General Form of Color Charge of the Quark

In Maxwell theory the constant electric charge e of the electron is consistent with the continuity equation $\partial_\mu j^\mu(x)=0$ where $j^\mu(x)$ is the current density of the electron where the repeated indices $\mu=0,1,2,3$ are summed. However, in Yang-Mills theory the Yang-Mills color current density $j^{\mu a}(x)$ of the quark satisfies the equation $D_\mu[A]j^{\mu a}(x)=0$ which is not a continuity equation ($\partial_\mu j^{\mu a}(x)\neq 0$) which implies that the color charge of the quark is not constant where a=1,2,...,8 are the color indices. Since the charge of a point particle is obtained from the zero ($\mu =0$) component of a corresponding current density by integrating over the entire (physically) allowed volume, the color charge $q^a(t)$ of the quark in Yang-Mills theory is time dependent. In this paper we derive the general form of eight time dependent fundamental color charges $q^a(t)$ of the quark in Yang-Mills theory in SU(3) where a=1,2,...,8.Comment: 52 pages latex, final version, accepted for publication in Eur. Phys. J. C. arXiv admin note: substantial text overlap with arXiv:1201.266

String Theory at LHC Using Higgs Production and Decay From String Balls

We study Higgs production and decay from TeV scale string balls in $pp$ collisions at $\sqrt{s}$ = 14 TeV at LHC. We present the results of total cross section of diphotons, invariant mass distribution of the diphotons and $p_T$ distribution of the diphotons and $ZZ$ pairs from Higgs from string balls at LHC. We find that the invariant mass distribution of diphotons from Higgs from string balls is not very sensitive to the increase in diphoton invariant mass. We find that for string mass scale $M_s$=2.5 TeV, which is the lower limit of the string mass scale set by the recent CMS collaboration at LHC, the $\frac{d\sigma}{dp_T}$ of high $p_T$ ($\ge$ 450 GeV) diphotons and $ZZ$ pairs produced from Higgs from string balls is larger than that from standard model Higgs. Hence in the absence of black hole production at LHC an enhancement of high $p_T$ diphotons and $ZZ$ pairs at LHC can be useful signatures for string theory at LHC. Since the matrix element for Higgs production in parton-parton collisions via string regge excitations is not available we compute $\frac{d\sigma}{dp_T}$ of photon production from string regge excitations and make a comparison with that from string balls at LHC. We find that for string mass scale $M_s$ = 2.5 TeV the $\frac{d\sigma_{photon}}{dp_T}$ from string regge excitations is larger than that from string balls and black holes at LHC.Comment: Title changed, New results on string regge excitations added, 18 pages latex, 7 figures, Accepted for publication in JHE