Gauge Invariant Noether's Theorem in Yang-Mills Theory

The gauge invariant definition of the spin dependent gluon distribution function from first principle is necessary to study the proton spin crisis at high energy colliders. In this paper we derive the gauge invariant Noether's theorem in Yang-Mills theory by using combined Lorentz transformation plus local non-abelian gauge transformation. We find that the definition of the gauge invariant spin (or orbital) angular momentum of the Yang-Mills field does not exist in Yang-Mills theory although the definition of the gauge invariant spin (or orbital) angular momentum of the quark exists. We show that the gauge invariant definition of the spin angular momentum of the Yang-Mills field in the literature is not correct because of the non-vanishing boundary surface term in Yang-Mills theory. We also find that the Belinfante-Rosenfeld tensor in Yang-Mills theory is not required to obtain the symmetric and gauge invariant energy-momentum tensor of the quark and the Yang-Mills field.Comment: 26 pages latex. arXiv admin note: text overlap with arXiv:1802.0286

String Theory at LHC Using Jet Production From String Regge Excitations vs String Balls

If we find extra dimensions in the second run of the LHC in the $pp$ collisions at $\sqrt{s}$ = 14 TeV, then the string mass scale $M_s$ can be $\sim$ TeV and we should produce QCD jets in $2 \rightarrow 2$ partonic collisions via string Regge excitations at the LHC. QCD jets can also be produced from string balls via thermal radiation at Hagedorn temperature. In this paper we study jet production from string Regge excitations vs string balls in $pp$ collisions at $\sqrt{s}$ = 14 TeV at LHC and make a comparison with the standard model QCD jets. We find that high $p_T$ jet production from string Regge excitations can be larger than that from string balls and from standard model QCD jets. We also find resonances in the jet production cross section in string Regge excitation scenario which is absent in the other two scenarios. Hence TeV scale high $p_T$ jets can be a good signature to study string Regge excitations in the $pp$ collisions at $\sqrt{s}$ = 14 TeV at the LHC.Comment: 14 pages latex, 4 .eps figures. arXiv admin note: text overlap with arXiv:0902.376

Proof of Factorization of J/ΨJ/\Psi Production in Non-Equilibrium QCD at RHIC and LHC

$J/\psi$ suppression/production is one of the main signature of quark-gluon plasma detection at RHIC and LHC. In order to study $j/\psi$ suppression/production in high energy heavy-ion collisions at RHIC and LHC, one needs to prove the factorization theorem of $j/\psi$ production in non-equilibrium QCD medium, otherwise one will predict infinite cross section of $j/\psi$. In this paper we prove factorization theorem of $j/\psi$ production in non-equilibrium QCD at RHIC and LHC at all order in coupling constant.Comment: 29 pages latex. arXiv admin note: substantial text overlap with arXiv:1509.01148; text overlap with arXiv:1506.02593, arXiv:1506.02651, arXiv:1508.0119

Correct Definition of the Gluon Distribution Function at High Energy Colliders

Unlike QED, since F_{\mu \nu}^a(x)F^{\mu \nu a}(0) in QCD contains cubic and quartic powers of the gluon field the present definition of the gluon distribution function at high energy colliders is not consistent with the number operator interpretation of the gluon. In this paper we derive the correct definition of the gluon distribution function at high energy colliders from first principles which is consistent with the number operator interpretation of the gluon and is gauge invariant and is consistent with the factorization theorem in QCD.Comment: 32 pages latex. arXiv admin note: substantial text overlap with arXiv:1506.0259

Non-Perturbative Quark-Antiquark Production From a Constant Chromo-Electric Field via the Schwinger Mechanism

We obtain an exact result for the non-perturbative quark (antiquark) production rate and its p_T distribution from a constant SU(3) chromo-electric field E^a with arbitary color index $a$ by directly evaluating the path integral. Unlike the WKB tunneling result, which depends only on one gauge invariant quantity |E|, the strength of the chromo-electric field, we find that the exact result for the p_T distribution for quark (antiquark) production rate depends on two independent Casimir (gauge) invariants, E^aE^a and [d_{abc}E^aE^bE^c]^2.Comment: 7 pages latex. To appear in Phys. Rev.

String Theory at LHC Using Supersymmetry Production From String Balls

If extra dimensions are found in the second run of LHC in the $pp$ collisions at $\sqrt{s}$ = 14 TeV then the string scale can be $\sim$ TeV, and we should produce string balls at LHC. In this paper we study supersymmetry (squark and gluino) production from string balls at LHC in $pp$ collisions at $\sqrt{s}$ = 14 TeV and compare that with the parton fusion results using pQCD. We find significant squark and gluino production from string balls at LHC which is comparable to parton fusion pQCD results. Hence, in the absence of black hole production at LHC, an enhancement in supersymmetry production can be a signature of TeV scale string physics at LHC.Comment: 18 pages latex, 7 .eps figures. arXiv admin note: substantial text overlap with arXiv:0902.3764, arXiv:1508.0635

Momentum Sum Rule Is Violated in The Operator Product Expansion in QCD At The High Energy Colliders

To prove the momentum sum rule in the operator product expansion (OPE) in QCD at high energy colliders it is assumed that $=2(P^+)^2$ where $|P>$ is the momentum eigenstate of the hadron $H$ with momentum $P^\mu$ and ${\hat T}^{++}(0)$ is the $++$ component of the gauge invariant color singlet energy-momentum tensor density operator ${\hat T}^{\mu \nu}(0)$ of all the quarks plus antiquarks plus gluons inside the hadron $H$. However, in this paper, we show that this relation $=2(P^+)^2$ is correct if ${\hat T}^{\mu \nu}(0)$ is the energy-momentum tensor density operator of the hadron but this relation $=2(P^+)^2$ is not correct if ${\hat T}^{\mu \nu}(0)$ is the gauge invariant color singlet energy-momentum tensor density operator of all the quarks plus antiquarks plus gluons inside the hadron. Hence we find that the momentum sum rule is violated in the operator product expansion (OPE) in QCD at high energy colliders.Comment: 11 pages late

Operator Product Expansion in QCD Is Not Consistent With Quantum Field Theory For Gluon Distribution Function

Since the operator product expansion (OPE) is applicable at short distance the OPE in QCD does not solve the long distance confinement problem involving hadron in QCD where the non-perturbative QCD is applicable. In this paper we show that the gauge invariant definition of the non-perturbative gluon distribution function inside the hadron consistent with the operator product expansion (OPE) in QCD at high energy colliders is not consistent with the gauge invariant definition of the non-perturbative gluon distribution function in the quantum field theory.Comment: 17 pages late

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

Correct Definition of Color Singlet P-Wave Non-Perturbative Matrix Element of Heavy Quarkonium Production

Recently we have proved factorization of infrared divergences in NRQCD S-wave heavy quarkonium production at high energy colliders at all orders in coupling constant. One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of non-canceling infrared divergences due to real soft gluons exchange, although no such infrared divergences are present in the color singlet S-wave heavy quarkonium. In this paper we find that since the non-perturbative matrix element of the color singlet P-wave heavy quarkonium production contains derivative operators, the gauge links are necessary to make it gauge invariant and be consistent with the factorization of such non-canceling infrared divergences at all orders in coupling constant.Comment: 18 pages latex, Final Version, Accepted for Publication in JHE