The Experts below are selected from a list of 18819 Experts worldwide ranked by ideXlab platform
Juan Tirao - One of the best experts on this subject based on the ideXlab platform.
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Matrix Valued Spherical Functions Associated to the Complex Projective Plane
Journal of Functional Analysis, 2002Co-Authors: F. A. Grünbaum, Inés Pacharoni, Juan TiraoAbstract:Abstract The main purpose of this paper is to compute all irreducible spherical functions on G=SU(3) of arbitrary type δ∈K, where K=S(U(2)×U(1))≃U(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the complex Projective Plane P2( C )=G/K. It is well known that there is a fruitful connection between the hypergeometric function of Euler and Gauss and the spherical functions of trivial type associated to a rank one symmetric pair (G, K). But the relation of spherical functions of types of dimension bigger than one with classical analysis has not been worked out even in the case of an example of a rank one pair. The entries of H can be described by solutions of two systems of ordinary differential equations. There is no ready-made approach to such a pair of systems or even to a single system of this kind. In our case the situation is very favorable and the solution to this pair of systems can be exhibited explicitly in terms of a special class of generalized hypergeometric functions p+1Fp.
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Matrix Valued Spherical Functions Associated to the Complex Projective Plane
arXiv: Representation Theory, 2001Co-Authors: F. A. Grünbaum, Inés Pacharoni, Juan TiraoAbstract:The main purpose of this paper is to compute all irreducible spherical functions on $G=\SU(3)$ of arbitrary type $\delta\in \hat K$, where $K={\mathrm{S}}(\mathrm{U}(2)\times\mathrm{U}(1))\simeq\mathrm{U}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a matrix valued function $H$ on the complex Projective Plane $P_2(\mathbb{C})=G/K$. It is well known that there is a fruitful connection between the hypergeometric function of Euler and Gauss and the spherical functions of trivial type associated to a rank one symmetric pair $(G,K)$. But the relation of spherical functions of types of dimension bigger than one with classical analysis, has not been worked out even in the case of an example of a rank one pair. The entries of $H$ are solutions of two systems of ordinary differential equations. There is no ready made approach to such a pair of systems, or even to a single system of this kind. In our case the situation is very favorable and the solution to this pair of systems can be exhibited explicitely in terms of a special class of generalized hypergeometric functions ${}_{p+1}F_p$.
Giacomo Cacciapaglia - One of the best experts on this subject based on the ideXlab platform.
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even tiers and resonances on the real Projective Plane
arXiv: High Energy Physics - Phenomenology, 2012Co-Authors: Giacomo Cacciapaglia, B KubikAbstract:In this work we focus on various phenomenological aspects of the lightest even tiers, (2,0) and (0,2), in models based on a Real Projective Plane in 6 dimensions. We discuss the spectrum of the levels due to loop corrections, and the limit when the two radii are equal, in which case the two levels mix with each other and a new basis is defined. We also discuss the dependence of the spectrum on the ratio of the two radii. These results are essential to understand the phenomenology of the model at colliders (LHC) and to predict the relic abundance of Dark Matter. Finally, we estimate the bounds on the radius from resonant decays of the even tiers at the LHC, showing that they can be in the 600 GeV range after the complete analysis of the 2011 data.
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the universal real Projective Plane lhc phenomenology at one loop
Journal of High Energy Physics, 2011Co-Authors: Giacomo Cacciapaglia, A. Deandrea, Jeremie LlodraperezAbstract:The Real Projective Plane is the lowest dimensional orbifold which, when combined with the usual Minkowski space-time, gives rise to a unique model in six flat dimensions possessing an exact Kaluza Klein (KK) parity as a relic symmetry of the broken six dimensional Lorentz group. As a consequence of this property, any model formulated on this background will include a stable Dark Matter candidate. Loop corrections play a crucial role because they remove mass degeneracy in the tiers of KK modes and induce new couplings which mediate decays. We study the full one loop structure of the corrections by means of counter-terms localised on the two singular points. As an application, the LHC phenomenology of the (2, 0) and (0, 2) tiers is discussed. We identify promising signatures with single and di-lepton, top anti-top and 4 tops: in the di-lepton channel, present data from CMS and ATLAS may already exclude KK masses up to 250 GeV, while by next year they may cover the whole mass range preferred by WMAP data.
A. Deandrea - One of the best experts on this subject based on the ideXlab platform.
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the universal real Projective Plane lhc phenomenology at one loop
Journal of High Energy Physics, 2011Co-Authors: Giacomo Cacciapaglia, A. Deandrea, Jeremie LlodraperezAbstract:The Real Projective Plane is the lowest dimensional orbifold which, when combined with the usual Minkowski space-time, gives rise to a unique model in six flat dimensions possessing an exact Kaluza Klein (KK) parity as a relic symmetry of the broken six dimensional Lorentz group. As a consequence of this property, any model formulated on this background will include a stable Dark Matter candidate. Loop corrections play a crucial role because they remove mass degeneracy in the tiers of KK modes and induce new couplings which mediate decays. We study the full one loop structure of the corrections by means of counter-terms localised on the two singular points. As an application, the LHC phenomenology of the (2, 0) and (0, 2) tiers is discussed. We identify promising signatures with single and di-lepton, top anti-top and 4 tops: in the di-lepton channel, present data from CMS and ATLAS may already exclude KK masses up to 250 GeV, while by next year they may cover the whole mass range preferred by WMAP data.
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The Universal Real Projective Plane: LHC phenomenology at one Loop
Journal of High Energy Physics, 2011Co-Authors: G. Cacciapaglia, A. Deandrea, J. Llodra-perezAbstract:The Real Projective Plane is the lowest dimensional orbifold which, when combined with the usual Minkowski space-time, gives rise to a unique model in six flat dimensions possessing an exact Kaluza Klein (KK) parity as a relic symmetry of the broken six dimensional Lorentz group. As a consequence of this property, any model formulated on this background will include a stable Dark Matter candidate. Loop corrections play a crucial role because they remove mass degeneracy in the tiers of KK modes and induce new couplings which mediate decays. We study the full one loop structure of the corrections by means of counter-terms localised on the two singular points. As an application, the phenomenology of the (2,0) and (0,2) tiers is discussed at the LHC. We identify promising signatures with single and di-lepton, top antitop and 4 tops: in the dilepton channel, present data from CMS and ATLAS may already exclude KK masses up to 250 GeV, while by next year they may cover the whole mass range preferred by WMAP data.
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Four tops on the real Projective Plane at LHC
Journal of High Energy Physics, 2011Co-Authors: G. Cacciapaglia, A. Deandrea, R. Chierici, L. Panizzi, S. Perries, S. TosiAbstract:We explore the four top signal ttbar ttbar at the 7 TeV Large Hadron Collider as a probe of physics beyond the standard model. Enhancement of the corresponding cross-section with respect to the Standard Model value can probe the electroweak symmetry breaking sector or test extra dimensional models with heavy Kaluza-Klein gluons and quarks. We perform a detailed analysis including background and detector simulation in the specific case of a universal extra-dimensional model with two extra dimensions compactified using the geometry of the real Projective Plane. For masses around 600 GeV, a discovery is possible for an effective cross section above 210 fb (36 fb) for 1/fb (10/fb) of integrated luminosity. This implies a branching ratio in tops of the (1,1) heavy photon above 13% (5%). Furthermore, the 4-top signal from the (2,0) and (0,2) tiers can be discovered with an integrated luminosity of 3.5/fb. The results of our simulation can be easily adapted to other models since the background processes are identical. Concerning the signal, typical production mechanisms for the ttbar ttbar signal are similar even if cross-section values may vary considerably depending on the model and the spectrum of the new particles.
G. Cacciapaglia - One of the best experts on this subject based on the ideXlab platform.
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The Universal Real Projective Plane: LHC phenomenology at one Loop
Journal of High Energy Physics, 2011Co-Authors: G. Cacciapaglia, A. Deandrea, J. Llodra-perezAbstract:The Real Projective Plane is the lowest dimensional orbifold which, when combined with the usual Minkowski space-time, gives rise to a unique model in six flat dimensions possessing an exact Kaluza Klein (KK) parity as a relic symmetry of the broken six dimensional Lorentz group. As a consequence of this property, any model formulated on this background will include a stable Dark Matter candidate. Loop corrections play a crucial role because they remove mass degeneracy in the tiers of KK modes and induce new couplings which mediate decays. We study the full one loop structure of the corrections by means of counter-terms localised on the two singular points. As an application, the phenomenology of the (2,0) and (0,2) tiers is discussed at the LHC. We identify promising signatures with single and di-lepton, top antitop and 4 tops: in the dilepton channel, present data from CMS and ATLAS may already exclude KK masses up to 250 GeV, while by next year they may cover the whole mass range preferred by WMAP data.
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Four tops on the real Projective Plane at LHC
Journal of High Energy Physics, 2011Co-Authors: G. Cacciapaglia, A. Deandrea, R. Chierici, L. Panizzi, S. Perries, S. TosiAbstract:We explore the four top signal ttbar ttbar at the 7 TeV Large Hadron Collider as a probe of physics beyond the standard model. Enhancement of the corresponding cross-section with respect to the Standard Model value can probe the electroweak symmetry breaking sector or test extra dimensional models with heavy Kaluza-Klein gluons and quarks. We perform a detailed analysis including background and detector simulation in the specific case of a universal extra-dimensional model with two extra dimensions compactified using the geometry of the real Projective Plane. For masses around 600 GeV, a discovery is possible for an effective cross section above 210 fb (36 fb) for 1/fb (10/fb) of integrated luminosity. This implies a branching ratio in tops of the (1,1) heavy photon above 13% (5%). Furthermore, the 4-top signal from the (2,0) and (0,2) tiers can be discovered with an integrated luminosity of 3.5/fb. The results of our simulation can be easily adapted to other models since the background processes are identical. Concerning the signal, typical production mechanisms for the ttbar ttbar signal are similar even if cross-section values may vary considerably depending on the model and the spectrum of the new particles.
Nicola Pace - One of the best experts on this subject based on the ideXlab platform.
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k nets embedded in a Projective Plane over a field
Combinatorica, 2015Co-Authors: Gabor Korchmaros, Gabor P Nagy, Nicola PaceAbstract:We investigate k-nets with k?4 embedded in the Projective Plane PG(2, $\mathbb{K}$ ) defined over a field $\mathbb{K}$ ; they are line configurations in PG(2, $\mathbb{K}$ ) consisting of k pairwise disjoint line-sets, called components, such that any two lines from distinct families are concurrent with exactly one line from each component. The size of each component of a k-net is the same, the order of the k-net. If $\mathbb{K}$ has zero characteristic, no embedded k-net for k?5 exists; see [11,14]. Here we prove that this holds true in positive characteristic p as long as p is sufficiently large compared with the order of the k-net. Our approach, different from that used in [11,14], also provides a new proof in characteristic zero.
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on small complete arcs and transitive a5 invariant arcs in the Projective Plane pg 2 q
Journal of Combinatorial Designs, 2014Co-Authors: Nicola PaceAbstract:Let q be an odd prime power such that q is a power of 5 or (mod 10). In this case, the Projective Plane admits a collineation group G isomorphic to the alternating group A5. Transitive G-invariant 30-arcs are shown to exist for every . The completeness is also investigated, and complete 30-arcs are found for . Surprisingly, they are the smallest known complete arcs in the Planes , and . Moreover, computational results are presented for the cases and . New upper bounds on the size of the smallest complete arc are obtained for .
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3 nets realizing a group in a Projective Plane
Journal of Algebraic Combinatorics, 2014Co-Authors: Gabor Korchmaros, Gabor P Nagy, Nicola PaceAbstract:In a Projective Plane $\mathit{PG}(2,\mathbb{K})$ defined over an algebraically closed field $\mathbb{K}$ of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614---1624, 2004), arises from Plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv. Math. 219:672---688, 2008), comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzua's 3-nets (Adv. Geom. 10:287---310, 2010) realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds in characteristic p>0 apart from three possible exceptions $\rm{Alt}_{4}$ , $\rm{Sym}_{4}$ , and $\rm{Alt}_{5}$ . Motivation for the study of finite 3-nets in the complex Plane comes from the study of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky in Compos. Math. 143:1069---1088, 2007; Miguel and Buzunariz in Graphs Comb. 25:469---488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672---688, 2008; Yuzvinsky in Compos. Math. 140:1614---1624, 2004; Yuzvinsky in Proc. Am. Math. Soc. 137:1641---1648, 2009).
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k nets embedded in a Projective Plane over a field
arXiv: Algebraic Geometry, 2013Co-Authors: Gabor Korchmaros, Gabor P Nagy, Nicola PaceAbstract:We investigate $k$-nets with $k\geq 4$ embedded in the Projective Plane $PG(2,\mathbb{K})$ defined over a field $\mathbb{K}$; they are line configurations in $PG(2,\mathbb{K})$ consisting of $k$ pairwise disjoint line-sets, called components, such that any two lines from distinct families are concurrent with exactly one line from each component. The size of each component of a $k$-net is the same, the order of the $k$-net. If $\mathbb{K}$ has zero characteristic, no embedded $k$-net for $k\geq 5$ exists; see [1,2]. Here we prove that this holds true in positive characteristic $p$ as long as $p$ is sufficiently large compared with the order of the $k$-net. Our approach, different from that used in [1,2], also provides a new proof in characteristic zero. [1] J. Stipins, Old and new examples of k-nets in P2, math.AG/0701046. [2] S. Yuzvinsky, A new bound on the number of special fibers in a pencil of curves, Proc. Amer. Math. Soc. 137 (2009), 1641-1648.
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3 nets realizing a group in a Projective Plane
arXiv: Algebraic Geometry, 2011Co-Authors: Gabor Korchmaros, Gabor P Nagy, Nicola PaceAbstract:In a Projective Plane PG(2,K) defined over an algebraically closed field K of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky, arises from Plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzua's 3-nets realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds true in characteristic p>0 apart from three possible exceptions Alt_4, Sym_4 and Alt_5.
