Документ взят из кэша поисковой машины. Адрес оригинального документа : http://nuclphys.sinp.msu.ru/conf/lpp14/190809/Krasnikov.pdf Дата изменения: Wed Sep 16 15:09:39 2009 Дата индексирования: Tue Oct 2 00:42:43 2012 Кодировка: Поисковые слова: ultraviolet

UNPARTICLES AS FIELDS WITH CONTINUOUSLY DISTRIBUTED MASSES
N.V.Krasnikov INR, Moscow


OUTLINE
1. Introduction 2. Fields with continuously distributed masses 3. Phenomenological implications 4. Conclusion


1.Introduction
Recently H.Georgi proposed a model of unparticles. The main speculation : suppose there is conformal invariant world (gauge theory with fermions with ultraviolet fixed point as an example). For such conformal world all 2point functions behave like D(pІ) ~(pІ)2+2d-3 , where is anomalous dimension of the operator O and d its naive dimension. As a consequence there is no single particle pole in the spectrum . The spectrum is continuous.


The main support of the possible existence of 4-dimensional conformal models is due to the fact that for some number of matter fields in gauge models one-loop beta function contribution is negative while twoloop correction is positive that leads to speculation about existence of fixed point For instance for QCD with nf flavours (s) = -02s(2)-1 ­ 13s(2)-3 + O(5s ) 0 = 11 - 2nf/3; 1 = 51 -19nf/3 For 8 < nf < 16 in PT we have fixed point.


Suppose conformal "unparticle world" and our world are connected due to nonrenormalizable interaction Li = c-nO(particle)O(unparticle) Due to assumed interactions two types of observable effects are possible: a. Production of unparticles at colliders :
qq qU gg gU

Unparticles being weekly interacting in our world are not detected and behave like neutrino


As a consequence we obtain that unparticles signature are events with missing transverse momentum and hadronic jet(s) like in ADD model which describes our 4 dimensional world plus gravity in (4 +n) dimensional world with compactification of n additional dimensions (tower of massive gravitons). b. Exchange of unparticles leads to additional propagators D(p2) (p2)- that change the SM predictions for cross sections like DY, production, ...


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In other words: Due to assumed interactions of particles and unparticles it is possible to produce unparticles in particle collisions . As a consequence of continuous spectrum of unparticles and weak interactions with particles unparticles are not detected . How to detect unparticles? 1. Missing Transverse Energy 2. Unparticle exchange leads to the modification of particle propagators. So study of processes like dimuon production allows to constrain particle-unparticle interactions

Some unparticle references: 1.H.Georgi, Phys.Rev.Lett. 98 221601(1997). Plus a lot of "unparticle exercises" , for instance: 2. K.Cheung et al, Collider Phenomenolgy of Unparticle Physics, arXiv:07063155


In this talk I show that the notion of an unparticle can be described as a particular case of a field with continuously distributed mass. I also review the models with continuously distributed masses and describe possible phenomenological implications for Large Hadron Collider(LHC) This talk is based on my papers: 1. N.V.K., Higgs boson with continuously distributed mass, Phys.Lett. B325(1994)430. 2. N.V.K., Unparticle as a field with continuously distributed mass, Int.J.Mod.Phys. 22 (2007) 5117. 3. N.V.K., LHC signatures for Z` models with continuously distributed mass, Mod.Phys.Lett. 23 (2008) 3233. Also I have to mention related work A.A.Slavnov, Theor.Math.Phys. 148(2006)339


2.Fields with continuously distributed mass Let us start with N free scalar fields k(xk) with masses mk . For the field (xk,mk,ck) = cji(xi,mj) free propagator has the form Dint(k2) = |cj|2(k2 ­ m2j + i)-1 = (t,cj,mj)(k2-t +i)-1dt , (t,cj,mj) = |cj|2(t ­m2j), n2 In the limit N , (t,cj,mj) (t) and Dint(k2) (t)(k2 - t ­i)-1dt For instance for m2k =m2 +kN-1 and |ck|2 =N-1 in the limit N (t) = (t-m2)(m2 +-t)-1


9 n2
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For spectral density (t) ~t-1 the propagator Dint(k2) (k2)-1 that corresponds to the case of unparticle propagator and the limiting field (x,(t)) = limN(x,mj,cj) describes unparticle field. It is possible to introduce self interacrion in standard way as Lint = -((x,(t))4 For finite (t)dt the asymptotics of the effective propagator coincides with free propagator D(p) (p2)-1 and the model is renormalizable. The generalization to the case of vector fields is straightforward. Consider the Lagrangian L = [(-1/4)F,kF,k + (1/2)m2k(A,k-k)2 Gauge invariance: A ,k A,k + k , k k + k

n3


10 n3
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For the field B = ckA,k in the limit N we obtain free unparticle vector field One can introduce gauge invariant interaction with fermion field in standard way Lint = e B For such model Feynman rules the same as in QED except the change photon propagator 1/k2 Dint(k2). Another approach to the fields with continuously distributed mass related with the introduction of additional space dimensions. The main peculiarity is that we postulate Poincare invariance only in 4-dimensional space-time but not Poincare invariance in (4+n)-dimensional space-time. Consider scalar field (x,, x4 ) in five-dimensional field interacting with the four-dimensional fermion field (x).


11 n4
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The scalar action has the form S1 = (1/2)[ ­ f(-42)]d5x This action is invariant only under 4dimensional Poincare group and 5dimensional free propagator is D0 = (kk ­ f(k24))-1 The interaction of 5-dimensional scalar field with 4-dimensional fermion field is Lint = g(x)(x)(x, x4 =0) One can say that fermion field lives on 4dimensional brane while scalar field lives in 5-dimensional world.


· For such interaction Feynman rules the standard as for 4-dimensional model except the use of effective scalar propagator Deff(k2) = (2)-1[k2-f(k24)+i]-1 dk4 One of possible generalizations to the gauge fields is to consider Yang-Mills in 4-dimensional space-time with standard action and matter fields in 5-dimensional space-time with the replacement of the mass m2 f(-42). So for such kind of models gauge field Aa(x) lives on fourdimensional brane, while mater field lives in 5-dimensional dimensional space-time and the Poincare invariance holds only in 4dimensional space-time.


SF = d5x[ (i + gTaAa - m(-24))] Feynman rules for such model coincide with standard except the use of fermion propagator i[p - m(p24)]-1 and additional integration (2)-1dp4 in fermion loop. For the case when m(p24) = 0 for |p4| < and m(p24) = for |p4| > the single difference between our model and 4-dimensional case is additional factor for each fermion loop due to additional integration over dp4 in fermion loop so the model is renormalizable and one loop -function is (g) = -g3(11N/3 - 2/3)/162 +O(g5)


Phenomenological implications
There are a lot of possible extensions of Standard Model with continuously distributed Higgs boson mass. For instance, consider SM in the unitary gauge and make replacement in free Higgs boson propagator (p2 - m2H)-1 Dint(p2) = (t)[p2 ­ t +i]-1dt For Dint(p2) = (p2 ­ m2H +iintmH)-1 we can interpret int as internal Higgs boson decay width into 5-th dimension. For large int >> tot,H we shall have additional suppression factor tot,H(tot,H + int) -1 for standard signatures like pp H +... + ... to be used at the LHC that can make the LHC Higgs boson discovery practically impossible.


Phenomenological implications
For Dint(p2) = |cn|2(p2 ­ m2n +i)-1 and for (mk ­ mk-1) bigger than detector resolution we shall have several peaks in the reactions pp + ... pp ZZ* + ... 4l + ... to be used for Higgs boson search at the LHC with factor |cn|2 suppression for each resonance that for big n makes the Higgs boson discovery at LHC extremely difficult or even impossible


Phenomenological implications
· It should be stressed that the proposed generalization of the SM model is renormalizable if the ultraviolet asymptotics of the Higgs boson propagator Dint(p2) coincides with free propagator D0(p2) = (p2 ) -1


Phenomenological implications
Another possible implications are models of Z` bosons with continuously distributed mass. Most models predict the existence of new narrow vector boson Z` with Total decay width tot = O(10-2)MZ` while in model with continuously distributed Z` boson mass Z` boson could be very broad and possible consequence is the existence of broad structure for dimuon mass distribution in the reaction pp +- + ...


Conclusions
1.Unparticles can be interpreted as fields with continuously distributed mass. 2.Fields with continuously distributed mass can be treated as fields in d >4 space-time and from experimental point of view it Is not necessary to require Poincare group in D-dimensional spacetime (only 4-dimensional Poincare group follow from experiment) 3. Renormalizable extensions at d > 4 are possible. 4. There are possible testable at the LHC phenomenological consequences like Higgs boson or Z` boson decaying into additional dimension(s)