS Kim, MJ Kim, SB Kim, SH Kim, YK Kim, M Kirby, M Kirk, L Kirsch, S Klimenko, P Koehn, K Kondo, J Konigsberg, A Korn, A Korytov, E Kovacs, J Kroll, M Kruse, SE Kuhlmann, K Kurino, T Kuwabara, AT Laasanen, N Lai, S Lami, S Lammel, J Lancaster, M Lancaster, R Lander, A Lath, G Latino, T LeCompte, K Lee, S Leone, JD Lewis, M Lindgren, TM Liss, JB Liu, YC Liu, DO Litvintsev, O Lobban, NS Lockyer, J Loken, M Loreti, D Lucchesi, P Lukens, S Lusin, L Lyons, J Lys, R Madrak, K Maeshima, P Maksimovic, L Malferrari, M Mangano, M Mariotti, G Martignon, A Martin, V Martin, JAJ Matthews, P Mazzanti, KS McFarland, P McIntyre, M Menguzzato, A Menzione, P Merkel, C Mesropian, A Meyer, T Miao, R Miller, JS Miller, H Minato, S Miscetti, M Mishina, G Mitselmakher, Y Miyazaki, N Moggi, E Moore, R Moore, Y Morita, T Moulik, M Mulhearn, A Mukherjee, T Muller, A Munar, P Murat, S Murgia, J Nachtman, V Nagaslaev, S Nahn, H Nakada, I Nakano, C Nelson, T Nelson, C Neu, D Neuberger, C Newman-Holmes, C-YP Ngan, H Niu, L Nodulman, A Nomerotski, SH Oh, YD Oh, T Ohmoto, T Ohsugi, R Oishi, T Okusawa, J Olsen, W Orejudos, C Pagliarone, F Palmonari, R Paoletti, V Papadimitriou, D Partos, J Patrick, G Pauletta, M Paulini, C Paus, D Pellett, L Pescara, TJ Phillips, G Piacentino, KT Pitts, A Pompos, L Pondrom, G Pope, F Prokoshin, J Proudfoot, F Ptohos, O Pukhov, G Punzi, A Rakitine, F Ratnikov, D Reher, A Reichold, P Renton, A Ribon, W Riegler, F Rimondi, L Ristori, M Riveline, WJ Robertson, T Rodrigo, S Rolli, L Rosenson, R Roser, R Rossin, C Rott, A Roy, A Ruiz, A Safonov, R St Denis, WK Sakumoto, D Saltzberg, C Sanchez, A Sansoni, L Santi, H Sato, P Savard, A Savoy-Navarro, P Schlabach, EE Schmidt, MP Schmidt, M Schmitt, L Scodellaro, A Scott, A Scribano, A Sedov, S Segler, S Seidel, Y Seiya, A Semenov, F Semeria, T Shah, MD Shapiro, PF Shepard, T Shibayama, M Shimojima, M Shochet, A Sidoti, J Siegrist, A Sill, P Sinervo, P Singh, AJ Slaughter, K Sliwa, C Smith, FD Snider, A Solodsky, J Spalding, T Speer, P Sphicas, F Spinella, M Spiropulu, L Spiegel, J Steele, A Stefanini, J Strologas, F Strumia, D Stuart, K Sumorok, T Suzuki, T Takano, R Takashima, K Takikawa, P Tamburello, M Tanaka, B Tannenbaum, M Tecchio, RJ Tesarek, PK Teng, K Terashi, S Tether, AS Thompson, E Thomson, R Thurman-Keup, P Tipton, S Tkaczyk, D Toback, K Tollefson, A Tollestrup, D Tonelli, H Toyoda, W Trischuk, JF de Troconiz, J Tseng, D Tsybychev, N Turini, F Ukegawa, T Vaiciulis, J Valls, E Vataga, S Vejcik, G Velev, G Veramendi, R Vidal, I Vila, R Vilar, I Volobouev, M von der Mey, D Vucinic, RG Wagner, RL Wagner, NB Wallace, Z Wan, C Wang, MJ Wang, SM Wang, B Ward, S Waschke, T Watanabe, D Waters, T Watts, R Webb, H Wenzel, WC Wester, AB Wicklund, E Wicklund, T Wilkes, HH Williams, P Wilson, BL Winer, D Winn, S Wolbers, D Wolinski, J Wolinski, S Wolinski, S Worm, X Wu, J Wyss, W Yao, GP Yeh, P Yeh, J Yoh, C Yosef, T Yoshida, I Yu, S Yu, Z Yu, A Zanetti, F Zetti, S Zucchelli, CDF Collaboration

Abstract:

We report on measurements of the Upsilon(1S), Upsilon(2S), and Upsilon(3S) differential cross sections (d(2)sigma/dp(T)dy)(/y/<0.4), as well as on the Upsilon(1S) polarization in p p macro collisions at square root of s = 1.8 TeV using a sample of 77+/-3 pb(-1) collected by the collider detector at Fermilab. The three resonances were reconstructed through the decay Upsilon-->mu(+)mu(-). The measured angular distribution of the muons in the Upsilon(1S) rest frame is consistent with unpolarized meson production.

Γ production and polarization in pp̄ collisions at √s = 1.8 TeV

Physical Review Letters 88:16 (2002) 1618021-1618026

Authors:

D Acosta, T Affolder, H Akimoto, MG Albrow, P Amaral, D Ambrose, D Amidei, K Anikeev, J Antos, G Apollinari, T Arisawa, A Artikov, T Asakawa, W Ashmanskas, F Azfar, P Azzi-Bacchetta, N Bacchetta, H Bachacou, S Bailey, P De Barbaro, A Barbaro-Galtieri, VE Barnes, BA Barnett, S Baroiant, M Barone, G Bauer, F Bedeschi, S Belforte, WH Bell, G Bellettini, J Bellinger, D Benjamin, J Bensinger, A Beretvas, JP Berge, J Berryhill, A Bhatti, M Binkley, D Bisello, M Bishai, RE Blair, C Blocker, K Bloom, B Blumenfeld, SR Blusk, A Bocci, A Bodek, G Bolla, Y Bonushkin, D Bortoletto, J Boudreau, A Brandl, S Van Den Brink, C Bromberg, M Brozovic, E Brubaker, N Bruner, E Buckley-Geer, J Budagov, HS Budd, K Burkett, G Busetto, A Byon-Wagner, KL Byrum, S Cabrera, P Calafiura, M Campbell, W Carithers, J Carlson, D Carlsmith, W Caskey, A Castro, D Cauz, A Cerri, AW Chan, PS Chang, PT Chang, J Chapman, C Chen, YC Chen, MT Cheng, M Chertok, G Chiarelli, I Chirikov-Zorin, G Chlachidze, F Chlebana, L Christofek, ML Chu, JY Chung, YS Chung, CI Ciobanu, AG Clark, AP Colijn

Abstract:

The differential cross sections for the γ(1S), γ(2S), and γ(3S) states and the γ(1S) polarization were measured. Fits of nonrelativistic quantumchromodynamics (NRQCD) matrix elements could describe the cross sections. The polarization systematic uncertainties were also indicated. The polarization measurement was made by fitting the shape of the uncorrected data.

Diffractive dijet production at sqrt[s] = 630 and 1800 GeV at the Fermilab Tevatron.

Phys Rev Lett 88:15 (2002) 151802

Authors:

D Acosta, T Affolder, H Akimoto, MG Albrow, P Amaral, D Ambrose, D Amidei, K Anikeev, J Antos, G Apollinari, T Arisawa, A Artikov, T Asakawa, W Ashmanskas, F Azfar, P Azzi-Bacchetta, N Bacchetta, H Bachacou, S Bailey, P de Barbaro, A Barbaro-Galtieri, VE Barnes, BA Barnett, S Baroiant, M Barone, G Bauer, F Bedeschi, S Belforte, WH Bell, G Bellettini, J Bellinger, D Benjamin, J Bensinger, A Beretvas, JP Berge, J Berryhill, A Bhatti, M Binkley, D Bisello, M Bishai, RE Blair, C Blocker, K Bloom, B Blumenfeld, SR Blusk, A Bocci, A Bodek, G Bolla, Y Bonushkin, K Borras, D Bortoletto, J Boudreau, A Brandl, S van den Brink, C Bromberg, M Brozovic, E Brubaker, N Bruner, E Buckley-Geer, J Budagov, HS Budd, K Burkett, G Busetto, A Byon-Wagner, KL Byrum, S Cabrera, P Calafiura, M Campbell, W Carithers, J Carlson, D Carlsmith, W Caskey, A Castro, D Cauz, A Cerri, AW Chan, PS Chang, PT Chang, J Chapman, C Chen, YC Chen, M-T Cheng, M Chertok, G Chiarelli, I Chirikov-Zorin, G Chlachidze, F Chlebana, L Christofek, ML Chu, JY Chung, YS Chung, CI Ciobanu, AG Clark, AP Colijn, A Connolly, ME Convery, J Conway, M Cordelli, J Cranshaw, R Cropp, R Culbertson, D Dagenhart, S D'Auria, F DeJongh, S Dell'Agnello, M Dell'Orso, S Demers, L Demortier, M Deninno, PF Derwent, T Devlin, JR Dittmann, A Dominguez, S Donati, J Done, M D'Onofrio, T Dorigo, N Eddy, K Einsweiler, JE Elias, E Engels, R Erbacher, D Errede, S Errede, Q Fan, H-C Fang, RG Feild, JP Fernandez, C Ferretti, RD Field, I Fiori, B Flaugher, GW Foster, M Franklin, J Freeman, J Friedman, Y Fukui, I Furic, S Galeotti, A Gallas, M Gallinaro, T Gao, M Garcia-Sciveres, AF Garfinkel, P Gatti, C Gay, DW Gerdes, P Giannetti, V Glagolev, D Glenzinski, M Gold, J Goldstein, I Gorelov, AT Goshaw, Y Gotra, K Goulianos, C Green, G Grim, P Gris, C Grosso-Pilcher, M Guenther, G Guillian, J Guimaraes da Costa, RM Haas, C Haber, SR Hahn, C Hall, T Handa, R Handler, W Hao, F Happacher, K Hara, AD Hardman, RM Harris, F Hartmann, K Hatakeyama, J Hauser, J Heinrich, A Heiss, M Herndon, C Hill, A Hocker, KD Hoffman, R Hollebeek, L Holloway, BT Huffman, R Hughes, J Huston, J Huth, H Ikeda, J Incandela, G Introzzi, A Ivanov, J Iwai, Y Iwata, E James, M Jones, U Joshi, H Kambara, T Kamon, T Kaneko, K Karr, S Kartal, H Kasha, Y Kato, TA Keaffaber, K Kelley, M Kelly, D Khazins, T Kikuchi, B Kilminster, BJ Kim, DH Kim, HS Kim, MJ Kim, SB Kim, SH Kim, YK Kim, M Kirby, M Kirk, L Kirsch, S Klimenko, P Koehn, K Kondo, J Konigsberg, A Korn, A Korytov, E Kovacs, J Kroll, M Kruse, SE Kuhlmann, K Kurino, T Kuwabara, AT Laasanen, N Lai, S Lami, S Lammel, J Lancaster, M Lancaster, R Lander, A Lath, G Latino, T LeCompte, AM Lee, K Lee, S Leone, JD Lewis, M Lindgren, TM Liss, JB Liu, YC Liu, DO Litvintsev, O Lobban, NS Lockyer, J Loken, M Loreti, D Lucchesi, P Lukens, S Lusin, L Lyons, J Lys, R Madrak, K Maeshima, P Maksimovic, L Malferrari, M Mangano, M Mariotti, G Martignon, A Martin, JAJ Matthews, J Mayer, P Mazzanti, KS McFarland, P McIntyre, M Menguzzato, A Menzione, P Merkel, C Mesropian, A Meyer, T Miao, R Miller, JS Miller, H Minato, S Miscetti, M Mishina, G Mitselmakher, Y Miyazaki, N Moggi, C Moore, E Moore, R Moore, Y Morita, T Moulik, M Mulhearn, A Mukherjee, T Muller, A Munar, P Murat, S Murgia, J Nachtman, V Nagaslaev, S Nahn, H Nakada, I Nakano, C Nelson, T Nelson, C Neu, D Neuberger, C Newman-Holmes, C-YP Ngan, H Niu, L Nodulman, A Nomerotski, SH Oh, YD Oh, T Ohmoto, T Ohsugi, R Oishi, T Okusawa, J Olsen, W Orejudos, C Pagliarone, F Palmonari, R Paoletti, V Papadimitriou, D Partos, J Patrick, G Pauletta, M Paulini, C Paus, D Pellett, L Pescara, TJ Phillips, G Piacentino, KT Pitts, A Pompos, L Pondrom, G Pope, M Popovic, F Prokoshin, J Proudfoot, F Ptohos, O Pukhov, G Punzi, A Rakitine, F Ratnikov, D Reher, A Reichold, P Renton, A Ribon, W Riegler, F Rimondi, L Ristori, M Riveline, WJ Robertson, A Robinson, T Rodrigo, S Rolli, L Rosenson, R Roser, R Rossin, C Rott, A Roy, A Ruiz, A Safonov, R St Denis, WK Sakumoto, D Saltzberg, C Sanchez, A Sansoni, L Santi, H Sato, P Savard, A Savoy-Navarro, P Schlabach, EE Schmidt, MP Schmidt, M Schmitt, L Scodellaro, A Scott, A Scribano, A Sedov, S Segler, S Seidel, Y Seiya, A Semenov, F Semeria, T Shah, MD Shapiro, PF Shepard, T Shibayama, M Shimojima, M Shochet, A Sidoti, J Siegrist, A Sill, P Sinervo, P Singh, AJ Slaughter, K Sliwa, C Smith, FD Snider, A Solodsky, J Spalding, T Speer, P Sphicas, F Spinella, M Spiropulu, L Spiegel, J Steele, A Stefanini, J Strologas, F Strumia, D Stuart, K Sumorok, T Suzuki, T Takano, R Takashima, K Takikawa, P Tamburello, M Tanaka, B Tannenbaum, M Tecchio, RJ Tesarek, PK Teng, K Terashi, S Tether, AS Thompson, E Thomson, R Thurman-Keup, P Tipton, S Tkaczyk, D Toback, K Tollefson, A Tollestrup, D Tonelli, H Toyoda, W Trischuk, JF de Troconiz, J Tseng, D Tsybychev, N Turini, F Ukegawa, T Vaiciulis, J Valls, S Vejcik, G Velev, G Veramendi, R Vidal, I Vila, R Vilar, I Volobouev, M von der Mey, D Vucinic, RG Wagner, RL Wagner, NB Wallace, Z Wan, C Wang, MJ Wang, SM Wang, B Ward, S Waschke, T Watanabe, D Waters, T Watts, R Webb, H Wenzel, WC Wester, AB Wicklund, E Wicklund, T Wilkes, HH Williams, P Wilson, BL Winer, D Winn, S Wolbers, D Wolinski, J Wolinski, S Wolinski, S Worm, X Wu, J Wyss, W Yao, GP Yeh, P Yeh, J Yoh, C Yosef, T Yoshida, I Yu, S Yu, Z Yu, A Zanetti, F Zetti, S Zucchelli, CDF Collaboration

Abstract:

We report a measurement of the diffractive structure function F(D)(jj) of the antiproton obtained from a study of dijet events produced in association with a leading antiproton in pp collisions at sqrt[s] = 630 GeV at the Fermilab Tevatron. The ratio of F(D)(jj) at sqrt[s] = 630 GeV to F(D)(jj) obtained from a similar measurement at sqrt[s] = 1800 GeV is compared with expectations from QCD factorization and other theoretical predictions. We also report a measurement of the xi ( x-Pomeron) and beta ( x of parton in Pomeron) dependence of F(D)(jj) at sqrt[s] = 1800 GeV. In the region 0.035

Soft and hard interactions in pp̄ collisions at √s=1800 and 630 GeV

Physical Review D Particles Fields Gravitation and Cosmology 65:7 A (2002) 720051-7200512

Authors:

D Acosta, T Affolder, H Akimoto, MG Albrow, P Amaral, D Ambrose, D Amidei, K Anikeev, J Antos, G Apollinari, T Arisawa, A Artikov, T Asakawa, W Ashmanskas, F Azfar, P Azzi-Bacchetta, N Bacchetta, H Bachacou, S Bailey, P de Barbaro, A Barbaro-Galtieri, VE Barnes, BA Barnett, S Baroiant, M Barone, G Bauer, F Bedeschi, S Belforte, WH Bell, G Bellettini, J Bellinger, D Benjamin, J Bensinger, A Beretvas, JP Berge, J Berryhill, A Bhatti, M Binkley, D Bisello, M Bishai, RE Blair, C Blocker, K Bloom, B Blumenfeld, SR Blusk, A Bocci, A Bodek, G Bolla, Y Bonushkin, D Bortoletto, J Boudreau, A Brandl, S van den Brink, C Bromberg, M Brozovic, E Brubaker, N Bruner, E Buckley-Geer, J Budagov, HS Budd, K Burkett, G Busetto, A Byon-Wagner, KL Byrum, S Cabrera, P Calafiura, M Campbell, W Carithers, J Carlson, D Carlsmith, W Caskey, A Castro, D Cauz, A Cerri, AW Chan, PS Chang, PT Chang, J Chapman, C Chen, YC Chen, MT Cheng, M Chertok, G Chiarelli, I Chirikov-Zorin, G Chlachidze, F Chlebana, L Christofek, ML Chu, JY Chung, YS Chung, CI Ciobanu, AG Clark, AP Colijn, A Connolly, M Convery, J Conway, M Cordelli, J Cranshaw, R Culbertson, D Dagenhart

Abstract:

We present a study of pp̄ of collisions at √s = 1800 and 630 GeV collected using a minimum bias trigger by the CDF experiment in which the data set is divided into two classes corresponding to "soft" and "hard" interactions. For each subsample, the analysis includes measurements of the multiplicity, transverse momentum (PT) spectrum, and the average PT and event-by-event PT dispersion as a function of multiplicity. A comparison of results shows distinct differences in the behavior of the two samples as a function of the center of mass (c.m.) energy. We find evidence that the properties of the soft sample are invariant as a function of c.m. energy.

Searches for new physics in events with a photon and b-quark jet at CDF

Physical Review D Particles Fields Gravitation and Cosmology 65:5 (2002) 520061-5200622

Authors:

T Affolder, H Akimoto, A Akopian, MG Albrow, P Amaral, D Amidei, K Anikeev, J Antos, G Apollinari, T Arisawa, A Artikov, T Asakawa, W Ashmanskas, F Azfar, P Azzi-Bacchetta, N Bacchetta, H Bachacou, S Bailey, P de Barbaro, A Barbaro-Galtieri, VE Barnes, BA Barnett, S Baroiant, M Barone, G Bauer, F Bedeschi, S Belforte, WH Bell, G Bellettini, J Bellinger, D Benjamin, J Bensinger, A Beretvas, JP Berge, J Berryhill, A Bhatti, M Binkley, D Bisello, M Bishai, RE Blair, C Blocker, K Bloom, B Blumenfeld, SR Blusk, A Bocci, A Bodek, W Bokhari, G Bolla, Y Bonushkin, D Bortoletto, J Boudreau, A Brandl, S van den Brink, C Bromberg, M Brozovic, E Brubaker, N Bruner, E Buckley-Geer, J Budagov, HS Budd, K Burkett, G Busetto, A Byon-Wagner, KL Byrum, S Cabrera, P Calafiura, M Campbell, W Carithers, J Carlson, D Carlsmith, W Caskey, A Castro, D Cauz, A Cerri, AW Chan, PS Chang, PT Chang, J Chapman, C Chen, YC Chen, MT Cheng, M Chertok, G Chiarelli, I Chirikov-Zorin, G Chlachidze, F Chlebana, L Christofek, ML Chu, YS Chung, CI Ciobanu, AG Clark, A Connolly, J Conway, M Cordelli, J Cranshaw, R Cropp, R Culbertson, D Dagenhart, S D'Auria, F DeJongh

Abstract:

We have searched for evidence of physics beyond the standard model in events that include an energetic photon and an energetic b-quark jet, produced in 85 pb-1 of p̄p collisions at 1.8 TeV at the Tevatron Collider at Fermilab. This signature, containing at least one gauge boson and a third-generation quark, could arise in the production and decay of a pair of new particles, such as those predicted by supersymmetry, leading to a production rate exceeding standard model predictions. We also search these events for anomalous production of missing transverse energy, additional jets and leptons (e, μ, and τ), and additional b quarks. We find no evidence for any anomalous production of γb or γb + X events. We present limits on two supersymmetric models: a model where the photon is produced in the decay χ̃20→ γχ̃10, and a model where the photon is produced in the neutralino decay into the gravitino LSP, χ̃10→ γG̃. We also present our limits in a model-independent form and test methods of applying model-independent limits.

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